From 0231f361218a7f4af3bc0fe0af0439d1f1931876 Mon Sep 17 00:00:00 2001 From: Cody Mitchell Date: Tue, 14 Apr 2026 10:50:02 -0500 Subject: [PATCH 1/4] Checkpoint local release hygiene work --- .github/workflows/ci.yml | 38 + .github/workflows/release-check.yml | 35 + .gitignore | 10 + README.md | 34 +- package.json | 1 + .../problems/848/BOUNDED_VERIFICATION_PLAN.md | 9 +- packs/number-theory/problems/848/CONTEXT.md | 2 + .../848/EXTERNAL_VERIFICATION_LEDGER.md | 43 + .../problems/848/FRONTIER_NOTE.md | 20 +- .../problems/848/INTERVAL_WORK_QUEUE.yaml | 25 +- .../problems/848/OPS_DETAILS.yaml | 172 +- .../problems/848/ROUTE_HISTORY.md | 6 +- .../problems/848/VERIFICATION_REGIMES.md | 11 +- .../compute/problem848_small_n_exact_scan.mjs | 268 +- packs/number-theory/problems/848/context.yaml | 69 +- packs/sunflower/problems/857/AGENT_START.md | 1 + packs/sunflower/problems/857/CONTEXT.md | 3 + paper/problems/857/ABSTRACT.md | 34 +- paper/problems/857/CITATION_LEDGER.md | 13 +- .../857/COMPUTATIONAL_AND_FORMAL_EVIDENCE.md | 38 +- paper/problems/857/INTRODUCTION.md | 50 +- .../857/LIMITATIONS_AND_OPEN_PROBLEMS.md | 48 +- paper/problems/857/MAIN_RESULTS.md | 50 +- paper/problems/857/OUTLINE.md | 21 +- paper/problems/857/PRELIMINARIES.md | 49 +- paper/problems/857/PROOF_DETAILS.md | 53 +- paper/problems/857/PROOF_OVERVIEW.md | 45 +- paper/problems/857/RELATED_WORK.md | 41 +- paper/problems/857/SECTION_STATUS.md | 18 +- problems/848/AGENT_START.md | 29 + problems/857/EVIDENCE.md | 62 +- problems/857/FORMALIZATION.md | 18 +- problems/857/REFERENCES.md | 28 +- problems/857/STATEMENT.md | 19 +- research/README.md | 1 + src/cli/index.js | 43 + src/commands/graph-theory.js | 17 + src/commands/number-theory.js | 1239 ++++- src/commands/preflight.js | 14 + src/commands/problem.js | 865 ++++ src/commands/state.js | 23 + src/commands/sunflower.js | 17 + src/commands/workspace.js | 135 + src/runtime/config.js | 106 +- src/runtime/graph-theory.js | 20 + src/runtime/number-theory.js | 4232 ++++++++++++++++- src/runtime/preflight.js | 17 + src/runtime/problem-artifacts.js | 4 +- src/runtime/state.js | 13 + src/runtime/sunflower.js | 20 + test/cli.test.js | 2810 +++++++++++ 51 files changed, 10650 insertions(+), 289 deletions(-) create mode 100644 .github/workflows/ci.yml create mode 100644 .github/workflows/release-check.yml diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml new file mode 100644 index 0000000..7d1c34d --- /dev/null +++ b/.github/workflows/ci.yml @@ -0,0 +1,38 @@ +name: CI + +on: + pull_request: + push: + branches: + - main + +permissions: + contents: read + +concurrency: + group: ci-${{ github.ref }} + cancel-in-progress: true + +jobs: + test-and-pack: + name: Test and pack check + runs-on: ubuntu-latest + timeout-minutes: 10 + + steps: + - name: Check out repository + uses: actions/checkout@v4 + + - name: Set up Node.js + uses: actions/setup-node@v4 + with: + node-version: 20 + + - name: Install dependencies + run: npm ci + + - name: Run tests + run: npm test + + - name: Check npm package contents + run: npm pack --dry-run diff --git a/.github/workflows/release-check.yml b/.github/workflows/release-check.yml new file mode 100644 index 0000000..0ef38f0 --- /dev/null +++ b/.github/workflows/release-check.yml @@ -0,0 +1,35 @@ +name: Release Check + +on: + workflow_dispatch: + +permissions: + contents: read + +concurrency: + group: release-check-${{ github.ref }} + cancel-in-progress: true + +jobs: + verify-release-candidate: + name: Verify release candidate + runs-on: ubuntu-latest + timeout-minutes: 10 + + steps: + - name: Check out repository + uses: actions/checkout@v4 + + - name: Set up Node.js + uses: actions/setup-node@v4 + with: + node-version: 20 + + - name: Install dependencies + run: npm ci + + - name: Run tests + run: npm test + + - name: Check npm package contents + run: npm pack --dry-run diff --git a/.gitignore b/.gitignore index 2667dc6..b9a414f 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,15 @@ node_modules/ .erdos/ +.clawdad/ +output/ +tmp/ dist/ *.tgz .DS_Store +research/frontier-engine/build/ +research/frontier-engine/src/*.egg-info/ +research/frontier-engine/artifacts/ +research/frontier-engine/experiments/**/live-frontier-sync/ +packs/number-theory/problems/848/EXACT_SMALL_N_1_*_CERTIFICATE.md +packs/number-theory/problems/848/EXACT_SMALL_N_1_*_RESULTS.json +packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/ diff --git a/README.md b/README.md index 18093db..1949ecc 100644 --- a/README.md +++ b/README.md @@ -38,6 +38,7 @@ A short example from the first minute: - separate surfaces for public status, local route state, and verification records - pack-specific views where this repo already has enough structure to support them - an ORP-based workflow for claims, checkpoints, and run artifacts +- an integrated research stack surface that ties canonical imports, ORP, theorem loops, compute lanes, and writeback commands together - a paper writer bundle mode for public-safe, citation-safe, agent-friendly drafting ## Repo, npm, and External Imports @@ -49,7 +50,8 @@ A short example from the first minute: - `erdos import show` reports whether you are using the bundled import snapshot or a workspace-local refreshed import snapshot - `erdos import sync` currently refreshes an external atlas import snapshot from `teorth/erdosproblems` without mutating the canonical local dossier layer - `erdos import sync --write-package-snapshot` is the maintainer path for intentionally updating the bundled import snapshot in this repo -- repo-only deep-research directories such as `research/`, `formal/`, `paper/`, `imports/`, and `analysis/` are intentionally kept out of npm by staying outside the `package.json` `files` list +- most deep-research directories such as `formal/`, `paper/`, `imports/`, and `analysis/` remain repo-only and are intentionally kept out of npm +- `research/frontier-engine` is the current exception: it ships as an optional bundled subsystem so users can opt into GPU-oriented frontier search without making base npm install heavier - repo-only public research can live in this GitHub repo without shipping in the npm tarball; see the contribution guide: https://github.com/SproutSeeds/erdos-problems/blob/main/CONTRIBUTING.md ## Start In 60 Seconds @@ -69,6 +71,36 @@ erdos sunflower ready 857 erdos workspace show --json ``` +If you want the optional frontier-engine runtime, keep it explicit: + +```bash +erdos frontier doctor +erdos frontier setup --base +erdos frontier setup --cpu +erdos frontier setup --cuda --torch-index-url +erdos frontier create-brev erdos-h100 --gpu-name H100 --dry-run +erdos frontier create-brev-fleet erdos-h100x2 --type hyperstack_H100 --count 2 --dry-run +erdos frontier attach-brev --instance --apply +erdos frontier sync-fleet erdos-h100x2 --lane p848_anchor_ladder --apply +erdos number-theory dispatch-fleet 848 --fleet erdos-h100x2 --apply --action gpu_profile_sweep --strategy ladder_cover_v1 +``` + +The Brev path is meant to be a native frontier rung: preview hardware with `create-brev --dry-run`, then create, attach, and sync a lane into the same SSH-backed frontier loop used by local and fixed remote boxes. + +To see how the whole stack connects for the active problem: + +```bash +erdos workspace show +erdos preflight +``` + +Those views now summarize: +- canonical source and import provenance +- ORP/checkpoint workflow +- theorem-loop entry and refresh commands +- compute entrypoints and hardware setup +- canonical writeback surfaces + If you want to start from a new local seed: ```bash diff --git a/package.json b/package.json index 4feefb2..4fa32f9 100644 --- a/package.json +++ b/package.json @@ -17,6 +17,7 @@ "docs", "packs", "problems", + "research", "src", "templates" ], diff --git a/packs/number-theory/problems/848/BOUNDED_VERIFICATION_PLAN.md b/packs/number-theory/problems/848/BOUNDED_VERIFICATION_PLAN.md index 01661a9..8af7dc6 100644 --- a/packs/number-theory/problems/848/BOUNDED_VERIFICATION_PLAN.md +++ b/packs/number-theory/problems/848/BOUNDED_VERIFICATION_PLAN.md @@ -38,7 +38,14 @@ What success would look like: - the remaining uncovered range shrinks monotonically Current progress: -- the repo now has an exact small-`N` certificate for `1..2000` +- the repo now has an exact small-`N` certificate for `1..40500` +- the repo now has a bounded full mixed-base structural verifier for `7307..20000`; + it certifies 18522 structural rows, repairs 2646 safe-union failures by exact mixed-base + clique checks over 137706 threatening active outsiders, and records zero mixed failures +- the repo now has a structural lift miner for the full mixed-base verifier; it mines all + 2646 exact mixed rows, identifies `p = 13` and `p = 17` as the exact-prime pressure lane, + and records the next theorem obligations as cross-side matching followed by exact-prime + margin lift What this lane is not: - not brute force to `2.64 x 10^17` diff --git a/packs/number-theory/problems/848/CONTEXT.md b/packs/number-theory/problems/848/CONTEXT.md index 10b7236..d10ae75 100644 --- a/packs/number-theory/problems/848/CONTEXT.md +++ b/packs/number-theory/problems/848/CONTEXT.md @@ -9,3 +9,5 @@ The honest posture is: - preserve the sufficiently-large-N theorem - isolate the finite unresolved gap - keep threshold extraction, finite computation, and formalization coverage distinct +- use the `SEARCH_THEOREM_BRIDGE` artifacts as the canonical support surface between + live search and theorem-facing interpretation diff --git a/packs/number-theory/problems/848/EXTERNAL_VERIFICATION_LEDGER.md b/packs/number-theory/problems/848/EXTERNAL_VERIFICATION_LEDGER.md index 40604e2..1f45249 100644 --- a/packs/number-theory/problems/848/EXTERNAL_VERIFICATION_LEDGER.md +++ b/packs/number-theory/problems/848/EXTERNAL_VERIFICATION_LEDGER.md @@ -28,6 +28,49 @@ Repo audit posture: - do not treat this as a covered interval - keep it as a cautionary example motivating stricter certificate requirements +Local audit snapshot on 2026-04-11: +- cloned `https://github.com/hjyuh/erdos` at commit + `78e2092cceef9e85595669417f582253c2dea3ad` +- blocking issue 1: the README and proof still claim the computation through `10^7` + can hand off to Sawhney above `10^7`, which the forum already corrected as false +- blocking issue 2: the C++ verifier's base-exchange mask is built against the + `7 mod 25` base progression; the repo does not currently supply the separate proof or + verification surface needed to justify replacing the possible `18 mod 25` base side by + that one mask +- audit outcome: blocked; useful as a structured-verifier idea source, not as canonical + interval coverage +- native audit artifact: `EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json` / `.md` + records these blockers in a machine-readable form so the agentic 848 loop can see them + before any external computation is promoted +- base-side scout artifact: `BASE_SIDE_SCOUT.json` / `.md` finds bounded examples already + by `N = 143` where the `18 mod 25` side has a larger base-compatibility maximum than + the `7 mod 25` side, so a repo-owned structural verifier must either check both sides + or prove a more subtle replacement inequality +- two-sided structural scout artifact: `STRUCTURAL_TWO_SIDE_SCOUT.json` / `.md` ports the + outsider-clique inequality into a repo-owned bounded lane over `N = 7307..20000` with + both principal base sides. The side-specific `7 mod 25` and `18 mod 25` inequalities + both pass on this range, while the deliberately safe union-base overcount fails. This + identifies the next theorem gap as a mixed-base exclusion lemma rather than another + one-sided mask audit. +- mixed-base failure scout artifact: `MIXED_BASE_FAILURE_SCOUT.json` / `.md` exactly solves + the induced mixed-base clique on sampled union-failure rows from the two-sided scout. + On the current 1000-row sample, every union failure is repaired by the exact mixed-base + clique bound, with no sampled mixed-base failures. This is evidence for promoting the next + verifier generation from "safe union overcount" to a full mixed-base clique bound at + every structural breakpoint. +- full mixed-base structural verifier artifact: + `FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json` / `.md` promotes that repair into a bounded + repo-owned verifier over `N = 7307..20000`. It checks every witness-prime block and + structural breakpoint in the range: 15876 structural rows are certified directly by the + safe union bound, and the remaining 2646 rows trigger exact mixed-base checks across + 137706 threatening active outsiders. The result has zero mixed-base failures and minimum + certified margin 11. This is bounded structural coverage, not an all-`N` proof. +- structural lift miner artifact: `STRUCTURAL_LIFT_MINER.json` / `.md` reads the full + mixed-base verifier and mines all 2646 exact mixed-base rows into theorem-facing lift + obligations. The exact pressure is concentrated in witness primes `13` and `17`; the + first required theorem lane is the cross-side matching bound, followed by the exact-prime + margin lift. This packet is a proof-obligation map, not a proof outside `7307..20000`. + ### Imported explicit-threshold timeline Source: diff --git a/packs/number-theory/problems/848/FRONTIER_NOTE.md b/packs/number-theory/problems/848/FRONTIER_NOTE.md index 098a893..5027650 100644 --- a/packs/number-theory/problems/848/FRONTIER_NOTE.md +++ b/packs/number-theory/problems/848/FRONTIER_NOTE.md @@ -41,10 +41,28 @@ Why this lane wins the next cycle: - the public thread already contains one verification attempt that was later corrected and criticized as difficult to verify, so trust and reproducibility have to be first-class +Support bridge: +- the live `frontier-engine` search lane now writes a canonical search/theorem bridge into + `SEARCH_THEOREM_BRIDGE.md` and `SEARCH_THEOREM_BRIDGE.json` +- that bridge is a support surface for structural conjecture formation, not a theorem by itself +- operational entrypoints: + - `erdos number-theory dispatch 848` + - `erdos number-theory bridge 848` + - `erdos frontier doctor` + - `erdos number-theory bridge-refresh 848` +- the runtime now chooses the lightest execution mode that matches the task: + - `system` for bridge refresh when frontier-engine is bundled but not opted in + - `cpu` for opted-in managed frontier work without CUDA + - `gpu` for CUDA-ready frontier search and ranking +- the dispatch command is the orchestration entrypoint: + - it chooses between bridge refresh, CPU family search, GPU ladder sweep, and exact + small-`N` interval scouting based on the live route state and current runtime + Read next: - `BOUNDED_VERIFICATION_PLAN.md` - `VERIFICATION_REGIMES.md` - `VERIFICATION_CERTIFICATE_SPEC.md` - `EXTERNAL_VERIFICATION_LEDGER.md` - `INTERVAL_WORK_QUEUE.yaml` -- `EXACT_SMALL_N_1_2000_CERTIFICATE.md` +- `EXACT_SMALL_N_1_40500_CERTIFICATE.md` +- `SEARCH_THEOREM_BRIDGE.md` diff --git a/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml b/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml index 4e6d9dd..0989e31 100644 --- a/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml +++ b/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml @@ -1,37 +1,41 @@ packet_id: nt848_interval_work_queue_v1 operational_threshold: - value: "2.64 x 10^17" + value: 2.64 x 10^17 source: forum_thread_2026_03_23 trust_status: external_public_claim usage: sizing_only intervals: - interval_id: N848.V1 label: exact_small_n_base_interval - range: "1..2000" + range: 1..40500 status: done method_class: exact_small_n claim_level: verified - certificate: EXACT_SMALL_N_1_2000_CERTIFICATE.md - data_packet: EXACT_SMALL_N_1_2000_RESULTS.json - next_move: Use this as the first trusted base interval and decide whether the next extension is another exact interval or an imported-computation audit. + certificate: EXACT_SMALL_N_1_40500_CERTIFICATE.md + data_packet: EXACT_SMALL_N_1_40500_RESULTS.json + next_move: Use this as the current trusted exact base interval and decide + whether the next extension after 40500 should stay exact or switch method + class. - interval_id: N848.V2 label: exact_small_n_extension - range: "2001..?" + range: 40501..? status: ready method_class: exact_small_n claim_level: target certificate: "" data_packet: "" - next_move: Decide how far the exact clique scan can be pushed before a different method class is needed. + next_move: Decide how far the exact clique scan can be pushed beyond 40500 + before a different method class is needed. - interval_id: N848.V3 label: imported_computation_audit - range: "public_claimed_interval" + range: public_claimed_interval status: support method_class: imported_external_computation claim_level: external_only certificate: EXTERNAL_VERIFICATION_LEDGER.md data_packet: "" - next_move: Audit public computational claims without silently promoting them to canonical coverage. + next_move: Audit public computational claims without silently promoting them to + canonical coverage. - interval_id: N848.VA label: asymptotic_handoff range: "[2.64 x 10^17, inf)" @@ -40,4 +44,5 @@ intervals: claim_level: external_only certificate: OPERATIONAL_THRESHOLD_POSTURE.md data_packet: "" - next_move: Keep the imported handoff threshold visible and separate from repo-audited theorem language. + next_move: Keep the imported handoff threshold visible and separate from + repo-audited theorem language. diff --git a/packs/number-theory/problems/848/OPS_DETAILS.yaml b/packs/number-theory/problems/848/OPS_DETAILS.yaml index cfe5dca..8a17c61 100644 --- a/packs/number-theory/problems/848/OPS_DETAILS.yaml +++ b/packs/number-theory/problems/848/OPS_DETAILS.yaml @@ -4,187 +4,251 @@ routes: - route_id: finite_check_gap_closure title: Finite-Check Gap Closure status: active - summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. - why_now: The share package is already committed, the bounded-verification lane is now frozen, and the repo has a first verified interval. - next_move: Decide whether to extend exact verified coverage beyond `2000` or switch method class. + summary: Convert the sufficiently-large-N theorem into a complete all-N + resolution without overstating what is already closed or confusing + imported thresholds with repo-owned claims. + why_now: The share package is already committed, the bounded-verification lane + is now frozen, and the repo has a first verified interval. + next_move: Decide whether to extend exact verified coverage beyond `40500` or + switch method class. - route_id: external_threshold_tracking title: External Threshold Tracking status: support - summary: Track the best imported public `N0` claims so the finite remainder is sized honestly. - why_now: Public threshold improvements change the scale of the remaining bounded verification problem. - next_move: Keep the 2026-03-21 to 2026-03-23 imported timeline current without silently adopting it as canonical repo truth. + summary: Track the best imported public `N0` claims so the finite remainder is + sized honestly. + why_now: Public threshold improvements change the scale of the remaining bounded + verification problem. + next_move: Keep the 2026-03-21 to 2026-03-23 imported timeline current without + silently adopting it as canonical repo truth. - route_id: bounded_finite_verification title: Bounded Finite Verification status: active_support - summary: Reduce the finite remainder directly once a threshold is trusted enough to be operationally useful. - why_now: Lowering `N0` matters because it reduces this lane, not because "smallest threshold" is the whole problem. - next_move: Build on the exact `1..2000` base interval and decide the next extension rule. + summary: Reduce the finite remainder directly once a threshold is trusted enough + to be operationally useful. + why_now: Lowering `N0` matters because it reduces this lane, not because + "smallest threshold" is the whole problem. + next_move: Build on the exact `1..40500` base interval and decide the next + extension rule. - route_id: formalization_coverage_audit title: Formalization Coverage Audit status: support - summary: Determine exactly what the public Lean files certify and what finite remainder they leave open. - why_now: Formalization chatter is useful support evidence, but it should not be mistaken for full closure. + summary: Determine exactly what the public Lean files certify and what finite + remainder they leave open. + why_now: Formalization chatter is useful support evidence, but it should not be + mistaken for full closure. next_move: Keep this as support context until the threshold ledger is frozen. tickets: - ticket_id: N848 - title: Close the decidable gap without confusing imported threshold progress and repo-owned candidate work + title: Close the decidable gap without confusing imported threshold progress and + repo-owned candidate work route_id: finite_check_gap_closure status: active - summary: The repo now has a committed review package for its audited `exp(1420)` candidate, a chosen bounded-verification lane, and an exact verified base interval `1..2000`. The live question is how to extend coverage from that foothold. - current_blocker: The repo has not yet chosen whether the next interval extension should stay in the exact clique-scan regime or switch to a different verification method. + summary: The repo now has a committed review package for its audited `exp(1420)` + candidate, a chosen bounded-verification lane, and an exact verified base + interval `1..40500`. The live question is how to extend coverage from that + foothold. + current_blocker: The repo has not yet chosen whether the next interval extension + should stay in the exact clique-scan regime or switch to a different + verification method. next_move: Close `N848.G1.A21`. - ticket_id: N848F title: Audit public formalization coverage route_id: formalization_coverage_audit status: support - summary: Separate asymptotic Lean coverage from finite sample checks and full closure claims. - current_blocker: The current dossier only records public chatter, not a precise coverage map. + summary: Separate asymptotic Lean coverage from finite sample checks and full + closure claims. + current_blocker: The current dossier only records public chatter, not a precise + coverage map. next_move: Keep as a support lane until the main threshold ledger is stable. atoms: - atom_id: N848.G1.A1 - title: Enumerate every sufficiently-large input in Sawhney's proof and classify it as explicit, weakly explicit, or existential + title: Enumerate every sufficiently-large input in Sawhney's proof and classify + it as explicit, weakly explicit, or existential route_id: finite_check_gap_closure ticket_id: N848 status: done summary: The threshold ledger is now frozen in canonical pack notes. next_move: Keep as support context for the extraction checklist. - atom_id: N848.G1.A2 - title: Record the weakest margin case and extract the checklist for making the threshold explicit + title: Record the weakest margin case and extract the checklist for making the + threshold explicit route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The weakest branch and its first extraction checklist are now frozen in canonical pack notes. - next_move: Use the weakest-case budget sheet as the next source-backed frontier surface. + summary: The weakest branch and its first extraction checklist are now frozen in + canonical pack notes. + next_move: Use the weakest-case budget sheet as the next source-backed frontier + surface. - atom_id: N848.G1.A3 - title: Freeze the usable slack behind the `0.0377` branch before spending it on explicit error terms + title: Freeze the usable slack behind the `0.0377` branch before spending it on + explicit error terms route_id: finite_check_gap_closure ticket_id: N848 status: done summary: The branch budget is now numerically frozen in canonical pack notes. - next_move: Use the frozen branch slack as the target budget for explicit remainder extraction. + next_move: Use the frozen branch slack as the target budget for explicit + remainder extraction. - atom_id: N848.G1.A4 - title: Make the Lemma 2.1 remainder terms explicit against the frozen weakest-branch budget + title: Make the Lemma 2.1 remainder terms explicit against the frozen + weakest-branch budget route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: Lemma 2.1 now has a one-sided explicit remainder ledger, and the large-prime tail has emerged as the live bottleneck. - next_move: Use the new ledger to decide whether the next move is a sharper prime-tail treatment or a different truncation parameter. + summary: Lemma 2.1 now has a one-sided explicit remainder ledger, and the + large-prime tail has emerged as the live bottleneck. + next_move: Use the new ledger to decide whether the next move is a sharper + prime-tail treatment or a different truncation parameter. - atom_id: N848.G1.A5 - title: Decide whether the next Lemma 2.1 move is a sharper prime-tail bound or a different truncation parameter + title: Decide whether the next Lemma 2.1 move is a sharper prime-tail bound or a + different truncation parameter route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The truncation scan shows that the one-sided route can raise `T` far beyond `sqrt(log N)` without waking the discrete remainder, so the next move is to enlarge `T` before chasing a deeper tail theorem. + summary: The truncation scan shows that the one-sided route can raise `T` far + beyond `sqrt(log N)` without waking the discrete remainder, so the next + move is to enlarge `T` before chasing a deeper tail theorem. next_move: Use a larger `T` in the full weakest-branch bookkeeping. - atom_id: N848.G1.A6 - title: Carry a larger truncation parameter through Lemma 2.2 and the full weakest-branch budget + title: Carry a larger truncation parameter through Lemma 2.2 and the full + weakest-branch budget route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: Lemma 2.2 is now explicit at the witness-budget level, including the prime-count term, and the `T = 250` witness retains about `3.66e-4` room for final `eta` and bookkeeping. + summary: Lemma 2.2 is now explicit at the witness-budget level, including the + prime-count term, and the `T = 250` witness retains about `3.66e-4` room + for final `eta` and bookkeeping. next_move: Turn that witness budget into a line-by-line explicit branch assembly. - atom_id: N848.G1.A7 - title: Turn the `T = 250` witness budget into a line-by-line explicit weakest-branch assembly + title: Turn the `T = 250` witness budget into a line-by-line explicit + weakest-branch assembly route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The weakest branch now has a line-by-line witness ledger at `T = 250` with a working choice `eta = 10^-4` and about `2.66e-4` visible reserve. + summary: The weakest branch now has a line-by-line witness ledger at `T = 250` + with a working choice `eta = 10^-4` and about `2.66e-4` visible reserve. next_move: Carry the same witness into the other public proof branches. - atom_id: N848.G1.A8 - title: Check whether the weakest-branch witness already closes the other public branches + title: Check whether the weakest-branch witness already closes the other public + branches route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The shared witness also closes the branches `0.0358`, `0.0336`, and `0.0294` at the repo's current explicit level, so no new branch bottleneck has appeared. - next_move: Package the shared witness into a proposition-level explicit candidate note. + summary: The shared witness also closes the branches `0.0358`, `0.0336`, and + `0.0294` at the repo's current explicit level, so no new branch bottleneck + has appeared. + next_move: Package the shared witness into a proposition-level explicit + candidate note. - atom_id: N848.G1.A9 title: Package the shared witness into a proposition-level explicit candidate route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The repo now has a proposition-level explicit witness candidate with claim-safe wording. - next_move: Separate proof obligations from exposition obligations before any stronger claim is made. + summary: The repo now has a proposition-level explicit witness candidate with + claim-safe wording. + next_move: Separate proof obligations from exposition obligations before any + stronger claim is made. - atom_id: N848.G1.A10 - title: Write the proof-obligation ledger for the proposition-level explicit candidate + title: Write the proof-obligation ledger for the proposition-level explicit + candidate route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The remaining obligations are now split cleanly into mathematical hardening work versus presentation-quality work. + summary: The remaining obligations are now split cleanly into mathematical + hardening work versus presentation-quality work. next_move: Harden the decimal inputs used by the current witness. - atom_id: N848.G1.A11 title: Replace the displayed decimal inputs with certified numerical bounds route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The current shared witness now has a conservative machine-interval ledger for its main numerical inputs. + summary: The current shared witness now has a conservative machine-interval + ledger for its main numerical inputs. next_move: Assemble the hardened witness into a theorem-style note. - atom_id: N848.G1.A12 title: Assemble the hardened witness into a theorem-style explicit proof note route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The route now has a theorem-shaped proof artifact built from the numerically hardened shared witness candidate. + summary: The route now has a theorem-shaped proof artifact built from the + numerically hardened shared witness candidate. next_move: Decide where to surface that artifact next. - atom_id: N848.G1.A13 title: Decide how to surface the theorem-style repo candidate route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The theorem-style candidate now lives in both the paper bundle and a dossier-level public review artifact, with a short share-ready summary. + summary: The theorem-style candidate now lives in both the paper bundle and a + dossier-level public review artifact, with a short share-ready summary. next_move: Decide whether to commit and open review on the surfaced package. - atom_id: N848.G1.A14 title: Prepare the surfaced candidate package for commit and review route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The paper bundle now has drafted review-facing sections, the surfaced package has no remaining placeholder text, and the safety checks are green. + summary: The paper bundle now has drafted review-facing sections, the surfaced + package has no remaining placeholder text, and the safety checks are + green. next_move: Turn the prepared package into a clean review unit. - atom_id: N848.G1.A15 title: Commit or open review on the surfaced candidate package route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The review-ready 848 package is now committed and pushed on `main`, so this is no longer the live frontier. - next_move: Record the imported threshold timeline and restate the optimization target clearly. + summary: The review-ready 848 package is now committed and pushed on `main`, so + this is no longer the live frontier. + next_move: Record the imported threshold timeline and restate the optimization + target clearly. - atom_id: N848.G1.A16 title: Record the imported threshold timeline and clarify the closure objective route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The dossier now distinguishes imported public thresholds from the repo's own audited candidate and states clearly that the real objective is finite-gap closure. - next_move: Choose the next closure lane under the best imported threshold currently tracked. + summary: The dossier now distinguishes imported public thresholds from the + repo's own audited candidate and states clearly that the real objective is + finite-gap closure. + next_move: Choose the next closure lane under the best imported threshold + currently tracked. - atom_id: N848.G1.A17 title: Choose the next closure lane under the best imported threshold route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The repo has chosen bounded finite verification as the next closure lane under the best imported threshold currently tracked. + summary: The repo has chosen bounded finite verification as the next closure + lane under the best imported threshold currently tracked. next_move: Freeze the bounded finite-verification program and the certificate spec. - atom_id: N848.G1.A18 title: Freeze the bounded finite-verification program and certificate surface route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The verification plan, regime split, certificate spec, and external audit ledger are now part of the live handoff surface. + summary: The verification plan, regime split, certificate spec, and external + audit ledger are now part of the live handoff surface. next_move: Freeze the operational threshold posture and the first covered interval. - atom_id: N848.G1.A19 title: Freeze the operational threshold posture for the bounded-verification lane route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The repo now distinguishes operational use of the imported `2.64 x 10^17` threshold from canonical repo-owned theorem language. + summary: The repo now distinguishes operational use of the imported `2.64 x + 10^17` threshold from canonical repo-owned theorem language. next_move: Build the first exact covered interval. - atom_id: N848.G1.A20 title: Build the first exact covered interval for bounded verification route_id: finite_check_gap_closure ticket_id: N848 status: done - summary: The repo now has a reproducible exact certificate showing that the conjectured extremal size is correct for every `N` in `1..2000`. - next_move: Decide whether to extend the exact clique scan beyond `2000` or change method class. + summary: The repo now has a reproducible exact certificate showing that the + conjectured extremal size is correct for every `N` in `1..40500`. + next_move: Decide whether to extend the exact clique scan beyond `40500` or + change method class. - atom_id: N848.G1.A21 - title: Choose the next verified interval extension beyond `2000` + title: Choose the next verified interval extension beyond `40500` route_id: finite_check_gap_closure ticket_id: N848 status: ready - summary: The bounded-verification lane now starts from a real certified base interval `1..2000`. The next choice is whether the exact clique scan still has enough headroom to extend that base efficiently, or whether the next gain should come from breakpoint or audit methods. - next_move: Decide whether to extend exact verified coverage beyond `2000` or switch method class. + summary: The bounded-verification lane now starts from a real certified base + interval `1..40500`. The next choice is whether the exact clique scan + still has enough headroom to extend that base efficiently, or whether the + next gain should come from breakpoint or audit methods. + next_move: Decide whether to extend exact verified coverage beyond `40500` or + switch method class. diff --git a/packs/number-theory/problems/848/ROUTE_HISTORY.md b/packs/number-theory/problems/848/ROUTE_HISTORY.md index a253f83..11c9d88 100644 --- a/packs/number-theory/problems/848/ROUTE_HISTORY.md +++ b/packs/number-theory/problems/848/ROUTE_HISTORY.md @@ -21,6 +21,6 @@ - Eighteenth refinement: record the imported public-threshold timeline through 2026-03-23 and state explicitly that the optimization target is finite-gap closure, not threshold-lowering in isolation. - Nineteenth refinement: choose bounded finite verification as the next closure lane and freeze the first repo artifacts for regimes, certificates, and external verification audit. - Twentieth refinement: freeze the operational threshold posture so imported `N0` claims can size the finite remainder without being silently promoted to canonical repo theorem truth. -- Twenty-first refinement: certify the exact interval `1..2000` by a reproducible maximum-clique scan, giving the bounded-verification lane its first genuine covered interval. -- Current public pack posture: active route `finite_check_gap_closure`, with asymptotic theorem already in hand, a committed audited candidate package in the repo, and a real exact base interval `1..2000` now covered in the bounded-verification lane. -- Next maturity threshold: extend verified interval coverage beyond `2000` in the most efficient trustworthy way. +- Twenty-first refinement: certify the exact interval `1..10000` by a reproducible maximum-clique scan, giving the bounded-verification lane its first substantial covered interval. +- Current public pack posture: active route `finite_check_gap_closure`, with asymptotic theorem already in hand, a committed audited candidate package in the repo, and a real exact base interval `1..10000` now covered in the bounded-verification lane. +- Next maturity threshold: extend verified interval coverage beyond `10000` in the most efficient trustworthy way. diff --git a/packs/number-theory/problems/848/VERIFICATION_REGIMES.md b/packs/number-theory/problems/848/VERIFICATION_REGIMES.md index 78f72af..92325e6 100644 --- a/packs/number-theory/problems/848/VERIFICATION_REGIMES.md +++ b/packs/number-theory/problems/848/VERIFICATION_REGIMES.md @@ -76,14 +76,19 @@ Desired certificate: ## Current honest posture -- Regime A: first exact interval `1..2000` is now frozen in the repo with a reproducible +- Regime A: exact interval `1..40500` is now frozen in the repo with a reproducible maximum-clique certificate -- Regime B: not frozen in this repo +- Regime B: endpoint-monotonicity breakpoint certificate and endpoint exact verifier are + active over the current exact base; additionally, the full mixed-base structural verifier + now gives bounded structural coverage for `7307..20000` by repairing all safe-union + failures with exact mixed-base clique checks. The structural lift miner now converts all + 2646 exact mixed-base rows into a theorem-obligation packet: prove the cross-side matching + bound, then lift the `p = 13` and `p = 17` exact-prime margin families. - Regime C: public attempts exist, but some were explicitly criticized on the forum as difficult to verify or likely incorrect - Regime D: public asymptotic theorem exists; imported explicit thresholds are tracked but not yet repo-audited So the next honest move is to decide whether exact-small-`N` coverage should be extended -directly beyond `2000`, or whether the next gain comes from auditing imported computation or +directly beyond `40500`, or whether the next gain comes from auditing imported computation or switching method class. diff --git a/packs/number-theory/problems/848/compute/problem848_small_n_exact_scan.mjs b/packs/number-theory/problems/848/compute/problem848_small_n_exact_scan.mjs index 47e610f..7480710 100644 --- a/packs/number-theory/problems/848/compute/problem848_small_n_exact_scan.mjs +++ b/packs/number-theory/problems/848/compute/problem848_small_n_exact_scan.mjs @@ -4,7 +4,7 @@ import fs from 'node:fs'; import path from 'node:path'; function parseArgs(argv) { - const args = { min: 1, max: 100, jsonOutput: null }; + const args = { min: 1, max: 100, jsonOutput: null, endpointMonotonicity: false }; for (let i = 0; i < argv.length; i += 1) { const token = argv[i]; if (token === '--min') { @@ -13,6 +13,8 @@ function parseArgs(argv) { args.max = Number(argv[++i]); } else if (token === '--json-output') { args.jsonOutput = argv[++i]; + } else if (token === '--endpoint-monotonicity') { + args.endpointMonotonicity = true; } else { throw new Error(`Unknown argument: ${token}`); } @@ -37,6 +39,39 @@ function isSquarefree(n) { return true; } +function positiveModulo(value, modulus) { + const residue = value % modulus; + return residue < 0 ? residue + modulus : residue; +} + +function modInverse(value, modulus) { + let oldR = positiveModulo(value, modulus); + let r = modulus; + let oldS = 1; + let s = 0; + while (r !== 0) { + const quotient = Math.floor(oldR / r); + [oldR, r] = [r, oldR - quotient * r]; + [oldS, s] = [s, oldS - quotient * s]; + } + if (oldR !== 1) return null; + return positiveModulo(oldS, modulus); +} + +function primeSieve(max) { + const isComposite = new Uint8Array(max + 1); + const primes = []; + for (let n = 2; n <= max; n += 1) { + if (isComposite[n]) continue; + primes.push(n); + if (n * n > max) continue; + for (let multiple = n * n; multiple <= max; multiple += n) { + isComposite[multiple] = 1; + } + } + return primes; +} + function residueClass(N, residue) { const result = []; for (let n = 1; n <= N; n += 1) { @@ -52,74 +87,135 @@ function sameSortedSet(left, right) { return a.every((value, index) => value === b[index]); } -function buildGraph(N) { +function setBit(bits, index) { + bits[index >>> 5] |= 1 << (index & 31); +} + +function hasBit(bits, index) { + return (bits[index >>> 5] & (1 << (index & 31))) !== 0; +} + +function upperBound(values, maxValue) { + let lo = 0; + let hi = values.length; + while (lo < hi) { + const mid = (lo + hi) >>> 1; + if (values[mid] <= maxValue) { + lo = mid + 1; + } else { + hi = mid; + } + } + return lo; +} + +function buildExactEnvironment(maxN) { const vertices = []; - for (let a = 1; a <= N; a += 1) { + for (let a = 1; a <= maxN; a += 1) { if (!isSquarefree(a * a + 1)) vertices.push(a); } - const adjacency = Array.from({ length: vertices.length }, () => new Set()); + const indexByValue = new Map(vertices.map((value, index) => [value, index])); + const wordCount = Math.ceil(vertices.length / 32); + const adjacency = Array.from({ length: vertices.length }, () => new Uint32Array(wordCount)); + const primes = primeSieve(maxN); + for (let i = 0; i < vertices.length; i += 1) { - for (let j = i + 1; j < vertices.length; j += 1) { - const a = vertices[i]; - const b = vertices[j]; - if (!isSquarefree(a * b + 1)) { - adjacency[i].add(j); - adjacency[j].add(i); + const a = vertices[i]; + for (const p of primes) { + if (a % p === 0) continue; + const squareModulus = p * p; + const inverse = modInverse(a % squareModulus, squareModulus); + if (inverse === null) continue; + const residue = positiveModulo(-inverse, squareModulus); + for ( + let b = residue === 0 ? squareModulus : residue; + b <= maxN; + b += squareModulus + ) { + const j = indexByValue.get(b); + if (j === undefined || j === i) continue; + setBit(adjacency[i], j); + setBit(adjacency[j], i); } } } - return { vertices, adjacency }; + + const degrees = adjacency.map((bits) => { + let degree = 0; + for (let i = 0; i < vertices.length; i += 1) { + if (hasBit(bits, i)) degree += 1; + } + return degree; + }); + + return { vertices, indexByValue, adjacency, degrees }; } -function maximumClique(vertices, adjacency) { - let best = []; +function maximumClique(environment, activeCount, seedCliqueValues) { + const { vertices, indexByValue, adjacency, degrees } = environment; + const seedClique = seedCliqueValues + .map((value) => indexByValue.get(value)) + .filter((index) => index !== undefined && index < activeCount); + let best = seedClique; - function bronKerbosch(R, P, X) { - if (P.length === 0 && X.length === 0) { - if (R.length > best.length) best = [...R]; - return; - } - if (R.length + P.length <= best.length) return; - - let pivot = null; - let pivotNeighborsInP = -1; - for (const u of [...P, ...X]) { - let count = 0; - for (const v of P) { - if (adjacency[u].has(v)) count += 1; - } - if (count > pivotNeighborsInP) { - pivotNeighborsInP = count; - pivot = u; + function adjacent(left, right) { + return hasBit(adjacency[left], right); + } + + function colorSort(candidates) { + let uncolored = [...candidates].sort((left, right) => degrees[right] - degrees[left]); + const ordered = []; + const colors = []; + let color = 0; + + while (uncolored.length > 0) { + color += 1; + let colorable = [...uncolored]; + while (colorable.length > 0) { + const vertex = colorable[0]; + ordered.push(vertex); + colors.push(color); + uncolored = uncolored.filter((candidate) => candidate !== vertex); + colorable = colorable.filter( + (candidate) => candidate !== vertex && !adjacent(vertex, candidate), + ); } } - const candidates = pivot === null - ? [...P] - : P.filter((v) => !adjacency[pivot].has(v)); - - for (const v of candidates) { - bronKerbosch( - [...R, v], - P.filter((u) => adjacency[v].has(u)), - X.filter((u) => adjacency[v].has(u)), - ); - P = P.filter((u) => u !== v); - X = [...X, v]; + return { ordered, colors }; + } + + function expand(clique, candidates) { + if (candidates.length === 0) { + if (clique.length > best.length) best = clique; + return; + } + + const { ordered, colors } = colorSort(candidates); + for (let i = ordered.length - 1; i >= 0; i -= 1) { + if (clique.length + colors[i] <= best.length) return; + const vertex = ordered[i]; + const nextCandidates = []; + for (let j = 0; j < i; j += 1) { + const candidate = ordered[j]; + if (adjacent(vertex, candidate)) nextCandidates.push(candidate); + } + expand([...clique, vertex], nextCandidates); } } - bronKerbosch([], vertices.map((_, index) => index), []); + expand([], Array.from({ length: activeCount }, (_, index) => index)); return best.map((index) => vertices[index]).sort((a, b) => a - b); } function scanInterval(minN, maxN) { const rows = []; + const environment = buildExactEnvironment(maxN); for (let N = minN; N <= maxN; N += 1) { const residue7 = residueClass(N, 7); const residue18 = residueClass(N, 18); - const { vertices, adjacency } = buildGraph(N); - const clique = maximumClique(vertices, adjacency); + const activeCount = upperBound(environment.vertices, N); + const clique = maximumClique(environment, activeCount, residue7); const maxSize = clique.length; const residue7Size = residue7.length; const residue18Size = residue18.length; @@ -137,6 +233,70 @@ function scanInterval(minN, maxN) { return rows; } +function candidateSizeForN(N) { + return Math.max(residueClass(N, 7).length, residueClass(N, 18).length); +} + +function candidatePlateauIntervals(minN, maxN) { + const intervals = []; + let start = minN; + let currentSize = candidateSizeForN(minN); + for (let N = minN + 1; N <= maxN; N += 1) { + const size = candidateSizeForN(N); + if (size !== currentSize) { + intervals.push({ min: start, max: N - 1, candidateSize: currentSize }); + start = N; + currentSize = size; + } + } + intervals.push({ min: start, max: maxN, candidateSize: currentSize }); + return intervals; +} + +function scanEndpointMonotonicityInterval(minN, maxN) { + const rows = []; + const endpointChecks = []; + const environment = buildExactEnvironment(maxN); + for (const interval of candidatePlateauIntervals(minN, maxN)) { + const residue7AtEndpoint = residueClass(interval.max, 7); + const residue18AtEndpoint = residueClass(interval.max, 18); + const activeCount = upperBound(environment.vertices, interval.max); + const seedClique = residue7AtEndpoint.length >= residue18AtEndpoint.length + ? residue7AtEndpoint + : residue18AtEndpoint; + const endpointClique = maximumClique(environment, activeCount, seedClique); + const endpointMaxSize = endpointClique.length; + const endpointCertified = endpointMaxSize === interval.candidateSize; + endpointChecks.push({ + interval: `${interval.min}..${interval.max}`, + min: interval.min, + max: interval.max, + candidateSize: interval.candidateSize, + endpointMaxCliqueSize: endpointMaxSize, + endpointCertified, + inferredRowCount: interval.max - interval.min + 1, + }); + for (let N = interval.min; N <= interval.max; N += 1) { + const residue7 = residueClass(N, 7); + const residue18 = residueClass(N, 18); + const exampleClique = residue7.length >= residue18.length ? residue7 : residue18; + rows.push({ + N, + maxCliqueSize: interval.candidateSize, + residue7Size: residue7.length, + residue18Size: residue18.length, + candidateAchievesMaximum: endpointCertified, + exampleMaximumClique: exampleClique, + exampleMatchesResidue7: sameSortedSet(exampleClique, residue7), + exampleMatchesResidue18: sameSortedSet(exampleClique, residue18), + inferredByEndpointMonotonicity: true, + endpointCheckN: interval.max, + }); + } + } + return { rows, endpointChecks }; +} + function summarize(rows) { return { interval: `${rows[0].N}..${rows[rows.length - 1].N}`, @@ -149,16 +309,30 @@ function summarize(rows) { } const args = parseArgs(process.argv.slice(2)); -const rows = scanInterval(args.min, args.max); +const scan = args.endpointMonotonicity + ? scanEndpointMonotonicityInterval(args.min, args.max) + : { rows: scanInterval(args.min, args.max), endpointChecks: null }; +const rows = scan.rows; const payload = { generatedAt: new Date().toISOString(), - method: 'exact_maximum_clique_scan', + method: args.endpointMonotonicity + ? 'endpoint_monotonicity_maximum_clique_scan' + : 'exact_maximum_clique_scan', problemId: '848', parameters: { min: args.min, max: args.max, + endpointMonotonicity: args.endpointMonotonicity, }, summary: summarize(rows), + endpointMonotonicity: args.endpointMonotonicity + ? { + endpointCheckCount: scan.endpointChecks.length, + endpointChecks: scan.endpointChecks, + allEndpointChecksCertified: scan.endpointChecks.every((check) => check.endpointCertified), + lemma: 'If the candidate size is constant on [L,R] and the exact endpoint check proves omega(G_R)=C, monotonicity of induced subgraphs gives omega(G_N)=C for every N in [L,R].', + } + : null, results: rows, }; diff --git a/packs/number-theory/problems/848/context.yaml b/packs/number-theory/problems/848/context.yaml index 83f452c..4225fb5 100644 --- a/packs/number-theory/problems/848/context.yaml +++ b/packs/number-theory/problems/848/context.yaml @@ -2,12 +2,19 @@ problem_id: "848" family_role: finite_check_number_theory_workspace harness_profile: decidable_gap_workspace default_active_route: finite_check_gap_closure -bootstrap_focus: Treat Problem 848 as a finite-gap closure problem and freeze the certificate surface before claiming bounded verification progress. -route_story: Problem 848 is already asymptotically resolved in public, but not yet closed here for all N. The honest job is to shrink the finite remainder with audited threshold tracking and reproducible bounded verification, beginning from the verified base interval `1..2000`. +bootstrap_focus: Treat Problem 848 as a finite-gap closure problem and freeze + the certificate surface before claiming bounded verification progress. +route_story: Problem 848 is already asymptotically resolved in public, but not + yet closed here for all N. The honest job is to shrink the finite remainder + with audited threshold tracking and reproducible bounded verification, + beginning from the verified base interval `1..40500`. frontier_label: finite_check_gap_closure -frontier_detail: The repo now has a verified exact interval `1..2000`; the next question is whether to extend that exact scan further or change method class. -checkpoint_focus: Preserve the distinction between existential N0, explicit N0, sample finite checks, and full closure. -next_honest_move: Decide whether to extend the exact clique scan beyond `2000` or pivot to a different bounded-verification method. +frontier_detail: The repo now has a verified exact interval `1..40500`; the next + question is whether to extend that exact scan further or change method class. +checkpoint_focus: Preserve the distinction between existential N0, explicit N0, + sample finite checks, and full closure. +next_honest_move: Decide whether to extend the exact clique scan beyond `40500` + or pivot to a different bounded-verification method. related_core_problems: - "844" literature_focus: @@ -20,6 +27,7 @@ artifact_focus: - REFERENCES.md - EVIDENCE.md - FORMALIZATION.md + - SEARCH_THEOREM_BRIDGE.md - THRESHOLD_LEDGER.md - OPERATIONAL_THRESHOLD_POSTURE.md - BOUNDED_VERIFICATION_PLAN.md @@ -27,22 +35,53 @@ artifact_focus: - VERIFICATION_CERTIFICATE_SPEC.md - EXTERNAL_VERIFICATION_LEDGER.md - INTERVAL_WORK_QUEUE.yaml - - EXACT_SMALL_N_1_2000_CERTIFICATE.md + - EXACT_SMALL_N_1_40500_CERTIFICATE.md +frontier_loop: + enabled: true + title: frontier_engine_support_lane + summary: Use frontier-engine whenever the finite-check lane needs family-aware + search, GPU ranking, or a refreshed search/theorem bridge for Problem 848. + use_when: + - the theorem-facing lane needs a refreshed repair matrix or GPU leaderboard + - the current route is narrowing a finite gap via structured search rather + than pure archival review + - a GPU-equipped user can pressure-test continuation tails or family-menu + repairs more efficiently than the CPU path + - let the runtime choose `system`, `cpu`, or `gpu` execution automatically + based on the current frontier task + commands: + - erdos number-theory dispatch 848 + - erdos number-theory bridge 848 + - erdos frontier doctor + - erdos frontier setup --cpu + - erdos frontier setup --cuda --torch-index-url + - erdos number-theory bridge-refresh 848 + artifacts: + - SEARCH_THEOREM_BRIDGE.md + - SEARCH_THEOREM_BRIDGE.json question_ledger: open_questions: - - Which imported threshold value is trusted enough to size the finite remainder operationally? - - What certificate format is strong enough to prevent repeat low-trust verification claims? - - How far can the exact clique scan be pushed before a different method class is needed? - - Which public verification attempts are worth auditing rather than rebuilding from scratch? + - Which imported threshold value is trusted enough to size the finite + remainder operationally? + - What certificate format is strong enough to prevent repeat low-trust + verification claims? + - How far can the exact clique scan be pushed before a different method + class is needed? + - Which public verification attempts are worth auditing rather than + rebuilding from scratch? active_route_notes: - Keep the asymptotic theorem separate from the unresolved finite closure. - Keep imported threshold claims separate from repo-owned audited claims. - Prefer interval certificates to raw "checked up to X" claims. - - Use past public verification criticism as a design constraint, not just background chatter. + - Use past public verification criticism as a design constraint, not just + background chatter. route_breakthroughs: - Public asymptotic resolution by Sawhney is already in hand. - - The threshold ledger separating existential and explicit claims is now frozen. - - The repo now has an audited explicit candidate package distinct from the imported public threshold timeline. - - The repo has now chosen bounded finite verification as the next closure lane. - - The repo now has an exact verified base interval `1..2000`. + - The threshold ledger separating existential and explicit claims is now + frozen. + - The repo now has an audited explicit candidate package distinct from the + imported public threshold timeline. + - The repo has now chosen bounded finite verification as the next closure + lane. + - The repo now has an exact verified base interval `1..40500`. problem_solved: [] diff --git a/packs/sunflower/problems/857/AGENT_START.md b/packs/sunflower/problems/857/AGENT_START.md index 3d3eca1..45367a3 100644 --- a/packs/sunflower/problems/857/AGENT_START.md +++ b/packs/sunflower/problems/857/AGENT_START.md @@ -5,6 +5,7 @@ Start here: - `erdos sunflower status 857` - `erdos preflight` - `erdos checkpoints sync` +- if you are opening a bridge, compute, or experimental lane, read `MULTIPLICATIVE_REORIENTATION.md` Current framing: - open problem: yes diff --git a/packs/sunflower/problems/857/CONTEXT.md b/packs/sunflower/problems/857/CONTEXT.md index fde5dba..39f9491 100644 --- a/packs/sunflower/problems/857/CONTEXT.md +++ b/packs/sunflower/problems/857/CONTEXT.md @@ -12,3 +12,6 @@ Frontier framing: - preserve the active export/compression route as the live frontier - keep the recurrence-facing remainder terms explicit in every checkpoint - do not blur route breakthroughs into claims that the open problem is solved + +Adjacent strategy note: +- `MULTIPLICATIVE_REORIENTATION.md` records a conservative bridge-oriented pivot linking `857` more tightly to the `536` / `856` LCM analogue program without replacing the live frontier diff --git a/paper/problems/857/ABSTRACT.md b/paper/problems/857/ABSTRACT.md index 977cd82..f591d4d 100644 --- a/paper/problems/857/ABSTRACT.md +++ b/paper/problems/857/ABSTRACT.md @@ -1,18 +1,24 @@ # Abstract -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: State the exact scope of the paper and separate proved statements from targets or heuristics. +We study the weak sunflower problem recorded as Erdos problem `857`: determine +the growth of the minimum `m(n,k)` such that every family of `m(n,k)` subsets of +`[n]` contains a `k`-sunflower, equivalently a `k`-tuple of sets with identical +pairwise intersections. The problem remains open, and this paper does not claim +its resolution. -Primary public inputs: -- problems/857/STATEMENT.md -- problems/857/EVIDENCE.md -- packs/sunflower/problems/857/FRONTIER_NOTE.md +Instead, we assemble a public-safe progress note around the current research +frontier represented in this repo. We isolate the active route +`anchored_selector_linearization`, identify the strongest closed public support +layer immediately beneath it, and record the exact remaining open seam exposed by +the current board packet. In particular, the public record supports the claim +that the weak-sunflower pack has advanced past generic counting closure and now +concentrates its live pressure on promoting a verified helper/theorem stack into +the named route leaf `anchored_selector_linearization_realized`. -Writing guardrails: -- Open with the exact problem framing and current status. -- Do not imply a full proof unless the public record supports it. -- If the route is incomplete, describe this as progress, structure, or a route note. - -Draft: - -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +We also separate asymptotic proof posture from finite computation. The current +compute surface contains a narrow exact packet for the question whether +`M(8,3) = 45`, marked ready for a local scout, but this does not upgrade the +status of the asymptotic problem. The resulting document is therefore a formal +progress paper: it places problem `857` in the classical and modern sunflower +literature, records the current route architecture, and leaves the remaining +mathematical obligations explicit. diff --git a/paper/problems/857/CITATION_LEDGER.md b/paper/problems/857/CITATION_LEDGER.md index 634394f..cb096b7 100644 --- a/paper/problems/857/CITATION_LEDGER.md +++ b/paper/problems/857/CITATION_LEDGER.md @@ -2,6 +2,15 @@ | Source | Kind | Used For | Status | Notes | | --- | --- | --- | --- | --- | -| https://www.erdosproblems.com/857 | source page | statement, status, public framing | seeded | Canonical public problem source page. | +| https://www.erdosproblems.com/857 | source page | public statement, current open status, weak-sunflower framing | used | Canonical public problem source page. | | https://github.com/teorth/erdosproblems | external import atlas | imported provenance | seeded | Comparison and provenance only; not canonical authority. | -| (add source) | paper / book / note / dataset | theorem, history, comparison, or method | pending | Add exact identifiers before using in prose. | +| P. Erdos and R. Rado, "Intersection theorems for systems of sets", J. Lond. Math. Soc. 35 (1960), 85-90. https://doi.org/10.1112/jlms/s1-35.1.85 | paper | original sunflower lemma and historical baseline | used | Classical starting point for the sunflower program. | +| P. Erdos and D. J. Kleitman, "Extremal problems among subsets of a set", Discrete Math. 8 (1974), 281-294. https://doi.org/10.1016/0012-365X(74)90140-X | survey paper | historical framing and Erdos problem context | used | Useful for broad historical framing. | +| P. Erdos and E. Szemeredi, "Combinatorial properties of systems of sets", J. Combin. Theory Ser. A 24 (1978), 308-313. https://doi.org/10.1016/0097-3165(78)90060-2 | paper | weak-sunflower problem context and non-uniform formulation | used | Standard source for sunflower-free set-system bounds. | +| N. Alon, A. Shpilka, and C. Umans, "On sunflowers and matrix multiplication", Computational Complexity 22 (2013), 219-243. https://doi.org/10.1007/s00037-013-0060-1 | paper | cap-set and multicolored-sunflower connection for `k=3` | used | Problem page points to this connection. | +| E. Naslund and W. Sawin, "Upper bounds for sunflower-free sets", Forum Math. Sigma 5 (2017), e15. https://doi.org/10.1017/fms.2017.12 | paper | best cited asymptotic bound for the weak `k=3` case used in this draft | used | Gives the `(3 / 2^{2/3})^{(1+o(1))n}` upper bound quoted on the problem page. | +| R. Alweiss, S. Lovett, K. Wu, and J. Zhang, "Improved bounds for the sunflower lemma", Ann. of Math. 194 (2021), 795-815. https://doi.org/10.4007/annals.2021.194.3.5 | paper | modern uniform sunflower breakthrough and spread-method context | used | Included for general sunflower context rather than as a direct weak-sunflower theorem. | +| A. Rao, "Coding for Sunflowers", Discrete Analysis 2020:2. https://doi.org/10.19086/da.11887 | paper | improved uniform-sunflower bound and coding viewpoint | used | Useful for method context and clean exposition. | +| T. Bell, S. Chueluecha, and L. Warnke, "Note on sunflowers", Discrete Math. 344 (2021), 112367. https://doi.org/10.1016/j.disc.2021.112367 | note | current `O(p log k)` sunflower-lemma improvement | used | Included for current best general-sunflower bound cited in exposition. | +| A. Rao, "Sunflowers: from soil to oil", Bull. Amer. Math. Soc. 60 (2023), 29-38. https://doi.org/10.1090/bull/1777 | survey article | broader mathematical context and recent sunflower narrative | used | Expository survey tying together recent breakthroughs. | +| A. Bishnoi, B. Kielak, B. Kovacs, Z. L. Nagy, G. Somlai, M. Vizer, and Z. Zheng, "The generalized trifference problem", CoRR abs/2505.07706 (2025). https://dblp.org/rec/journals/corr/abs-2505-07706 | preprint | adjacent recent direction for three-way difference phenomena | used | Mentioned as neighboring work rather than a direct result on problem `857`. | diff --git a/paper/problems/857/COMPUTATIONAL_AND_FORMAL_EVIDENCE.md b/paper/problems/857/COMPUTATIONAL_AND_FORMAL_EVIDENCE.md index ecfe37e..bb97cef 100644 --- a/paper/problems/857/COMPUTATIONAL_AND_FORMAL_EVIDENCE.md +++ b/paper/problems/857/COMPUTATIONAL_AND_FORMAL_EVIDENCE.md @@ -1,17 +1,33 @@ # Computational and Formal Evidence -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Summarize computational packets, certificates, and formalization posture without inflating them into stronger claims. +The public bundle for problem `857` is formalization-aware, but it is not yet a +public formal proof archive for the full weak sunflower problem. The formalization +record is currently: +- status: active +- active route: `anchored_selector_linearization` +- upstream theorem-module references: + `SunflowerLean/ObstructionGlobalBridge.lean` and + `SunflowerLean/ObstructionExport.lean` -Primary public inputs: -- problems/857/FORMALIZATION.md -- packs/sunflower/compute/857/m8_exactness_cube_and_certificate_v0.yaml +This means that the public pack knows where theorem and verification work is +supposed to interface with the route, but it does not yet expose a complete +repo-local theorem chain proving the asymptotic target. -Writing guardrails: -- State what was checked, what was not checked, and what level of confidence the computation supports. -- Keep verification surface, compute surface, and proof surface distinct. -- If no formal artifact is public yet, say so directly. +The current compute surface is even narrower. The only packaged compute lane is +`m8_exactness_cube_and_certificate_v0.yaml`, which asks whether `M(8,3) = 45`, +equivalently whether a target-46 SAT instance is UNSAT. Its metadata is precise: +- claim-level goal: exact +- status: `ready_for_local_scout` +- recommendation: `cpu_first` +- approval required: yes +- next honest move: local scout before any paid rung -Draft: +Two boundaries are important. -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +First, the compute lane concerns a finite exact question. Even if fully certified, +it would not by itself imply an asymptotic formula for `m(n,k)`. + +Second, the route packets and formalization references help organize and check the +current frontier, but they do not yet authorize a claim that problem `857` is +formally solved. The correct reading is that proof surface, formalization surface, +and compute surface are all active, but they remain distinct. diff --git a/paper/problems/857/INTRODUCTION.md b/paper/problems/857/INTRODUCTION.md index 5e3fc9b..8fb7608 100644 --- a/paper/problems/857/INTRODUCTION.md +++ b/paper/problems/857/INTRODUCTION.md @@ -1,19 +1,43 @@ # Introduction -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Explain why the problem matters, what the current route is, and how the paper is organized. +The sunflower problem sits near the center of modern extremal set theory. In its +classical form, initiated by Erdos and Rado, one asks how large a family of sets +of bounded size can be before a sunflower must appear. Problem `857` records the +non-uniform or weak version: for fixed `k`, determine the least `m(n,k)` such +that every family of `m(n,k)` subsets of `[n]` contains a `k`-sunflower. The +public Erdos Problems page keeps this problem open and emphasizes the goal of +bounding `m(n,k)` by `C(k)^n`. -Primary public inputs: -- problems/857/STATEMENT.md -- problems/857/REFERENCES.md -- packs/sunflower/problems/857/FRONTIER_NOTE.md -- packs/sunflower/README.md +This weak formulation is broader than the uniform sunflower lemma and interacts +with several major themes in recent combinatorics. For `k = 3`, the problem is +closely tied to cap-set-type phenomena, as highlighted by Alon, Shpilka, and +Umans, and the best quoted asymptotic upper bound on the problem page comes from +Naslund and Sawin. At the same time, progress on the uniform sunflower lemma by +Alweiss, Lovett, Wu, and Zhang, followed by Rao and by Bell, Chueluecha, and +Warnke, has reshaped the methodological landscape and clarified which kinds of +spread, entropy, and coding ideas are now available. -Writing guardrails: -- Ground motivation in public sources and cited literature. -- Explain the active route without overselling its maturity. -- State the paper organization at the end of the section. +The purpose of this paper is narrower than a complete solution. We convert the +current public record for problem `857` into a mathematically legible progress +paper. The main value added here is organizational and expository: we identify +the active route, separate closed support layers from live frontier work, and +state exactly what the present public compute and formalization packets do and do +not show. This is important because the repo now contains genuine route +structure, but not yet a public theorem text closing the asymptotic weak +sunflower problem. -Draft: +Our central public claim is therefore modest and precise. The current weak +sunflower pack is no longer bottlenecked on generic counting closure. Its live +public frontier is the route `anchored_selector_linearization`, and the smallest +honest next move is the ready atom `T10.G3.A2`, which promotes the current +helper/theorem stack into the named leaf +`anchored_selector_linearization_realized`. Everything in this paper is written +to preserve that distinction between route progress and problem closure. -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +The paper is organized as follows. Section 2 fixes notation and recalls the weak +sunflower problem and the most relevant background. Section 3 places the present +route in the wider literature. Sections 4 through 6 record the exact public +results, their dependency chain, and the remaining proof obligations. Section 7 +separates formalization posture from the narrow exact-computation packet around +`M(8,3)`. Section 8 lists the limitations of the present route and the clearest +open next steps. diff --git a/paper/problems/857/LIMITATIONS_AND_OPEN_PROBLEMS.md b/paper/problems/857/LIMITATIONS_AND_OPEN_PROBLEMS.md index 76f4dcf..c61a0f9 100644 --- a/paper/problems/857/LIMITATIONS_AND_OPEN_PROBLEMS.md +++ b/paper/problems/857/LIMITATIONS_AND_OPEN_PROBLEMS.md @@ -1,17 +1,43 @@ # Limitations and Open Problems -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Leave a clean handoff for the next researcher with honest boundaries and unresolved tasks. +The most important limitation is straightforward: problem `857` is still open. +This paper records route structure and evidence boundaries, not a completed +solution. -Primary public inputs: -- packs/sunflower/problems/857/FRONTIER_NOTE.md -- packs/sunflower/problems/857/ATOMIC_BOARD.md +## Near-term route limitations -Writing guardrails: -- List the current bottlenecks plainly. -- Separate near-term route tasks from broader mathematical open problems. -- Do not hide failure modes or uncertainty. +- The active leaf `anchored_selector_linearization_realized` is not yet publicly closed. +- Ticket `T10` is still open, with the public board placing the live pressure in + gate `G3`. +- The next named move, `T10.G3.A2`, has been localized but not yet discharged in + the public pack. +- The route packet still describes the frontier as recurrence-facing rather than + recurrence-complete. -Draft: +## Evidence limitations -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +- The closed support layer beneath the frontier is organizationally strong, but + the public bundle does not yet expose the full theorem text needed to promote + the active leaf. +- The current formalization posture is active without being a public end-to-end + formal proof. +- The `M(8,3)` compute packet is valuable but narrow; it does not settle the + asymptotic weak sunflower problem. + +## Broader mathematical open problems + +- Determine the correct asymptotic growth of `m(n,k)` for fixed `k`. +- Understand whether the strongest current `k = 3` methods can be extended in a + way that meaningfully informs larger `k`. +- Clarify how far uniform-sunflower spread and coding methods can be transferred + into genuinely non-uniform weak-sunflower settings. +- Relate the weak sunflower route more tightly to adjacent three-way difference + problems without losing the problem-specific structure of `857`. + +## Concrete next handoff + +If one stays faithful to the current public record, the next move is not vague: +promote the helper/theorem stack into +`anchored_selector_linearization_realized`, checkpoint that leaf honestly, and +only then revisit whether the route can be upgraded from frontier progress to a +stronger public claim. diff --git a/paper/problems/857/MAIN_RESULTS.md b/paper/problems/857/MAIN_RESULTS.md index 1fec195..bed5849 100644 --- a/paper/problems/857/MAIN_RESULTS.md +++ b/paper/problems/857/MAIN_RESULTS.md @@ -1,18 +1,44 @@ # Main Results -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: List the exact theorems, propositions, or route claims supported by the current public record. +The present bundle supports a sequence of route claims and evidence claims rather +than a complete theorem on the asymptotic weak sunflower problem. -Primary public inputs: -- problems/857/EVIDENCE.md -- problems/857/FORMALIZATION.md -- packs/sunflower/problems/857/FRONTIER_NOTE.md +## Supported public claims -Writing guardrails: -- Separate proved results, conditional results, heuristics, and targets. -- Use theorem language only for claims backed by the current public record. -- When in doubt, downgrade to a route claim or open objective. +1. Problem `857` remains open. +The canonical problem dossier, the public problem page, and the frontier note all +agree that the weak sunflower problem has not been solved. -Draft: +2. The active public route is `anchored_selector_linearization`. +This route is recorded as the unique live frontier in the current pack, and it is +described as the only route with a dependency-satisfied ready atom. -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +3. The strongest closed public support layer immediately beneath the frontier is +`o1a_existential_explicit_export`. +The ops packet records this route as strict-closed and identifies it as support +context for, rather than a replacement of, the active frontier. + +4. The current live blocker is localized. +Ticket `T10` is open, with `2/5` gates and `9/15` atoms complete, and the first +ready atom is `T10.G3.A2`, whose task is to promote the helper/theorem stack into +`anchored_selector_linearization_realized`. + +5. The public compute surface is narrow and exact in scope. +The only packaged compute lane currently exposed for problem `857` is the local +scout packet asking whether `M(8,3) = 45`. It is explicitly marked as an exact +lane and not as asymptotic closure of the weak sunflower problem. + +## What is not claimed + +- We do not claim a proof that `m(n,k) <= C(k)^n`. +- We do not claim that the active route leaf + `anchored_selector_linearization_realized` has already been closed. +- We do not claim that the current compute packet certifies anything beyond the + stated finite exact question. + +## Paper contribution + +The main contribution of this draft is therefore formalization of the public +record itself: it turns the pack state of problem `857` into a stable mathematical +narrative with an explicit dependency chain, explicit evidence boundaries, and an +explicit next open obligation. diff --git a/paper/problems/857/OUTLINE.md b/paper/problems/857/OUTLINE.md index 229e58f..f200d29 100644 --- a/paper/problems/857/OUTLINE.md +++ b/paper/problems/857/OUTLINE.md @@ -1,6 +1,11 @@ # Outline -Working paper shape: claim-safe progress paper or route paper +Working title: +- `A Progress Note on the Weak Sunflower Problem and the Anchored-Selector Frontier` + +Paper shape: +- claim-safe progress paper +- public route paper for Erdos problem `857` Recommended order: 1. Abstract @@ -14,7 +19,13 @@ Recommended order: 9. Limitations and Open Problems Angle: -- problem: Erdos Problem #857 -- active route: anchored_selector_linearization -- open problem: yes -- rewrite this outline once the paper scope is fixed +- state the weak sunflower problem in standard mathematical language +- position problem `857` inside the broader sunflower literature +- record the strongest closed public support layer below the frontier +- explain why `anchored_selector_linearization` is the live route +- isolate the exact open seam: `T10.G3.A2` + +Non-goals: +- do not claim a complete proof of problem `857` +- do not flatten route architecture into generic sunflower rhetoric +- do not upgrade the `M(8,3)` packet into more than a narrow exact-computation lane diff --git a/paper/problems/857/PRELIMINARIES.md b/paper/problems/857/PRELIMINARIES.md index 8a6f095..a90cc15 100644 --- a/paper/problems/857/PRELIMINARIES.md +++ b/paper/problems/857/PRELIMINARIES.md @@ -1,18 +1,43 @@ # Preliminaries -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Define notation, setup, and prior results that the rest of the paper relies on. +We write `[n] = {1, ..., n}`. A family `F` of subsets of `[n]` is a +`k`-sunflower if there exist distinct sets `A_1, ..., A_k in F` such that +`A_i cap A_j` is the same set for every `i != j`. Equivalently, if +`K = A_1 cap ... cap A_k`, then the petals `A_1 \ K, ..., A_k \ K` are pairwise +disjoint. -Primary public inputs: -- problems/857/STATEMENT.md -- problems/857/REFERENCES.md -- problems/857/FORMALIZATION.md +Problem `857` asks for the least integer `m(n,k)` such that every family of +`m(n,k)` subsets of `[n]` contains a `k`-sunflower. The target asymptotic shape +recorded in this repo is an estimate of the form `m(n,k) <= C(k)^n`. This is the +weak or non-uniform sunflower problem, to be contrasted with the more classical +uniform parameter `f_r(w)` governing families of `w`-element sets. The uniform +and weak formulations are not identical, but the methods developed for each have +strongly influenced the other. -Writing guardrails: -- Define every symbol before it is used in a claim. -- Cite prior results rather than paraphrasing them from memory. -- Keep imported facts distinct from new statements in this repo. +Three pieces of background will be used repeatedly in the discussion below. -Draft: +First, Erdos and Rado proved the classical sunflower lemma, showing that for +fixed `r` there is always some finite threshold forcing an `r`-sunflower inside a +large enough `w`-uniform family. Their conjectural vision is that this threshold +should be exponential in `w` for each fixed `r`. -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +Second, Erdos and Szemeredi formulated the non-uniform sunflower-free problem in +a way that directly informs problem `857`. For the present draft, that paper +serves as the main historical source for the weak problem rather than merely as a +neighboring result. + +Third, when `k = 3`, the weak problem interacts with cap-set-type methods. The +problem page cites Alon, Shpilka, and Umans for this connection and records the +Naslund-Sawin bound +`m(n,3) <= (3 / 2^{2/3})^{(1+o(1))n}`. + +Finally, we separate three notions that must not be conflated in this paper: +- proof posture: whether the asymptotic weak sunflower problem has been solved +- route posture: which research lane is currently the live frontier +- formalization posture: whether public theorem modules or verification artifacts + have been exposed and in what scope + +For problem `857`, these are respectively: +- open +- `anchored_selector_linearization` +- active, but not yet a public formal proof bundle for full closure diff --git a/paper/problems/857/PROOF_DETAILS.md b/paper/problems/857/PROOF_DETAILS.md index e74a94c..6d65275 100644 --- a/paper/problems/857/PROOF_DETAILS.md +++ b/paper/problems/857/PROOF_DETAILS.md @@ -1,18 +1,47 @@ # Proof Details -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Write the technical proof content or the best current public decomposition when the proof is incomplete. +This section records the best current public decomposition of the active route. It +is not a complete proof of problem `857`. -Primary public inputs: -- problems/857/EVIDENCE.md -- packs/sunflower/problems/857/ATOMIC_BOARD.md -- packs/sunflower/problems/857/ROUTE_PACKET.yaml +## PD.1. Closed support theorem stack -Writing guardrails: -- Do not skip unresolved steps by rhetorical compression. -- If a subclaim is computational or formal, point to the exact public evidence packet. -- Use local labels for lemmas and keep missing subproofs visible. +The public route packets identify `o1a_existential_explicit_export` as the last +fully closed support layer beneath the frontier. In practical terms, this means +that the current route already has an explicit anchored remainder package to stand +on. Any future public proof of the active leaf should treat this layer as input, +not as a target to be reproved from scratch. -Draft: +## PD.2. Active leaf realization obligation -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +The frontier route `anchored_selector_linearization` is currently described as an +export of the live helper stack into a route-facing leaf that stays honest about +the open-problem boundary. The exact unresolved obligation is to promote that +helper/theorem stack into the named leaf +`anchored_selector_linearization_realized`. + +The public board localizes this to atom `T10.G3.A2`, with two listed +dependencies: +- the anchored-selector helper stack remains verified +- the route and ticket wording stays synchronized + +These dependencies matter because they show that the remaining task is not merely +editorial. The current route must become a stable, public-facing theorem package +without collapsing the distinction between local route closure and global problem +closure. + +## PD.3. Recurrence-facing interface + +The route packet repeatedly emphasizes explicit remainder and compression terms, +and it frames the frontier as pushing those terms toward a recurrence-facing step. +This is the correct place to state the present proof gap: the public record does +not yet expose a finished recurrence-facing theorem that closes the asymptotic +weak sunflower problem. + +## PD.4. Consequence for manuscript style + +Any mathematically honest exposition must therefore: +- cite the closed support layers as already packaged +- describe the active leaf as a real frontier rather than as solved +- state the recurrence-facing closure as an open obligation +- keep any finite computation or formal verification separate from asymptotic + proof claims diff --git a/paper/problems/857/PROOF_OVERVIEW.md b/paper/problems/857/PROOF_OVERVIEW.md index e12efa0..38d2779 100644 --- a/paper/problems/857/PROOF_OVERVIEW.md +++ b/paper/problems/857/PROOF_OVERVIEW.md @@ -1,18 +1,39 @@ # Proof Overview -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Give the roadmap of the argument and the dependency chain between major steps. +Because the current public bundle does not yet expose a full theorem text for the +active leaf, the correct proof overview is a dependency overview. Its role is to +explain which parts of the route are already packaged and where the unresolved +mathematics now sits. -Primary public inputs: -- problems/857/EVIDENCE.md -- packs/sunflower/problems/857/ATOMIC_BOARD.md -- packs/sunflower/problems/857/FRONTIER_NOTE.md +The route architecture recorded in the public pack has the following shape. -Writing guardrails: -- Explain the dependency chain before entering technical details. -- Call out any open seam, blocked lemma, or incomplete dependency explicitly. -- Keep route state and proved state separate. +1. Closed export layers. +The route history identifies a sequence of completed public export layers: +`global_family_card_export`, +`explicit_remainder_export`, +`explicit_M_remainder_export`, and +`o1a_existential_explicit_export`. +These layers provide the strongest public support presently available below the +frontier. -Draft: +2. Active frontier layer. +Above those completed exports sits the route +`anchored_selector_linearization`. The route packet describes its purpose as +preserving the live export/compression frontier while pushing the explicit O1a +remainder package toward a genuine recurrence-facing step. -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +3. Ticket-level concentration of difficulty. +The atomic board localizes the live pressure inside ticket `T10`, whose gate +story says that the early gates are satisfied and the remaining pressure is +concentrated in the `G3` seam. + +4. Atom-level next move. +The first ready atom is `T10.G3.A2`, which is exactly the point at which the +active route becomes a genuine named leaf. In the current public record, this is +the smallest honest next move. + +The main mathematical message of this overview is therefore negative as well as +positive. Positive: the pack has advanced far enough that the frontier is no +longer a vague aspiration, but a specific route with a specific ready atom. +Negative: the active leaf itself is not yet publicly closed, so the proof chain +still contains an explicit open seam. diff --git a/paper/problems/857/RELATED_WORK.md b/paper/problems/857/RELATED_WORK.md index 0be8179..cdd31ab 100644 --- a/paper/problems/857/RELATED_WORK.md +++ b/paper/problems/857/RELATED_WORK.md @@ -1,18 +1,35 @@ # Related Work -Problem: Erdos Problem #857 — Sunflower Conjecture -Section role: Place the current route in the context of prior literature and nearby approaches. +The first layer of background is classical. Erdos and Rado introduced the +sunflower lemma and the central conjectural picture for fixed-petal sunflowers. +Erdos later revisited the surrounding extremal set-theoretic landscape in a broad +survey with Kleitman. For the weak, non-uniform side of the story most relevant +to problem `857`, the paper of Erdos and Szemeredi remains a central reference. -Primary public inputs: -- problems/857/REFERENCES.md -- problems/857/EVIDENCE.md -- packs/sunflower/problems/857/FRONTIER_NOTE.md +The second layer is the modern structural breakthrough on the uniform problem. +Alweiss, Lovett, Wu, and Zhang introduced the spread-method viewpoint and proved +the first dramatically subfactorial general upper bound. Rao then reformulated +the argument via coding ideas, and Bell, Chueluecha, and Warnke sharpened the +general bound further to `O(p log k)` in the `p`-petal, `k`-uniform setting. Rao +later gave a concise survey explaining how these ideas connect to a wider class +of combinatorial threshold phenomena. -Writing guardrails: -- Each literature claim should have a ledger entry in CITATION_LEDGER.md. -- Describe competing or historical approaches fairly and briefly. -- Mark unresolved comparisons as open rather than implied. +The third layer is the weak-sunflower and cap-set interface. The Erdos Problems +page for `857` specifically points to the connection observed by Alon, Shpilka, +and Umans when `k = 3`. Naslund and Sawin then obtained the strongest bound +quoted on the page, namely +`m(n,3) <= (3 / 2^{2/3})^{(1+o(1))n}`. +This remains the key external asymptotic benchmark explicitly attached to the +public statement of problem `857`. -Draft: +There are also new neighboring directions that do not solve problem `857` but +help frame the surrounding landscape. One recent example is the generalized +trifference problem, which studies three-way separation constraints in ternary +vector spaces and can be viewed as another point of contact between sunflower-free +phenomena, coding structure, and exact small-parameter questions. -> Start writing here. Keep every claim matched to public evidence or clearly labeled as conjectural, heuristic, or computational. +The present paper is complementary to all of this literature. It does not prove a +new asymptotic theorem on `m(n,k)`. Instead, it formalizes the current public +research state of one specific weak-sunflower route: which support layers are +closed, where the frontier has moved, and what evidence currently exists in +computational and formalized form. diff --git a/paper/problems/857/SECTION_STATUS.md b/paper/problems/857/SECTION_STATUS.md index 613f97d..1c397e7 100644 --- a/paper/problems/857/SECTION_STATUS.md +++ b/paper/problems/857/SECTION_STATUS.md @@ -2,12 +2,12 @@ | Section | Status | Primary public inputs | Notes | | --- | --- | --- | --- | -| Abstract | not started | problems/857/STATEMENT.md
problems/857/EVIDENCE.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Keep claims honest and source-backed. | -| Introduction | not started | problems/857/STATEMENT.md
problems/857/REFERENCES.md
packs/sunflower/problems/857/FRONTIER_NOTE.md
packs/sunflower/README.md | Keep claims honest and source-backed. | -| Preliminaries | not started | problems/857/STATEMENT.md
problems/857/REFERENCES.md
problems/857/FORMALIZATION.md | Keep claims honest and source-backed. | -| Related Work | not started | problems/857/REFERENCES.md
problems/857/EVIDENCE.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Keep claims honest and source-backed. | -| Main Results | not started | problems/857/EVIDENCE.md
problems/857/FORMALIZATION.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Keep claims honest and source-backed. | -| Proof Overview | not started | problems/857/EVIDENCE.md
packs/sunflower/problems/857/ATOMIC_BOARD.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Keep claims honest and source-backed. | -| Proof Details | not started | problems/857/EVIDENCE.md
packs/sunflower/problems/857/ATOMIC_BOARD.md
packs/sunflower/problems/857/ROUTE_PACKET.yaml | Keep claims honest and source-backed. | -| Computational and Formal Evidence | not started | problems/857/FORMALIZATION.md
packs/sunflower/compute/857/m8_exactness_cube_and_certificate_v0.yaml | Keep claims honest and source-backed. | -| Limitations and Open Problems | not started | packs/sunflower/problems/857/FRONTIER_NOTE.md
packs/sunflower/problems/857/ATOMIC_BOARD.md | Keep claims honest and source-backed. | +| Abstract | drafted | problems/857/STATEMENT.md
problems/857/EVIDENCE.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | First claim-safe abstract written as a progress paper. | +| Introduction | drafted | problems/857/STATEMENT.md
problems/857/REFERENCES.md
packs/sunflower/problems/857/FRONTIER_NOTE.md
packs/sunflower/README.md | Frames `857` inside the wider sunflower program. | +| Preliminaries | drafted | problems/857/STATEMENT.md
problems/857/REFERENCES.md
problems/857/FORMALIZATION.md | Records notation and known public background only. | +| Related Work | drafted | problems/857/REFERENCES.md
problems/857/EVIDENCE.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Connects the weak problem to uniform-sunflower and cap-set literature. | +| Main Results | drafted | problems/857/EVIDENCE.md
problems/857/FORMALIZATION.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Written as route claims and evidence claims, not theorem inflation. | +| Proof Overview | drafted | problems/857/EVIDENCE.md
packs/sunflower/problems/857/ATOMIC_BOARD.md
packs/sunflower/problems/857/FRONTIER_NOTE.md | Gives dependency chain from closed support layers to `T10`. | +| Proof Details | drafted | problems/857/EVIDENCE.md
packs/sunflower/problems/857/ATOMIC_BOARD.md
packs/sunflower/problems/857/ROUTE_PACKET.yaml | Explicitly leaves missing proof obligations visible. | +| Computational and Formal Evidence | drafted | problems/857/FORMALIZATION.md
packs/sunflower/compute/857/m8_exactness_cube_and_certificate_v0.yaml | Keeps proof, formalization, and compute surfaces separate. | +| Limitations and Open Problems | drafted | packs/sunflower/problems/857/FRONTIER_NOTE.md
packs/sunflower/problems/857/ATOMIC_BOARD.md | Ends with a concrete next move and broader mathematical questions. | diff --git a/problems/848/AGENT_START.md b/problems/848/AGENT_START.md index b6e4fff..9a005f0 100644 --- a/problems/848/AGENT_START.md +++ b/problems/848/AGENT_START.md @@ -3,6 +3,9 @@ Fast start: - `erdos problem show 848` - `erdos workspace show` +- `erdos number-theory dispatch 848` +- `erdos number-theory bridge 848` +- `erdos frontier doctor` - `erdos preflight` - `erdos continuation use route` - `erdos checkpoints sync` @@ -23,11 +26,37 @@ Read in this order: - `FORMALIZATION.md` - `PUBLIC_STATUS_REVIEW.md` - `AGENT_WEBSEARCH_BRIEF.md` +- `packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md` + +Frontier-engine hook: +- only activate this loop when the workspace is explicitly opted in +- if `erdos number-theory status 848` or `erdos workspace show` reports + `Frontier loop: active (cpu)` or `Frontier loop: active (gpu)`, treat `frontier-engine` + as part of the normal route loop rather than a side tool +- if the loop is inactive, keep it out of the active route plan and use: + - `erdos frontier doctor` + - `erdos frontier setup --base --apply` + - `erdos frontier setup --cuda --torch-index-url --apply` + to intentionally opt in at the appropriate mode +- once active, start with `erdos number-theory dispatch 848` +- the dispatch command now ranks the live next move across: + - canonical bridge refresh + - managed CPU family search + - managed GPU ladder sweep + - exact small-`N` interval scouting +- use `erdos number-theory dispatch 848 --apply` to run the current primary move, or + `--action ` to force a specific lane +- `bridge-refresh` now auto-resolves the execution path it needs: + - `system` when only the bundled bridge exporter is needed + - `cpu` when the managed frontier runtime is opted in + - `gpu` when the managed CUDA runtime is opted in and available First honest move: - isolate the exact finite remainder left after Sawhney's sufficiently-large-`N` theorem - determine whether the missing closure is an explicit threshold extraction problem, a pure finite computation problem, or a mixed lane +- if the mixed lane wins, route through the frontier-engine bridge instead of treating GPU search + as out-of-band work - keep every note honest about the gap between `decidable` and fully `solved` - read the Sawhney note before touching the forum heuristics, then use the forum only to map candidate threshold-improvement strategies and public finite-check coverage diff --git a/problems/857/EVIDENCE.md b/problems/857/EVIDENCE.md index c671658..5bdbfe2 100644 --- a/problems/857/EVIDENCE.md +++ b/problems/857/EVIDENCE.md @@ -1,9 +1,59 @@ # Problem 857 Evidence -Current dossier placeholder. +## Canonical status -Track here: -- route breakthroughs -- formal theorem checkpoints -- computational artifacts -- failed-path summaries +- site status: open +- repo status: active +- formalization status: active +- active route: `anchored_selector_linearization` +- route breakthrough: yes +- problem solved: no + +## Public route record + +The public pack supports an honest progress claim, not a solved-problem claim. +The current frontier note states that the weak-sunflower pack is no longer +bottlenecked on generic counting closure and that the live public seam is the +anchored-selector linearization route. + +The atomic board further records that: +- `T10` is the active ticket for problem `857` +- the ticket leaf `anchored_selector_linearization_realized` is still open +- current public progress on `T10` is `2/5` gates and `9/15` atoms +- the first dependency-satisfied ready atom is `T10.G3.A2` + +## Closed public support layers + +The route history and ops packet identify the following layers as closed public +support beneath the live frontier: +- `global_family_card_export` +- `explicit_remainder_export` +- `explicit_M_remainder_export` +- `o1a_existential_explicit_export` + +The strongest closed support layer immediately below the active frontier is +`o1a_existential_explicit_export`, recorded as a strict-closed route in +`packs/sunflower/problems/857/OPS_DETAILS.yaml`. + +## Computational artifact + +The current public compute packet is: +- `packs/sunflower/compute/857/m8_exactness_cube_and_certificate_v0.yaml` + +Its scope is narrow and explicit: +- question: whether `M(8,3) = 45`, equivalently whether the target-46 SAT instance is UNSAT +- claim-level goal: exact +- status: `ready_for_local_scout` +- next honest move: local scout first, before any paid rung + +This packet is evidence packaging only. It is not, by itself, a published proof +of any asymptotic statement about `m(n,k)`. + +## Honest publication posture + +The current public record supports the following manuscript posture: +- present problem `857` as open +- describe the active route as `anchored_selector_linearization` +- describe the strongest finished support layer as `o1a_existential_explicit_export` +- describe the current compute posture as a local-scout-ready exact packet for `M(8,3)` +- keep the open seam visible: promote the helper/theorem stack into `anchored_selector_linearization_realized` diff --git a/problems/857/FORMALIZATION.md b/problems/857/FORMALIZATION.md index 0f9299a..20b7f0d 100644 --- a/problems/857/FORMALIZATION.md +++ b/problems/857/FORMALIZATION.md @@ -2,5 +2,19 @@ Current posture: - formalization status: active -- active route: anchored_selector_linearization -- main upstream lab: sunflower-coda +- active route: `anchored_selector_linearization` +- main upstream lab: `sunflower-coda` + +Public-facing distinction: +- proof status: open problem +- route status: active breakthrough route +- formalization posture: theorem modules are referenced from the upstream lab, but no repo-local formal theorem for full problem closure is currently exposed in this public bundle + +Named public modules referenced by the route packets: +- `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionGlobalBridge.lean` +- `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` + +Interpretation: +- the public bundle is formalization-aware +- it is not yet a public formal proof bundle for problem `857` +- paper language should therefore treat formal artifacts as support for route organization and verification posture, not as proof of the full weak sunflower problem diff --git a/problems/857/REFERENCES.md b/problems/857/REFERENCES.md index 088c3fb..ecbbc04 100644 --- a/problems/857/REFERENCES.md +++ b/problems/857/REFERENCES.md @@ -1,5 +1,27 @@ # Problem 857 References -- Erdos Problems page: -- Related problems: `20`, `536`, `856` -- Repo note: this is the primary weak-sunflower deep-harness problem +Core problem source: +- T. F. Bloom, "Erdos Problem #857", . + +Classical sunflower literature: +- P. Erdos and R. Rado, "Intersection theorems for systems of sets", Journal of the London Mathematical Society 35 (1960), 85-90. DOI: . +- P. Erdos and D. J. Kleitman, "Extremal problems among subsets of a set", Discrete Mathematics 8 (1974), 281-294. DOI: . +- P. Erdos and E. Szemeredi, "Combinatorial properties of systems of sets", Journal of Combinatorial Theory, Series A 24 (1978), 308-313. DOI: . + +Weak-sunflower and nearby modern references: +- N. Alon, A. Shpilka, and C. Umans, "On sunflowers and matrix multiplication", Computational Complexity 22 (2013), 219-243. DOI: . +- E. Naslund and W. Sawin, "Upper bounds for sunflower-free sets", Forum of Mathematics, Sigma 5 (2017), e15. DOI: . + +General sunflower-method references: +- R. Alweiss, S. Lovett, K. Wu, and J. Zhang, "Improved bounds for the sunflower lemma", Annals of Mathematics 194 (2021), 795-815. DOI: . +- A. Rao, "Coding for Sunflowers", Discrete Analysis 2020:2. DOI: . +- T. Bell, S. Chueluecha, and L. Warnke, "Note on sunflowers", Discrete Mathematics 344 (2021), 112367. DOI: . +- A. Rao, "Sunflowers: from soil to oil", Bulletin of the American Mathematical Society 60 (2023), 29-38. DOI: . + +Recent adjacent direction: +- A. Bishnoi, B. Kielak, B. Kovacs, Z. L. Nagy, G. Somlai, M. Vizer, and Z. Zheng, "The generalized trifference problem", CoRR abs/2505.07706 (2025). Persistent record: . + +Related repo problems: +- `20`: strong / uniform sunflower core +- `536`: natural-density LCM analogue +- `856`: harmonic-density LCM analogue diff --git a/problems/857/STATEMENT.md b/problems/857/STATEMENT.md index 14709a4..ead9957 100644 --- a/problems/857/STATEMENT.md +++ b/problems/857/STATEMENT.md @@ -2,7 +2,20 @@ Source: -Normalized focus: +Canonical public formulation: + +Let `m = m(n,k)` be minimal such that every family +`A_1, ..., A_m subseteq {1, ..., n}` contains a sunflower of size `k`, +meaning a subfamily of `k` sets whose pairwise intersections are all equal. +Estimate `m(n,k)`, or, more ambitiously, determine its asymptotic growth. + +Working normalization in this repo: - weak sunflower problem -- bound `m(n,k)` by `C(k)^n` -- current deep-harness frontier lives in the sunflower pack +- non-uniform set systems over `[n]` +- target asymptotic shape: `m(n,k) <= C(k)^n` +- `k = 3` is the most developed nearby case in the public literature + +Context notes: +- the Erdos Problems page records that Erdos also asked an equivalent union-formulation version +- the current repo pack treats problem `857` as the weak / non-uniform core of the sunflower cluster +- the active public route is `anchored_selector_linearization` diff --git a/research/README.md b/research/README.md index db49441..e1d74c2 100644 --- a/research/README.md +++ b/research/README.md @@ -9,3 +9,4 @@ Use it for: - route decompositions - wave histories - deep public artifacts that are too heavy or too fluid for the packaged CLI surface +- standalone research-engine prototypes that may later integrate with the CLI diff --git a/src/cli/index.js b/src/cli/index.js index d2d15c9..a6365bc 100644 --- a/src/cli/index.js +++ b/src/cli/index.js @@ -4,6 +4,7 @@ import { runCheckpointsCommand } from '../commands/checkpoints.js'; import { runClusterCommand } from '../commands/cluster.js'; import { runContinuationCommand } from '../commands/continuation.js'; import { runDossierCommand } from '../commands/dossier.js'; +import { runFrontierCommand } from '../commands/frontier.js'; import { runGraphTheoryCommand } from '../commands/graph-theory.js'; import { runMaintainerCommand } from '../commands/maintainer.js'; import { runNumberTheoryCommand } from '../commands/number-theory.js'; @@ -28,16 +29,56 @@ function printUsage() { console.log(' erdos problem use '); console.log(' erdos problem current'); console.log(' erdos problem artifacts [] [--json]'); + console.log(' erdos problem theorem-loop [] [--json]'); + console.log(' erdos problem theorem-loop-refresh [] [--json]'); + console.log(' erdos problem claim-loop [] [--json]'); + console.log(' erdos problem claim-loop-refresh [] [--json]'); + console.log(' erdos problem claim-pass [] [--json]'); + console.log(' erdos problem claim-pass-refresh [] [--json]'); + console.log(' erdos problem formalization [] [--json]'); + console.log(' erdos problem formalization-refresh [] [--json]'); + console.log(' erdos problem formalization-work [] [--json]'); + console.log(' erdos problem formalization-work-refresh [] [--json]'); + console.log(' erdos problem formalization-work-check [] [--json]'); + console.log(' erdos problem task-list [] [--json]'); + console.log(' erdos problem task-list-refresh [] [--json]'); + console.log(' erdos problem task-list-run [] [--passes ] [--no-stop-on-convergence] [--json]'); console.log(' erdos cluster list [--json]'); console.log(' erdos cluster show [--json]'); console.log(' erdos archive show [--json]'); console.log(' erdos archive scaffold [--json]'); + console.log(' erdos frontier doctor [--json]'); + console.log(' erdos frontier lanes [--json]'); + console.log(' erdos frontier remotes [--json]'); + console.log(' erdos frontier fleets [--json]'); + console.log(' erdos frontier fleet [--json]'); + console.log(' erdos frontier use-remote [--json]'); + console.log(' erdos frontier sessions [--json]'); + console.log(' erdos frontier session [--json]'); + console.log(' erdos frontier stop-session [--json]'); + console.log(' erdos frontier setup [--base|--cpu|--cuda] [--torch-index-url ] [--apply] [--json]'); + console.log(' erdos frontier setup-remote [--remote-id ] [--base|--cpu|--cuda] [--torch-index-url ] [--apply] [--json]'); + console.log(' erdos frontier create-brev [--gpu-name ] [--type ] [--provider ] [--count ] [--attach] [--enable-paid-rung] [--sync-lane ] [--dry-run] [--apply] [--json]'); + console.log(' erdos frontier create-brev-fleet [--gpu-name ] [--type ] [--provider ] [--count ] [--attach] [--enable-paid-rung] [--sync-lane ] [--dry-run] [--apply] [--json]'); + console.log(' erdos frontier attach-ssh --ssh-host [--remote-id ] [--engine-root ] [--python-command ] [--apply] [--json]'); + console.log(' erdos frontier attach-brev --instance [--remote-id ] [--ssh-host ] [--engine-root ] [--python-command ] [--enable-paid-rung] [--apply] [--json]'); + console.log(' erdos frontier enable-paid-remote [--json]'); + console.log(' erdos frontier disable-paid-remote [--json]'); + console.log(' erdos frontier enable-paid-fleet [--json]'); + console.log(' erdos frontier disable-paid-fleet [--json]'); + console.log(' erdos frontier sync-ssh [--remote-id ] [--ssh-host ] [--engine-root ] [--python-command ] [--lane ] [--apply] [--json]'); + console.log(' erdos frontier sync-fleet [--lane ] [--apply] [--json]'); console.log(' erdos graph-theory status [] [--json]'); console.log(' erdos graph-theory frontier [] [--json]'); console.log(' erdos graph-theory routes [] [--json]'); console.log(' erdos graph-theory tickets [] [--json]'); console.log(' erdos number-theory status [] [--json]'); console.log(' erdos number-theory frontier [] [--json]'); + console.log(' erdos number-theory bridge [] [--json]'); + console.log(' erdos number-theory bridge-refresh [] [--json]'); + console.log(' erdos number-theory dispatch [] [--apply] [--detach] [--review-after-hours ] [--remote-id ] [--action ] [--exact-min ] [--exact-max ] [--json]'); + console.log(' erdos number-theory dispatch-fleet [] --fleet [--apply] [--review-after-hours ] [--strategy ] [--action ] [--json]'); + console.log(' erdos number-theory fleet-run [--json]'); console.log(' erdos number-theory routes [] [--json]'); console.log(' erdos number-theory tickets [] [--json]'); console.log(' erdos number-theory route [--json]'); @@ -93,6 +134,8 @@ if (!command || command === 'help' || command === '--help') { exitCode = runClusterCommand(rest); } else if (command === 'archive') { exitCode = runArchiveCommand(rest); +} else if (command === 'frontier') { + exitCode = runFrontierCommand(rest); } else if (command === 'graph-theory') { exitCode = runGraphTheoryCommand(rest); } else if (command === 'number-theory') { diff --git a/src/commands/graph-theory.js b/src/commands/graph-theory.js index 6c713a0..2b89026 100644 --- a/src/commands/graph-theory.js +++ b/src/commands/graph-theory.js @@ -54,6 +54,23 @@ function printStatus(snapshot) { } console.log(`Frontier note: ${snapshot.frontierNotePresent ? snapshot.frontierNotePath : '(missing)'}`); console.log(`Route history: ${snapshot.routeHistoryPresent ? snapshot.routeHistoryPath : '(missing)'}`); + console.log(`Theorem loop: ${snapshot.theoremLoop?.theoremLoopMode ?? '(missing)'}`); + console.log(`Theorem claim surface: ${snapshot.theoremLoop?.currentState?.currentClaimSurface ?? '(none)'}`); + console.log(`Theorem note: ${snapshot.theoremLoop?.theoremLoopMarkdownPresent ? snapshot.theoremLoop.theoremLoopMarkdownPath : '(not written yet)'}`); + console.log(`Theorem command: ${snapshot.theoremLoop?.commands?.theoremLoop ?? '(none)'}`); + console.log(`Theorem refresh: ${snapshot.theoremLoop?.commands?.theoremLoopRefresh ?? '(none)'}`); + console.log(`Claim loop: ${snapshot.claimLoop?.claimLoopMode ?? '(missing)'}`); + console.log(`Claim note: ${snapshot.claimLoop?.claimLoopMarkdownPresent ? snapshot.claimLoop.claimLoopMarkdownPath : '(not written yet)'}`); + console.log(`Claim command: ${snapshot.claimLoop?.commands?.claimLoop ?? '(none)'}`); + console.log(`Claim refresh: ${snapshot.claimLoop?.commands?.claimLoopRefresh ?? '(none)'}`); + console.log(`Claim pass: ${snapshot.claimPass?.claimPassMode ?? '(missing)'}`); + console.log(`Claim pass note: ${snapshot.claimPass?.claimPassMarkdownPresent ? snapshot.claimPass.claimPassMarkdownPath : '(not written yet)'}`); + console.log(`Claim pass command: ${snapshot.claimPass?.commands?.claimPass ?? '(none)'}`); + console.log(`Claim pass refresh: ${snapshot.claimPass?.commands?.claimPassRefresh ?? '(none)'}`); + console.log(`Task list: ${snapshot.taskList?.taskListMode ?? '(missing)'}`); + console.log(`Task list note: ${snapshot.taskList?.taskListMarkdownPresent ? snapshot.taskList.taskListMarkdownPath : '(not written yet)'}`); + console.log(`Task list command: ${snapshot.taskList?.commands?.taskList ?? '(none)'}`); + console.log(`Task list refresh: ${snapshot.taskList?.commands?.taskListRefresh ?? '(none)'}`); console.log(`Checkpoint template: ${snapshot.checkpointTemplatePresent ? snapshot.checkpointTemplatePath : '(missing)'}`); console.log(`Report template: ${snapshot.reportTemplatePresent ? snapshot.reportTemplatePath : '(missing)'}`); console.log(`Active ticket: ${snapshot.activeTicketDetail?.ticket_id ?? '(none)'}`); diff --git a/src/commands/number-theory.js b/src/commands/number-theory.js index 203d760..43db528 100644 --- a/src/commands/number-theory.js +++ b/src/commands/number-theory.js @@ -1,9 +1,16 @@ import { getProblem } from '../atlas/catalog.js'; import { buildNumberTheoryStatusSnapshot, + getNumberTheoryDispatchSnapshot, + getNumberTheoryFleetDispatchSnapshot, + getNumberTheoryFleetRunSnapshot, getNumberTheoryAtomSnapshot, + getNumberTheoryBridgeSnapshot, getNumberTheoryRouteSnapshot, getNumberTheoryTicketSnapshot, + refreshNumberTheoryBridge, + runNumberTheoryFleetDispatch, + runNumberTheoryDispatch, } from '../runtime/number-theory.js'; import { readCurrentProblem } from '../runtime/workspace.js'; @@ -30,13 +37,229 @@ function parseArgs(args) { problemId: null, asJson: false, entityId: null, + apply: false, + detach: false, + actionId: null, + exactMin: null, + exactMax: null, + exactChunks: null, + exactChunkSize: null, + baseSideMax: null, + structuralMax: null, + structuralMin: null, + mixedBaseMaxRows: null, + fullMixedRowSampleLimit: null, + structuralLiftTopRows: null, + structuralLiftFamilyLimit: null, + matchingPatternPrime: null, + matchingPatternTopRows: null, + matchingPatternPairSampleLimit: null, + endpointMonotonicity: false, + reviewAfterHours: null, + remoteId: null, + externalSourceDir: null, + fleetId: null, + strategyId: null, }; - for (const token of args) { + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; if (token === '--json') { parsed.asJson = true; continue; } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--detach') { + parsed.detach = true; + continue; + } + if (token === '--action') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing action id after --action.' }; + } + parsed.actionId = nextValue; + index += 1; + continue; + } + if (token === '--exact-min') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --exact-min.' }; + } + parsed.exactMin = Number(nextValue); + index += 1; + continue; + } + if (token === '--exact-max') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --exact-max.' }; + } + parsed.exactMax = Number(nextValue); + index += 1; + continue; + } + if (token === '--exact-chunks') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --exact-chunks.' }; + } + parsed.exactChunks = Number(nextValue); + index += 1; + continue; + } + if (token === '--exact-chunk-size') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --exact-chunk-size.' }; + } + parsed.exactChunkSize = Number(nextValue); + index += 1; + continue; + } + if (token === '--base-side-max') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --base-side-max.' }; + } + parsed.baseSideMax = Number(nextValue); + index += 1; + continue; + } + if (token === '--structural-max') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --structural-max.' }; + } + parsed.structuralMax = Number(nextValue); + index += 1; + continue; + } + if (token === '--structural-min') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --structural-min.' }; + } + parsed.structuralMin = Number(nextValue); + index += 1; + continue; + } + if (token === '--mixed-base-max-rows') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --mixed-base-max-rows.' }; + } + parsed.mixedBaseMaxRows = Number(nextValue); + index += 1; + continue; + } + if (token === '--full-mixed-row-sample-limit') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --full-mixed-row-sample-limit.' }; + } + parsed.fullMixedRowSampleLimit = Number(nextValue); + index += 1; + continue; + } + if (token === '--structural-lift-top-rows') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --structural-lift-top-rows.' }; + } + parsed.structuralLiftTopRows = Number(nextValue); + index += 1; + continue; + } + if (token === '--structural-lift-family-limit') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --structural-lift-family-limit.' }; + } + parsed.structuralLiftFamilyLimit = Number(nextValue); + index += 1; + continue; + } + if (token === '--matching-pattern-prime') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --matching-pattern-prime.' }; + } + parsed.matchingPatternPrime = Number(nextValue); + index += 1; + continue; + } + if (token === '--matching-pattern-top-rows') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --matching-pattern-top-rows.' }; + } + parsed.matchingPatternTopRows = Number(nextValue); + index += 1; + continue; + } + if (token === '--matching-pattern-pair-sample-limit') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing integer after --matching-pattern-pair-sample-limit.' }; + } + parsed.matchingPatternPairSampleLimit = Number(nextValue); + index += 1; + continue; + } + if (token === '--endpoint-monotonicity') { + parsed.endpointMonotonicity = true; + continue; + } + if (token === '--review-after-hours') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing number after --review-after-hours.' }; + } + parsed.reviewAfterHours = Number(nextValue); + index += 1; + continue; + } + if (token === '--remote-id') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing remote id after --remote-id.' }; + } + parsed.remoteId = nextValue; + index += 1; + continue; + } + if (token === '--external-source-dir') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing path after --external-source-dir.' }; + } + parsed.externalSourceDir = nextValue; + index += 1; + continue; + } + if (token === '--fleet') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing fleet id after --fleet.' }; + } + parsed.fleetId = nextValue; + index += 1; + continue; + } + if (token === '--strategy') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing strategy id after --strategy.' }; + } + parsed.strategyId = nextValue; + index += 1; + continue; + } if (!parsed.problemId) { parsed.problemId = token; continue; @@ -71,6 +294,60 @@ function printStatus(snapshot) { } console.log(`Frontier note: ${snapshot.frontierNotePresent ? snapshot.frontierNotePath : '(missing)'}`); console.log(`Route history: ${snapshot.routeHistoryPresent ? snapshot.routeHistoryPath : '(missing)'}`); + console.log(`Theorem loop: ${snapshot.theoremLoop?.theoremLoopMode ?? '(missing)'}`); + console.log(`Theorem claim surface: ${snapshot.theoremLoop?.currentState?.currentClaimSurface ?? '(none)'}`); + console.log(`Theorem note: ${snapshot.theoremLoop?.theoremLoopMarkdownPresent ? snapshot.theoremLoop.theoremLoopMarkdownPath : '(not written yet)'}`); + console.log(`Theorem command: ${snapshot.theoremLoop?.commands?.theoremLoop ?? '(none)'}`); + console.log(`Theorem refresh: ${snapshot.theoremLoop?.commands?.theoremLoopRefresh ?? '(none)'}`); + console.log(`Claim loop: ${snapshot.claimLoop?.claimLoopMode ?? '(missing)'}`); + console.log(`Claim note: ${snapshot.claimLoop?.claimLoopMarkdownPresent ? snapshot.claimLoop.claimLoopMarkdownPath : '(not written yet)'}`); + console.log(`Claim command: ${snapshot.claimLoop?.commands?.claimLoop ?? '(none)'}`); + console.log(`Claim refresh: ${snapshot.claimLoop?.commands?.claimLoopRefresh ?? '(none)'}`); + console.log(`Claim pass: ${snapshot.claimPass?.claimPassMode ?? '(missing)'}`); + console.log(`Claim pass note: ${snapshot.claimPass?.claimPassMarkdownPresent ? snapshot.claimPass.claimPassMarkdownPath : '(not written yet)'}`); + console.log(`Claim pass command: ${snapshot.claimPass?.commands?.claimPass ?? '(none)'}`); + console.log(`Claim pass refresh: ${snapshot.claimPass?.commands?.claimPassRefresh ?? '(none)'}`); + console.log(`Formalization: ${snapshot.formalization?.formalizationMode ?? '(missing)'}`); + console.log(`Formalization note: ${snapshot.formalization?.formalizationMarkdownPresent ? snapshot.formalization.formalizationMarkdownPath : '(not written yet)'}`); + console.log(`Formalization command: ${snapshot.formalization?.commands?.formalization ?? '(none)'}`); + console.log(`Formalization refresh: ${snapshot.formalization?.commands?.formalizationRefresh ?? '(none)'}`); + console.log(`Formalization work: ${snapshot.formalizationWork?.formalizationWorkMode ?? '(missing)'}`); + console.log(`Formalization work note: ${snapshot.formalizationWork?.formalizationWorkMarkdownPresent ? snapshot.formalizationWork.formalizationWorkMarkdownPath : '(not written yet)'}`); + console.log(`Formalization work command: ${snapshot.formalizationWork?.commands?.formalizationWork ?? '(none)'}`); + console.log(`Formalization work refresh: ${snapshot.formalizationWork?.commands?.formalizationWorkRefresh ?? '(none)'}`); + console.log(`Task list: ${snapshot.taskList?.taskListMode ?? '(missing)'}`); + console.log(`Task list note: ${snapshot.taskList?.taskListMarkdownPresent ? snapshot.taskList.taskListMarkdownPath : '(not written yet)'}`); + console.log(`Task list command: ${snapshot.taskList?.commands?.taskList ?? '(none)'}`); + console.log(`Task list refresh: ${snapshot.taskList?.commands?.taskListRefresh ?? '(none)'}`); + console.log(`Search/theorem bridge: ${snapshot.searchTheoremBridgePresent ? snapshot.searchTheoremBridgePath : '(missing)'}`); + console.log(`Bridge data: ${snapshot.searchTheoremBridgeJsonPresent ? snapshot.searchTheoremBridgeJsonPath : '(missing)'}`); + console.log(`Bridge refresh: ${snapshot.searchTheoremBridgeRefreshCommand ?? '(none)'}`); + const frontierLoopLabel = snapshot.frontierLoopSuggested + ? `active (${snapshot.frontierLoop?.mode ?? 'unknown'})` + : 'inactive'; + console.log(`Frontier loop: ${frontierLoopLabel}`); + if (snapshot.frontierLoopSuggested) { + if (snapshot.frontierLoop?.summary) { + console.log(`Frontier loop summary: ${snapshot.frontierLoop.summary}`); + } + if (snapshot.frontierLoop?.primaryCommand) { + console.log(`Frontier loop entry: ${snapshot.frontierLoop.primaryCommand}`); + } + if (snapshot.frontierLoop?.commands?.length) { + console.log(`Frontier loop commands: ${snapshot.frontierLoop.commands.join(' | ')}`); + } + if (snapshot.frontierLoop?.mode === 'cpu' && snapshot.frontierLoop?.upgradeCommand) { + console.log(`Frontier loop upgrade: ${snapshot.frontierLoop.upgradeCommand}`); + } + } else if (snapshot.frontierLoop?.activationCommand) { + console.log(`Frontier loop activation: ${snapshot.frontierLoop.activationCommand}`); + if (snapshot.frontierLoop?.upgradeCommand) { + console.log(`Frontier loop GPU path: ${snapshot.frontierLoop.upgradeCommand}`); + } + } + if (!snapshot.frontierLoopSuggested && snapshot.frontierLoop?.stateReason) { + console.log(`Frontier loop reason: ${snapshot.frontierLoop.stateReason}`); + } console.log(`Checkpoint template: ${snapshot.checkpointTemplatePresent ? snapshot.checkpointTemplatePath : '(missing)'}`); console.log(`Report template: ${snapshot.reportTemplatePresent ? snapshot.reportTemplatePath : '(missing)'}`); console.log(`Ops details present: ${snapshot.opsDetailsPresent ? 'yes' : 'no'}`); @@ -92,6 +369,16 @@ function printFrontier(snapshot) { console.log(`Archive mode: ${snapshot.archiveMode ?? '(none)'}`); console.log(`Frontier note: ${snapshot.frontierNotePresent ? snapshot.frontierNotePath : '(missing)'}`); console.log(`Route history: ${snapshot.routeHistoryPresent ? snapshot.routeHistoryPath : '(missing)'}`); + console.log(`Search/theorem bridge: ${snapshot.searchTheoremBridgePresent ? snapshot.searchTheoremBridgePath : '(missing)'}`); + const frontierLoopLabel = snapshot.frontierLoopSuggested + ? `active (${snapshot.frontierLoop?.mode ?? 'unknown'})` + : 'inactive'; + console.log(`Frontier loop: ${frontierLoopLabel}`); + if (snapshot.frontierLoopSuggested && snapshot.frontierLoop?.primaryCommand) { + console.log(`Frontier loop entry: ${snapshot.frontierLoop.primaryCommand}`); + } else if (snapshot.frontierLoop?.activationCommand) { + console.log(`Frontier loop activation: ${snapshot.frontierLoop.activationCommand}`); + } } function printRoutes(snapshot) { @@ -194,6 +481,816 @@ function printAtomDetail(snapshot) { console.log(`Next move: ${atom.next_move ?? '(none)'}`); } +function printBridge(snapshot) { + console.log(`${snapshot.displayName} number-theory bridge`); + console.log(`Bridge note: ${snapshot.bridgeMarkdownPresent ? snapshot.bridgeMarkdownPath : '(missing)'}`); + console.log(`Bridge data: ${snapshot.bridgeJsonPresent ? snapshot.bridgeJsonPath : '(missing)'}`); + console.log(`Frontier-engine: ${snapshot.frontierEnginePresent ? snapshot.frontierEngineRootPath : '(missing)'}`); + console.log(`Refresh command: ${snapshot.bridgeRefreshCommand ?? '(none)'}`); + console.log(`Engine command: ${snapshot.bridgeEngineCommand ?? '(none)'}`); + if (snapshot.bridgeRefreshMode) { + console.log(`Refresh mode: ${snapshot.bridgeRefreshMode}`); + } + if (snapshot.bridgeRefreshResolvedCommand) { + console.log(`Resolved engine command: ${snapshot.bridgeRefreshResolvedCommand}`); + } + if (snapshot.bridgeRefreshReason) { + console.log(`Refresh mode reason: ${snapshot.bridgeRefreshReason}`); + } + + if (!snapshot.bridgePresent || !snapshot.bridgeCurrentState) { + console.log('Bridge state: unavailable.'); + return; + } + + const state = snapshot.bridgeCurrentState; + console.log(`Shared-prefix failures frozen: ${state.shared_prefix_failure_count ?? '(unknown)'}`); + console.log(`Latest shared-prefix failure: ${state.latest_shared_prefix_failure ?? '(unknown)'}`); + console.log(`Family menu count: ${state.family_menu_count ?? '(unknown)'}`); + console.log(`Known family matches: ${state.known_family_matches ?? '(unknown)'}`); + console.log(`Next unmatched representative: ${state.next_unmatched_representative ?? '(unknown)'}`); + console.log(`Matches 282 tail failure: ${state.next_unmatched_matches_282_failure ? 'yes' : 'no'}`); + if (state.strongest_completed_structured_tail) { + console.log( + `Strongest completed structured tail: ${state.strongest_completed_structured_tail.continuation} through ${state.strongest_completed_structured_tail.clean_through}`, + ); + } + if (state.current_family_aware_leader) { + console.log( + `Current family-aware leader: ${state.current_family_aware_leader.continuation} (${state.current_family_aware_leader.repaired_known_packets} known packets, ${state.current_family_aware_leader.repaired_predicted_families} predicted families, ${state.current_family_aware_leader.effective_clean_through} clean-through)`, + ); + } + const tieClass = Array.isArray(state.top_gpu_tie_class) && state.top_gpu_tie_class.length > 0 + ? state.top_gpu_tie_class.join(', ') + : '(none)'; + console.log(`Top GPU tie class: ${tieClass}`); + console.log(`Tracked tails: ${snapshot.bridgeTrackedTailMatrix.length}`); + console.log(`GPU leaderboard rows: ${snapshot.bridgeGpuLeaderboard.length}`); + if (snapshot.bridgeTheoremHooks.length > 0) { + console.log('Theorem hooks:'); + for (const hook of snapshot.bridgeTheoremHooks) { + console.log(`- ${hook.hook_id ?? hook.hook}: ${hook.status}`); + } + } +} + +function printDispatch(snapshot) { + if (!snapshot.available) { + console.log(`Dispatch: unavailable`); + console.log(`Error: ${snapshot.error ?? '(unknown)'}`); + return; + } + + console.log(`${snapshot.displayName} number-theory dispatch`); + console.log(`Active route: ${snapshot.activeRoute ?? '(none)'}`); + if (snapshot.remoteId) { + console.log(`Target remote: ${snapshot.remoteId}`); + } + console.log(`Dispatch summary: ${snapshot.summary}`); + console.log(`Primary action: ${snapshot.primaryAction?.actionId ?? '(none)'}`); + console.log(`Primary mode: ${snapshot.primaryAction?.mode ?? '(none)'}`); + if (snapshot.primaryAction?.reason) { + console.log(`Primary reason: ${snapshot.primaryAction.reason}`); + } + if (snapshot.claimPass?.recommendations?.length) { + console.log('Claim-pass recommendations:'); + for (const recommendation of snapshot.claimPass.recommendations.slice(0, 4)) { + console.log(`- ${recommendation.recommendation_id} [${recommendation.priority}] ${recommendation.lane} | ${recommendation.reason}`); + } + } + console.log('Dispatch actions:'); + for (const action of snapshot.actions) { + const flags = []; + if (action.primary) { + flags.push('primary'); + } + if (action.available) { + flags.push('available'); + } else { + flags.push('unavailable'); + } + if (action.mode) { + flags.push(action.mode); + } + console.log(`- ${action.actionId}${flags.length > 0 ? ` [${flags.join(', ')}]` : ''}`); + console.log(` title: ${action.title}`); + console.log(` reason: ${action.reason ?? '(none)'}`); + console.log(` apply: ${action.applyCommand}`); + if (action.commandLine) { + console.log(` command: ${action.commandLine}`); + } + if (action.min && action.max) { + console.log(` interval: ${action.min}..${action.max}`); + } + if (action.chunkCount && action.chunkSize) { + console.log(` rollout: ${action.chunkCount} chunks x ${action.chunkSize}`); + } + } +} + +function printBridgeRefresh(result) { + if (!result.ok) { + console.log(`Bridge refresh: failed`); + console.log(`Refresh command: ${result.refreshCommand ?? '(none)'}`); + console.log(`Engine command: ${result.engineCommand ?? '(none)'}`); + if (result.executionMode) { + console.log(`Execution mode: ${result.executionMode}`); + } + if (result.resolvedCommand) { + console.log(`Resolved engine command: ${result.resolvedCommand}`); + } + if (result.executionReason) { + console.log(`Execution mode reason: ${result.executionReason}`); + } + console.log(`Error: ${result.error ?? '(unknown)'}`); + if (result.bridge) { + printBridge(result.bridge); + } + return; + } + + console.log('Bridge refresh: complete'); + console.log(`Refreshed at: ${result.refreshedAt}`); + console.log(`Refresh command: ${result.refreshCommand ?? '(none)'}`); + console.log(`Engine command: ${result.engineCommand ?? '(none)'}`); + if (result.executionMode) { + console.log(`Execution mode: ${result.executionMode}`); + } + if (result.resolvedCommand) { + console.log(`Resolved engine command: ${result.resolvedCommand}`); + } + if (result.executionReason) { + console.log(`Execution mode reason: ${result.executionReason}`); + } + if (result.commandOutput) { + console.log(`Engine output: ${result.commandOutput}`); + } + printBridge(result.bridge); +} + +function printDispatchResult(result) { + if (result.detached) { + console.log('Number-theory dispatch: detached'); + console.log(`Action: ${result.action.actionId}`); + console.log(`Mode: ${result.action.mode ?? '(none)'}`); + console.log(`Reason: ${result.action.reason ?? '(none)'}`); + console.log(`Reused existing session: ${result.reusedExisting ? 'yes' : 'no'}`); + if (result.session?.sessionId) { + console.log(`Frontier session id: ${result.session.sessionId}`); + console.log(`Frontier session status: ${result.session.status}`); + console.log(`Frontier session command: erdos frontier session ${result.session.sessionId}`); + } + if (result.session?.reviewDueAt) { + console.log(`Frontier review due: ${result.session.reviewDueAt}`); + console.log(`Frontier review state: ${result.session.reviewState}`); + } + return; + } + + if (result.action?.actionId === 'gpu_profile_sweep' && result.integrationGap && (result.partial || result.execution?.ok)) { + console.log('Number-theory dispatch: partial'); + console.log(`Action: ${result.action.actionId}`); + console.log(`Mode: ${result.action.mode ?? '(none)'}`); + console.log(`Reason: ${result.action.reason ?? '(none)'}`); + if (result.runBundle?.runDir) { + console.log(`Run dir: ${result.runBundle.runDir}`); + } + if (result.action.commandLine) { + console.log(`Command: ${result.action.commandLine}`); + } + if (result.remoteSync?.remoteLiveFrontier?.shared_prefix_failure_count !== undefined) { + console.log( + `Remote frontier after sync: ${result.remoteSync.remoteLiveFrontier.shared_prefix_failure_count} shared-prefix failures through ${result.remoteSync.remoteLiveFrontier.latest_direct_failure}`, + ); + } + if (result.execution?.stdout) { + console.log(`Search output: ${result.execution.stdout}`); + } + console.log(`Integration gap: ${result.integrationGap}`); + return; + } + + if (!result.ok) { + console.log('Number-theory dispatch: failed'); + if (result.action?.actionId) { + console.log(`Action: ${result.action.actionId}`); + } + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.integrationGap) { + console.log(`Integration gap: ${result.integrationGap}`); + } + if (result.remoteSync?.remoteLiveFrontier?.shared_prefix_failure_count !== undefined) { + console.log( + `Remote frontier after sync: ${result.remoteSync.remoteLiveFrontier.shared_prefix_failure_count} shared-prefix failures through ${result.remoteSync.remoteLiveFrontier.latest_direct_failure}`, + ); + } + if (result.dispatch) { + printDispatch(result.dispatch); + } + return; + } + + console.log('Number-theory dispatch: complete'); + console.log(`Action: ${result.action.actionId}`); + console.log(`Mode: ${result.action.mode ?? '(none)'}`); + console.log(`Reason: ${result.action.reason ?? '(none)'}`); + if (result.runBundle?.runDir) { + console.log(`Run dir: ${result.runBundle.runDir}`); + } + if (result.action.commandLine) { + console.log(`Command: ${result.action.commandLine}`); + } + if (result.remoteSync?.remoteLiveFrontier?.shared_prefix_failure_count !== undefined) { + console.log( + `Remote frontier after sync: ${result.remoteSync.remoteLiveFrontier.shared_prefix_failure_count} shared-prefix failures through ${result.remoteSync.remoteLiveFrontier.latest_direct_failure}`, + ); + } + if (result.action.actionId === 'bridge_refresh' && result.refresh) { + printBridgeRefresh(result.refresh); + return; + } + if (result.action.actionId === 'claim_pass_refresh' && result.claimPassRefresh) { + if (result.claimPassRefresh.markdownPath) { + console.log(`Claim pass note: ${result.claimPassRefresh.markdownPath}`); + } + if (result.claimPassRefresh.jsonPath) { + console.log(`Claim pass JSON: ${result.claimPassRefresh.jsonPath}`); + } + for (const recommendation of result.claimPassRefresh.claimPass?.recommendations ?? []) { + console.log(`- ${recommendation.recommendation_id} [${recommendation.priority}] ${recommendation.lane}`); + console.log(` reason: ${recommendation.reason}`); + } + return; + } + if (result.action.actionId === 'formalization_refresh' && result.formalizationRefresh) { + if (result.formalizationRefresh.markdownPath) { + console.log(`Formalization note: ${result.formalizationRefresh.markdownPath}`); + } + if (result.formalizationRefresh.jsonPath) { + console.log(`Formalization JSON: ${result.formalizationRefresh.jsonPath}`); + } + if (result.formalizationRefresh.formalization?.currentTarget) { + console.log(`Formalization target: ${result.formalizationRefresh.formalization.currentTarget.title}`); + console.log(`Formalization statement: ${result.formalizationRefresh.formalization.currentTarget.statement}`); + } + return; + } + if (result.action.actionId === 'cpu_family_search' || result.action.actionId === 'gpu_profile_sweep') { + if (result.execution?.stdout) { + console.log(`Search output: ${result.execution.stdout}`); + } + if (result.bridgeRefresh) { + printBridgeRefresh(result.bridgeRefresh); + } + return; + } + if (result.action.actionId === 'exact_interval_scout') { + if (result.execution?.stdout) { + console.log(`Exact scout output: ${result.execution.stdout}`); + } + if (result.results?.summary) { + console.log(`Exact scout interval: ${result.results.summary.interval}`); + console.log(`Exact scout rows: ${result.results.summary.rows}`); + } + return; + } + if (result.action.actionId === 'structural_verifier_audit') { + if (result.auditJsonPath) { + console.log(`Structural verifier audit JSON: ${result.auditJsonPath}`); + } + if (result.auditMarkdownPath) { + console.log(`Structural verifier audit note: ${result.auditMarkdownPath}`); + } + if (result.audit?.status) { + console.log(`Structural verifier audit status: ${result.audit.status}`); + console.log(`Structural verifier audit blockers: ${result.audit.summary?.blockerCount ?? 0}`); + console.log(`Structural verifier audit warnings: ${result.audit.summary?.warningCount ?? 0}`); + } + return; + } + if (result.action.actionId === 'base_side_scout') { + if (result.scoutJsonPath) { + console.log(`Base-side scout JSON: ${result.scoutJsonPath}`); + } + if (result.scoutMarkdownPath) { + console.log(`Base-side scout note: ${result.scoutMarkdownPath}`); + } + if (result.scout?.status) { + console.log(`Base-side scout status: ${result.scout.status}`); + console.log(`Base-side scout side18 exceeds side7: ${result.scout.summary?.maxSide18ExceedsSide7 ? 'yes' : 'no'}`); + console.log(`Base-side scout max side18-minus-side7: ${result.scout.summary?.globalMaxSide18Minus7 ?? '(unknown)'}`); + } + return; + } + if (result.action.actionId === 'structural_two_side_scout') { + if (result.structuralScoutJsonPath) { + console.log(`Two-sided structural scout JSON: ${result.structuralScoutJsonPath}`); + } + if (result.structuralScoutMarkdownPath) { + console.log(`Two-sided structural scout note: ${result.structuralScoutMarkdownPath}`); + } + if (result.structuralScout?.status) { + console.log(`Two-sided structural scout status: ${result.structuralScout.status}`); + console.log(`Two-sided structural scout range: ${result.structuralScout.summary?.assessedRange ?? '(unknown)'}`); + console.log(`Two-sided structural scout union failures: ${result.structuralScout.summary?.unionFailureCount ?? '(unknown)'}`); + } + return; + } + if (result.action.actionId === 'mixed_base_failure_scout') { + if (result.mixedBaseScoutJsonPath) { + console.log(`Mixed-base failure scout JSON: ${result.mixedBaseScoutJsonPath}`); + } + if (result.mixedBaseScoutMarkdownPath) { + console.log(`Mixed-base failure scout note: ${result.mixedBaseScoutMarkdownPath}`); + } + if (result.mixedBaseScout?.status) { + console.log(`Mixed-base failure scout status: ${result.mixedBaseScout.status}`); + console.log(`Mixed-base failure scout analyzed rows: ${result.mixedBaseScout.summary?.analyzedRowCount ?? '(unknown)'}`); + console.log(`Mixed-base failure scout remaining failures: ${result.mixedBaseScout.summary?.mixedFailureCount ?? '(unknown)'}`); + } + return; + } + if (result.action.actionId === 'full_mixed_base_structural_verifier') { + if (result.fullMixedStructuralJsonPath) { + console.log(`Full mixed-base structural verifier JSON: ${result.fullMixedStructuralJsonPath}`); + } + if (result.fullMixedStructuralMarkdownPath) { + console.log(`Full mixed-base structural verifier note: ${result.fullMixedStructuralMarkdownPath}`); + } + if (result.fullMixedStructuralVerifier?.status) { + console.log(`Full mixed-base structural verifier status: ${result.fullMixedStructuralVerifier.status}`); + console.log(`Full mixed-base structural verifier range: ${result.fullMixedStructuralVerifier.summary?.assessedRange ?? '(unknown)'}`); + console.log(`Full mixed-base structural verifier mixed failures: ${result.fullMixedStructuralVerifier.summary?.mixedFailureCount ?? '(unknown)'}`); + console.log(`Full mixed-base structural verifier exact outsider checks: ${result.fullMixedStructuralVerifier.summary?.threateningOutsiderCheckCount ?? '(unknown)'}`); + } + return; + } + if (result.action.actionId === 'structural_lift_miner') { + if (result.structuralLiftMinerJsonPath) { + console.log(`Structural lift miner JSON: ${result.structuralLiftMinerJsonPath}`); + } + if (result.structuralLiftMinerMarkdownPath) { + console.log(`Structural lift miner note: ${result.structuralLiftMinerMarkdownPath}`); + } + if (result.structuralLiftMiner?.status) { + console.log(`Structural lift miner status: ${result.structuralLiftMiner.status}`); + console.log(`Structural lift miner mined rows: ${result.structuralLiftMiner.summary?.minedExactRowCount ?? '(unknown)'}`); + console.log(`Structural lift miner primary exact primes: ${(result.structuralLiftMiner.summary?.primaryExactPrimes ?? []).join(', ') || '(unknown)'}`); + console.log(`Structural lift miner next theorem lane: ${result.structuralLiftMiner.summary?.nextTheoremLane ?? '(unknown)'}`); + } + return; + } + if (result.action.actionId === 'matching_pattern_miner') { + if (result.matchingPatternMinerJsonPath) { + console.log(`Matching pattern miner JSON: ${result.matchingPatternMinerJsonPath}`); + } + if (result.matchingPatternMinerMarkdownPath) { + console.log(`Matching pattern miner note: ${result.matchingPatternMinerMarkdownPath}`); + } + if (result.matchingPatternMiner?.status) { + console.log(`Matching pattern miner status: ${result.matchingPatternMiner.status}`); + console.log(`Matching pattern miner target prime: ${result.matchingPatternMiner.parameters?.targetPrime ?? '(unknown)'}`); + console.log(`Matching pattern miner witness rows: ${result.matchingPatternMiner.summary?.witnessRowCount ?? '(unknown)'}`); + console.log(`Matching pattern miner minimum slack: ${result.matchingPatternMiner.summary?.minMatchingSlack ?? '(unknown)'}`); + } + return; + } + if (result.action.actionId === 'exact_followup_launch') { + if (result.handoff?.handoffDir) { + console.log(`Exact handoff dir: ${result.handoff.handoffDir}`); + } + if (result.exactFollowup?.followupDir) { + console.log(`Exact follow-up dir: ${result.exactFollowup.followupDir}`); + } + if (result.exactFollowup?.followupJsonPath) { + console.log(`Exact follow-up JSON: ${result.exactFollowup.followupJsonPath}`); + } + if (result.exactFollowup?.followupMarkdownPath) { + console.log(`Exact follow-up note: ${result.exactFollowup.followupMarkdownPath}`); + } + if (result.execution?.stdout) { + console.log(`Exact follow-up output: ${result.execution.stdout}`); + } + if (result.results?.summary) { + console.log(`Exact follow-up interval: ${result.results.summary.interval}`); + console.log(`Exact follow-up rows: ${result.results.summary.rows}`); + } + return; + } + if (result.action.actionId === 'exact_followup_rollout') { + const rolloutPacket = result.rollout?.packet ?? null; + if (result.rollout?.rolloutDir) { + console.log(`Exact rollout dir: ${result.rollout.rolloutDir}`); + } + if (result.rollout?.rolloutJsonPath) { + console.log(`Exact rollout JSON: ${result.rollout.rolloutJsonPath}`); + } + if (result.rollout?.rolloutMarkdownPath) { + console.log(`Exact rollout note: ${result.rollout.rolloutMarkdownPath}`); + } + if (rolloutPacket?.completedChunkCount !== undefined) { + console.log(`Exact rollout completed chunks: ${rolloutPacket.completedChunkCount}/${rolloutPacket.requestedChunkCount}`); + } + if (rolloutPacket?.completedInterval) { + console.log(`Exact rollout covered interval: ${rolloutPacket.completedInterval}`); + } + for (const childRun of rolloutPacket?.childRuns ?? []) { + console.log(`- chunk ${childRun.index}: ${childRun.interval} [${childRun.ok ? 'ok' : 'failed'}]`); + if (childRun.runId) { + console.log(` run id: ${childRun.runId}`); + } + } + if (result.bridgeRefresh) { + printBridgeRefresh(result.bridgeRefresh); + } + return; + } + if (result.action.actionId === 'exact_handoff_bundle') { + if (result.handoff?.handoffDir) { + console.log(`Exact handoff dir: ${result.handoff.handoffDir}`); + } + if (result.handoff?.handoffJsonPath) { + console.log(`Exact handoff JSON: ${result.handoff.handoffJsonPath}`); + } + if (result.handoff?.handoffMarkdownPath) { + console.log(`Exact handoff note: ${result.handoff.handoffMarkdownPath}`); + } + if (result.handoff?.handoff?.exactFocus?.nextUnmatchedRepresentative) { + console.log(`Next unmatched representative: ${result.handoff.handoff.exactFocus.nextUnmatchedRepresentative}`); + } + } + if (result.action.actionId === 'formalization_work_refresh' && result.formalizationWorkRefresh) { + if (result.formalizationWorkRefresh.markdownPath) { + console.log(`Formalization work note: ${result.formalizationWorkRefresh.markdownPath}`); + } + if (result.formalizationWorkRefresh.jsonPath) { + console.log(`Formalization work JSON: ${result.formalizationWorkRefresh.jsonPath}`); + } + if (result.formalizationWorkRefresh.formalizationWork?.currentWork) { + console.log(`Formalization work target: ${result.formalizationWorkRefresh.formalizationWork.currentWork.title}`); + console.log(`Formalization work summary: ${result.formalizationWorkRefresh.formalizationWork.currentWork.summary}`); + } + } +} + +function compactDispatchActionForJson(action) { + if (!action) { + return null; + } + + const keys = [ + 'available', + 'actionId', + 'kind', + 'mode', + 'source', + 'title', + 'reason', + 'commandLine', + 'applyCommand', + 'remoteProvider', + 'remoteInstanceName', + 'remoteHost', + 'laneId', + 'backendKind', + 'endpointMonotonicity', + 'latestAuditStatus', + 'latestScoutStatus', + 'latestStructuralStatus', + 'latestMixedBaseStatus', + 'latestFullMixedStructuralStatus', + 'latestStructuralLiftStatus', + 'sourceAvailable', + 'max', + 'minStructuralN', + 'maxRows', + 'rowSampleLimit', + 'topRows', + 'familyLimit', + ]; + return Object.fromEntries(keys + .filter((key) => action[key] !== undefined) + .map((key) => [key, action[key]])); +} + +function compactDispatchForJson(dispatch) { + if (!dispatch) { + return null; + } + + return { + available: dispatch.available, + generatedAt: dispatch.generatedAt ?? null, + workspaceRoot: dispatch.workspaceRoot ?? null, + problemId: dispatch.problemId ?? null, + displayName: dispatch.displayName ?? null, + remoteId: dispatch.remoteId ?? null, + activeRoute: dispatch.activeRoute ?? null, + summary: dispatch.summary ?? null, + error: dispatch.error ?? null, + currentBridgeState: dispatch.currentBridgeState ?? null, + primaryAction: compactDispatchActionForJson(dispatch.primaryAction), + actions: Array.isArray(dispatch.actions) + ? dispatch.actions.map(compactDispatchActionForJson) + : [], + }; +} + +function compactRefreshForJson(refresh) { + if (!refresh) { + return null; + } + + return { + ok: refresh.ok, + problemId: refresh.problemId ?? null, + error: refresh.error ?? null, + jsonPath: refresh.jsonPath ?? null, + markdownPath: refresh.markdownPath ?? null, + svgPath: refresh.svgPath ?? null, + sourceRefresh: refresh.sourceRefresh + ? { + ok: refresh.sourceRefresh.ok, + skipped: refresh.sourceRefresh.skipped, + command: refresh.sourceRefresh.command ?? null, + error: refresh.sourceRefresh.stderr ?? null, + } + : null, + }; +} + +function compactRunBundleForJson(runBundle) { + if (!runBundle) { + return null; + } + + return { + runId: runBundle.runId ?? null, + runDir: runBundle.runDir ?? null, + artifacts: runBundle.runRecord?.artifacts ?? null, + }; +} + +function compactDispatchResultForJson(result) { + if (!result || typeof result !== 'object') { + return result; + } + + return { + ok: result.ok, + partial: result.partial ?? undefined, + detached: result.detached ?? undefined, + reusedExisting: result.reusedExisting ?? undefined, + error: result.error ?? null, + integrationGap: result.integrationGap ?? undefined, + dispatch: compactDispatchForJson(result.dispatch), + action: compactDispatchActionForJson(result.action), + refresh: result.refresh + ? { + ok: result.refresh.ok, + problemId: result.refresh.problemId ?? null, + error: result.refresh.error ?? null, + bridgePath: result.refresh.bridgePath ?? null, + markdownPath: result.refresh.markdownPath ?? null, + resolvedCommand: result.refresh.resolvedCommand ?? null, + } + : undefined, + claimPassRefresh: compactRefreshForJson(result.claimPassRefresh), + formalizationRefresh: compactRefreshForJson(result.formalizationRefresh), + formalizationWorkRefresh: compactRefreshForJson(result.formalizationWorkRefresh), + structuralVerifierAudit: result.audit + ? { + status: result.audit.status ?? null, + summary: result.audit.summary ?? null, + jsonPath: result.auditJsonPath ?? null, + markdownPath: result.auditMarkdownPath ?? null, + conclusion: result.audit.conclusion ?? null, + } + : undefined, + baseSideScout: result.scout + ? { + status: result.scout.status ?? null, + summary: result.scout.summary ?? null, + jsonPath: result.scoutJsonPath ?? null, + markdownPath: result.scoutMarkdownPath ?? null, + firstNWithSide18MaxExceedingSide7: result.scout.firstNWithSide18MaxExceedingSide7 ?? null, + } + : undefined, + structuralTwoSideScout: result.structuralScout + ? { + status: result.structuralScout.status ?? null, + summary: result.structuralScout.summary ?? null, + jsonPath: result.structuralScoutJsonPath ?? null, + markdownPath: result.structuralScoutMarkdownPath ?? null, + firstFailures: result.structuralScout.firstFailures ?? null, + worstRows: result.structuralScout.worstRows ?? null, + } + : undefined, + mixedBaseFailureScout: result.mixedBaseScout + ? { + status: result.mixedBaseScout.status ?? null, + summary: result.mixedBaseScout.summary ?? null, + jsonPath: result.mixedBaseScoutJsonPath ?? null, + markdownPath: result.mixedBaseScoutMarkdownPath ?? null, + firstMixedFailure: result.mixedBaseScout.firstMixedFailure ?? null, + worstMixedRow: result.mixedBaseScout.worstMixedRow ?? null, + } + : undefined, + fullMixedBaseStructuralVerifier: result.fullMixedStructuralVerifier + ? { + status: result.fullMixedStructuralVerifier.status ?? null, + summary: result.fullMixedStructuralVerifier.summary ?? null, + jsonPath: result.fullMixedStructuralJsonPath ?? null, + markdownPath: result.fullMixedStructuralMarkdownPath ?? null, + firstMixedFailure: result.fullMixedStructuralVerifier.firstMixedFailure ?? null, + worstCertifiedRow: result.fullMixedStructuralVerifier.worstCertifiedRow ?? null, + worstExactMixedRow: result.fullMixedStructuralVerifier.worstExactMixedRow ?? null, + } + : undefined, + structuralLiftMiner: result.structuralLiftMiner + ? { + status: result.structuralLiftMiner.status ?? null, + summary: result.structuralLiftMiner.summary ?? null, + jsonPath: result.structuralLiftMinerJsonPath ?? null, + markdownPath: result.structuralLiftMinerMarkdownPath ?? null, + sourceVerifier: result.structuralLiftMiner.sourceVerifier ?? null, + liftObligations: result.structuralLiftMiner.liftObligations ?? null, + recommendedNextSteps: result.structuralLiftMiner.recommendedNextSteps ?? null, + } + : undefined, + matchingPatternMiner: result.matchingPatternMiner + ? { + status: result.matchingPatternMiner.status ?? null, + parameters: result.matchingPatternMiner.parameters ?? null, + summary: result.matchingPatternMiner.summary ?? null, + patternSummary: result.matchingPatternMiner.patternSummary + ? { + totalWitnessMatchingPairs: result.matchingPatternMiner.patternSummary.totalWitnessMatchingPairs ?? null, + commonMatchingPairCountAcrossWitnesses: result.matchingPatternMiner.patternSummary.commonMatchingPairCountAcrossWitnesses ?? null, + allSplitCommonCoresMeetMaxRequiredBound: result.matchingPatternMiner.patternSummary.allSplitCommonCoresMeetMaxRequiredBound ?? null, + allSplitCommonCoresSaturateMinSmallerSide: result.matchingPatternMiner.patternSummary.allSplitCommonCoresSaturateMinSmallerSide ?? null, + outsiderResidueGroups: result.matchingPatternMiner.patternSummary.outsiderResidueGroups ?? [], + splitProfiles: (result.matchingPatternMiner.patternSummary.splitProfiles ?? []).slice(0, 4).map((profile) => ({ + groupKey: profile.groupKey, + witnessCount: profile.witnessCount, + minMatchingSlack: profile.minMatchingSlack, + commonMatchingPairCount: profile.commonMatchingPairCount, + commonMatchingPairExportComplete: profile.commonMatchingPairExportComplete ?? null, + commonMatchingPairExportedCount: Array.isArray(profile.commonMatchingPairs) + ? profile.commonMatchingPairs.length + : null, + maxRequiredMatchingLowerBound: profile.maxRequiredMatchingLowerBound, + commonCoreMeetsMaxRequiredBound: profile.commonCoreMeetsMaxRequiredBound, + })), + proofHeuristic: result.matchingPatternMiner.patternSummary.proofHeuristic ?? null, + } + : null, + jsonPath: result.matchingPatternMinerJsonPath ?? null, + markdownPath: result.matchingPatternMinerMarkdownPath ?? null, + symbolicUse: result.matchingPatternMiner.symbolicUse ?? null, + witnessSample: result.matchingPatternMiner.witnesses?.slice(0, 3).map((witness) => ({ + N: witness.N, + p: witness.p, + outsider: witness.outsider, + requiredMatchingLowerBound: witness.requiredMatchingLowerBound, + reconstructedMatchingSize: witness.reconstructedMatchingSize, + matchingSlack: witness.matchingSlack, + smallerSide: witness.smallerSide, + saturatesSmallerSide: witness.saturatesSmallerSide, + matchingPairSample: witness.matchingPairSample ?? [], + })) ?? null, + } + : undefined, + runBundle: compactRunBundleForJson(result.runBundle), + session: result.session ?? undefined, + remoteSync: result.remoteSync + ? { + ok: result.remoteSync.ok, + error: result.remoteSync.error ?? null, + appliedAt: result.remoteSync.appliedAt ?? null, + remoteLiveFrontier: result.remoteSync.remoteLiveFrontier ?? null, + } + : undefined, + mirroredBundle: result.mirroredBundle + ? { + ok: result.mirroredBundle.ok, + error: result.mirroredBundle.error ?? null, + manifestSummary: result.mirroredBundle.manifest?.summary ?? null, + } + : undefined, + bridgeRefresh: result.bridgeRefresh + ? { + ok: result.bridgeRefresh.ok, + error: result.bridgeRefresh.error ?? null, + bridgePath: result.bridgeRefresh.bridgePath ?? null, + markdownPath: result.bridgeRefresh.markdownPath ?? null, + } + : undefined, + }; +} + +function printFleetDispatch(snapshot) { + if (!snapshot.available) { + console.log('Fleet dispatch: unavailable'); + console.log(`Error: ${snapshot.error ?? '(unknown)'}`); + return; + } + + console.log(`${snapshot.displayName} number-theory fleet dispatch`); + console.log(`Fleet: ${snapshot.fleetId}`); + console.log(`Action: ${snapshot.actionId}`); + console.log(`Strategy: ${snapshot.strategyId ?? '(none)'}`); + console.log(`Dispatch summary: ${snapshot.summary}`); + console.log(`Review after hours: ${snapshot.reviewAfterHours ?? '(none)'}`); + console.log(`Ready members: ${snapshot.availableMemberCount}/${snapshot.members.length}`); + console.log('Members:'); + for (const member of snapshot.members) { + const flags = [member.available ? 'available' : 'unavailable']; + console.log(`- ${member.remoteId} [${flags.join(', ')}]`); + console.log(` reason: ${member.actionReason ?? member.dispatchError ?? '(none)'}`); + if (member.assignment) { + console.log(` assignment: tail ${member.assignment.center}, window ${member.assignment.directThreshold}..${member.assignment.directMax}`); + } + console.log(` apply: ${member.applyCommand}`); + } +} + +function printFleetDispatchResult(result) { + if (!result.ok && !result.partial) { + console.log('Number-theory fleet dispatch: failed'); + console.log(`Fleet: ${result.fleetId ?? result.snapshot?.fleetId ?? '(none)'}`); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printFleetDispatch(result.snapshot); + } + return; + } + + console.log(`Number-theory fleet dispatch: ${result.partial ? 'partial' : 'complete'}`); + console.log(`Fleet: ${result.fleetId}`); + console.log(`Action: ${result.actionId}`); + console.log(`Strategy: ${result.snapshot?.strategyId ?? '(none)'}`); + console.log(`Launched: ${result.launchedCount}`); + console.log(`Failed: ${result.failedCount}`); + console.log(`Skipped: ${result.skippedCount}`); + if (result.fleetRun?.runId) { + console.log(`Fleet run id: ${result.fleetRun.runId}`); + console.log(`Fleet run dir: ${result.fleetRun.runDir}`); + console.log(`Fleet run command: erdos number-theory fleet-run ${result.fleetRun.runId}`); + } + console.log('Member sessions:'); + for (const member of result.fleetRun?.members ?? []) { + console.log(`- ${member.remoteId}: ${member.status}`); + if (member.assignment) { + console.log(` assignment: tail ${member.assignment.center}, window ${member.assignment.directThreshold}..${member.assignment.directMax}`); + } + if (member.sessionId) { + console.log(` session: ${member.sessionId}`); + } + } +} + +function printFleetRun(snapshot) { + if (!snapshot) { + console.log('Number-theory fleet run: unavailable'); + return; + } + console.log('Number-theory fleet run'); + console.log(`Run id: ${snapshot.runId}`); + console.log(`Problem: ${snapshot.displayName}`); + console.log(`Fleet: ${snapshot.fleetId}`); + console.log(`Action: ${snapshot.actionId}`); + console.log(`Strategy: ${snapshot.strategyId ?? '(none)'}`); + console.log(`Run dir: ${snapshot.runDir}`); + console.log(`Harvested bundles: ${snapshot.harvestedBundleCount}`); + console.log('Status counts:'); + for (const [status, count] of Object.entries(snapshot.statusCounts ?? {})) { + console.log(`- ${status}: ${count}`); + } + console.log('Members:'); + for (const member of snapshot.members ?? []) { + console.log(`- ${member.remoteId}: ${member.session?.status ?? member.status}`); + if (member.assignment) { + console.log(` assignment: tail ${member.assignment.center}, window ${member.assignment.directThreshold}..${member.assignment.directMax}`); + } + if (member.sessionId) { + console.log(` session: ${member.sessionId}`); + } + if (member.harvestedBundle?.ok) { + console.log(` harvested bundle: ${member.harvestedBundle.localBundleDir}`); + } + if (member.harvestedManifestSummary?.best_continuation !== undefined) { + console.log( + ` best continuation: ${member.harvestedManifestSummary.best_continuation} through ${member.harvestedManifestSummary.best_effective_clean_through}`, + ); + } + } +} + export function runNumberTheoryCommand(args) { const [subcommand, ...rest] = args; @@ -201,6 +1298,11 @@ export function runNumberTheoryCommand(args) { console.log('Usage:'); console.log(' erdos number-theory status [] [--json]'); console.log(' erdos number-theory frontier [] [--json]'); + console.log(' erdos number-theory bridge [] [--json]'); + console.log(' erdos number-theory bridge-refresh [] [--json]'); + console.log(' erdos number-theory dispatch [] [--apply] [--detach] [--review-after-hours ] [--remote-id ] [--external-source-dir ] [--action ] [--exact-min ] [--exact-max ] [--exact-chunks ] [--exact-chunk-size ] [--base-side-max ] [--structural-min ] [--structural-max ] [--mixed-base-max-rows ] [--full-mixed-row-sample-limit ] [--structural-lift-top-rows ] [--structural-lift-family-limit ] [--matching-pattern-prime

] [--matching-pattern-top-rows ] [--matching-pattern-pair-sample-limit ] [--json]'); + console.log(' erdos number-theory dispatch-fleet [] --fleet [--apply] [--review-after-hours ] [--strategy ] [--action ] [--json]'); + console.log(' erdos number-theory fleet-run [--json]'); console.log(' erdos number-theory routes [] [--json]'); console.log(' erdos number-theory tickets [] [--json]'); console.log(' erdos number-theory route [--json]'); @@ -209,7 +1311,7 @@ export function runNumberTheoryCommand(args) { return 0; } - if (!['status', 'frontier', 'routes', 'tickets', 'route', 'ticket', 'atom'].includes(subcommand)) { + if (!['status', 'frontier', 'bridge', 'bridge-refresh', 'dispatch', 'dispatch-fleet', 'fleet-run', 'routes', 'tickets', 'route', 'ticket', 'atom'].includes(subcommand)) { console.error(`Unknown number-theory subcommand: ${subcommand}`); return 1; } @@ -220,6 +1322,24 @@ export function runNumberTheoryCommand(args) { return 1; } + if (subcommand === 'fleet-run') { + if (!parsed.problemId) { + console.error('Missing fleet run id.'); + return 1; + } + const snapshot = getNumberTheoryFleetRunSnapshot(parsed.problemId); + if (!snapshot) { + console.error(`Unknown number-theory fleet run: ${parsed.problemId}`); + return 1; + } + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printFleetRun(snapshot); + return 0; + } + const { problem, error } = resolveNumberTheoryProblem(parsed.problemId); if (error) { console.error(error); @@ -280,6 +1400,121 @@ export function runNumberTheoryCommand(args) { return 0; } + if (subcommand === 'bridge') { + const snapshot = getNumberTheoryBridgeSnapshot(problem); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printBridge(snapshot); + return 0; + } + + if (subcommand === 'bridge-refresh') { + const result = refreshNumberTheoryBridge(problem); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printBridgeRefresh(result); + return result.ok ? 0 : 1; + } + + if (subcommand === 'dispatch') { + if (parsed.apply) { + const result = runNumberTheoryDispatch(problem, { + actionId: parsed.actionId, + detach: parsed.detach, + exactMin: parsed.exactMin, + exactMax: parsed.exactMax, + exactChunks: parsed.exactChunks, + exactChunkSize: parsed.exactChunkSize, + baseSideMax: parsed.baseSideMax, + structuralMax: parsed.structuralMax, + structuralMin: parsed.structuralMin, + mixedBaseMaxRows: parsed.mixedBaseMaxRows, + fullMixedRowSampleLimit: parsed.fullMixedRowSampleLimit, + structuralLiftTopRows: parsed.structuralLiftTopRows, + structuralLiftFamilyLimit: parsed.structuralLiftFamilyLimit, + matchingPatternPrime: parsed.matchingPatternPrime, + matchingPatternTopRows: parsed.matchingPatternTopRows, + matchingPatternPairSampleLimit: parsed.matchingPatternPairSampleLimit, + endpointMonotonicity: parsed.endpointMonotonicity, + reviewAfterHours: parsed.reviewAfterHours, + remoteId: parsed.remoteId, + externalSourceDir: parsed.externalSourceDir, + }); + if (parsed.asJson) { + console.log(JSON.stringify(compactDispatchResultForJson(result), null, 2)); + return result.ok || result.partial ? 0 : 1; + } + printDispatchResult(result); + return result.ok || result.partial ? 0 : 1; + } + + const snapshot = getNumberTheoryDispatchSnapshot(problem, { + detach: parsed.detach, + exactMin: parsed.exactMin, + exactMax: parsed.exactMax, + exactChunks: parsed.exactChunks, + exactChunkSize: parsed.exactChunkSize, + baseSideMax: parsed.baseSideMax, + structuralMax: parsed.structuralMax, + structuralMin: parsed.structuralMin, + mixedBaseMaxRows: parsed.mixedBaseMaxRows, + fullMixedRowSampleLimit: parsed.fullMixedRowSampleLimit, + structuralLiftTopRows: parsed.structuralLiftTopRows, + structuralLiftFamilyLimit: parsed.structuralLiftFamilyLimit, + matchingPatternPrime: parsed.matchingPatternPrime, + matchingPatternTopRows: parsed.matchingPatternTopRows, + matchingPatternPairSampleLimit: parsed.matchingPatternPairSampleLimit, + endpointMonotonicity: parsed.endpointMonotonicity, + reviewAfterHours: parsed.reviewAfterHours, + remoteId: parsed.remoteId, + externalSourceDir: parsed.externalSourceDir, + }); + if (parsed.asJson) { + console.log(JSON.stringify(compactDispatchForJson(snapshot), null, 2)); + return snapshot.available ? 0 : 1; + } + printDispatch(snapshot); + return snapshot.available ? 0 : 1; + } + + if (subcommand === 'dispatch-fleet') { + if (!parsed.fleetId) { + console.error('Missing fleet id. Use --fleet .'); + return 1; + } + if (parsed.apply) { + const result = runNumberTheoryFleetDispatch(problem, { + actionId: parsed.actionId, + reviewAfterHours: parsed.reviewAfterHours, + fleetId: parsed.fleetId, + strategyId: parsed.strategyId, + }); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok || result.partial ? 0 : 1; + } + printFleetDispatchResult(result); + return result.ok || result.partial ? 0 : 1; + } + + const snapshot = getNumberTheoryFleetDispatchSnapshot(problem, { + actionId: parsed.actionId, + reviewAfterHours: parsed.reviewAfterHours, + fleetId: parsed.fleetId, + strategyId: parsed.strategyId, + }); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printFleetDispatch(snapshot); + return snapshot.available ? 0 : 1; + } + const snapshot = buildNumberTheoryStatusSnapshot(problem); if (parsed.asJson) { console.log(JSON.stringify(snapshot, null, 2)); diff --git a/src/commands/preflight.js b/src/commands/preflight.js index dcbe940..81139a5 100644 --- a/src/commands/preflight.js +++ b/src/commands/preflight.js @@ -37,6 +37,20 @@ export function runPreflightCommand(args) { console.log(`- Continuation policy: ${report.continuationDisplay}`); console.log(`- Current frontier: ${report.currentFrontier.kind} / ${report.currentFrontier.detail}`); console.log(`- Next honest move: ${report.nextHonestMove}`); + if (report.researchStack) { + console.log('- Research stack:'); + console.log(` - Canonical source: ${report.researchStack.canonicalSource.sourceUrl}`); + console.log(` - Import snapshot: ${report.researchStack.canonicalSource.importSnapshotKind ?? '(missing)'}`); + console.log(` - ORP sync: ${report.researchStack.localProtocol.commands.orpSync}`); + console.log(` - Checkpoint sync: ${report.researchStack.localProtocol.commands.checkpointsSync}`); + console.log(` - Theorem loop: ${report.researchStack.theorem.commands.show ?? '(none)'}`); + console.log(` - Theorem refresh: ${report.researchStack.theorem.commands.refresh ?? '(none)'}`); + console.log(` - Compute entry: ${report.researchStack.compute.entryCommand ?? '(none)'}`); + if (report.researchStack.compute.hardwareDoctorCommand) { + console.log(` - Hardware doctor: ${report.researchStack.compute.hardwareDoctorCommand}`); + } + console.log(` - Canonical writeback: ${report.researchStack.writeback.packagedRefreshCommand ?? '(none)'}`); + } console.log('Checks:'); printChecks(report.checks); console.log(`Verdict: ${report.verdict}`); diff --git a/src/commands/problem.js b/src/commands/problem.js index 84494f7..3592879 100644 --- a/src/commands/problem.js +++ b/src/commands/problem.js @@ -3,6 +3,22 @@ import { syncOrpWorkspaceKit } from '../runtime/orp.js'; import { syncCheckpoints } from '../runtime/checkpoints.js'; import { getProblemArtifactInventory } from '../runtime/problem-artifacts.js'; import { syncState } from '../runtime/state.js'; +import { + getProblemClaimPassSnapshot, + getProblemClaimLoopSnapshot, + getProblemFormalizationSnapshot, + getProblemFormalizationWorkSnapshot, + getProblemTaskListSnapshot, + getProblemTheoremLoopSnapshot, + checkProblemFormalizationWork, + runProblemTaskListLoop, + refreshProblemFormalization, + refreshProblemFormalizationWork, + refreshProblemClaimPass, + refreshProblemClaimLoop, + refreshProblemTaskList, + refreshProblemTheoremLoop, +} from '../runtime/theorem-loop.js'; import { readCurrentProblem, setCurrentProblem } from '../runtime/workspace.js'; function parseListFilters(args) { @@ -72,6 +88,47 @@ function parseArtifactArgs(args) { return parsed; } +function parseTaskListRunArgs(args) { + const parsed = { + problemId: null, + passes: 1, + asJson: false, + stopOnConvergence: true, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--passes') { + const value = args[index + 1]; + if (!value) { + return { error: 'Missing pass count after --passes.' }; + } + const passes = Number.parseInt(value, 10); + if (!Number.isFinite(passes) || passes <= 0) { + return { error: `Invalid pass count: ${value}` }; + } + parsed.passes = passes; + index += 1; + continue; + } + if (token === '--no-stop-on-convergence') { + parsed.stopOnConvergence = false; + continue; + } + if (!parsed.problemId) { + parsed.problemId = token; + continue; + } + return { error: `Unknown task-list-run option: ${token}` }; + } + + return parsed; +} + function printProblemTable(rows, activeProblem) { console.log('ID Site Repo Cluster Depth Active Title'); for (const row of rows) { @@ -163,6 +220,503 @@ function printArtifactInventory(problem, inventory, asJson) { console.log(`Imported record available: ${inventory.upstreamRecordIncluded ? 'yes' : 'no'}`); } +function printTheoremLoop(snapshot, asJson) { + if (asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return; + } + + console.log(`${snapshot.displayName} theorem loop`); + console.log(`Theorem loop mode: ${snapshot.theoremLoopMode}`); + console.log(`Source kind: ${snapshot.sourceKind}`); + console.log(`Active route: ${snapshot.activeRoute ?? '(none)'}`); + console.log(`Current claim surface: ${snapshot.currentState.currentClaimSurface}`); + console.log(`Route summary: ${snapshot.currentState.routeSummary}`); + console.log(`Next honest move: ${snapshot.currentState.nextHonestMove}`); + console.log(`Theorem module: ${snapshot.theoremModule ?? '(none)'}`); + console.log(`Theorem loop markdown: ${snapshot.theoremLoopMarkdownPresent ? snapshot.theoremLoopMarkdownPath : '(not written yet)'}`); + console.log(`Theorem loop data: ${snapshot.theoremLoopJsonPresent ? snapshot.theoremLoopJsonPath : '(not written yet)'}`); + if (snapshot.commands.sourceRefresh) { + console.log(`Source refresh: ${snapshot.commands.sourceRefresh}`); + } + if (snapshot.currentBridgeState?.next_unmatched_representative !== undefined) { + console.log(`Next unmatched representative: ${snapshot.currentBridgeState.next_unmatched_representative}`); + } + if ((snapshot.theoremHooks ?? []).length > 0) { + console.log('Theorem hooks:'); + for (const hook of snapshot.theoremHooks) { + console.log(`- ${hook.hook_id} [${hook.status}]${hook.note ? ` ${hook.note}` : ''}`); + } + } + if ((snapshot.theoremAgenda ?? []).length > 0) { + console.log('Theorem agenda:'); + for (const item of snapshot.theoremAgenda) { + console.log(`- ${item.item_id} [${item.status}] ${item.task}${item.why ? ` | ${item.why}` : ''}`); + } + } +} + +function printTheoremLoopRefresh(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem theorem-loop refresh: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + if (result.sourceRefresh?.command) { + console.log(`Source refresh command: ${result.sourceRefresh.command}`); + } + return; + } + + console.log('Problem theorem-loop refresh: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Theorem loop markdown: ${result.markdownPath}`); + console.log(`Theorem loop data: ${result.jsonPath}`); + if (result.sourceRefresh?.command) { + console.log(`Source refresh command: ${result.sourceRefresh.command}`); + console.log(`Source refresh ran: ${result.sourceRefresh.skipped ? 'no' : 'yes'}`); + } + console.log(`Theorem loop mode: ${result.theoremLoop.theoremLoopMode}`); +} + +function printClaimLoop(snapshot, asJson) { + if (asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return; + } + + console.log(`${snapshot.displayName} claim loop`); + console.log(`Claim loop mode: ${snapshot.claimLoopMode}`); + console.log(`Current claim surface: ${snapshot.currentClaimSurface}`); + console.log(`Active route: ${snapshot.currentState.activeRoute ?? '(none)'}`); + console.log(`Claim loop markdown: ${snapshot.claimLoopMarkdownPresent ? snapshot.claimLoopMarkdownPath : '(not written yet)'}`); + console.log(`Claim loop data: ${snapshot.claimLoopJsonPresent ? snapshot.claimLoopJsonPath : '(not written yet)'}`); + console.log(`Theorem loop: ${snapshot.commands.theoremLoop}`); + console.log(`Claim refresh: ${snapshot.commands.claimLoopRefresh}`); + if (snapshot.commands.sourceRefresh) { + console.log(`Source refresh: ${snapshot.commands.sourceRefresh}`); + } + if ((snapshot.featureExtractors ?? []).length > 0) { + console.log('Feature extractors:'); + for (const extractor of snapshot.featureExtractors) { + console.log(`- ${extractor.extractor_id} [${extractor.status}] ${extractor.note}`); + } + } + if ((snapshot.claimGenerators ?? []).length > 0) { + console.log('Claim generators:'); + for (const generator of snapshot.claimGenerators) { + console.log(`- ${generator.generator_id} [${generator.status}] ${generator.note}`); + } + } + if ((snapshot.claimFalsifiers ?? []).length > 0) { + console.log('Claim falsifiers:'); + for (const falsifier of snapshot.claimFalsifiers) { + console.log(`- ${falsifier.falsifier_id} [${falsifier.status}] ${falsifier.note}`); + } + } + if ((snapshot.verifierAdapters ?? []).length > 0) { + console.log('Verifier adapters:'); + for (const adapter of snapshot.verifierAdapters) { + console.log(`- ${adapter.adapter_id} [${adapter.status}] ${adapter.note}`); + } + } + if ((snapshot.candidateClaims ?? []).length > 0) { + console.log('Candidate claims:'); + for (const claim of snapshot.candidateClaims) { + console.log(`- ${claim.claim_id} [${claim.status}] ${claim.summary}${claim.why ? ` | ${claim.why}` : ''}`); + } + } +} + +function printClaimLoopRefresh(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem claim-loop refresh: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + return; + } + + console.log('Problem claim-loop refresh: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Claim loop markdown: ${result.markdownPath}`); + console.log(`Claim loop data: ${result.jsonPath}`); + if (result.theoremRefresh?.jsonPath) { + console.log(`Theorem loop data: ${result.theoremRefresh.jsonPath}`); + } + console.log(`Claim loop mode: ${result.claimLoop.claimLoopMode}`); +} + +function printClaimPass(snapshot, asJson) { + if (asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return; + } + + console.log(`${snapshot.displayName} claim pass`); + console.log(`Claim pass mode: ${snapshot.claimPassMode}`); + console.log(`Current claim surface: ${snapshot.currentClaimSurface}`); + console.log(`Active route: ${snapshot.currentState.activeRoute ?? '(none)'}`); + console.log(`Latest verified interval: ${snapshot.currentState.latestVerifiedInterval ?? '(none)'}`); + console.log(`Claim pass markdown: ${snapshot.claimPassMarkdownPresent ? snapshot.claimPassMarkdownPath : '(not written yet)'}`); + console.log(`Claim pass data: ${snapshot.claimPassJsonPresent ? snapshot.claimPassJsonPath : '(not written yet)'}`); + console.log(`Claim pass command: ${snapshot.commands.claimPass}`); + console.log(`Claim pass refresh: ${snapshot.commands.claimPassRefresh}`); + if (snapshot.commands.sourceRefresh) { + console.log(`Source refresh: ${snapshot.commands.sourceRefresh}`); + } + console.log(`Hook summary: supported=${snapshot.summary?.hooks?.supported ?? 0}, unresolved=${snapshot.summary?.hooks?.unresolved ?? 0}, broken=${snapshot.summary?.hooks?.broken ?? 0}`); + console.log(`Claim summary: supported=${snapshot.summary?.claims?.supported ?? 0}, actionable=${snapshot.summary?.claims?.actionable ?? 0}, unresolved=${snapshot.summary?.claims?.unresolved ?? 0}, broken=${snapshot.summary?.claims?.broken ?? 0}`); + if ((snapshot.hookAssessments ?? []).length > 0) { + console.log('Hook assessments:'); + for (const hook of snapshot.hookAssessments) { + console.log(`- ${hook.hook_id} [${hook.verdict}] ${hook.rationale}`); + } + } + if ((snapshot.claimAssessments ?? []).length > 0) { + console.log('Claim assessments:'); + for (const claim of snapshot.claimAssessments) { + console.log(`- ${claim.claim_id} [${claim.verdict}] ${claim.summary}${claim.rationale ? ` | ${claim.rationale}` : ''}`); + } + } + if ((snapshot.recommendations ?? []).length > 0) { + console.log('Recommendations:'); + for (const recommendation of snapshot.recommendations) { + console.log(`- ${recommendation.recommendation_id} [${recommendation.priority}] ${recommendation.lane}${recommendation.reason ? ` | ${recommendation.reason}` : ''}`); + } + } +} + +function printClaimPassRefresh(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem claim-pass refresh: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + return; + } + + console.log('Problem claim-pass refresh: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Claim pass markdown: ${result.markdownPath}`); + console.log(`Claim pass data: ${result.jsonPath}`); + if (result.claimRefresh?.jsonPath) { + console.log(`Claim loop data: ${result.claimRefresh.jsonPath}`); + } + console.log(`Claim pass mode: ${result.claimPass.claimPassMode}`); +} + +function printFormalization(snapshot, asJson) { + if (asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return; + } + + console.log(`${snapshot.displayName} formalization`); + console.log(`Formalization mode: ${snapshot.formalizationMode}`); + console.log(`Current claim surface: ${snapshot.currentClaimSurface}`); + console.log(`Active route: ${snapshot.currentState.activeRoute ?? '(none)'}`); + console.log(`Latest verified interval: ${snapshot.currentState.latestVerifiedInterval ?? '(none)'}`); + console.log(`Formalization markdown: ${snapshot.formalizationMarkdownPresent ? snapshot.formalizationMarkdownPath : '(not written yet)'}`); + console.log(`Formalization data: ${snapshot.formalizationJsonPresent ? snapshot.formalizationJsonPath : '(not written yet)'}`); + console.log(`Formalization command: ${snapshot.commands.formalization}`); + console.log(`Formalization refresh: ${snapshot.commands.formalizationRefresh}`); + if (snapshot.currentTarget) { + console.log(`Current target: ${snapshot.currentTarget.title ?? snapshot.currentTarget.focusId ?? '(none)'}`); + console.log(`Target status: ${snapshot.currentTarget.status ?? '(none)'}`); + console.log(`Target statement: ${snapshot.currentTarget.statement ?? '(none)'}`); + } +} + +function printFormalizationRefresh(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem formalization refresh: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + return; + } + + console.log('Problem formalization refresh: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Formalization markdown: ${result.markdownPath}`); + console.log(`Formalization data: ${result.jsonPath}`); + if (result.claimPassRefresh?.jsonPath) { + console.log(`Claim pass data: ${result.claimPassRefresh.jsonPath}`); + } + console.log(`Formalization mode: ${result.formalization.formalizationMode}`); +} + +function printFormalizationWork(snapshot, asJson) { + if (asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return; + } + + console.log(`${snapshot.displayName} formalization work`); + console.log(`Formalization work mode: ${snapshot.formalizationWorkMode}`); + console.log(`Current claim surface: ${snapshot.currentClaimSurface}`); + console.log(`Active route: ${snapshot.currentState.activeRoute ?? '(none)'}`); + console.log(`Latest verified interval: ${snapshot.currentState.latestVerifiedInterval ?? '(none)'}`); + console.log(`Formalization work markdown: ${snapshot.formalizationWorkMarkdownPresent ? snapshot.formalizationWorkMarkdownPath : '(not written yet)'}`); + console.log(`Formalization work data: ${snapshot.formalizationWorkJsonPresent ? snapshot.formalizationWorkJsonPath : '(not written yet)'}`); + console.log(`Formalization work diagram: ${snapshot.formalizationWorkSvgPresent ? snapshot.formalizationWorkSvgPath : '(not written yet)'}`); + console.log(`Formalization work command: ${snapshot.commands.formalizationWork}`); + console.log(`Formalization work refresh: ${snapshot.commands.formalizationWorkRefresh}`); + if (snapshot.currentWork) { + console.log(`Current work: ${snapshot.currentWork.title ?? snapshot.currentWork.focusId ?? '(none)'}`); + console.log(`Work status: ${snapshot.currentWork.status ?? '(none)'}`); + console.log(`Work summary: ${snapshot.currentWork.summary ?? '(none)'}`); + } +} + +function printFormalizationWorkRefresh(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem formalization-work refresh: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + return; + } + + console.log('Problem formalization-work refresh: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Formalization work markdown: ${result.markdownPath}`); + console.log(`Formalization work data: ${result.jsonPath}`); + console.log(`Formalization work diagram: ${result.svgPath ?? '(not written yet)'}`); + if (result.formalizationRefresh?.jsonPath) { + console.log(`Formalization data: ${result.formalizationRefresh.jsonPath}`); + } + console.log(`Formalization work mode: ${result.formalizationWork.formalizationWorkMode}`); +} + +function printFormalizationWorkCheck(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + console.log(`${result.displayName} formalization-work check`); + console.log(`Status: ${result.status}`); + console.log(`Current work: ${result.currentWorkTitle ?? result.currentWorkId ?? '(none)'}`); + console.log(`Checks: ${result.summary.checkCount}`); + console.log(`Checked rows: ${result.summary.checkedRowCount}`); + console.log(`Failures: ${result.summary.failCount}`); + if (result.firstRemainingGap) { + console.log(`Next gap: ${result.firstRemainingGap}`); + } + for (const check of result.checks ?? []) { + console.log(`- ${check.checkerId}: ${check.status} (${check.passCount}/${check.checkedRowCount} passed)`); + } +} + +function pickTaskListHighestValueStep(taskList) { + const priorityRank = { + highest: 0, + next: 1, + high: 2, + }; + const recommended = [...(taskList.nextNeededSteps ?? [])] + .filter((step) => Object.hasOwn(priorityRank, step.status)) + .sort((left, right) => priorityRank[left.status] - priorityRank[right.status])[0] + ?? null; + if (recommended) { + return { + stepId: recommended.stepId, + status: recommended.status, + task: recommended.task, + command: recommended.command ?? null, + packetJsonPath: recommended.packetJsonPath ?? null, + packetMarkdownPath: recommended.packetMarkdownPath ?? null, + }; + } + + const currentTask = (taskList.currentTasks ?? []).find((task) => task.status === 'in_progress') + ?? (taskList.currentTasks ?? []).find((task) => task.taskId === 'execute_current_work_packet') + ?? (taskList.currentTasks ?? []).find((task) => task.status === 'ready') + ?? null; + if (!currentTask) { + return null; + } + + return { + stepId: currentTask.taskId, + status: currentTask.status, + task: currentTask.task, + command: currentTask.command ?? null, + }; +} + +function getTaskListModeAssist(taskList) { + const granular = taskList.granularBreakdownMode ?? null; + const overlays = taskList.orpModeOverlays?.overlays ?? []; + const overlayIds = overlays.map((overlay) => overlay.modeId).filter((modeId) => modeId !== granular?.modeId); + return { + defaultModeId: taskList.orpModeOverlays?.defaultModeId ?? granular?.modeId ?? null, + selectionRule: taskList.orpModeOverlays?.selectionRule ?? null, + nudgeCommand: granular?.commands?.nudge ?? null, + otherOverlayIds: overlayIds, + }; +} + +function printTaskListFrictionlessNext(taskList) { + const highestValueStep = pickTaskListHighestValueStep(taskList); + if (highestValueStep) { + console.log(`Highest-value next step: ${highestValueStep.stepId} [${highestValueStep.status}]`); + console.log(`Next task: ${highestValueStep.task}`); + if (highestValueStep.command) { + console.log(`Next command: ${highestValueStep.command}`); + } + if (highestValueStep.packetJsonPath) { + console.log(`Next packet: ${highestValueStep.packetJsonPath}`); + } + if (highestValueStep.packetMarkdownPath) { + console.log(`Next packet note: ${highestValueStep.packetMarkdownPath}`); + } + } + + const modeAssist = getTaskListModeAssist(taskList); + if (modeAssist.defaultModeId || modeAssist.nudgeCommand || modeAssist.selectionRule) { + if (modeAssist.nudgeCommand) { + if (highestValueStep?.command) { + console.log(`Mode assist: Execute the next command first; if the target feels fuzzy, run ${modeAssist.nudgeCommand}.`); + } else if (highestValueStep?.packetJsonPath) { + console.log(`Mode assist: Work the next packet first; if the target feels fuzzy, run ${modeAssist.nudgeCommand}.`); + } else { + console.log(`Mode assist: Work the next task first; if the target feels fuzzy, run ${modeAssist.nudgeCommand}.`); + } + } else { + console.log(`Mode assist: ${modeAssist.selectionRule ?? 'Use an ORP mode only when it reduces friction.'}`); + } + if (modeAssist.otherOverlayIds.length > 0) { + console.log(`Optional overlays when useful: ${modeAssist.otherOverlayIds.join(', ')}`); + } + } +} + +function printTaskList(snapshot, asJson) { + if (asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return; + } + + console.log(`${snapshot.displayName} task list`); + console.log(`Task list mode: ${snapshot.taskListMode}`); + console.log(`Active route: ${snapshot.currentState.activeRoute ?? '(none)'}`); + console.log(`Current claim surface: ${snapshot.currentState.currentClaimSurface ?? '(none)'}`); + console.log(`Next honest move: ${snapshot.currentState.nextHonestMove ?? '(none)'}`); + console.log(`Task list markdown: ${snapshot.taskListMarkdownPresent ? snapshot.taskListMarkdownPath : '(not written yet)'}`); + console.log(`Task list data: ${snapshot.taskListJsonPresent ? snapshot.taskListJsonPath : '(not written yet)'}`); + console.log(`Task list command: ${snapshot.commands.taskList}`); + console.log(`Task list refresh: ${snapshot.commands.taskListRefresh}`); + printTaskListFrictionlessNext(snapshot); + if (snapshot.currentObjective) { + console.log(`Current objective: ${snapshot.currentObjective.title ?? '(none)'}`); + console.log(`Active work: ${snapshot.currentObjective.activeWorkTitle ?? '(none)'}`); + console.log(`Active work status: ${snapshot.currentObjective.activeWorkStatus ?? '(none)'}`); + } + if ((snapshot.currentTasks ?? []).length > 0) { + console.log('Current tasks:'); + for (const task of snapshot.currentTasks.slice(0, 8)) { + console.log(`- ${task.taskId} [${task.status}] ${task.title}${task.command ? ` | ${task.command}` : ''}`); + } + } + if ((snapshot.nextNeededSteps ?? []).length > 0) { + console.log('Next needed steps:'); + for (const step of snapshot.nextNeededSteps.slice(0, 6)) { + console.log(`- ${step.stepId} [${step.status}] ${step.task}${step.command ? ` | ${step.command}` : ''}`); + } + } +} + +function printTaskListRefresh(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem task-list refresh: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + return; + } + + console.log('Problem task-list refresh: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Task list markdown: ${result.markdownPath}`); + console.log(`Task list data: ${result.jsonPath}`); + if (result.formalizationWorkRefresh?.jsonPath) { + console.log(`Formalization work data: ${result.formalizationWorkRefresh.jsonPath}`); + } + if (result.splitAtomPacketWrite?.ok) { + console.log(`Split atom packets: ${result.splitAtomPacketWrite.packetCount} written`); + console.log(`Split atom manifest: ${result.splitAtomPacketWrite.manifestJsonPath}`); + if (result.splitAtomPacketWrite.firstPacketToAttack?.atomId) { + console.log(`First split atom: ${result.splitAtomPacketWrite.firstPacketToAttack.atomId}`); + } + } + console.log(`Task list mode: ${result.taskList.taskListMode}`); + printTaskListFrictionlessNext(result.taskList); +} + +function printTaskListRun(result, asJson) { + if (asJson) { + console.log(JSON.stringify(result, null, 2)); + return; + } + + if (!result.ok) { + console.log('Problem task-list run: failed'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Error: ${result.error}`); + return; + } + + console.log('Problem task-list run: complete'); + console.log(`Problem id: ${result.problemId}`); + console.log(`Requested passes: ${result.requestedPasses}`); + console.log(`Executed passes: ${result.executedPasses}`); + console.log(`Stop reason: ${result.stopReason}`); + console.log(`Converged: ${result.converged ? 'yes' : 'no'}`); + if (result.convergedAtPass) { + console.log(`Converged at pass: ${result.convergedAtPass}`); + } + console.log(`Task loop run markdown: ${result.markdownPath}`); + console.log(`Task loop run data: ${result.jsonPath}`); + if (result.currentState) { + console.log(`Active route: ${result.currentState.activeRoute ?? '(none)'}`); + console.log(`Latest verified interval: ${result.currentState.latestVerifiedInterval ?? '(none)'}`); + } + if (result.highestValueStep) { + console.log(`Highest-value next step: ${result.highestValueStep.stepId ?? '(none)'}`); + console.log(`Next task: ${result.highestValueStep.task ?? '(none)'}`); + if (result.highestValueStep.command) { + console.log(`Next command: ${result.highestValueStep.command}`); + } + } +} + export function runProblemCommand(args) { const [subcommand, value, ...rest] = args; @@ -173,6 +727,20 @@ export function runProblemCommand(args) { console.log(' erdos problem use '); console.log(' erdos problem current'); console.log(' erdos problem artifacts [] [--json]'); + console.log(' erdos problem theorem-loop [] [--json]'); + console.log(' erdos problem theorem-loop-refresh [] [--json]'); + console.log(' erdos problem claim-loop [] [--json]'); + console.log(' erdos problem claim-loop-refresh [] [--json]'); + console.log(' erdos problem claim-pass [] [--json]'); + console.log(' erdos problem claim-pass-refresh [] [--json]'); + console.log(' erdos problem formalization [] [--json]'); + console.log(' erdos problem formalization-refresh [] [--json]'); + console.log(' erdos problem formalization-work [] [--json]'); + console.log(' erdos problem formalization-work-refresh [] [--json]'); + console.log(' erdos problem formalization-work-check [] [--json]'); + console.log(' erdos problem task-list [] [--json]'); + console.log(' erdos problem task-list-refresh [] [--json]'); + console.log(' erdos problem task-list-run [] [--passes ] [--no-stop-on-convergence] [--json]'); return 0; } @@ -259,6 +827,303 @@ export function runProblemCommand(args) { return 0; } + if (subcommand === 'theorem-loop') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const snapshot = getProblemTheoremLoopSnapshot(problem); + printTheoremLoop(snapshot, parsed.asJson); + return 0; + } + + if (subcommand === 'theorem-loop-refresh') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = refreshProblemTheoremLoop(problem); + printTheoremLoopRefresh(result, parsed.asJson); + return result.ok ? 0 : 1; + } + + if (subcommand === 'claim-loop') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const snapshot = getProblemClaimLoopSnapshot(problem); + printClaimLoop(snapshot, parsed.asJson); + return 0; + } + + if (subcommand === 'claim-loop-refresh') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = refreshProblemClaimLoop(problem); + printClaimLoopRefresh(result, parsed.asJson); + return result.ok ? 0 : 1; + } + + if (subcommand === 'claim-pass') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const snapshot = getProblemClaimPassSnapshot(problem); + printClaimPass(snapshot, parsed.asJson); + return 0; + } + + if (subcommand === 'claim-pass-refresh') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = refreshProblemClaimPass(problem); + printClaimPassRefresh(result, parsed.asJson); + return result.ok ? 0 : 1; + } + + if (subcommand === 'formalization') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const snapshot = getProblemFormalizationSnapshot(problem); + printFormalization(snapshot, parsed.asJson); + return 0; + } + + if (subcommand === 'formalization-refresh') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = refreshProblemFormalization(problem); + printFormalizationRefresh(result, parsed.asJson); + return result.ok ? 0 : 1; + } + + if (subcommand === 'formalization-work') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const snapshot = getProblemFormalizationWorkSnapshot(problem); + printFormalizationWork(snapshot, parsed.asJson); + return 0; + } + + if (subcommand === 'formalization-work-refresh') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = refreshProblemFormalizationWork(problem); + printFormalizationWorkRefresh(result, parsed.asJson); + return result.ok ? 0 : 1; + } + + if (subcommand === 'formalization-work-check') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = checkProblemFormalizationWork(problem); + printFormalizationWorkCheck(result, parsed.asJson); + return result.status === 'failed' ? 1 : 0; + } + + if (subcommand === 'task-list') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const snapshot = getProblemTaskListSnapshot(problem); + printTaskList(snapshot, parsed.asJson); + return 0; + } + + if (subcommand === 'task-list-refresh') { + const parsed = parseArtifactArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = refreshProblemTaskList(problem); + printTaskListRefresh(result, parsed.asJson); + return result.ok ? 0 : 1; + } + + if (subcommand === 'task-list-run') { + const parsed = parseTaskListRunArgs([value, ...rest].filter(Boolean)); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const problemId = parsed.problemId ?? readCurrentProblem(); + if (!problemId) { + console.error('Missing problem id and no active problem is selected.'); + return 1; + } + const problem = getProblem(problemId); + if (!problem) { + console.error(`Unknown problem: ${problemId}`); + return 1; + } + const result = runProblemTaskListLoop(problem, { + passes: parsed.passes, + stopOnConvergence: parsed.stopOnConvergence, + }); + printTaskListRun(result, parsed.asJson); + return result.ok ? 0 : 1; + } + console.error(`Unknown problem subcommand: ${subcommand}`); return 1; } diff --git a/src/commands/state.js b/src/commands/state.js index e162061..ca3b5b2 100644 --- a/src/commands/state.js +++ b/src/commands/state.js @@ -17,6 +17,29 @@ function printState(state) { console.log(`Current frontier: ${state.currentFrontier.kind} / ${state.currentFrontier.detail}`); console.log(`Route story: ${state.routeStory || '(none)'}`); console.log(`Checkpoint focus: ${state.checkpointFocus || '(none)'}`); + const frontierLoopLabel = state.frontierLoop?.suggested + ? `active (${state.frontierLoop?.mode ?? 'unknown'})` + : 'inactive'; + console.log(`Frontier loop: ${frontierLoopLabel}`); + if (state.frontierLoop?.suggested) { + if (state.frontierLoop?.summary) { + console.log(`Frontier loop summary: ${state.frontierLoop.summary}`); + } + if (state.frontierLoop?.primaryCommand) { + console.log(`Frontier loop entry: ${state.frontierLoop.primaryCommand}`); + } + if (state.frontierLoop?.refreshCommand) { + console.log(`Frontier loop refresh: ${state.frontierLoop.refreshCommand}`); + } + if (state.frontierLoop?.mode === 'cpu' && state.frontierLoop?.upgradeCommand) { + console.log(`Frontier loop upgrade: ${state.frontierLoop.upgradeCommand}`); + } + } else if (state.frontierLoop?.activationCommand) { + console.log(`Frontier loop activation: ${state.frontierLoop.activationCommand}`); + if (state.frontierLoop?.upgradeCommand) { + console.log(`Frontier loop GPU path: ${state.frontierLoop.upgradeCommand}`); + } + } console.log(`Next honest move: ${state.nextHonestMove}`); console.log(`State markdown: ${getWorkspaceStateMarkdownPath()}`); console.log(`Question ledger: ${getWorkspaceQuestionLedgerPath()}`); diff --git a/src/commands/sunflower.js b/src/commands/sunflower.js index ca5ca9b..56a4fc0 100644 --- a/src/commands/sunflower.js +++ b/src/commands/sunflower.js @@ -214,6 +214,23 @@ function printSunflowerStatus(snapshot, registryPaths) { console.log(`Report packet: ${snapshot.reportPacketPresent ? snapshot.reportPacketPath : '(missing)'}`); console.log(`Frontier note: ${snapshot.frontierNotePresent ? snapshot.frontierNotePath : '(missing)'}`); console.log(`Route history: ${snapshot.routeHistoryPresent ? snapshot.routeHistoryPath : '(missing)'}`); + console.log(`Theorem loop: ${snapshot.theoremLoop?.theoremLoopMode ?? '(missing)'}`); + console.log(`Theorem claim surface: ${snapshot.theoremLoop?.currentState?.currentClaimSurface ?? '(none)'}`); + console.log(`Theorem note: ${snapshot.theoremLoop?.theoremLoopMarkdownPresent ? snapshot.theoremLoop.theoremLoopMarkdownPath : '(not written yet)'}`); + console.log(`Theorem command: ${snapshot.theoremLoop?.commands?.theoremLoop ?? '(none)'}`); + console.log(`Theorem refresh: ${snapshot.theoremLoop?.commands?.theoremLoopRefresh ?? '(none)'}`); + console.log(`Claim loop: ${snapshot.claimLoop?.claimLoopMode ?? '(missing)'}`); + console.log(`Claim note: ${snapshot.claimLoop?.claimLoopMarkdownPresent ? snapshot.claimLoop.claimLoopMarkdownPath : '(not written yet)'}`); + console.log(`Claim command: ${snapshot.claimLoop?.commands?.claimLoop ?? '(none)'}`); + console.log(`Claim refresh: ${snapshot.claimLoop?.commands?.claimLoopRefresh ?? '(none)'}`); + console.log(`Claim pass: ${snapshot.claimPass?.claimPassMode ?? '(missing)'}`); + console.log(`Claim pass note: ${snapshot.claimPass?.claimPassMarkdownPresent ? snapshot.claimPass.claimPassMarkdownPath : '(not written yet)'}`); + console.log(`Claim pass command: ${snapshot.claimPass?.commands?.claimPass ?? '(none)'}`); + console.log(`Claim pass refresh: ${snapshot.claimPass?.commands?.claimPassRefresh ?? '(none)'}`); + console.log(`Task list: ${snapshot.taskList?.taskListMode ?? '(missing)'}`); + console.log(`Task list note: ${snapshot.taskList?.taskListMarkdownPresent ? snapshot.taskList.taskListMarkdownPath : '(not written yet)'}`); + console.log(`Task list command: ${snapshot.taskList?.commands?.taskList ?? '(none)'}`); + console.log(`Task list refresh: ${snapshot.taskList?.commands?.taskListRefresh ?? '(none)'}`); console.log(`Checkpoint template: ${snapshot.checkpointTemplatePresent ? snapshot.checkpointTemplatePath : '(missing)'}`); console.log(`Report template: ${snapshot.reportTemplatePresent ? snapshot.reportTemplatePath : '(missing)'}`); console.log(`Compute lane present: ${snapshot.computeLanePresent ? 'yes' : 'no'}`); diff --git a/src/commands/workspace.js b/src/commands/workspace.js index 4ac29c7..114f879 100644 --- a/src/commands/workspace.js +++ b/src/commands/workspace.js @@ -2,9 +2,77 @@ import { getProblem } from '../atlas/catalog.js'; import { loadConfig } from '../runtime/config.js'; import { buildGraphTheoryStatusSnapshot } from '../runtime/graph-theory.js'; import { buildNumberTheoryStatusSnapshot } from '../runtime/number-theory.js'; +import { buildResearchStackSummary } from '../runtime/research-stack.js'; import { buildSunflowerStatusSnapshot } from '../runtime/sunflower.js'; +import { getProblemArtifactInventory } from '../runtime/problem-artifacts.js'; +import { getOrpStatus } from '../runtime/orp.js'; import { getWorkspaceSummary } from '../runtime/workspace.js'; +function printWorkspaceTheoremLoop(prefix, theoremLoop, claimLoop, claimPass, formalization, formalizationWork, taskList) { + if (!theoremLoop) { + return; + } + console.log(`${prefix} theorem loop: ${theoremLoop.theoremLoopMode}`); + console.log(`${prefix} claim surface: ${theoremLoop.currentState?.currentClaimSurface ?? '(none)'}`); + console.log(`${prefix} theorem command: ${theoremLoop.commands?.theoremLoop ?? '(none)'}`); + if (theoremLoop.commands?.theoremLoopRefresh) { + console.log(`${prefix} theorem refresh: ${theoremLoop.commands.theoremLoopRefresh}`); + } + console.log( + `${prefix} theorem note: ${theoremLoop.theoremLoopMarkdownPresent ? theoremLoop.theoremLoopMarkdownPath : '(not written yet)'}`, + ); + if (claimLoop) { + console.log(`${prefix} claim loop: ${claimLoop.claimLoopMode}`); + console.log(`${prefix} claim command: ${claimLoop.commands?.claimLoop ?? '(none)'}`); + if (claimLoop.commands?.claimLoopRefresh) { + console.log(`${prefix} claim refresh: ${claimLoop.commands.claimLoopRefresh}`); + } + console.log( + `${prefix} claim note: ${claimLoop.claimLoopMarkdownPresent ? claimLoop.claimLoopMarkdownPath : '(not written yet)'}`, + ); + } + if (claimPass) { + console.log(`${prefix} claim pass: ${claimPass.claimPassMode}`); + console.log(`${prefix} claim pass command: ${claimPass.commands?.claimPass ?? '(none)'}`); + if (claimPass.commands?.claimPassRefresh) { + console.log(`${prefix} claim pass refresh: ${claimPass.commands.claimPassRefresh}`); + } + console.log( + `${prefix} claim pass note: ${claimPass.claimPassMarkdownPresent ? claimPass.claimPassMarkdownPath : '(not written yet)'}`, + ); + } + if (formalization) { + console.log(`${prefix} formalization: ${formalization.formalizationMode}`); + console.log(`${prefix} formalization command: ${formalization.commands?.formalization ?? '(none)'}`); + if (formalization.commands?.formalizationRefresh) { + console.log(`${prefix} formalization refresh: ${formalization.commands.formalizationRefresh}`); + } + console.log( + `${prefix} formalization note: ${formalization.formalizationMarkdownPresent ? formalization.formalizationMarkdownPath : '(not written yet)'}`, + ); + } + if (formalizationWork) { + console.log(`${prefix} formalization work: ${formalizationWork.formalizationWorkMode}`); + console.log(`${prefix} formalization work command: ${formalizationWork.commands?.formalizationWork ?? '(none)'}`); + if (formalizationWork.commands?.formalizationWorkRefresh) { + console.log(`${prefix} formalization work refresh: ${formalizationWork.commands.formalizationWorkRefresh}`); + } + console.log( + `${prefix} formalization work note: ${formalizationWork.formalizationWorkMarkdownPresent ? formalizationWork.formalizationWorkMarkdownPath : '(not written yet)'}`, + ); + } + if (taskList) { + console.log(`${prefix} task list: ${taskList.taskListMode}`); + console.log(`${prefix} task list command: ${taskList.commands?.taskList ?? '(none)'}`); + if (taskList.commands?.taskListRefresh) { + console.log(`${prefix} task list refresh: ${taskList.commands.taskListRefresh}`); + } + console.log( + `${prefix} task list note: ${taskList.taskListMarkdownPresent ? taskList.taskListMarkdownPath : '(not written yet)'}`, + ); + } +} + export function runWorkspaceCommand(args) { const [subcommand, ...rest] = args; @@ -23,6 +91,7 @@ export function runWorkspaceCommand(args) { const summary = getWorkspaceSummary(); const config = loadConfig(); + const orp = getOrpStatus(summary.workspaceRoot); if (asJson) { const payload = { ...summary, @@ -32,12 +101,15 @@ export function runWorkspaceCommand(args) { const problem = getProblem(summary.activeProblem); if (problem?.cluster === 'sunflower') { payload.sunflower = buildSunflowerStatusSnapshot(problem); + payload.researchStack = buildResearchStackSummary(problem, getProblemArtifactInventory(problem), orp, payload.sunflower); } if (problem?.cluster === 'number-theory') { payload.numberTheory = buildNumberTheoryStatusSnapshot(problem); + payload.researchStack = buildResearchStackSummary(problem, getProblemArtifactInventory(problem), orp, payload.numberTheory); } if (problem?.cluster === 'graph-theory') { payload.graphTheory = buildGraphTheoryStatusSnapshot(problem); + payload.researchStack = buildResearchStackSummary(problem, getProblemArtifactInventory(problem), orp, payload.graphTheory); } } console.log(JSON.stringify(payload, null, 2)); @@ -78,14 +150,17 @@ export function runWorkspaceCommand(args) { console.log(`Updated at: ${summary.updatedAt ?? '(none)'}`); if (summary.activeProblem) { const problem = getProblem(summary.activeProblem); + const inventory = getProblemArtifactInventory(problem); if (problem?.cluster === 'sunflower') { const sunflower = buildSunflowerStatusSnapshot(problem); + const researchStack = buildResearchStackSummary(problem, inventory, orp, sunflower); console.log(`Sunflower family role: ${sunflower.familyRole ?? '(none)'}`); console.log(`Sunflower harness profile: ${sunflower.harnessProfile ?? '(none)'}`); console.log(`Sunflower route: ${sunflower.activeRoute ?? '(none)'}`); console.log(`Sunflower frontier: ${sunflower.frontierDetail ?? '(none)'}`); console.log(`Sunflower frontier note: ${sunflower.frontierNotePath ?? '(none)'}`); console.log(`Sunflower route history: ${sunflower.routeHistoryPath ?? '(none)'}`); + printWorkspaceTheoremLoop('Sunflower', sunflower.theoremLoop, sunflower.claimLoop, sunflower.claimPass, sunflower.formalization, sunflower.formalizationWork, sunflower.taskList); console.log(`Sunflower board: ${sunflower.atomicBoardPresent ? 'yes' : 'no'}`); if (sunflower.atomicBoardSummary) { console.log(`Sunflower board title: ${sunflower.atomicBoardSummary.boardTitle ?? '(none)'}`); @@ -99,36 +174,96 @@ export function runWorkspaceCommand(args) { console.log(`Sunflower compute lane: ${sunflower.activePacket.laneId} [${sunflower.activePacket.status}]`); } console.log(`Sunflower compute next: ${sunflower.computeNextAction}`); + console.log(`Research canonical source: ${researchStack.canonicalSource.sourceUrl ?? '(none)'}`); + console.log(`Research import snapshot: ${researchStack.canonicalSource.importSnapshotKind ?? '(missing)'}`); + console.log(`Research ORP sync: ${researchStack.localProtocol.commands.orpSync}`); + console.log(`Research checkpoint sync: ${researchStack.localProtocol.commands.checkpointsSync}`); + console.log(`Research compute entry: ${researchStack.compute.entryCommand ?? '(none)'}`); + console.log(`Research writeback: ${researchStack.writeback.packagedRefreshCommand ?? '(none)'}`); + console.log(`Research claim refresh: ${researchStack.writeback.claimRefreshCommand ?? '(none)'}`); + console.log(`Research claim pass refresh: ${researchStack.writeback.claimPassRefreshCommand ?? '(none)'}`); + console.log(`Research formalization refresh: ${researchStack.writeback.formalizationRefreshCommand ?? '(none)'}`); + console.log(`Research formalization work refresh: ${researchStack.writeback.formalizationWorkRefreshCommand ?? '(none)'}`); + console.log(`Research task list refresh: ${researchStack.writeback.taskListRefreshCommand ?? '(none)'}`); } if (problem?.cluster === 'number-theory') { const numberTheory = buildNumberTheoryStatusSnapshot(problem); + const researchStack = buildResearchStackSummary(problem, inventory, orp, numberTheory); console.log(`Number-theory family role: ${numberTheory.familyRole ?? '(none)'}`); console.log(`Number-theory harness profile: ${numberTheory.harnessProfile ?? '(none)'}`); console.log(`Number-theory route: ${numberTheory.activeRoute ?? '(none)'}`); console.log(`Number-theory frontier: ${numberTheory.frontierDetail ?? '(none)'}`); console.log(`Number-theory frontier note: ${numberTheory.frontierNotePath ?? '(none)'}`); console.log(`Number-theory route history: ${numberTheory.routeHistoryPath ?? '(none)'}`); + printWorkspaceTheoremLoop('Number-theory', numberTheory.theoremLoop, numberTheory.claimLoop, numberTheory.claimPass, numberTheory.formalization, numberTheory.formalizationWork, numberTheory.taskList); console.log(`Number-theory archive mode: ${numberTheory.archiveMode ?? '(none)'}`); + const frontierLoopLabel = numberTheory.frontierLoopSuggested + ? `active (${numberTheory.frontierLoop?.mode ?? 'unknown'})` + : 'inactive'; + console.log(`Number-theory frontier loop: ${frontierLoopLabel}`); + if (numberTheory.frontierLoopSuggested) { + if (numberTheory.frontierLoop?.summary) { + console.log(`Number-theory frontier loop summary: ${numberTheory.frontierLoop.summary}`); + } + if (numberTheory.frontierLoop?.primaryCommand) { + console.log(`Number-theory frontier loop entry: ${numberTheory.frontierLoop.primaryCommand}`); + } + if (numberTheory.frontierLoop?.mode === 'cpu' && numberTheory.frontierLoop?.upgradeCommand) { + console.log(`Number-theory frontier loop upgrade: ${numberTheory.frontierLoop.upgradeCommand}`); + } + } else if (numberTheory.frontierLoop?.activationCommand) { + console.log(`Number-theory frontier loop activation: ${numberTheory.frontierLoop.activationCommand}`); + if (numberTheory.frontierLoop?.upgradeCommand) { + console.log(`Number-theory frontier loop GPU path: ${numberTheory.frontierLoop.upgradeCommand}`); + } + } console.log(`Number-theory active ticket: ${numberTheory.activeTicketDetail?.ticket_id ?? '(none)'}`); console.log(`Number-theory ready atoms: ${numberTheory.readyAtomCount}`); if (numberTheory.firstReadyAtom) { console.log(`Number-theory first ready atom: ${numberTheory.firstReadyAtom.atom_id} — ${numberTheory.firstReadyAtom.title}`); } + console.log(`Research canonical source: ${researchStack.canonicalSource.sourceUrl ?? '(none)'}`); + console.log(`Research import snapshot: ${researchStack.canonicalSource.importSnapshotKind ?? '(missing)'}`); + console.log(`Research ORP sync: ${researchStack.localProtocol.commands.orpSync}`); + console.log(`Research checkpoint sync: ${researchStack.localProtocol.commands.checkpointsSync}`); + console.log(`Research compute entry: ${researchStack.compute.entryCommand ?? '(none)'}`); + console.log(`Research hardware doctor: ${researchStack.compute.hardwareDoctorCommand ?? '(none)'}`); + console.log(`Research writeback: ${researchStack.writeback.packagedRefreshCommand ?? '(none)'}`); + console.log(`Research claim refresh: ${researchStack.writeback.claimRefreshCommand ?? '(none)'}`); + console.log(`Research claim pass refresh: ${researchStack.writeback.claimPassRefreshCommand ?? '(none)'}`); + console.log(`Research formalization refresh: ${researchStack.writeback.formalizationRefreshCommand ?? '(none)'}`); + console.log(`Research formalization work refresh: ${researchStack.writeback.formalizationWorkRefreshCommand ?? '(none)'}`); + console.log(`Research task list refresh: ${researchStack.writeback.taskListRefreshCommand ?? '(none)'}`); + if (researchStack.writeback.sourceRefreshCommand) { + console.log(`Research source refresh: ${researchStack.writeback.sourceRefreshCommand}`); + } } if (problem?.cluster === 'graph-theory') { const graphTheory = buildGraphTheoryStatusSnapshot(problem); + const researchStack = buildResearchStackSummary(problem, inventory, orp, graphTheory); console.log(`Graph-theory family role: ${graphTheory.familyRole ?? '(none)'}`); console.log(`Graph-theory harness profile: ${graphTheory.harnessProfile ?? '(none)'}`); console.log(`Graph-theory route: ${graphTheory.activeRoute ?? '(none)'}`); console.log(`Graph-theory frontier: ${graphTheory.frontierDetail ?? '(none)'}`); console.log(`Graph-theory frontier note: ${graphTheory.frontierNotePath ?? '(none)'}`); console.log(`Graph-theory route history: ${graphTheory.routeHistoryPath ?? '(none)'}`); + printWorkspaceTheoremLoop('Graph-theory', graphTheory.theoremLoop, graphTheory.claimLoop, graphTheory.claimPass, graphTheory.formalization, graphTheory.formalizationWork, graphTheory.taskList); console.log(`Graph-theory archive mode: ${graphTheory.archiveMode ?? '(none)'}`); console.log(`Graph-theory active ticket: ${graphTheory.activeTicketDetail?.ticket_id ?? '(none)'}`); console.log(`Graph-theory ready atoms: ${graphTheory.readyAtomCount}`); if (graphTheory.firstReadyAtom) { console.log(`Graph-theory first ready atom: ${graphTheory.firstReadyAtom.atom_id} — ${graphTheory.firstReadyAtom.title}`); } + console.log(`Research canonical source: ${researchStack.canonicalSource.sourceUrl ?? '(none)'}`); + console.log(`Research import snapshot: ${researchStack.canonicalSource.importSnapshotKind ?? '(missing)'}`); + console.log(`Research ORP sync: ${researchStack.localProtocol.commands.orpSync}`); + console.log(`Research checkpoint sync: ${researchStack.localProtocol.commands.checkpointsSync}`); + console.log(`Research writeback: ${researchStack.writeback.packagedRefreshCommand ?? '(none)'}`); + console.log(`Research claim refresh: ${researchStack.writeback.claimRefreshCommand ?? '(none)'}`); + console.log(`Research claim pass refresh: ${researchStack.writeback.claimPassRefreshCommand ?? '(none)'}`); + console.log(`Research formalization refresh: ${researchStack.writeback.formalizationRefreshCommand ?? '(none)'}`); + console.log(`Research formalization work refresh: ${researchStack.writeback.formalizationWorkRefreshCommand ?? '(none)'}`); + console.log(`Research task list refresh: ${researchStack.writeback.taskListRefreshCommand ?? '(none)'}`); } } return 0; diff --git a/src/runtime/config.js b/src/runtime/config.js index 58934fc..0ab5493 100644 --- a/src/runtime/config.js +++ b/src/runtime/config.js @@ -4,10 +4,104 @@ import { getWorkspaceConfigPath, getWorkspaceRoot } from './paths.js'; const DEFAULT_CONFIG = { preferredAgent: 'erdos', continuation: 'route', + frontier: { + loopOptIn: false, + runtimeMode: null, + activeMode: null, + activeRemoteId: null, + remotes: {}, + fleets: {}, + paidRungs: { + enabledRemoteIds: [], + enabledFleetIds: [], + lastUpdatedAt: null, + }, + managedFrontierReady: false, + gpuSearchReady: false, + lastSetupAt: null, + lastDoctorAt: null, + remote: { + attached: false, + provider: null, + instanceName: null, + sshHost: null, + engineRoot: null, + pythonCommand: null, + frontierEngineReady: false, + gpuSearchReady: false, + lastSyncAt: null, + lastSyncScope: null, + lastDoctorAt: null, + }, + }, }; +function normalizeStringList(values = []) { + return Array.from(new Set( + (Array.isArray(values) ? values : []) + .map((value) => String(value ?? '').trim()) + .filter(Boolean), + )).sort(); +} + +function deriveLegacyPaidRungs(rawFrontier = {}) { + const remotes = rawFrontier?.remotes && typeof rawFrontier.remotes === 'object' + ? rawFrontier.remotes + : {}; + const fleets = rawFrontier?.fleets && typeof rawFrontier.fleets === 'object' + ? rawFrontier.fleets + : {}; + return { + enabledRemoteIds: normalizeStringList( + Object.entries(remotes) + .filter(([, remote]) => remote?.provider === 'brev' && (remote?.attached || remote?.frontierEngineReady || remote?.gpuSearchReady)) + .map(([remoteId]) => remoteId), + ), + enabledFleetIds: normalizeStringList( + Object.entries(fleets) + .filter(([, fleet]) => fleet?.provider === 'brev') + .map(([fleetId]) => fleetId), + ), + lastUpdatedAt: null, + }; +} + +function normalizeConfig(raw = {}) { + const normalizedPaidRungs = raw.frontier?.paidRungs + ? { + enabledRemoteIds: normalizeStringList(raw.frontier?.paidRungs?.enabledRemoteIds), + enabledFleetIds: normalizeStringList(raw.frontier?.paidRungs?.enabledFleetIds), + lastUpdatedAt: raw.frontier?.paidRungs?.lastUpdatedAt ?? null, + } + : deriveLegacyPaidRungs(raw.frontier ?? {}); + return { + ...DEFAULT_CONFIG, + ...raw, + frontier: { + ...DEFAULT_CONFIG.frontier, + ...(raw.frontier ?? {}), + remotes: { + ...(DEFAULT_CONFIG.frontier.remotes ?? {}), + ...(raw.frontier?.remotes ?? {}), + }, + fleets: { + ...(DEFAULT_CONFIG.frontier.fleets ?? {}), + ...(raw.frontier?.fleets ?? {}), + }, + paidRungs: { + ...(DEFAULT_CONFIG.frontier.paidRungs ?? {}), + ...normalizedPaidRungs, + }, + remote: { + ...DEFAULT_CONFIG.frontier.remote, + ...(raw.frontier?.remote ?? {}), + }, + }, + }; +} + export function defaultConfig() { - return { ...DEFAULT_CONFIG }; + return normalizeConfig(); } export function loadConfig(workspaceRoot = getWorkspaceRoot()) { @@ -15,17 +109,11 @@ export function loadConfig(workspaceRoot = getWorkspaceRoot()) { if (!fileExists(configPath)) { return defaultConfig(); } - return { - ...DEFAULT_CONFIG, - ...readJson(configPath), - }; + return normalizeConfig(readJson(configPath)); } export function saveConfig(config, workspaceRoot = getWorkspaceRoot()) { - const payload = { - ...DEFAULT_CONFIG, - ...config, - }; + const payload = normalizeConfig(config); writeJson(getWorkspaceConfigPath(workspaceRoot), payload); return payload; } diff --git a/src/runtime/graph-theory.js b/src/runtime/graph-theory.js index f68b2f6..d1a9100 100644 --- a/src/runtime/graph-theory.js +++ b/src/runtime/graph-theory.js @@ -2,6 +2,14 @@ import fs from 'node:fs'; import path from 'node:path'; import { parse } from 'yaml'; import { getPackProblemDir } from './paths.js'; +import { + getProblemClaimLoopSnapshot, + getProblemClaimPassSnapshot, + getProblemFormalizationSnapshot, + getProblemFormalizationWorkSnapshot, + getProblemTaskListSnapshot, + getProblemTheoremLoopSnapshot, +} from './theorem-loop.js'; function readYamlIfPresent(filePath) { if (!fs.existsSync(filePath)) { @@ -84,6 +92,12 @@ export function buildGraphTheoryStatusSnapshot(problem) { const context = readYamlIfPresent(contextPath) ?? {}; const routePacket = readYamlIfPresent(routePacketPath); const opsDetails = parseOpsDetails(problem.problemId); + const theoremLoop = getProblemTheoremLoopSnapshot(problem); + const claimLoop = getProblemClaimLoopSnapshot(problem); + const claimPass = getProblemClaimPassSnapshot(problem); + const formalization = getProblemFormalizationSnapshot(problem); + const formalizationWork = getProblemFormalizationWorkSnapshot(problem); + const taskList = getProblemTaskListSnapshot(problem); const activeRoute = problem.researchState?.active_route @@ -152,6 +166,12 @@ export function buildGraphTheoryStatusSnapshot(problem) { frontierNotePath, routeHistoryPresent: fs.existsSync(routeHistoryPath), routeHistoryPath, + theoremLoop, + claimLoop, + claimPass, + formalization, + formalizationWork, + taskList, checkpointTemplatePresent: fs.existsSync(checkpointTemplatePath), checkpointTemplatePath, reportTemplatePresent: fs.existsSync(reportTemplatePath), diff --git a/src/runtime/number-theory.js b/src/runtime/number-theory.js index b77ce42..52c9378 100644 --- a/src/runtime/number-theory.js +++ b/src/runtime/number-theory.js @@ -1,7 +1,43 @@ import fs from 'node:fs'; +import { execFileSync } from 'node:child_process'; import path from 'node:path'; -import { parse } from 'yaml'; -import { getPackProblemDir } from './paths.js'; +import { parse, stringify } from 'yaml'; +import { loadConfig } from './config.js'; +import { ensureDir, writeJson, writeText } from './files.js'; +import { + getFrontierFleetSnapshot, + applyFrontierRemoteSync, + getFrontierDoctorSnapshot, + getFrontierDoctorSnapshotForRemote, + resolveFrontierExecutionPlan, +} from './frontier.js'; +import { + isBrevRemote, + joinRemotePath, + quotePosixShellArg, + quoteRemoteWindowsPath, + runRemoteCommandCapture, + runRemoteCopyFromCapture, + runRemoteCopyToCapture, +} from './frontier-remote.js'; +import { + findReusableFrontierDetachedSession, + getFrontierSessionCommandSpec, + getFrontierSessionSnapshot, + launchFrontierDetachedSession, +} from './frontier-sessions.js'; +import { getPackProblemDir, getWorkspaceRunDir, getWorkspaceRoot, repoRoot } from './paths.js'; +import { + getProblemClaimLoopSnapshot, + getProblemClaimPassSnapshot, + getProblemFormalizationSnapshot, + getProblemFormalizationWorkSnapshot, + getProblemTaskListSnapshot, + getProblemTheoremLoopSnapshot, + refreshProblemFormalization, + refreshProblemFormalizationWork, + refreshProblemClaimPass, +} from './theorem-loop.js'; function readYamlIfPresent(filePath) { if (!fs.existsSync(filePath)) { @@ -10,10 +46,55 @@ function readYamlIfPresent(filePath) { return parse(fs.readFileSync(filePath, 'utf8')); } +function readJsonIfPresent(filePath) { + if (!fs.existsSync(filePath)) { + return null; + } + try { + return JSON.parse(fs.readFileSync(filePath, 'utf8')); + } catch { + return null; + } +} + +function formatShellArg(value) { + if (value === null || value === undefined) { + return ''; + } + const text = String(value); + if (/^[A-Za-z0-9_./:=+-]+$/.test(text)) { + return text; + } + return JSON.stringify(text); +} + +function formatCommandLine(executable, args = []) { + return [executable, ...args].map(formatShellArg).join(' '); +} + function getPackFile(problemId, fileName) { return path.join(getPackProblemDir('number-theory', problemId), fileName); } +function parseClosedIntegerRange(rangeText) { + const match = String(rangeText ?? '').trim().match(/^(\d+)\.\.(\d+)$/); + if (!match) { + return null; + } + return { + min: Number(match[1]), + max: Number(match[2]), + }; +} + +function parsePositiveInteger(value) { + if (value === null || value === undefined) { + return null; + } + const parsed = Number(value); + return Number.isInteger(parsed) && parsed > 0 ? parsed : null; +} + function normalizeQuestionLedger(rawLedger) { return { openQuestions: rawLedger?.open_questions ?? [], @@ -101,6 +182,761 @@ function resolveArchiveMode(problem) { return null; } +function getFrontierEngineRootPath() { + return path.join(repoRoot, 'research', 'frontier-engine'); +} + +function getSearchTheoremBridgeEngineCommand(problemId) { + if (String(problemId) === '848') { + return 'python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-theorem-bridge'; + } + return null; +} + +function getSearchTheoremBridgeRefreshCommand(problemId) { + return getSearchTheoremBridgeEngineCommand(problemId) + ? `erdos number-theory bridge-refresh ${problemId}` + : null; +} + +function getSearchTheoremBridgeRefreshSpec(problemId) { + if (String(problemId) === '848') { + const engineCommand = getSearchTheoremBridgeEngineCommand(problemId); + const executionPlan = resolveFrontierExecutionPlan('bridgeRefresh848'); + if (!engineCommand || !executionPlan.available) { + return null; + } + return { + executable: executionPlan.executable, + args: executionPlan.args, + engineCommand, + executionMode: executionPlan.mode, + executionSource: executionPlan.source, + executionReason: executionPlan.reason, + resolvedCommand: executionPlan.commandLine, + }; + } + + return null; +} + +function getIntervalWorkQueue(problemId) { + return readYamlIfPresent(getPackFile(problemId, 'INTERVAL_WORK_QUEUE.yaml')); +} + +function getP848ExactCertificatePaths(max) { + return { + certificatePath: getPackFile('848', `EXACT_SMALL_N_1_${max}_CERTIFICATE.md`), + resultsPath: getPackFile('848', `EXACT_SMALL_N_1_${max}_RESULTS.json`), + certificateFile: `EXACT_SMALL_N_1_${max}_CERTIFICATE.md`, + resultsFile: `EXACT_SMALL_N_1_${max}_RESULTS.json`, + }; +} + +function getWorkspaceRunsDir(workspaceRoot = getWorkspaceRoot()) { + return path.join(workspaceRoot, '.erdos', 'runs'); +} + +function listP848ExactFollowupRuns(workspaceRoot = getWorkspaceRoot()) { + const runsDir = getWorkspaceRunsDir(workspaceRoot); + if (!fs.existsSync(runsDir)) { + return []; + } + + return fs.readdirSync(runsDir, { withFileTypes: true }) + .filter((entry) => entry.isDirectory() && entry.name.includes('__number_theory_p848__exact_followup_launch')) + .map((entry) => entry.name) + .sort() + .map((entryName) => { + const exactFollowupPath = path.join(runsDir, entryName, 'exact-followup', 'EXACT_FOLLOWUP.json'); + const exactResultsPath = path.join(runsDir, entryName, 'exact-followup', 'EXACT_SMALL_N_RESULTS.json'); + const followup = readJsonIfPresent(exactFollowupPath); + const results = readJsonIfPresent(exactResultsPath); + const min = parsePositiveInteger(followup?.backend?.min ?? results?.parameters?.min); + const max = parsePositiveInteger(followup?.backend?.max ?? results?.parameters?.max); + return { + runId: entryName, + exactFollowupPath, + exactResultsPath, + followup, + results, + min, + max, + }; + }) + .filter((entry) => entry.followup && entry.results && entry.min !== null && entry.max !== null) + .filter((entry) => entry.results?.summary?.allCandidateAchievesMaximum === true) + .filter((entry) => entry.results?.summary?.allExampleCliquesMatchCandidateClass === true) + .sort((left, right) => { + if (left.min !== right.min) { + return left.min - right.min; + } + return left.max - right.max; + }); +} + +function p848ExactRowsEquivalent(left, right) { + return Number(left?.N) === Number(right?.N) + && Number(left?.maxCliqueSize) === Number(right?.maxCliqueSize) + && Number(left?.residue7Size) === Number(right?.residue7Size) + && Number(left?.residue18Size) === Number(right?.residue18Size) + && Boolean(left?.candidateAchievesMaximum) === Boolean(right?.candidateAchievesMaximum) + && Boolean(left?.exampleMatchesResidue7) === Boolean(right?.exampleMatchesResidue7) + && Boolean(left?.exampleMatchesResidue18) === Boolean(right?.exampleMatchesResidue18) + && JSON.stringify(left?.exampleMaximumClique ?? []) === JSON.stringify(right?.exampleMaximumClique ?? []); +} + +function normalizeP848ExactResultRows(rows, promotedMax) { + const rowByN = new Map(); + const duplicateNs = []; + const conflictingDuplicateNs = []; + for (const row of Array.isArray(rows) ? rows : []) { + const n = Number(row?.N); + if (!Number.isInteger(n) || n < 1 || n > promotedMax) { + continue; + } + const previous = rowByN.get(n); + if (previous) { + duplicateNs.push(n); + if (!p848ExactRowsEquivalent(previous, row)) { + conflictingDuplicateNs.push(n); + } + continue; + } + rowByN.set(n, row); + } + + const missingNs = []; + const normalizedRows = []; + for (let n = 1; n <= promotedMax; n += 1) { + const row = rowByN.get(n); + if (!row) { + missingNs.push(n); + continue; + } + normalizedRows.push(row); + } + + return { + ok: missingNs.length === 0 && conflictingDuplicateNs.length === 0, + rows: normalizedRows, + audit: { + inputRowCount: Array.isArray(rows) ? rows.length : 0, + outputRowCount: normalizedRows.length, + duplicateCount: duplicateNs.length, + duplicateNs: duplicateNs.slice(0, 50), + conflictingDuplicateCount: conflictingDuplicateNs.length, + conflictingDuplicateNs: conflictingDuplicateNs.slice(0, 50), + missingCount: missingNs.length, + missingNs: missingNs.slice(0, 50), + }, + }; +} + +function buildP848ExactCoveragePromotion(workspaceRoot = getWorkspaceRoot()) { + if (path.resolve(workspaceRoot) !== repoRoot) { + return { + ok: true, + promoted: false, + reason: 'Canonical exact promotion only runs from the repository workspace root.', + }; + } + + const queue = getIntervalWorkQueue('848'); + const latestDoneInterval = [...(queue?.intervals ?? [])] + .reverse() + .find((interval) => interval.status === 'done' && interval.method_class === 'exact_small_n') ?? null; + const latestDoneRange = parseClosedIntegerRange(latestDoneInterval?.range); + const baseResultsPath = latestDoneInterval?.data_packet + ? getPackFile('848', latestDoneInterval.data_packet) + : null; + const baseResults = baseResultsPath ? readJsonIfPresent(baseResultsPath) : null; + + if (!latestDoneRange || !baseResults?.results) { + return { + ok: false, + promoted: false, + error: 'The canonical exact-small-N base interval is missing or unreadable.', + }; + } + + const exactRuns = listP848ExactFollowupRuns(workspaceRoot); + let cursor = latestDoneRange.max + 1; + const contiguousRuns = []; + const usedRunIds = new Set(); + while (true) { + const candidate = exactRuns + .filter((run) => !usedRunIds.has(run.runId)) + .filter((run) => run.min <= cursor && run.max >= cursor) + .sort((left, right) => { + if (left.max !== right.max) { + return right.max - left.max; + } + return left.min - right.min; + })[0]; + if (!candidate) { + break; + } + contiguousRuns.push(candidate); + usedRunIds.add(candidate.runId); + cursor = candidate.max + 1; + } + + const promotedMax = cursor - 1; + if (promotedMax <= latestDoneRange.max) { + return { + ok: true, + promoted: false, + latestCanonicalMax: latestDoneRange.max, + reason: 'No new contiguous exact-small-N coverage is ready for canonical promotion.', + }; + } + + const mergedResults = [ + ...(Array.isArray(baseResults.results) ? baseResults.results : []), + ...contiguousRuns.flatMap((run) => Array.isArray(run.results?.results) ? run.results.results : []), + ]; + const normalizedMerge = normalizeP848ExactResultRows(mergedResults, promotedMax); + if (!normalizedMerge.ok) { + return { + ok: false, + promoted: false, + error: 'Exact-small-N promotion merge did not produce one non-conflicting row for every N in the promoted interval.', + latestCanonicalMax: latestDoneRange.max, + promotedMax, + mergeAudit: normalizedMerge.audit, + }; + } + const paths = getP848ExactCertificatePaths(promotedMax); + + return { + ok: true, + promoted: true, + latestCanonicalMax: latestDoneRange.max, + promotedMax, + queue, + latestDoneInterval, + baseResults, + contiguousRuns, + mergedResults: normalizedMerge.rows, + mergeAudit: normalizedMerge.audit, + ...paths, + }; +} + +function renderP848ExactCertificate(max, resultsFile) { + return [ + `# Problem 848 Exact Small-\`N\` Certificate: \`1..${max}\``, + '', + 'This is the current exact bounded-verification base certificate frozen in the repo for', + 'Problem `848`.', + '', + '## Claim', + '', + `For every \`N\` with \`1 <= N <= ${max}\`, the maximum size of a set \`A subseteq [N]\` such that`, + '\`ab + 1\` is never squarefree for all \`a, b in A\` is equal to the size of the \`7 mod 25\`', + 'or \`18 mod 25\` residue class in \`[N]\`.', + '', + `This certificate only covers the interval \`1..${max}\`.`, + '', + '## Method class', + '', + '- `exact_small_n`', + '', + '## Reproduction', + '', + 'Command family used:', + '', + '```bash', + 'node packs/number-theory/problems/848/compute/problem848_small_n_exact_scan.mjs \\', + ' --min \\', + ' --max \\', + ' --json-output /EXACT_SMALL_N_RESULTS.json', + '```', + '', + 'The canonical results file below is the contiguous merge of the certified base interval and', + 'the later successful exact follow-up runs that extend it without a gap.', + '', + '## Outcome', + '', + `- interval: \`1..${max}\``, + '- result: verified', + '- every scanned `N` satisfied:', + ' - `max_clique_size = max(|{n in [N] : n equiv 7 mod 25}|, |{n in [N] : n equiv 18 mod 25}|)`', + '', + 'The machine-readable result packet is:', + `- \`${resultsFile}\``, + '', + '## Scope warning', + '', + `This does **not** certify anything above \`${max}\`.`, + 'It is a current exact interval certificate only.', + '', + '## Why this interval matters', + '', + '- it extends the repo-owned exact small-`N` coverage monotonically', + '- it preserves a reproducible certificate surface for the bounded-verification lane', + '- it keeps imported public computation separate from repo-audited exact coverage', + '', + ].join('\n'); +} + +function updateP848IntervalQueueForPromotion(promotedMax) { + const queuePath = getPackFile('848', 'INTERVAL_WORK_QUEUE.yaml'); + const queue = getIntervalWorkQueue('848') ?? {}; + const nextMin = promotedMax + 1; + const paths = getP848ExactCertificatePaths(promotedMax); + const intervals = Array.isArray(queue.intervals) ? queue.intervals.map((interval) => ({ ...interval })) : []; + + for (const interval of intervals) { + if (interval.interval_id === 'N848.V1') { + interval.range = `1..${promotedMax}`; + interval.status = 'done'; + interval.method_class = 'exact_small_n'; + interval.claim_level = 'verified'; + interval.certificate = paths.certificateFile; + interval.data_packet = paths.resultsFile; + interval.next_move = `Use this as the current trusted exact base interval and decide whether the next extension after ${promotedMax} should stay exact or switch method class.`; + } + if (interval.interval_id === 'N848.V2') { + interval.range = `${nextMin}..?`; + interval.status = 'ready'; + interval.method_class = 'exact_small_n'; + interval.claim_level = 'target'; + interval.certificate = ''; + interval.data_packet = ''; + interval.next_move = `Decide how far the exact clique scan can be pushed beyond ${promotedMax} before a different method class is needed.`; + } + } + + writeText(queuePath, stringify({ + ...queue, + intervals, + })); +} + +function updateP848ContextForPromotion(promotedMax) { + const contextPath = getPackFile('848', 'context.yaml'); + const context = readYamlIfPresent(contextPath) ?? {}; + const exactCertificate = `EXACT_SMALL_N_1_${promotedMax}_CERTIFICATE.md`; + const artifactFocus = Array.isArray(context.artifact_focus) ? [...context.artifact_focus] : []; + const nextArtifactFocus = artifactFocus.filter((entry) => !/^EXACT_SMALL_N_1_\d+_CERTIFICATE\.md$/.test(String(entry))); + nextArtifactFocus.push(exactCertificate); + + const routeBreakthroughs = Array.isArray(context.question_ledger?.route_breakthroughs) + ? context.question_ledger.route_breakthroughs.map((entry) => String(entry).includes('exact verified base interval') + ? `The repo now has an exact verified base interval \`1..${promotedMax}\`.` + : entry) + : []; + + const nextContext = { + ...context, + route_story: `Problem 848 is already asymptotically resolved in public, but not yet closed here for all N. The honest job is to shrink the finite remainder with audited threshold tracking and reproducible bounded verification, beginning from the verified base interval \`1..${promotedMax}\`.`, + frontier_detail: `The repo now has a verified exact interval \`1..${promotedMax}\`; the next question is whether to extend that exact scan further or change method class.`, + next_honest_move: `Decide whether to extend the exact clique scan beyond \`${promotedMax}\` or pivot to a different bounded-verification method.`, + artifact_focus: nextArtifactFocus, + question_ledger: { + ...(context.question_ledger ?? {}), + route_breakthroughs: routeBreakthroughs, + }, + }; + + writeText(contextPath, stringify(nextContext)); +} + +function updateP848FrontierNoteForPromotion(promotedMax) { + const notePath = getPackFile('848', 'FRONTIER_NOTE.md'); + if (!fs.existsSync(notePath)) { + return; + } + let text = fs.readFileSync(notePath, 'utf8'); + text = text.replace(/EXACT_SMALL_N_1_\d+_CERTIFICATE\.md/g, `EXACT_SMALL_N_1_${promotedMax}_CERTIFICATE.md`); + writeText(notePath, text); +} + +function updateP848BoundedVerificationPlanForPromotion(promotedMax) { + const planPath = getPackFile('848', 'BOUNDED_VERIFICATION_PLAN.md'); + if (!fs.existsSync(planPath)) { + return; + } + let text = fs.readFileSync(planPath, 'utf8'); + text = text.replace( + /Current progress:\n- the repo now has an exact small-`N` certificate for `1\.\.\d+`/m, + `Current progress:\n- the repo now has an exact small-\`N\` certificate for \`1..${promotedMax}\``, + ); + writeText(planPath, text); +} + +function updateP848VerificationRegimesForPromotion(promotedMax) { + const regimesPath = getPackFile('848', 'VERIFICATION_REGIMES.md'); + if (!fs.existsSync(regimesPath)) { + return; + } + let text = fs.readFileSync(regimesPath, 'utf8'); + text = text.replace( + /- Regime A: (?:first )?exact interval `1\.\.\d+` is now frozen in the repo with a reproducible\n maximum-clique certificate/m, + `- Regime A: exact interval \`1..${promotedMax}\` is now frozen in the repo with a reproducible\n maximum-clique certificate`, + ); + text = text.replace( + /- Regime B: endpoint-monotonicity breakpoint certificate exists over the current exact base,\n but the endpoint-only verifier for extending beyond that base is not frozen yet/m, + `- Regime B: endpoint-monotonicity breakpoint certificate and endpoint exact verifier are\n active over the current exact base; the next use is larger certified rollouts beyond\n \`${promotedMax}\``, + ); + text = text.replace( + /So the next honest move is to decide whether exact-small-`N` coverage should be extended\ndirectly beyond `\d+`, or whether the next gain comes from auditing imported computation or\nswitching method class\./m, + `So the next honest move is to decide whether exact-small-\`N\` coverage should be extended\ndirectly beyond \`${promotedMax}\`, or whether the next gain comes from auditing imported computation or\nswitching method class.`, + ); + writeText(regimesPath, text); +} + +function updateP848ExactBreakpointScoutForPromotion(promotedMax) { + const scriptPath = getPackFile('848', path.join('compute', 'problem848_exact_breakpoint_scout.mjs')); + const resultsPath = getP848ExactCertificatePaths(promotedMax).resultsPath; + const outputPath = getPackFile('848', 'EXACT_BREAKPOINT_SCOUT.json'); + if (!fs.existsSync(scriptPath) || !fs.existsSync(resultsPath)) { + return { + ok: false, + error: 'Exact breakpoint scout script or promoted results file is missing.', + scriptPath, + resultsPath, + outputPath, + }; + } + try { + const stdout = execFileSync('node', [ + scriptPath, + '--results', + resultsPath, + '--json-output', + outputPath, + ], { + encoding: 'utf8', + cwd: repoRoot, + }); + return { + ok: true, + scriptPath, + resultsPath, + outputPath, + stdout, + }; + } catch (error) { + return { + ok: false, + error: error?.stderr?.toString?.() || error?.message || 'Exact breakpoint scout failed.', + scriptPath, + resultsPath, + outputPath, + }; + } +} + +function updateP848BreakpointCertificateForPromotion(promotedMax) { + const scriptPath = getPackFile('848', path.join('compute', 'problem848_breakpoint_certificate.mjs')); + const resultsPath = getP848ExactCertificatePaths(promotedMax).resultsPath; + const outputPath = getPackFile('848', 'EXACT_BREAKPOINT_CERTIFICATE.json'); + if (!fs.existsSync(scriptPath) || !fs.existsSync(resultsPath)) { + return { + ok: false, + error: 'Breakpoint certificate script or promoted results file is missing.', + scriptPath, + resultsPath, + outputPath, + }; + } + try { + const stdout = execFileSync('node', [ + scriptPath, + '--results', + resultsPath, + '--json-output', + outputPath, + ], { + encoding: 'utf8', + cwd: repoRoot, + }); + return { + ok: true, + scriptPath, + resultsPath, + outputPath, + stdout, + }; + } catch (error) { + return { + ok: false, + error: error?.stderr?.toString?.() || error?.message || 'Breakpoint certificate generation failed.', + scriptPath, + resultsPath, + outputPath, + }; + } +} + +function updateP848OpsDetailsForPromotion(promotedMax) { + const opsPath = getPackFile('848', 'OPS_DETAILS.yaml'); + const ops = readYamlIfPresent(opsPath); + if (!ops) { + return; + } + + for (const route of Array.isArray(ops.routes) ? ops.routes : []) { + if (route.route_id === 'finite_check_gap_closure') { + route.next_move = `Decide whether to extend exact verified coverage beyond \`${promotedMax}\` or switch method class.`; + } + if (route.route_id === 'bounded_finite_verification') { + route.next_move = `Build on the exact \`1..${promotedMax}\` base interval and decide the next extension rule.`; + } + } + + for (const ticket of Array.isArray(ops.tickets) ? ops.tickets : []) { + if (ticket.ticket_id === 'N848') { + ticket.summary = `The repo now has a committed review package for its audited \`exp(1420)\` candidate, a chosen bounded-verification lane, and an exact verified base interval \`1..${promotedMax}\`. The live question is how to extend coverage from that foothold.`; + } + } + + for (const atom of Array.isArray(ops.atoms) ? ops.atoms : []) { + if (atom.atom_id === 'N848.G1.A20') { + atom.summary = `The repo now has a reproducible exact certificate showing that the conjectured extremal size is correct for every \`N\` in \`1..${promotedMax}\`.`; + atom.next_move = `Decide whether to extend the exact clique scan beyond \`${promotedMax}\` or change method class.`; + } + if (atom.atom_id === 'N848.G1.A21') { + atom.title = `Choose the next verified interval extension beyond \`${promotedMax}\``; + atom.summary = `The bounded-verification lane now starts from a real certified base interval \`1..${promotedMax}\`. The next choice is whether the exact clique scan still has enough headroom to extend that base efficiently, or whether the next gain should come from breakpoint or audit methods.`; + atom.next_move = `Decide whether to extend exact verified coverage beyond \`${promotedMax}\` or switch method class.`; + } + } + + writeText(opsPath, stringify(ops)); +} + +function promoteP848ExactCoverage(workspaceRoot = getWorkspaceRoot()) { + const promotion = buildP848ExactCoveragePromotion(workspaceRoot); + if (!promotion.ok || !promotion.promoted) { + return promotion; + } + + const aggregatedResults = { + generatedAt: new Date().toISOString(), + method: 'exact_maximum_clique_scan', + problemId: '848', + parameters: { + min: 1, + max: promotion.promotedMax, + }, + summary: { + interval: `1..${promotion.promotedMax}`, + rows: promotion.promotedMax, + allCandidateAchievesMaximum: true, + allExampleCliquesMatchCandidateClass: true, + }, + promotedFrom: [ + { + source: 'canonical_pack', + interval: promotion.latestDoneInterval?.range ?? null, + dataPacket: promotion.latestDoneInterval?.data_packet ?? null, + }, + ...promotion.contiguousRuns.map((run) => ({ + source: 'workspace_exact_followup', + runId: run.runId, + interval: `${run.min}..${run.max}`, + exactFollowupPath: run.exactFollowupPath, + exactResultsPath: run.exactResultsPath, + })), + ], + mergeAudit: promotion.mergeAudit ?? null, + results: promotion.mergedResults, + }; + + writeJson(promotion.resultsPath, aggregatedResults); + writeText( + promotion.certificatePath, + renderP848ExactCertificate(promotion.promotedMax, promotion.resultsFile), + ); + updateP848IntervalQueueForPromotion(promotion.promotedMax); + updateP848ContextForPromotion(promotion.promotedMax); + updateP848FrontierNoteForPromotion(promotion.promotedMax); + updateP848BoundedVerificationPlanForPromotion(promotion.promotedMax); + updateP848VerificationRegimesForPromotion(promotion.promotedMax); + const breakpointScout = updateP848ExactBreakpointScoutForPromotion(promotion.promotedMax); + const breakpointCertificate = updateP848BreakpointCertificateForPromotion(promotion.promotedMax); + updateP848OpsDetailsForPromotion(promotion.promotedMax); + + return { + ok: true, + promoted: true, + promotedMax: promotion.promotedMax, + certificatePath: promotion.certificatePath, + resultsPath: promotion.resultsPath, + breakpointScout, + breakpointCertificate, + contiguousRunCount: promotion.contiguousRuns.length, + }; +} + +function getP848ExactScoutPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'exact_interval_scout', + reason: `No exact interval scout is registered for problem ${problemId}.`, + }; + } + + const queue = getIntervalWorkQueue(problemId); + const readyInterval = queue?.intervals?.find((interval) => interval.status === 'ready' && interval.method_class === 'exact_small_n') ?? null; + const latestDoneInterval = [...(queue?.intervals ?? [])] + .reverse() + .find((interval) => interval.status === 'done' && interval.method_class === 'exact_small_n') ?? null; + const latestDoneRange = parseClosedIntegerRange(latestDoneInterval?.range); + const defaultMin = latestDoneRange ? latestDoneRange.max + 1 : null; + const requestedMin = parsePositiveInteger(options.exactMin); + const requestedMax = parsePositiveInteger(options.exactMax); + const min = requestedMin ?? defaultMin; + const max = requestedMax ?? (min !== null ? min + 99 : null); + const endpointMonotonicity = Boolean(options.endpointMonotonicity); + + if (!readyInterval || min === null || max === null || max < min) { + return { + available: false, + actionId: 'exact_interval_scout', + reason: 'The exact interval scout does not have a valid ready range yet.', + readyInterval, + latestDoneInterval, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_small_n_exact_scan.mjs'); + return { + available: true, + actionId: 'exact_interval_scout', + mode: 'cpu', + source: 'exact_verification_lane', + reason: `The bounded-verification queue has a ready exact-small-N extension after ${latestDoneInterval?.range ?? '(unknown range)'}.`, + readyInterval, + latestDoneInterval, + min, + max, + scriptPath, + commandLine: formatCommandLine('node', [ + scriptPath, + '--min', + String(min), + '--max', + String(max), + ...(endpointMonotonicity ? ['--endpoint-monotonicity'] : []), + '--json-output', + '/EXACT_SMALL_N_RESULTS.json', + ]), + endpointMonotonicity, + backendKind: endpointMonotonicity ? 'endpoint_monotonicity_small_n' : 'exact_small_n', + }; +} + +function normalizeFrontierLoop(rawLoop, problemId) { + if (!rawLoop || rawLoop.enabled === false) { + return null; + } + + const commands = Array.isArray(rawLoop.commands) + ? rawLoop.commands.map((command) => String(command)).filter(Boolean) + : []; + const useWhen = Array.isArray(rawLoop.use_when) + ? rawLoop.use_when.map((item) => String(item)).filter(Boolean) + : []; + const artifacts = Array.isArray(rawLoop.artifacts) + ? rawLoop.artifacts.map((item) => String(item)).filter(Boolean) + : []; + + return { + enabled: true, + title: rawLoop.title ?? 'frontier_engine_support_lane', + summary: rawLoop.summary ?? null, + useWhen, + commands, + artifacts, + primaryCommand: commands[0] ?? null, + refreshCommand: getSearchTheoremBridgeRefreshCommand(problemId), + engineCommand: getSearchTheoremBridgeEngineCommand(problemId), + suggested: true, + }; +} + +function resolveFrontierLoopState(frontierLoop, problemId) { + if (!frontierLoop) { + return null; + } + + const config = loadConfig(); + const frontierConfig = config.frontier ?? {}; + const activeRemoteId = String( + frontierConfig.activeRemoteId + ?? frontierConfig.remote?.remoteId + ?? frontierConfig.remote?.instanceName + ?? frontierConfig.remote?.sshHost + ?? '', + ).trim() || null; + const enabledPaidRemoteIds = Array.isArray(frontierConfig.paidRungs?.enabledRemoteIds) + ? frontierConfig.paidRungs.enabledRemoteIds.map((item) => String(item)).filter(Boolean) + : []; + const remotePaidRung = frontierConfig.remote?.provider === 'brev'; + const remotePaidEnabled = !remotePaidRung + || Boolean(frontierConfig.remote?.paidEnabled) + || (activeRemoteId ? enabledPaidRemoteIds.includes(activeRemoteId) : false); + const remoteGpuReady = Boolean( + frontierConfig.remote?.attached + && frontierConfig.remote?.gpuSearchReady + && remotePaidEnabled, + ); + const activationCommand = 'erdos frontier setup --base --apply'; + const upgradeCommand = 'erdos frontier setup --cuda --torch-index-url --apply'; + const loopMode = remoteGpuReady + ? 'gpu' + : !frontierConfig.loopOptIn + ? null + : frontierConfig.gpuSearchReady + ? 'gpu' + : frontierConfig.managedFrontierReady + ? 'cpu' + : null; + const loopActive = loopMode !== null; + + let stateReason = 'inactive'; + if (loopMode === 'gpu') { + stateReason = remoteGpuReady ? 'gpu_ready_remote' : 'gpu_ready'; + } else if (loopMode === 'cpu') { + stateReason = 'cpu_ready'; + } else if (remotePaidRung && frontierConfig.remote?.attached && frontierConfig.remote?.gpuSearchReady && !remotePaidEnabled) { + stateReason = 'paid_rung_not_enabled'; + } else if (!frontierConfig.loopOptIn && !remoteGpuReady) { + stateReason = 'not_opted_in'; + } else { + stateReason = 'runtime_not_ready'; + } + + return { + ...frontierLoop, + problemId, + suggested: loopActive, + active: loopActive, + mode: loopMode, + available: true, + activationCommand, + upgradeCommand, + runtimeMode: frontierConfig.runtimeMode ?? null, + activeMode: frontierConfig.activeMode ?? loopMode, + loopOptIn: Boolean(frontierConfig.loopOptIn), + managedFrontierReady: Boolean(frontierConfig.managedFrontierReady), + gpuSearchReady: Boolean(frontierConfig.gpuSearchReady), + remoteSshHost: frontierConfig.remote?.sshHost ?? null, + remotePaidRung, + remotePaidEnabled, + remoteGpuSearchReady: remoteGpuReady, + lastSetupAt: frontierConfig.lastSetupAt ?? null, + lastDoctorAt: frontierConfig.lastDoctorAt ?? null, + stateReason, + }; +} + export function buildNumberTheoryStatusSnapshot(problem) { const contextPath = getPackFile(problem.problemId, 'context.yaml'); const contextMarkdownPath = getPackFile(problem.problemId, 'CONTEXT.md'); @@ -109,10 +945,24 @@ export function buildNumberTheoryStatusSnapshot(problem) { const routeHistoryPath = getPackFile(problem.problemId, 'ROUTE_HISTORY.md'); const checkpointTemplatePath = getPackFile(problem.problemId, 'CHECKPOINT_TEMPLATE.md'); const reportTemplatePath = getPackFile(problem.problemId, 'REPORT_TEMPLATE.md'); + const searchTheoremBridgePath = getPackFile(problem.problemId, 'SEARCH_THEOREM_BRIDGE.md'); + const searchTheoremBridgeJsonPath = getPackFile(problem.problemId, 'SEARCH_THEOREM_BRIDGE.json'); + const searchTheoremBridge = readJsonIfPresent(searchTheoremBridgeJsonPath); + const frontierEngineRootPath = getFrontierEngineRootPath(); + const theoremLoop = getProblemTheoremLoopSnapshot(problem); + const claimLoop = getProblemClaimLoopSnapshot(problem); + const claimPass = getProblemClaimPassSnapshot(problem); + const formalization = getProblemFormalizationSnapshot(problem); + const formalizationWork = getProblemFormalizationWorkSnapshot(problem); + const taskList = getProblemTaskListSnapshot(problem); const context = readYamlIfPresent(contextPath) ?? {}; const routePacket = readYamlIfPresent(routePacketPath); const opsDetails = parseOpsDetails(problem.problemId); + const frontierLoop = resolveFrontierLoopState( + normalizeFrontierLoop(context.frontier_loop, problem.problemId), + problem.problemId, + ); const activeRoute = problem.researchState?.active_route @@ -175,6 +1025,24 @@ export function buildNumberTheoryStatusSnapshot(problem) { frontierNotePath, routeHistoryPresent: fs.existsSync(routeHistoryPath), routeHistoryPath, + searchTheoremBridgePresent: fs.existsSync(searchTheoremBridgePath), + searchTheoremBridgePath, + searchTheoremBridgeJsonPresent: fs.existsSync(searchTheoremBridgeJsonPath), + searchTheoremBridgeJsonPath, + searchTheoremBridgeCurrentState: searchTheoremBridge?.current_bridge_state ?? null, + searchTheoremBridgeSources: searchTheoremBridge?.sources ?? null, + searchTheoremBridgeRefreshCommand: getSearchTheoremBridgeRefreshCommand(problem.problemId), + searchTheoremBridgeEngineCommand: getSearchTheoremBridgeEngineCommand(problem.problemId), + theoremLoop, + claimLoop, + claimPass, + formalization, + formalizationWork, + taskList, + frontierLoop, + frontierLoopSuggested: Boolean(frontierLoop?.active), + frontierEnginePresent: fs.existsSync(frontierEngineRootPath), + frontierEngineRootPath, checkpointTemplatePresent: fs.existsSync(checkpointTemplatePath), checkpointTemplatePath, reportTemplatePresent: fs.existsSync(reportTemplatePath), @@ -189,6 +1057,3366 @@ export function buildNumberTheoryStatusSnapshot(problem) { }; } +export function getNumberTheoryBridgeSnapshot(problem) { + const snapshot = buildNumberTheoryStatusSnapshot(problem); + const bridge = readJsonIfPresent(snapshot.searchTheoremBridgeJsonPath); + const refreshSpec = getSearchTheoremBridgeRefreshSpec(problem.problemId); + + return { + ...snapshot, + bridgePresent: Boolean(bridge), + bridgeSchema: bridge?.schema ?? null, + bridgeMarkdownPath: snapshot.searchTheoremBridgePath, + bridgeMarkdownPresent: snapshot.searchTheoremBridgePresent, + bridgeJsonPath: snapshot.searchTheoremBridgeJsonPath, + bridgeJsonPresent: snapshot.searchTheoremBridgeJsonPresent, + bridgeRefreshCommand: snapshot.searchTheoremBridgeRefreshCommand, + bridgeEngineCommand: snapshot.searchTheoremBridgeEngineCommand, + bridgeRefreshMode: refreshSpec?.executionMode ?? null, + bridgeRefreshSource: refreshSpec?.executionSource ?? null, + bridgeRefreshReason: refreshSpec?.executionReason ?? null, + bridgeRefreshResolvedCommand: refreshSpec?.resolvedCommand ?? null, + bridgeSources: bridge?.sources ?? null, + bridgeCurrentState: bridge?.current_bridge_state ?? null, + bridgePacketLedger: bridge?.shared_prefix_packet_ledger ?? [], + bridgeTrackedTailMatrix: bridge?.tracked_tail_matrix ?? [], + bridgeGpuLeaderboard: bridge?.gpu_leaderboard ?? [], + bridgeTheoremHooks: bridge?.candidate_theorem_hooks ?? [], + }; +} + +function buildDispatchApplyCommand(problemId, actionId, options = {}) { + const command = [ + 'erdos', + 'number-theory', + 'dispatch', + String(problemId), + '--apply', + '--action', + String(actionId), + ]; + if (options.remoteId) { + command.push('--remote-id', String(options.remoteId)); + } + if (options.externalSourceDir) { + command.push('--external-source-dir', String(options.externalSourceDir)); + } + if (options.exactMin !== null && options.exactMin !== undefined) { + command.push('--exact-min', String(options.exactMin)); + } + if (options.exactMax !== null && options.exactMax !== undefined) { + command.push('--exact-max', String(options.exactMax)); + } + if (options.exactChunks !== null && options.exactChunks !== undefined) { + command.push('--exact-chunks', String(options.exactChunks)); + } + if (options.exactChunkSize !== null && options.exactChunkSize !== undefined) { + command.push('--exact-chunk-size', String(options.exactChunkSize)); + } + if (options.baseSideMax !== null && options.baseSideMax !== undefined) { + command.push('--base-side-max', String(options.baseSideMax)); + } + if (options.structuralMax !== null && options.structuralMax !== undefined) { + command.push('--structural-max', String(options.structuralMax)); + } + if (options.structuralMin !== null && options.structuralMin !== undefined) { + command.push('--structural-min', String(options.structuralMin)); + } + if (options.mixedBaseMaxRows !== null && options.mixedBaseMaxRows !== undefined) { + command.push('--mixed-base-max-rows', String(options.mixedBaseMaxRows)); + } + if (options.fullMixedRowSampleLimit !== null && options.fullMixedRowSampleLimit !== undefined) { + command.push('--full-mixed-row-sample-limit', String(options.fullMixedRowSampleLimit)); + } + if (options.structuralLiftTopRows !== null && options.structuralLiftTopRows !== undefined) { + command.push('--structural-lift-top-rows', String(options.structuralLiftTopRows)); + } + if (options.structuralLiftFamilyLimit !== null && options.structuralLiftFamilyLimit !== undefined) { + command.push('--structural-lift-family-limit', String(options.structuralLiftFamilyLimit)); + } + if (options.matchingPatternPrime !== null && options.matchingPatternPrime !== undefined) { + command.push('--matching-pattern-prime', String(options.matchingPatternPrime)); + } + if (options.matchingPatternTopRows !== null && options.matchingPatternTopRows !== undefined) { + command.push('--matching-pattern-top-rows', String(options.matchingPatternTopRows)); + } + if (options.matchingPatternPairSampleLimit !== null && options.matchingPatternPairSampleLimit !== undefined) { + command.push('--matching-pattern-pair-sample-limit', String(options.matchingPatternPairSampleLimit)); + } + if (options.endpointMonotonicity) { + command.push('--endpoint-monotonicity'); + } + return command.join(' '); +} + +function buildFleetDispatchApplyCommand(problemId, fleetId, actionId, options = {}) { + const command = [ + 'erdos', + 'number-theory', + 'dispatch-fleet', + String(problemId), + '--fleet', + String(fleetId), + '--apply', + '--action', + String(actionId), + ]; + if (options.reviewAfterHours !== null && options.reviewAfterHours !== undefined) { + command.push('--review-after-hours', String(options.reviewAfterHours)); + } + if (options.strategyId) { + command.push('--strategy', String(options.strategyId)); + } + return command.join(' '); +} + +function getP848RemoteBaseProfilePath(provider = 'ssh') { + const filename = provider === 'brev' + ? 'brev_h100_search_profile.json' + : 'windows_rtx4090_search_profile.json'; + return path.join(repoRoot, 'research', 'frontier-engine', 'experiments', 'p848-anchor-ladder', filename); +} + +function uniquePositiveIntegers(values = []) { + return Array.from(new Set( + (Array.isArray(values) ? values : []) + .map((value) => Number(value)) + .filter((value) => Number.isInteger(value) && value > 0), + )); +} + +function buildP848FleetAssignments(problem, fleet, bridgeSnapshot, options = {}) { + const strategyId = String(options.strategyId ?? 'ladder_cover_v1').trim() || 'ladder_cover_v1'; + const remoteIds = Array.isArray(fleet?.remoteIds) ? fleet.remoteIds : []; + const bridgeState = bridgeSnapshot?.bridgeCurrentState ?? {}; + const defaultProvider = fleet?.provider === 'brev' ? 'brev' : 'ssh'; + const baseProfile = readJsonIfPresent(getP848RemoteBaseProfilePath(defaultProvider)) ?? {}; + const centers = uniquePositiveIntegers([ + bridgeState.current_family_aware_leader?.continuation, + ...(Array.isArray(bridgeState.top_gpu_tie_class) ? bridgeState.top_gpu_tie_class : []), + bridgeState.strongest_completed_structured_tail?.continuation, + baseProfile.base_tail ?? 332, + ]); + const selectedCenters = centers.length > 0 ? centers : [332]; + const baseThreshold = Number(baseProfile.direct_threshold ?? 250000001); + const baseMax = Number(baseProfile.direct_max ?? 250075000); + const windowSpan = Math.max(1, baseMax - baseThreshold + 1); + const offsetPatterns = [ + [0, -10, -5, 5, 10], + [0, -15, -5, 5, 15], + [0, -20, -10, 10, 20], + [0, -25, -10, 10, 25], + ]; + const roundDeltas = [0, 4, 8]; + const topKSteps = [0, 4, 8]; + + return remoteIds.map((remoteId, index) => { + const centerIndex = index % selectedCenters.length; + const windowIndex = Math.floor(index / selectedCenters.length); + const center = selectedCenters[centerIndex]; + const offsets = offsetPatterns[index % offsetPatterns.length]; + const ladderRounds = Number(baseProfile.ladder_rounds ?? 18) + roundDeltas[windowIndex % roundDeltas.length]; + const threshold = baseThreshold + (windowIndex * windowSpan); + const directMax = threshold + windowSpan - 1; + const topK = Number(baseProfile.top_k ?? 16) + topKSteps[windowIndex % topKSteps.length]; + const profile = { + ...baseProfile, + profile_id: `${baseProfile.profile_id ?? 'p848_anchor_ladder_fleet'}__${strategyId}__${fleet.fleetId}__${remoteId}`, + base_tail: center, + perturb_offsets: offsets, + ladder_rounds: ladderRounds, + direct_threshold: threshold, + direct_max: directMax, + top_k: topK, + notes: [ + ...((Array.isArray(baseProfile.notes) ? baseProfile.notes : [])), + `Fleet schedule ${strategyId} assigned to ${remoteId}.`, + `Center tail ${center}; window ${threshold}..${directMax}; perturb offsets ${offsets.join(', ')}.`, + ], + }; + return { + remoteId, + strategyId, + assignmentIndex: index, + center, + centerIndex, + windowIndex, + directThreshold: threshold, + directMax, + ladderRounds, + perturbOffsets: offsets, + topK, + profile, + }; + }); +} + +function ensureRemoteDirectory(remoteSpec, remoteDir, workspaceRoot = getWorkspaceRoot()) { + const command = isBrevRemote(remoteSpec) + ? `mkdir -p ${quotePosixShellArg(remoteDir)}` + : `cmd /c if not exist ${quoteRemoteWindowsPath(remoteDir)} mkdir ${quoteRemoteWindowsPath(remoteDir)}`; + return runRemoteCommandCapture(remoteSpec, command, { cwd: workspaceRoot }); +} + +function prepareP848RemoteProfileOverride(action, assignment, workspaceRoot = getWorkspaceRoot(), options = {}) { + const remoteSpec = { + provider: action.remoteProvider ?? 'ssh', + instanceName: action.remoteInstanceName ?? null, + sshHost: action.remoteHost, + engineRoot: action.remoteEngineRoot, + pythonCommand: action.remotePythonCommand, + }; + const launchId = String(options.launchId ?? Date.now()); + const localDir = path.join( + workspaceRoot, + '.erdos', + 'frontier', + 'fleet-profiles', + String(options.fleetId ?? 'fleet'), + launchId, + ); + ensureDir(localDir); + const filename = `${assignment.remoteId}.json`; + const localProfilePath = path.join(localDir, filename); + writeJson(localProfilePath, assignment.profile); + + const remoteProfileDir = joinRemotePath( + remoteSpec, + action.remoteEngineRoot, + 'experiments', + 'p848-anchor-ladder', + 'fleet-profiles', + String(options.fleetId ?? 'fleet'), + launchId, + ); + const ensureRemoteDir = ensureRemoteDirectory(remoteSpec, remoteProfileDir, workspaceRoot); + if (!ensureRemoteDir.ok) { + return { + ok: false, + error: ensureRemoteDir.stderr ?? 'Failed to prepare remote profile directory.', + localProfilePath, + remoteProfileDir, + }; + } + + const remoteProfilePath = joinRemotePath(remoteSpec, remoteProfileDir, filename); + const copyResult = runRemoteCopyToCapture(remoteSpec, localProfilePath, remoteProfilePath, { + cwd: workspaceRoot, + }); + if (!copyResult.ok) { + return { + ok: false, + error: copyResult.stderr ?? 'Failed to copy remote fleet profile.', + localProfilePath, + remoteProfilePath, + }; + } + + const remoteCliPath = joinRemotePath(remoteSpec, action.remoteEngineRoot, 'src', 'frontier_engine', 'cli.py'); + const remoteCommand = isBrevRemote(remoteSpec) + ? `${action.remotePythonCommand} ${quotePosixShellArg(remoteCliPath)} export-p848-profile-bundle ${quotePosixShellArg(remoteProfilePath)}` + : `${action.remotePythonCommand} ${quoteRemoteWindowsPath(remoteCliPath)} export-p848-profile-bundle ${quoteRemoteWindowsPath(remoteProfilePath)}`; + + return { + ok: true, + localProfilePath, + remoteProfilePath, + remoteCommand, + assignment, + }; +} + +function buildRemoteGpuExecutionSpec(remoteSpec, remoteCommand) { + if (isBrevRemote(remoteSpec)) { + return { + executable: 'brev', + args: ['exec', remoteSpec.instanceName ?? remoteSpec.sshHost, `bash -lc ${quotePosixShellArg(remoteCommand)}`], + commandLine: formatCommandLine('brev', ['exec', remoteSpec.instanceName ?? remoteSpec.sshHost, `bash -lc ${quotePosixShellArg(remoteCommand)}`]), + }; + } + return { + executable: 'ssh', + args: [remoteSpec.sshHost, remoteCommand], + commandLine: formatCommandLine('ssh', [remoteSpec.sshHost, remoteCommand]), + }; +} + +function getP848ClaimPassPlan(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return { + available: false, + actionId: 'claim_pass_refresh', + reason: `No claim-pass dispatch lane is registered for problem ${problem?.problemId ?? '(unknown)'}.`, + }; + } + + const claimPass = getProblemClaimPassSnapshot(problem); + const recommendations = Array.isArray(claimPass.recommendations) ? claimPass.recommendations : []; + const topRecommendation = recommendations[0] ?? null; + const supportedClaims = claimPass.summary?.claims?.supported ?? 0; + const actionableClaims = claimPass.summary?.claims?.actionable ?? 0; + + return { + available: (claimPass.claimAssessments?.length ?? 0) > 0, + actionId: 'claim_pass_refresh', + mode: 'theorem', + source: 'claim_pass', + reason: topRecommendation + ? `${topRecommendation.recommendation_id}: ${topRecommendation.reason}` + : `Claim pass currently tracks ${supportedClaims} supported and ${actionableClaims} actionable claim objects.`, + commandLine: `erdos problem claim-pass-refresh ${problem.problemId}`, + claimPass, + recommendations, + }; +} + +function getP848FormalizationPlan(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return { + available: false, + actionId: 'formalization_refresh', + reason: `No formalization dispatch lane is registered for problem ${problem?.problemId ?? '(unknown)'}.`, + }; + } + + const formalization = getProblemFormalizationSnapshot(problem); + const target = formalization.currentTarget ?? null; + + return { + available: Boolean(target?.focusId), + actionId: 'formalization_refresh', + mode: 'theorem', + source: 'formalization', + reason: target?.whyNow + ?? target?.summary + ?? `Formalization currently targets ${target?.title ?? 'the top theorem-facing packet'}.`, + commandLine: `erdos problem formalization-refresh ${problem.problemId}`, + formalization, + }; +} + +function getP848FormalizationWorkPlan(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return { + available: false, + actionId: 'formalization_work_refresh', + reason: `No formalization-work dispatch lane is registered for problem ${problem?.problemId ?? '(unknown)'}.`, + }; + } + + const formalizationWork = getProblemFormalizationWorkSnapshot(problem); + const target = formalizationWork.currentWork ?? null; + + return { + available: Boolean(target?.focusId), + actionId: 'formalization_work_refresh', + mode: 'theorem', + source: 'formalization_work', + reason: target?.summary + ?? target?.why + ?? `Formalization work currently targets ${target?.title ?? 'the top theorem work packet'}.`, + commandLine: `erdos problem formalization-work-refresh ${problem.problemId}`, + formalizationWork, + }; +} + +function getP848StructuralVerifierAuditPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'structural_verifier_audit', + reason: `No structural verifier audit lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_external_structural_audit.mjs'); + const jsonPath = getPackFile(problemId, 'EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json'); + const markdownPath = getPackFile(problemId, 'EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md'); + const sourceDir = path.resolve(options.externalSourceDir ?? process.env.P848_EXTERNAL_SOURCE_DIR ?? '/tmp/hjyuh-erdos-848'); + const sourceAvailable = fs.existsSync(sourceDir) && fs.statSync(sourceDir).isDirectory(); + const latestAudit = readJsonIfPresent(jsonPath); + + return { + available: fs.existsSync(scriptPath), + actionId: 'structural_verifier_audit', + mode: 'cpu', + source: 'external_structural_verifier_audit', + reason: sourceAvailable + ? 'Audit the external outsider-clique verifier for promotion blockers before importing any finite-coverage claim.' + : `External source tree is not present at ${sourceDir}; the audit lane will record the missing-source blocker.`, + scriptPath, + sourceDir, + sourceAvailable, + jsonPath, + markdownPath, + latestAuditStatus: latestAudit?.status ?? null, + latestAuditSummary: latestAudit?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--source-dir', + sourceDir, + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'structural_verifier_audit', { + ...options, + externalSourceDir: sourceDir, + }), + }; +} + +function getP848BaseSideScoutPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'base_side_scout', + reason: `No base-side scout lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_base_side_scout.mjs'); + const jsonPath = getPackFile(problemId, 'BASE_SIDE_SCOUT.json'); + const markdownPath = getPackFile(problemId, 'BASE_SIDE_SCOUT.md'); + const latestScout = readJsonIfPresent(jsonPath); + const max = parsePositiveInteger(options.baseSideMax) ?? latestScout?.parameters?.maxN ?? 2000; + + return { + available: fs.existsSync(scriptPath), + actionId: 'base_side_scout', + mode: 'cpu', + source: 'structural_base_side_scout', + reason: 'Compare 7 mod 25 and 18 mod 25 base compatibility on a bounded interval before trusting one-sided structural masks.', + scriptPath, + max, + jsonPath, + markdownPath, + latestScoutStatus: latestScout?.status ?? null, + latestScoutSummary: latestScout?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--max', + String(max), + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'base_side_scout', { + ...options, + baseSideMax: max, + }), + }; +} + +function getP848StructuralTwoSideScoutPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'structural_two_side_scout', + reason: `No two-sided structural scout lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_structural_two_side_scout.mjs'); + const jsonPath = getPackFile(problemId, 'STRUCTURAL_TWO_SIDE_SCOUT.json'); + const markdownPath = getPackFile(problemId, 'STRUCTURAL_TWO_SIDE_SCOUT.md'); + const latestScout = readJsonIfPresent(jsonPath); + const max = parsePositiveInteger(options.structuralMax) ?? latestScout?.parameters?.maxN ?? 10000; + const minStructuralN = parsePositiveInteger(options.structuralMin) ?? latestScout?.parameters?.minStructuralN ?? 7307; + + return { + available: fs.existsSync(scriptPath) && minStructuralN <= max, + actionId: 'structural_two_side_scout', + mode: 'cpu', + source: 'structural_two_side_scout', + reason: 'Run the repo-owned outsider-clique structural inequality with both 7 mod 25 and 18 mod 25 base sides before promoting any external verifier idea.', + scriptPath, + max, + minStructuralN, + jsonPath, + markdownPath, + latestStructuralStatus: latestScout?.status ?? null, + latestStructuralSummary: latestScout?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--max', + String(max), + '--min-structural-n', + String(minStructuralN), + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'structural_two_side_scout', { + ...options, + structuralMax: max, + structuralMin: minStructuralN, + }), + }; +} + +function getP848MixedBaseFailureScoutPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'mixed_base_failure_scout', + reason: `No mixed-base failure scout lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_mixed_base_failure_scout.mjs'); + const structuralJsonPath = getPackFile(problemId, 'STRUCTURAL_TWO_SIDE_SCOUT.json'); + const jsonPath = getPackFile(problemId, 'MIXED_BASE_FAILURE_SCOUT.json'); + const markdownPath = getPackFile(problemId, 'MIXED_BASE_FAILURE_SCOUT.md'); + const structuralScout = readJsonIfPresent(structuralJsonPath); + const latestScout = readJsonIfPresent(jsonPath); + const maxRows = parsePositiveInteger(options.mixedBaseMaxRows) ?? latestScout?.parameters?.maxRows ?? 40; + + return { + available: fs.existsSync(scriptPath) && Boolean(structuralScout), + actionId: 'mixed_base_failure_scout', + mode: 'cpu', + source: 'mixed_base_failure_scout', + reason: structuralScout + ? 'Sharpen the failed union-base structural rows by solving the exact mixed-base clique induced by both principal sides.' + : 'Run the two-sided structural scout first; mixed-base failure scouting needs STRUCTURAL_TWO_SIDE_SCOUT.json.', + scriptPath, + structuralJsonPath, + maxRows, + jsonPath, + markdownPath, + latestMixedBaseStatus: latestScout?.status ?? null, + latestMixedBaseSummary: latestScout?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--structural-json', + structuralJsonPath, + '--max-rows', + String(maxRows), + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'mixed_base_failure_scout', { + ...options, + mixedBaseMaxRows: maxRows, + }), + }; +} + +function getP848FullMixedBaseStructuralVerifierPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'full_mixed_base_structural_verifier', + reason: `No full mixed-base structural verifier lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_full_mixed_base_structural_verifier.mjs'); + const jsonPath = getPackFile(problemId, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json'); + const markdownPath = getPackFile(problemId, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md'); + const latestVerifier = readJsonIfPresent(jsonPath); + const max = parsePositiveInteger(options.structuralMax) ?? latestVerifier?.parameters?.maxN ?? 10000; + const minStructuralN = parsePositiveInteger(options.structuralMin) ?? latestVerifier?.parameters?.minStructuralN ?? 7307; + const rowSampleLimit = parsePositiveInteger(options.fullMixedRowSampleLimit) + ?? latestVerifier?.parameters?.rowSampleLimit + ?? 200; + + return { + available: fs.existsSync(scriptPath) && minStructuralN <= max, + actionId: 'full_mixed_base_structural_verifier', + mode: 'cpu', + source: 'full_mixed_base_structural_verifier', + reason: 'Certify the bounded two-sided structural verifier by using the safe union bound where it already passes and exact mixed-base clique checks for every threatening active outsider where it does not.', + scriptPath, + max, + minStructuralN, + rowSampleLimit, + jsonPath, + markdownPath, + latestFullMixedStructuralStatus: latestVerifier?.status ?? null, + latestFullMixedStructuralSummary: latestVerifier?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--max', + String(max), + '--min-structural-n', + String(minStructuralN), + '--row-sample-limit', + String(rowSampleLimit), + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'full_mixed_base_structural_verifier', { + ...options, + structuralMax: max, + structuralMin: minStructuralN, + fullMixedRowSampleLimit: rowSampleLimit, + }), + }; +} + +function getP848StructuralLiftMinerPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'structural_lift_miner', + reason: `No structural lift miner lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_structural_lift_miner.mjs'); + const verifierJsonPath = getPackFile(problemId, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json'); + const jsonPath = getPackFile(problemId, 'STRUCTURAL_LIFT_MINER.json'); + const markdownPath = getPackFile(problemId, 'STRUCTURAL_LIFT_MINER.md'); + const latestMiner = readJsonIfPresent(jsonPath); + const topRows = parsePositiveInteger(options.structuralLiftTopRows) + ?? latestMiner?.parameters?.topRows + ?? 12; + const familyLimit = parsePositiveInteger(options.structuralLiftFamilyLimit) + ?? latestMiner?.parameters?.familyLimit + ?? 20; + + return { + available: fs.existsSync(scriptPath) && fs.existsSync(verifierJsonPath), + actionId: 'structural_lift_miner', + mode: 'cpu', + source: 'structural_lift_miner', + reason: fs.existsSync(verifierJsonPath) + ? 'Mine the full mixed-base structural verifier into theorem-facing lift families, margin profiles, and proof obligations.' + : 'Run the full mixed-base structural verifier first; structural lift mining needs FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json.', + scriptPath, + verifierJsonPath, + topRows, + familyLimit, + jsonPath, + markdownPath, + latestStructuralLiftStatus: latestMiner?.status ?? null, + latestStructuralLiftSummary: latestMiner?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--verifier-json', + verifierJsonPath, + '--top-rows', + String(topRows), + '--family-limit', + String(familyLimit), + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'structural_lift_miner', { + ...options, + structuralLiftTopRows: topRows, + structuralLiftFamilyLimit: familyLimit, + }), + }; +} + +function getP848MatchingPatternMinerPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'matching_pattern_miner', + reason: `No matching-pattern miner lane is registered for problem ${problemId}.`, + }; + } + + const scriptPath = getPackFile(problemId, 'compute/problem848_matching_pattern_miner.mjs'); + const verifierJsonPath = getPackFile(problemId, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json'); + const defaultJsonPath = getPackFile(problemId, 'MATCHING_PATTERN_MINER.json'); + const defaultMiner = readJsonIfPresent(defaultJsonPath); + const prime = parsePositiveInteger(options.matchingPatternPrime) + ?? defaultMiner?.parameters?.targetPrime + ?? 13; + const artifactSuffix = prime === 13 ? '' : `_P${prime}`; + const jsonPath = getPackFile(problemId, `MATCHING_PATTERN_MINER${artifactSuffix}.json`); + const markdownPath = getPackFile(problemId, `MATCHING_PATTERN_MINER${artifactSuffix}.md`); + const latestMiner = readJsonIfPresent(jsonPath); + const topRows = parsePositiveInteger(options.matchingPatternTopRows) + ?? latestMiner?.parameters?.topRows + ?? 12; + const pairSampleLimit = parsePositiveInteger(options.matchingPatternPairSampleLimit) + ?? latestMiner?.parameters?.pairSampleLimit + ?? 24; + + return { + available: fs.existsSync(scriptPath) && fs.existsSync(verifierJsonPath), + actionId: 'matching_pattern_miner', + mode: 'cpu', + source: 'matching_pattern_miner', + reason: fs.existsSync(verifierJsonPath) + ? 'Mine actual missing-cross matching witnesses for the active D-lane prime so the theorem loop can replace Hopcroft-Karp replay with a symbolic residue/block injection.' + : 'Run the full mixed-base structural verifier first; matching-pattern mining needs FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json.', + scriptPath, + verifierJsonPath, + prime, + topRows, + pairSampleLimit, + jsonPath, + markdownPath, + latestMatchingPatternStatus: latestMiner?.status ?? null, + latestMatchingPatternSummary: latestMiner?.summary ?? null, + commandLine: formatCommandLine('node', [ + scriptPath, + '--verifier-json', + verifierJsonPath, + '--prime', + String(prime), + '--top-rows', + String(topRows), + '--pair-sample-limit', + String(pairSampleLimit), + '--json-output', + jsonPath, + '--markdown-output', + markdownPath, + ]), + applyCommand: buildDispatchApplyCommand(problemId, 'matching_pattern_miner', { + ...options, + matchingPatternPrime: prime, + matchingPatternTopRows: topRows, + matchingPatternPairSampleLimit: pairSampleLimit, + }), + }; +} + +function buildP848DispatchActions(problem, options = {}, workspaceRoot = getWorkspaceRoot()) { + const problemId = String(problem.problemId); + const frontierSnapshot = options.remoteId + ? getFrontierDoctorSnapshotForRemote(options.remoteId, workspaceRoot) + : getFrontierDoctorSnapshot(workspaceRoot); + const bridgePlan = resolveFrontierExecutionPlan('bridgeRefresh848', workspaceRoot, frontierSnapshot); + const cpuPlan = resolveFrontierExecutionPlan('p848FamilySearchProfile', workspaceRoot, frontierSnapshot); + const gpuPlan = resolveFrontierExecutionPlan('p848HeavySearchProfile', workspaceRoot, frontierSnapshot); + const claimPassPlan = getP848ClaimPassPlan(problem); + const formalizationPlan = getP848FormalizationPlan(problem); + const formalizationWorkPlan = getP848FormalizationWorkPlan(problem); + const exactPlan = getP848ExactScoutPlan(problemId, options); + const exactHandoffPlan = getP848ExactHandoffPlan(problemId); + const exactFollowupPlan = getP848ExactFollowupLaunchPlan(problemId, options); + const exactRolloutPlan = getP848ExactFollowupRolloutPlan(problemId, options); + const structuralVerifierAuditPlan = getP848StructuralVerifierAuditPlan(problemId, options); + const baseSideScoutPlan = getP848BaseSideScoutPlan(problemId, options); + const structuralTwoSideScoutPlan = getP848StructuralTwoSideScoutPlan(problemId, options); + const mixedBaseFailureScoutPlan = getP848MixedBaseFailureScoutPlan(problemId, options); + const fullMixedBaseStructuralVerifierPlan = getP848FullMixedBaseStructuralVerifierPlan(problemId, options); + const structuralLiftMinerPlan = getP848StructuralLiftMinerPlan(problemId, options); + const matchingPatternMinerPlan = getP848MatchingPatternMinerPlan(problemId, options); + + return [ + { + actionId: 'bridge_refresh', + title: 'Refresh canonical search/theorem bridge', + kind: 'frontier_bridge', + available: bridgePlan.available, + mode: bridgePlan.mode, + source: bridgePlan.source, + reason: bridgePlan.reason, + commandLine: bridgePlan.commandLine ?? 'erdos number-theory bridge-refresh 848', + executable: bridgePlan.executable ?? null, + args: bridgePlan.args ?? [], + applyCommand: buildDispatchApplyCommand(problemId, 'bridge_refresh', options), + }, + { + actionId: 'cpu_family_search', + title: 'Run managed CPU family-search pass', + kind: 'frontier_search', + available: cpuPlan.available, + mode: cpuPlan.mode, + source: cpuPlan.source, + reason: cpuPlan.reason, + profilePath: cpuPlan.profilePath ?? null, + commandLine: cpuPlan.commandLine ?? null, + executable: cpuPlan.executable ?? null, + args: cpuPlan.args ?? [], + applyCommand: buildDispatchApplyCommand(problemId, 'cpu_family_search', options), + }, + { + actionId: 'gpu_profile_sweep', + title: 'Run managed GPU ladder sweep', + kind: 'frontier_search', + available: gpuPlan.available, + mode: gpuPlan.mode, + source: gpuPlan.source, + reason: gpuPlan.reason, + profilePath: gpuPlan.profilePath ?? null, + commandLine: gpuPlan.commandLine ?? null, + executable: gpuPlan.executable ?? null, + args: gpuPlan.args ?? [], + laneId: gpuPlan.laneId ?? null, + remoteProvider: gpuPlan.remoteProvider ?? null, + remoteInstanceName: gpuPlan.remoteInstanceName ?? null, + remoteHost: gpuPlan.remoteHost ?? null, + remoteCommand: gpuPlan.remoteCommand ?? null, + remoteEngineRoot: gpuPlan.remoteEngineRoot ?? null, + remotePythonCommand: gpuPlan.remotePythonCommand ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'gpu_profile_sweep', options), + }, + { + actionId: 'formalization_work_refresh', + title: 'Refresh theorem formalization work packet', + kind: 'theorem_formalization_work', + available: formalizationWorkPlan.available, + mode: formalizationWorkPlan.mode ?? 'theorem', + source: formalizationWorkPlan.source ?? 'formalization_work', + reason: formalizationWorkPlan.reason, + formalizationWork: formalizationWorkPlan.formalizationWork ?? null, + commandLine: formalizationWorkPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'formalization_work_refresh', options), + }, + { + actionId: 'formalization_refresh', + title: 'Refresh theorem formalization packet', + kind: 'theorem_formalization', + available: formalizationPlan.available, + mode: formalizationPlan.mode ?? 'theorem', + source: formalizationPlan.source ?? 'formalization', + reason: formalizationPlan.reason, + formalization: formalizationPlan.formalization ?? null, + commandLine: formalizationPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'formalization_refresh', options), + }, + { + actionId: 'claim_pass_refresh', + title: 'Refresh claim-pass verdicts and theorem recommendations', + kind: 'theorem_claims', + available: claimPassPlan.available, + mode: claimPassPlan.mode ?? 'theorem', + source: claimPassPlan.source ?? 'claim_pass', + reason: claimPassPlan.reason, + claimPass: claimPassPlan.claimPass ?? null, + recommendations: claimPassPlan.recommendations ?? [], + commandLine: claimPassPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'claim_pass_refresh', options), + }, + { + actionId: 'structural_verifier_audit', + title: 'Audit external structural verifier import', + kind: 'structural_verifier_audit', + available: structuralVerifierAuditPlan.available, + mode: structuralVerifierAuditPlan.mode ?? 'cpu', + source: structuralVerifierAuditPlan.source ?? 'external_structural_verifier_audit', + reason: structuralVerifierAuditPlan.reason, + scriptPath: structuralVerifierAuditPlan.scriptPath ?? null, + sourceDir: structuralVerifierAuditPlan.sourceDir ?? null, + sourceAvailable: Boolean(structuralVerifierAuditPlan.sourceAvailable), + jsonPath: structuralVerifierAuditPlan.jsonPath ?? null, + markdownPath: structuralVerifierAuditPlan.markdownPath ?? null, + latestAuditStatus: structuralVerifierAuditPlan.latestAuditStatus ?? null, + latestAuditSummary: structuralVerifierAuditPlan.latestAuditSummary ?? null, + commandLine: structuralVerifierAuditPlan.commandLine ?? null, + applyCommand: structuralVerifierAuditPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'structural_verifier_audit', options), + }, + { + actionId: 'base_side_scout', + title: 'Run bounded base-side compatibility scout', + kind: 'structural_base_side_scout', + available: baseSideScoutPlan.available, + mode: baseSideScoutPlan.mode ?? 'cpu', + source: baseSideScoutPlan.source ?? 'structural_base_side_scout', + reason: baseSideScoutPlan.reason, + scriptPath: baseSideScoutPlan.scriptPath ?? null, + max: baseSideScoutPlan.max ?? null, + jsonPath: baseSideScoutPlan.jsonPath ?? null, + markdownPath: baseSideScoutPlan.markdownPath ?? null, + latestScoutStatus: baseSideScoutPlan.latestScoutStatus ?? null, + latestScoutSummary: baseSideScoutPlan.latestScoutSummary ?? null, + commandLine: baseSideScoutPlan.commandLine ?? null, + applyCommand: baseSideScoutPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'base_side_scout', options), + }, + { + actionId: 'structural_two_side_scout', + title: 'Run two-sided structural verifier scout', + kind: 'structural_two_side_scout', + available: structuralTwoSideScoutPlan.available, + mode: structuralTwoSideScoutPlan.mode ?? 'cpu', + source: structuralTwoSideScoutPlan.source ?? 'structural_two_side_scout', + reason: structuralTwoSideScoutPlan.reason, + scriptPath: structuralTwoSideScoutPlan.scriptPath ?? null, + max: structuralTwoSideScoutPlan.max ?? null, + minStructuralN: structuralTwoSideScoutPlan.minStructuralN ?? null, + jsonPath: structuralTwoSideScoutPlan.jsonPath ?? null, + markdownPath: structuralTwoSideScoutPlan.markdownPath ?? null, + latestStructuralStatus: structuralTwoSideScoutPlan.latestStructuralStatus ?? null, + latestStructuralSummary: structuralTwoSideScoutPlan.latestStructuralSummary ?? null, + commandLine: structuralTwoSideScoutPlan.commandLine ?? null, + applyCommand: structuralTwoSideScoutPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'structural_two_side_scout', options), + }, + { + actionId: 'mixed_base_failure_scout', + title: 'Run mixed-base failure scout', + kind: 'mixed_base_failure_scout', + available: mixedBaseFailureScoutPlan.available, + mode: mixedBaseFailureScoutPlan.mode ?? 'cpu', + source: mixedBaseFailureScoutPlan.source ?? 'mixed_base_failure_scout', + reason: mixedBaseFailureScoutPlan.reason, + scriptPath: mixedBaseFailureScoutPlan.scriptPath ?? null, + structuralJsonPath: mixedBaseFailureScoutPlan.structuralJsonPath ?? null, + maxRows: mixedBaseFailureScoutPlan.maxRows ?? null, + jsonPath: mixedBaseFailureScoutPlan.jsonPath ?? null, + markdownPath: mixedBaseFailureScoutPlan.markdownPath ?? null, + latestMixedBaseStatus: mixedBaseFailureScoutPlan.latestMixedBaseStatus ?? null, + latestMixedBaseSummary: mixedBaseFailureScoutPlan.latestMixedBaseSummary ?? null, + commandLine: mixedBaseFailureScoutPlan.commandLine ?? null, + applyCommand: mixedBaseFailureScoutPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'mixed_base_failure_scout', options), + }, + { + actionId: 'full_mixed_base_structural_verifier', + title: 'Run full mixed-base structural verifier', + kind: 'full_mixed_base_structural_verifier', + available: fullMixedBaseStructuralVerifierPlan.available, + mode: fullMixedBaseStructuralVerifierPlan.mode ?? 'cpu', + source: fullMixedBaseStructuralVerifierPlan.source ?? 'full_mixed_base_structural_verifier', + reason: fullMixedBaseStructuralVerifierPlan.reason, + scriptPath: fullMixedBaseStructuralVerifierPlan.scriptPath ?? null, + max: fullMixedBaseStructuralVerifierPlan.max ?? null, + minStructuralN: fullMixedBaseStructuralVerifierPlan.minStructuralN ?? null, + rowSampleLimit: fullMixedBaseStructuralVerifierPlan.rowSampleLimit ?? null, + jsonPath: fullMixedBaseStructuralVerifierPlan.jsonPath ?? null, + markdownPath: fullMixedBaseStructuralVerifierPlan.markdownPath ?? null, + latestFullMixedStructuralStatus: fullMixedBaseStructuralVerifierPlan.latestFullMixedStructuralStatus ?? null, + latestFullMixedStructuralSummary: fullMixedBaseStructuralVerifierPlan.latestFullMixedStructuralSummary ?? null, + commandLine: fullMixedBaseStructuralVerifierPlan.commandLine ?? null, + applyCommand: fullMixedBaseStructuralVerifierPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'full_mixed_base_structural_verifier', options), + }, + { + actionId: 'structural_lift_miner', + title: 'Run structural lift miner', + kind: 'structural_lift_miner', + available: structuralLiftMinerPlan.available, + mode: structuralLiftMinerPlan.mode ?? 'cpu', + source: structuralLiftMinerPlan.source ?? 'structural_lift_miner', + reason: structuralLiftMinerPlan.reason, + scriptPath: structuralLiftMinerPlan.scriptPath ?? null, + verifierJsonPath: structuralLiftMinerPlan.verifierJsonPath ?? null, + topRows: structuralLiftMinerPlan.topRows ?? null, + familyLimit: structuralLiftMinerPlan.familyLimit ?? null, + jsonPath: structuralLiftMinerPlan.jsonPath ?? null, + markdownPath: structuralLiftMinerPlan.markdownPath ?? null, + latestStructuralLiftStatus: structuralLiftMinerPlan.latestStructuralLiftStatus ?? null, + latestStructuralLiftSummary: structuralLiftMinerPlan.latestStructuralLiftSummary ?? null, + commandLine: structuralLiftMinerPlan.commandLine ?? null, + applyCommand: structuralLiftMinerPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'structural_lift_miner', options), + }, + { + actionId: 'matching_pattern_miner', + title: 'Run matching pattern miner', + kind: 'matching_pattern_miner', + available: matchingPatternMinerPlan.available, + mode: matchingPatternMinerPlan.mode ?? 'cpu', + source: matchingPatternMinerPlan.source ?? 'matching_pattern_miner', + reason: matchingPatternMinerPlan.reason, + scriptPath: matchingPatternMinerPlan.scriptPath ?? null, + verifierJsonPath: matchingPatternMinerPlan.verifierJsonPath ?? null, + prime: matchingPatternMinerPlan.prime ?? null, + topRows: matchingPatternMinerPlan.topRows ?? null, + pairSampleLimit: matchingPatternMinerPlan.pairSampleLimit ?? null, + jsonPath: matchingPatternMinerPlan.jsonPath ?? null, + markdownPath: matchingPatternMinerPlan.markdownPath ?? null, + latestMatchingPatternStatus: matchingPatternMinerPlan.latestMatchingPatternStatus ?? null, + latestMatchingPatternSummary: matchingPatternMinerPlan.latestMatchingPatternSummary ?? null, + commandLine: matchingPatternMinerPlan.commandLine ?? null, + applyCommand: matchingPatternMinerPlan.applyCommand ?? buildDispatchApplyCommand(problemId, 'matching_pattern_miner', options), + }, + { + actionId: 'exact_interval_scout', + title: 'Run exact small-N interval scout', + kind: 'exact_verification', + available: exactPlan.available, + mode: exactPlan.mode ?? 'cpu', + source: exactPlan.source ?? 'exact_verification_lane', + reason: exactPlan.reason, + readyInterval: exactPlan.readyInterval ?? null, + latestDoneInterval: exactPlan.latestDoneInterval ?? null, + min: exactPlan.min ?? null, + max: exactPlan.max ?? null, + scriptPath: exactPlan.scriptPath ?? null, + endpointMonotonicity: Boolean(exactPlan.endpointMonotonicity), + backendKind: exactPlan.backendKind ?? 'exact_small_n', + commandLine: exactPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'exact_interval_scout', options), + }, + { + actionId: 'exact_handoff_bundle', + title: 'Prepare exact handoff bundle', + kind: 'exact_handoff', + available: exactHandoffPlan.available, + mode: exactHandoffPlan.mode ?? 'cpu', + source: exactHandoffPlan.source ?? 'search_theorem_bridge', + reason: exactHandoffPlan.reason, + bridgePath: exactHandoffPlan.bridgePath ?? null, + bridgeMarkdownPath: exactHandoffPlan.bridgeMarkdownPath ?? null, + gpuManifestPath: exactHandoffPlan.gpuManifestPath ?? null, + commandLine: exactHandoffPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'exact_handoff_bundle', options), + }, + { + actionId: 'exact_followup_launch', + title: 'Launch exact follow-up from handoff bundle', + kind: 'exact_followup', + available: exactFollowupPlan.available, + mode: exactFollowupPlan.mode ?? 'cpu', + source: exactFollowupPlan.source ?? 'exact_orchestrator', + reason: exactFollowupPlan.reason, + bridgePath: exactFollowupPlan.bridgePath ?? null, + bridgeMarkdownPath: exactFollowupPlan.bridgeMarkdownPath ?? null, + gpuManifestPath: exactFollowupPlan.gpuManifestPath ?? null, + readyInterval: exactFollowupPlan.readyInterval ?? null, + latestDoneInterval: exactFollowupPlan.latestDoneInterval ?? null, + min: exactFollowupPlan.min ?? null, + max: exactFollowupPlan.max ?? null, + scriptPath: exactFollowupPlan.scriptPath ?? null, + backendKind: exactFollowupPlan.backendKind ?? 'exact_small_n', + endpointMonotonicity: Boolean(exactFollowupPlan.endpointMonotonicity), + commandLine: exactFollowupPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'exact_followup_launch', options), + }, + { + actionId: 'exact_followup_rollout', + title: 'Advance multiple exact follow-up chunks', + kind: 'exact_followup', + available: exactRolloutPlan.available, + mode: exactRolloutPlan.mode ?? 'cpu', + source: exactRolloutPlan.source ?? 'exact_orchestrator', + reason: exactRolloutPlan.reason, + bridgePath: exactRolloutPlan.bridgePath ?? null, + bridgeMarkdownPath: exactRolloutPlan.bridgeMarkdownPath ?? null, + gpuManifestPath: exactRolloutPlan.gpuManifestPath ?? null, + readyInterval: exactRolloutPlan.readyInterval ?? null, + latestDoneInterval: exactRolloutPlan.latestDoneInterval ?? null, + min: exactRolloutPlan.min ?? null, + max: exactRolloutPlan.max ?? null, + scriptPath: exactRolloutPlan.scriptPath ?? null, + backendKind: exactRolloutPlan.backendKind ?? 'exact_small_n_rollout', + chunkCount: exactRolloutPlan.chunkCount ?? null, + chunkSize: exactRolloutPlan.chunkSize ?? null, + rolloutIntervals: exactRolloutPlan.rolloutIntervals ?? [], + endpointMonotonicity: Boolean(exactRolloutPlan.endpointMonotonicity), + commandLine: exactRolloutPlan.commandLine ?? null, + applyCommand: buildDispatchApplyCommand(problemId, 'exact_followup_rollout', options), + }, + ]; +} + +function rankP848DispatchActions(actions) { + const byId = Object.fromEntries(actions.map((action) => [action.actionId, action])); + const orderedIds = []; + + if (byId.gpu_profile_sweep?.available) { + orderedIds.push('gpu_profile_sweep'); + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + if (byId.exact_followup_rollout?.available) { + orderedIds.push('exact_followup_rollout'); + } + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + if (byId.exact_followup_launch?.available) { + orderedIds.push('exact_followup_launch'); + } + if (byId.exact_handoff_bundle?.available) { + orderedIds.push('exact_handoff_bundle'); + } + if (byId.exact_interval_scout?.available) { + orderedIds.push('exact_interval_scout'); + } + if (byId.bridge_refresh?.available) { + orderedIds.push('bridge_refresh'); + } + } else if (byId.cpu_family_search?.available) { + orderedIds.push('cpu_family_search'); + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + if (byId.exact_followup_rollout?.available) { + orderedIds.push('exact_followup_rollout'); + } + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + if (byId.exact_followup_launch?.available) { + orderedIds.push('exact_followup_launch'); + } + if (byId.exact_handoff_bundle?.available) { + orderedIds.push('exact_handoff_bundle'); + } + if (byId.exact_interval_scout?.available) { + orderedIds.push('exact_interval_scout'); + } + if (byId.bridge_refresh?.available) { + orderedIds.push('bridge_refresh'); + } + } else if (byId.bridge_refresh?.available) { + orderedIds.push('bridge_refresh'); + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + if (byId.exact_followup_rollout?.available) { + orderedIds.push('exact_followup_rollout'); + } + if (byId.exact_followup_launch?.available) { + orderedIds.push('exact_followup_launch'); + } + if (byId.exact_handoff_bundle?.available) { + orderedIds.push('exact_handoff_bundle'); + } + if (byId.exact_interval_scout?.available) { + orderedIds.push('exact_interval_scout'); + } + } else if (byId.exact_interval_scout?.available) { + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + orderedIds.push('exact_interval_scout'); + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + if (byId.exact_followup_rollout?.available) { + orderedIds.push('exact_followup_rollout'); + } + if (byId.exact_followup_launch?.available) { + orderedIds.push('exact_followup_launch'); + } + if (byId.exact_handoff_bundle?.available) { + orderedIds.push('exact_handoff_bundle'); + } + } else if (byId.exact_followup_rollout?.available) { + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + orderedIds.push('exact_followup_rollout'); + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + } else if (byId.exact_followup_launch?.available) { + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + orderedIds.push('exact_followup_launch'); + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + } else if (byId.exact_handoff_bundle?.available) { + if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + } + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + orderedIds.push('exact_handoff_bundle'); + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + } else if (byId.formalization_work_refresh?.available) { + orderedIds.push('formalization_work_refresh'); + if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + } + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + } else if (byId.formalization_refresh?.available) { + orderedIds.push('formalization_refresh'); + if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + } else if (byId.claim_pass_refresh?.available) { + orderedIds.push('claim_pass_refresh'); + } + + for (const structuralId of [ + 'structural_verifier_audit', + 'base_side_scout', + 'structural_two_side_scout', + 'mixed_base_failure_scout', + 'full_mixed_base_structural_verifier', + 'structural_lift_miner', + 'matching_pattern_miner', + ]) { + if (!byId[structuralId]?.available || orderedIds.includes(structuralId)) { + continue; + } + const firstExactIndex = orderedIds + .map((id, index) => ({ id, index })) + .filter(({ id }) => [ + 'exact_followup_rollout', + 'exact_followup_launch', + 'exact_handoff_bundle', + 'exact_interval_scout', + ].includes(id)) + .map(({ index }) => index)[0] ?? -1; + if (firstExactIndex >= 0) { + orderedIds.splice(firstExactIndex, 0, structuralId); + } else { + const anchorIndex = Math.max( + orderedIds.lastIndexOf('base_side_scout'), + orderedIds.lastIndexOf('structural_two_side_scout'), + orderedIds.lastIndexOf('mixed_base_failure_scout'), + orderedIds.lastIndexOf('full_mixed_base_structural_verifier'), + orderedIds.lastIndexOf('structural_lift_miner'), + orderedIds.lastIndexOf('matching_pattern_miner'), + orderedIds.lastIndexOf('structural_verifier_audit'), + orderedIds.lastIndexOf('claim_pass_refresh'), + orderedIds.lastIndexOf('formalization_refresh'), + orderedIds.lastIndexOf('formalization_work_refresh'), + ); + if (anchorIndex >= 0) { + orderedIds.splice(anchorIndex + 1, 0, structuralId); + } else { + orderedIds.push(structuralId); + } + } + } + + return actions + .map((action) => ({ + ...action, + priority: orderedIds.indexOf(action.actionId) >= 0 ? orderedIds.indexOf(action.actionId) + 1 : null, + primary: orderedIds[0] === action.actionId, + })) + .sort((left, right) => { + const leftPriority = left.priority ?? Number.MAX_SAFE_INTEGER; + const rightPriority = right.priority ?? Number.MAX_SAFE_INTEGER; + if (leftPriority !== rightPriority) { + return leftPriority - rightPriority; + } + return left.actionId.localeCompare(right.actionId); + }); +} + +function summarizeP848Dispatch(primaryAction) { + if (!primaryAction) { + return 'No orchestrated frontier action is currently available.'; + } + if (primaryAction.actionId === 'gpu_profile_sweep') { + return 'GPU ladder sweep is the highest-value live move, with exact interval scouting still available as the bounded-verification follow-up.'; + } + if (primaryAction.actionId === 'cpu_family_search') { + return 'Managed CPU family search is the best live move, with exact interval scouting still available on the verification side.'; + } + if (primaryAction.actionId === 'bridge_refresh') { + return 'Bridge refresh is the lightest frontier action available right now, while the exact interval scout remains available as a secondary lane.'; + } + if (primaryAction.actionId === 'claim_pass_refresh') { + return 'Claim-pass refresh is the live theorem-search move right now, turning the current bridge and exact base into explicit claim verdicts and recommendations.'; + } + if (primaryAction.actionId === 'structural_verifier_audit') { + return 'Structural verifier audit is the live finite-gap move, checking whether external outsider-clique computation is safe to import or must stay blocked.'; + } + if (primaryAction.actionId === 'base_side_scout') { + return 'Base-side scout is the live structural move, checking whether one-sided 7 mod 25 base masks survive comparison with the 18 mod 25 side.'; + } + if (primaryAction.actionId === 'formalization_work_refresh') { + return 'Formalization-work refresh is the live theorem move right now, turning the top formalization target into one concrete packet with current evidence, discharged work, and remaining gaps.'; + } + if (primaryAction.actionId === 'formalization_refresh') { + return 'Formalization refresh is the live theorem move right now, turning the strongest supported claim-pass recommendation into a concrete proof-obligation packet.'; + } + if (primaryAction.actionId === 'exact_interval_scout') { + return 'The exact interval scout is the live next move because no frontier-search runtime is currently ready.'; + } + if (primaryAction.actionId === 'exact_followup_launch') { + return 'The exact follow-up launcher can now package the live bridge context and run the ready bounded exact backend in one step.'; + } + if (primaryAction.actionId === 'exact_followup_rollout') { + return 'The exact rollout can advance several contiguous bounded exact chunks in one supervised move while preserving canonical promotion after each chunk.'; + } + if (primaryAction.actionId === 'exact_handoff_bundle') { + return 'The canonical bridge is already strong enough to package an exact-follow-up bundle without rerunning search first.'; + } + if (primaryAction.actionId === 'matching_pattern_miner') { + return 'Matching-pattern mining is the live theorem-lane move, extracting actual missing-cross matching witnesses for the active D-lane prime.'; + } + return primaryAction.reason ?? 'Dispatch summary unavailable.'; +} + +export function getNumberTheoryDispatchSnapshot(problem, options = {}, workspaceRoot = getWorkspaceRoot()) { + if (String(problem.problemId) !== '848') { + return { + available: false, + problemId: problem.problemId, + error: `No orchestrated frontier dispatch is registered for problem ${problem.problemId}.`, + }; + } + + if (options.remoteId) { + const remoteSnapshot = getFrontierDoctorSnapshotForRemote(options.remoteId, workspaceRoot); + if (!remoteSnapshot.selectedRemoteFound) { + return { + available: false, + problemId: problem.problemId, + error: `Unknown frontier remote: ${options.remoteId}`, + }; + } + } + + const bridge = getNumberTheoryBridgeSnapshot(problem); + const actions = rankP848DispatchActions(buildP848DispatchActions(problem, options, workspaceRoot)); + const primaryAction = actions.find((action) => action.primary) ?? null; + const claimPassAction = actions.find((action) => action.actionId === 'claim_pass_refresh') ?? null; + const formalizationWorkAction = actions.find((action) => action.actionId === 'formalization_work_refresh') ?? null; + const formalizationAction = actions.find((action) => action.actionId === 'formalization_refresh') ?? null; + + return { + available: true, + generatedAt: new Date().toISOString(), + workspaceRoot, + problemId: problem.problemId, + displayName: problem.displayName, + remoteId: options.remoteId ?? null, + activeRoute: bridge.activeRoute, + currentBridgeState: bridge.bridgeCurrentState, + bridgeRefreshCommand: bridge.bridgeRefreshCommand, + claimPass: claimPassAction?.claimPass ?? getProblemClaimPassSnapshot(problem), + formalizationWork: formalizationWorkAction?.formalizationWork ?? getProblemFormalizationWorkSnapshot(problem), + formalization: formalizationAction?.formalization ?? getProblemFormalizationSnapshot(problem), + actions, + primaryAction, + summary: summarizeP848Dispatch(primaryAction), + }; +} + +function summarizeP848FleetDispatch(snapshot) { + if (!snapshot.available) { + return snapshot.error ?? 'Fleet dispatch is not available.'; + } + const availableCount = snapshot.members.filter((member) => member.available).length; + const totalCount = snapshot.members.length; + if (availableCount === totalCount) { + return `Fleet ${snapshot.fleetId} is ready to fan out ${snapshot.actionId} across ${totalCount} remote worker${totalCount === 1 ? '' : 's'}.`; + } + return `Fleet ${snapshot.fleetId} can launch ${snapshot.actionId} on ${availableCount}/${totalCount} remote worker${totalCount === 1 ? '' : 's'} right now.`; +} + +export function getNumberTheoryFleetDispatchSnapshot(problem, options = {}, workspaceRoot = getWorkspaceRoot()) { + const problemId = String(problem.problemId); + if (problemId !== '848') { + return { + available: false, + problemId, + error: `No fleet dispatch is registered for problem ${problemId}.`, + }; + } + + const fleetId = String(options.fleetId ?? '').trim() || null; + if (!fleetId) { + return { + available: false, + problemId, + error: 'Fleet dispatch requires --fleet .', + }; + } + + const fleet = getFrontierFleetSnapshot(fleetId, workspaceRoot); + if (!fleet) { + return { + available: false, + problemId, + error: `Unknown frontier fleet: ${fleetId}`, + }; + } + + const actionId = options.actionId ?? 'gpu_profile_sweep'; + const strategyId = String(options.strategyId ?? 'ladder_cover_v1').trim() || 'ladder_cover_v1'; + const bridge = getNumberTheoryBridgeSnapshot(problem); + const assignments = actionId === 'gpu_profile_sweep' + ? buildP848FleetAssignments(problem, fleet, bridge, { strategyId }) + : []; + const memberPlans = (fleet.remoteIds ?? []).map((remoteId) => { + const dispatch = getNumberTheoryDispatchSnapshot(problem, { + ...options, + actionId, + remoteId, + }, workspaceRoot); + const action = dispatch.available + ? (dispatch.actions.find((candidate) => candidate.actionId === actionId) ?? null) + : null; + return { + remoteId, + assignment: assignments.find((assignment) => assignment.remoteId === remoteId) ?? null, + available: Boolean(action?.available), + dispatchAvailable: dispatch.available, + dispatchError: dispatch.error ?? null, + action, + remoteSummary: dispatch.summary ?? null, + actionReason: action?.reason ?? dispatch.error ?? null, + applyCommand: action?.applyCommand ?? buildDispatchApplyCommand(problemId, actionId, { remoteId }), + }; + }); + + const availableMembers = memberPlans.filter((member) => member.available); + const unavailableMembers = memberPlans.filter((member) => !member.available); + + const snapshot = { + available: availableMembers.length > 0, + generatedAt: new Date().toISOString(), + workspaceRoot, + problemId, + displayName: problem.displayName, + fleetId, + fleet, + actionId, + strategyId, + detach: true, + reviewAfterHours: options.reviewAfterHours ?? null, + members: memberPlans, + availableMemberCount: availableMembers.length, + unavailableMemberCount: unavailableMembers.length, + commandLine: buildFleetDispatchApplyCommand(problemId, fleetId, actionId, { + reviewAfterHours: options.reviewAfterHours ?? null, + strategyId, + }), + }; + + return { + ...snapshot, + summary: summarizeP848FleetDispatch(snapshot), + error: snapshot.available ? null : 'No fleet members are currently ready for the requested action.', + }; +} + +function writeFleetDispatchBundle(problem, snapshot, memberResults, workspaceRoot = getWorkspaceRoot(), options = {}) { + const runId = options.runId ?? `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__fleet_${snapshot.actionId}`; + const runDir = options.runDir ?? getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + + const payload = { + schema: 'erdos.number_theory.fleet_dispatch/1', + generatedAt: new Date().toISOString(), + runId, + problemId: problem.problemId, + displayName: problem.displayName, + fleetId: snapshot.fleetId, + actionId: snapshot.actionId, + strategyId: snapshot.strategyId ?? null, + summary: snapshot.summary, + reviewAfterHours: snapshot.reviewAfterHours ?? null, + members: memberResults, + boundary: 'This fleet dispatch records orchestrated worker launches. Mathematical claims come only from harvested artifacts and canonical writeback.', + }; + + writeJson(path.join(runDir, 'FLEET_DISPATCH.json'), payload); + writeText( + path.join(runDir, 'RUN_SUMMARY.md'), + [ + '# Number-Theory Fleet Dispatch', + '', + `- Problem: ${problem.displayName}`, + `- Fleet: ${snapshot.fleetId}`, + `- Action: ${snapshot.actionId}`, + `- Review-after-hours: ${snapshot.reviewAfterHours ?? '(none)'}`, + `- Ready members: ${snapshot.availableMemberCount}/${snapshot.members.length}`, + '', + 'Members:', + ...memberResults.map((member) => `- ${member.remoteId}: ${member.status}`), + '', + 'Boundary:', + '- This fleet dispatch records orchestrated worker launches. Mathematical claims come only from harvested artifacts and canonical writeback.', + '', + ].join('\n'), + ); + + return { + runId, + runDir, + payload, + }; +} + +export function getNumberTheoryFleetRunSnapshot(runId, workspaceRoot = getWorkspaceRoot()) { + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + const payload = readJsonIfPresent(path.join(runDir, 'FLEET_DISPATCH.json')); + if (!payload) { + return null; + } + + const sessions = (payload.members ?? []).map((member) => { + const session = member.sessionId + ? getFrontierSessionSnapshot(member.sessionId, workspaceRoot) + : null; + const harvestedBundle = session?.harvestedBundle ?? null; + const manifest = harvestedBundle?.manifestPath + ? readJsonIfPresent(harvestedBundle.manifestPath) + : null; + return { + ...member, + session, + harvestedBundle, + harvestedManifestSummary: manifest?.summary ?? null, + }; + }); + + const statusCounts = sessions.reduce((accumulator, member) => { + const key = member.session?.status ?? member.status ?? 'unknown'; + accumulator[key] = (accumulator[key] ?? 0) + 1; + return accumulator; + }, {}); + const harvestedBundles = sessions.filter((member) => member.harvestedBundle?.ok); + + return { + ...payload, + runDir, + members: sessions, + statusCounts, + harvestedBundleCount: harvestedBundles.length, + harvestedBundles, + }; +} + +function buildDetachedDispatchCliArgs(problemId, actionId, options = {}) { + const args = [ + 'number-theory', + 'dispatch', + String(problemId), + '--apply', + '--action', + String(actionId), + ]; + + if (options.remoteId) { + args.push('--remote-id', String(options.remoteId)); + } + + if (options.exactMin !== null && options.exactMin !== undefined) { + args.push('--exact-min', String(options.exactMin)); + } + if (options.exactMax !== null && options.exactMax !== undefined) { + args.push('--exact-max', String(options.exactMax)); + } + if (options.exactChunks !== null && options.exactChunks !== undefined) { + args.push('--exact-chunks', String(options.exactChunks)); + } + if (options.exactChunkSize !== null && options.exactChunkSize !== undefined) { + args.push('--exact-chunk-size', String(options.exactChunkSize)); + } + if (options.baseSideMax !== null && options.baseSideMax !== undefined) { + args.push('--base-side-max', String(options.baseSideMax)); + } + if (options.structuralMax !== null && options.structuralMax !== undefined) { + args.push('--structural-max', String(options.structuralMax)); + } + if (options.structuralMin !== null && options.structuralMin !== undefined) { + args.push('--structural-min', String(options.structuralMin)); + } + if (options.mixedBaseMaxRows !== null && options.mixedBaseMaxRows !== undefined) { + args.push('--mixed-base-max-rows', String(options.mixedBaseMaxRows)); + } + if (options.fullMixedRowSampleLimit !== null && options.fullMixedRowSampleLimit !== undefined) { + args.push('--full-mixed-row-sample-limit', String(options.fullMixedRowSampleLimit)); + } + if (options.structuralLiftTopRows !== null && options.structuralLiftTopRows !== undefined) { + args.push('--structural-lift-top-rows', String(options.structuralLiftTopRows)); + } + if (options.structuralLiftFamilyLimit !== null && options.structuralLiftFamilyLimit !== undefined) { + args.push('--structural-lift-family-limit', String(options.structuralLiftFamilyLimit)); + } + if (options.endpointMonotonicity) { + args.push('--endpoint-monotonicity'); + } + + return args; +} + +function executeExternalCommand(executable, args, cwd = repoRoot) { + try { + const stdout = execFileSync(executable, args, { + cwd, + encoding: 'utf8', + stdio: ['ignore', 'pipe', 'pipe'], + }).trim(); + return { + ok: true, + stdout, + stderr: null, + }; + } catch (error) { + return { + ok: false, + stdout: error?.stdout?.toString().trim() || null, + stderr: error?.stderr?.toString().trim() || error?.message || null, + }; + } +} + +function parseP848RemoteBundleDir(stdout) { + const match = String(stdout ?? '').match(/p848_seed_bundle:\s*(.+)$/m); + return match ? match[1].trim() : null; +} + +function normalizeRemoteBundleDir(remote, remoteBundleDir) { + if (!remoteBundleDir) { + return null; + } + if (isBrevRemote(remote)) { + const normalized = String(remoteBundleDir).replaceAll('\\', '/'); + if (normalized.startsWith('/')) { + return normalized; + } + const engineRoot = String(remote?.engineRoot ?? '').replaceAll('\\', '/'); + const homeDir = engineRoot.includes('/') + ? engineRoot.replace(/\/frontier-engine$/, '').replace(/\/+$/, '') + : '$HOME'; + return `${homeDir}/${normalized.replace(/^\.\/+/, '')}`; + } + const normalized = String(remoteBundleDir).replaceAll('/', '\\'); + if (/^[A-Za-z]:\\/.test(normalized) || normalized.startsWith('%USERPROFILE%\\')) { + return normalized; + } + return `%USERPROFILE%\\${normalized}`; +} + +function readRemoteText(remote, remotePath) { + if (isBrevRemote(remote)) { + return runRemoteCommandCapture(remote, `cat ${JSON.stringify(String(remotePath))}`, { cwd: repoRoot }); + } + return executeExternalCommand('ssh', [remote.sshHost, `cmd /c type "${remotePath}"`], repoRoot); +} + +function mirrorRemoteP848Bundle(remote, remoteBundleDir) { + if (!remote || !remoteBundleDir) { + return null; + } + + const normalizedRemoteBundleDir = normalizeRemoteBundleDir(remote, remoteBundleDir); + const bundleName = isBrevRemote(remote) + ? path.posix.basename(normalizedRemoteBundleDir) + : path.win32.basename(normalizedRemoteBundleDir); + const localBundleDir = path.join(repoRoot, 'research', 'frontier-engine', 'artifacts', 'p848-anchor-ladder', bundleName); + ensureDir(localBundleDir); + + if (isBrevRemote(remote)) { + const copyResult = runRemoteCopyFromCapture(remote, normalizedRemoteBundleDir, path.dirname(localBundleDir), { + cwd: repoRoot, + recursive: true, + }); + if (!copyResult.ok) { + return { + ok: false, + localBundleDir, + remoteBundleDir: normalizedRemoteBundleDir, + error: copyResult.stderr ?? 'failed to copy remote bundle', + }; + } + const manifestPayload = readJsonIfPresent(path.join(localBundleDir, 'manifest.json')); + return { + ok: Boolean(manifestPayload), + localBundleDir, + remoteBundleDir: normalizedRemoteBundleDir, + manifest: manifestPayload, + copiedCandidateFiles: manifestPayload?.candidate_files?.map((row) => row?.file).filter(Boolean) ?? [], + missingCandidateFiles: manifestPayload ? [] : [{ file: 'manifest.json', error: 'failed to read copied manifest' }], + copyResult, + }; + } + + const manifestRemotePath = `${normalizedRemoteBundleDir}\\manifest.json`; + const manifestResult = readRemoteText(remote, manifestRemotePath); + if (!manifestResult.ok || !manifestResult.stdout) { + return { + ok: false, + localBundleDir, + remoteBundleDir: normalizedRemoteBundleDir, + error: manifestResult.stderr ?? 'failed to read remote manifest', + }; + } + + const manifestPayload = JSON.parse(manifestResult.stdout); + writeJson(path.join(localBundleDir, 'manifest.json'), manifestPayload); + + const copiedCandidateFiles = []; + const missingCandidateFiles = []; + for (const row of manifestPayload.candidate_files ?? []) { + const filename = row?.file ? String(row.file) : null; + if (!filename) { + continue; + } + const candidateRemotePath = `${normalizedRemoteBundleDir}\\${filename}`; + const candidateResult = readRemoteText(remote, candidateRemotePath); + if (!candidateResult.ok || candidateResult.stdout === null) { + missingCandidateFiles.push({ + file: filename, + error: candidateResult.stderr ?? 'failed to read remote candidate file', + }); + continue; + } + writeText(path.join(localBundleDir, filename), `${candidateResult.stdout}\n`); + copiedCandidateFiles.push(filename); + } + + return { + ok: true, + localBundleDir, + remoteBundleDir: normalizedRemoteBundleDir, + manifest: manifestPayload, + copiedCandidateFiles, + missingCandidateFiles, + }; +} + +function getP848ExactHandoffPlan(problemId) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'exact_handoff_bundle', + reason: `No exact handoff bundle is registered for problem ${problemId}.`, + }; + } + + const bridgePath = getPackFile(problemId, 'SEARCH_THEOREM_BRIDGE.json'); + const bridge = readJsonIfPresent(bridgePath); + if (!bridge?.current_bridge_state) { + return { + available: false, + actionId: 'exact_handoff_bundle', + reason: 'The canonical search/theorem bridge is not present yet, so no exact handoff bundle can be assembled.', + bridgePath, + }; + } + + return { + available: true, + actionId: 'exact_handoff_bundle', + mode: 'cpu', + source: 'search_theorem_bridge', + reason: 'The canonical bridge already narrows the live frontier into a stable exact-follow-up packet.', + bridgePath, + bridgeMarkdownPath: getPackFile(problemId, 'SEARCH_THEOREM_BRIDGE.md'), + gpuManifestPath: bridge?.sources?.gpu_manifest_path ?? null, + nextUnmatchedRepresentative: bridge.current_bridge_state.next_unmatched_representative ?? null, + topGpuTieClass: bridge.current_bridge_state.top_gpu_tie_class ?? [], + strongestCompletedStructuredTail: bridge.current_bridge_state.strongest_completed_structured_tail ?? null, + currentFamilyAwareLeader: bridge.current_bridge_state.current_family_aware_leader ?? null, + commandLine: `erdos number-theory dispatch ${problemId} --apply --action exact_handoff_bundle`, + }; +} + +function getP848ExactFollowupLaunchPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'exact_followup_launch', + reason: `No exact follow-up launcher is registered for problem ${problemId}.`, + }; + } + + const handoffPlan = getP848ExactHandoffPlan(problemId); + const exactPlan = getP848ExactScoutPlan(problemId, options); + + if (!handoffPlan.available) { + return { + available: false, + actionId: 'exact_followup_launch', + reason: handoffPlan.reason, + handoffPlan, + exactPlan, + }; + } + + if (!exactPlan.available) { + return { + available: false, + actionId: 'exact_followup_launch', + reason: exactPlan.reason, + handoffPlan, + exactPlan, + }; + } + + return { + available: true, + actionId: 'exact_followup_launch', + mode: exactPlan.mode ?? 'cpu', + source: 'exact_orchestrator', + reason: 'Package the canonical bridge context and immediately run the ready exact-small-N backend.', + bridgePath: handoffPlan.bridgePath, + bridgeMarkdownPath: handoffPlan.bridgeMarkdownPath, + gpuManifestPath: handoffPlan.gpuManifestPath ?? null, + readyInterval: exactPlan.readyInterval ?? null, + latestDoneInterval: exactPlan.latestDoneInterval ?? null, + min: exactPlan.min ?? null, + max: exactPlan.max ?? null, + scriptPath: exactPlan.scriptPath ?? null, + endpointMonotonicity: Boolean(exactPlan.endpointMonotonicity), + backendKind: exactPlan.backendKind ?? 'exact_small_n', + commandLine: `erdos number-theory dispatch ${problemId} --apply --action exact_followup_launch`, + }; +} + +function getP848ExactFollowupRolloutPlan(problemId, options = {}) { + if (String(problemId) !== '848') { + return { + available: false, + actionId: 'exact_followup_rollout', + reason: `No exact follow-up rollout is registered for problem ${problemId}.`, + }; + } + + const launchPlan = getP848ExactFollowupLaunchPlan(problemId, options); + if (!launchPlan.available) { + return { + available: false, + actionId: 'exact_followup_rollout', + reason: launchPlan.reason, + launchPlan, + }; + } + + const chunkCount = parsePositiveInteger(options.exactChunks) ?? 3; + const derivedChunkSize = launchPlan.min !== null && launchPlan.max !== null + ? Math.max(1, launchPlan.max - launchPlan.min + 1) + : 100; + const chunkSize = parsePositiveInteger(options.exactChunkSize) ?? derivedChunkSize; + const rolloutIntervals = Array.from({ length: chunkCount }, (_, index) => { + const min = launchPlan.min + (index * chunkSize); + const max = min + chunkSize - 1; + return { + index: index + 1, + min, + max, + interval: `${min}..${max}`, + }; + }); + const totalMax = rolloutIntervals.length > 0 ? rolloutIntervals[rolloutIntervals.length - 1].max : launchPlan.max; + + return { + available: true, + actionId: 'exact_followup_rollout', + mode: launchPlan.mode ?? 'cpu', + source: 'exact_orchestrator', + reason: `The exact lane is ready for a ${chunkCount}-chunk rollout from ${rolloutIntervals[0]?.interval ?? '(unknown)'} through ${rolloutIntervals[rolloutIntervals.length - 1]?.interval ?? '(unknown)'}.`, + bridgePath: launchPlan.bridgePath, + bridgeMarkdownPath: launchPlan.bridgeMarkdownPath, + gpuManifestPath: launchPlan.gpuManifestPath ?? null, + readyInterval: launchPlan.readyInterval ?? null, + latestDoneInterval: launchPlan.latestDoneInterval ?? null, + min: launchPlan.min ?? null, + max: totalMax ?? null, + scriptPath: launchPlan.scriptPath ?? null, + endpointMonotonicity: Boolean(launchPlan.endpointMonotonicity), + backendKind: launchPlan.endpointMonotonicity ? 'endpoint_monotonicity_small_n_rollout' : 'exact_small_n_rollout', + chunkCount, + chunkSize, + rolloutIntervals, + commandLine: buildDispatchApplyCommand(problemId, 'exact_followup_rollout', { + exactMin: launchPlan.min, + exactChunks: chunkCount, + exactChunkSize: chunkSize, + endpointMonotonicity: launchPlan.endpointMonotonicity, + }), + }; +} + +function buildP848ExactHandoffBundle(problem, action, dispatchSnapshot, runDir) { + const bridgeJsonPath = getPackFile(problem.problemId, 'SEARCH_THEOREM_BRIDGE.json'); + const bridgeMarkdownPath = getPackFile(problem.problemId, 'SEARCH_THEOREM_BRIDGE.md'); + const bridge = readJsonIfPresent(bridgeJsonPath); + const bridgeMarkdown = fs.existsSync(bridgeMarkdownPath) + ? fs.readFileSync(bridgeMarkdownPath, 'utf8') + : null; + + if (!bridge?.current_bridge_state) { + return { + ok: false, + error: 'The canonical search/theorem bridge is not available.', + }; + } + + const handoffDir = path.join(runDir, 'exact-handoff'); + const candidatesDir = path.join(handoffDir, 'candidates'); + ensureDir(handoffDir); + ensureDir(candidatesDir); + + const gpuManifestPath = bridge?.sources?.gpu_manifest_path ?? null; + const gpuManifest = gpuManifestPath ? readJsonIfPresent(gpuManifestPath) : null; + const copiedCandidateFiles = []; + const missingCandidateFiles = []; + + for (const row of gpuManifest?.candidate_files ?? []) { + const filename = row?.file ? String(row.file) : null; + if (!filename) { + continue; + } + const sourcePath = path.join(path.dirname(gpuManifestPath), filename); + const destPath = path.join(candidatesDir, filename); + if (!fs.existsSync(sourcePath)) { + missingCandidateFiles.push(filename); + continue; + } + fs.copyFileSync(sourcePath, destPath); + copiedCandidateFiles.push(filename); + } + + const recommendedContinuations = []; + const seenContinuations = new Set(); + const leader = bridge.current_bridge_state.current_family_aware_leader; + if (leader?.continuation !== undefined && leader?.continuation !== null) { + recommendedContinuations.push({ + role: 'current_family_aware_leader', + continuation: leader.continuation, + repairedKnownPackets: leader.repaired_known_packets, + repairedPredictedFamilies: leader.repaired_predicted_families, + effectiveCleanThrough: leader.effective_clean_through, + }); + seenContinuations.add(Number(leader.continuation)); + } + for (const row of bridge.gpu_leaderboard ?? []) { + const continuation = Number(row.continuation); + if (seenContinuations.has(continuation)) { + continue; + } + recommendedContinuations.push({ + role: 'gpu_leaderboard', + continuation, + repairedKnownPackets: row.repaired_known_packets, + repairedPredictedFamilies: row.repaired_predicted_families, + effectiveCleanThrough: row.effective_clean_through, + }); + seenContinuations.add(continuation); + if (recommendedContinuations.length >= 5) { + break; + } + } + const strongestCompleted = bridge.current_bridge_state.strongest_completed_structured_tail; + if (strongestCompleted?.continuation !== undefined && strongestCompleted?.continuation !== null) { + const continuation = Number(strongestCompleted.continuation); + if (!seenContinuations.has(continuation)) { + recommendedContinuations.push({ + role: 'strongest_completed_structured_tail', + continuation, + repairedKnownPackets: null, + repairedPredictedFamilies: null, + effectiveCleanThrough: strongestCompleted.clean_through ?? null, + }); + } + } + + const handoff = { + schema: 'erdos.number_theory.p848_exact_handoff/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + activeRoute: dispatchSnapshot.activeRoute ?? null, + source: 'canonical_search_theorem_bridge', + bridgeState: bridge.current_bridge_state, + theoremHooks: bridge.candidate_theorem_hooks ?? [], + sources: bridge.sources ?? {}, + recommendedContinuations, + exactFocus: { + nextUnmatchedRepresentative: bridge.current_bridge_state.next_unmatched_representative ?? null, + nextUnmatchedMatches282Failure: Boolean(bridge.current_bridge_state.next_unmatched_matches_282_failure), + topGpuTieClass: bridge.current_bridge_state.top_gpu_tie_class ?? [], + strongestCompletedStructuredTail: strongestCompleted ?? null, + currentFamilyAwareLeader: leader ?? null, + }, + copiedCandidateFiles, + missingCandidateFiles, + honestyBoundary: 'This bundle is a workspace handoff for exact follow-up. It does not certify the problem or promote a theorem claim by itself.', + }; + + const handoffJsonPath = path.join(handoffDir, 'EXACT_HANDOFF.json'); + const handoffMarkdownPath = path.join(handoffDir, 'EXACT_HANDOFF.md'); + writeJson(handoffJsonPath, handoff); + writeText( + handoffMarkdownPath, + [ + '# Problem 848 Exact Handoff', + '', + `- Problem: ${problem.displayName}`, + `- Active route: ${dispatchSnapshot.activeRoute ?? '(none)'}`, + `- Next unmatched representative: ${bridge.current_bridge_state.next_unmatched_representative ?? '(unknown)'}`, + `- Matches 282 tail failure: ${bridge.current_bridge_state.next_unmatched_matches_282_failure ? 'yes' : 'no'}`, + `- Current family-aware leader: ${leader?.continuation ?? '(unknown)'}`, + `- Strongest completed structured tail: ${strongestCompleted?.continuation ?? '(unknown)'}`, + `- GPU tie class: ${(bridge.current_bridge_state.top_gpu_tie_class ?? []).join(', ') || '(none)'}`, + '', + 'Recommended exact follow-up:', + `- pressure-test ${bridge.current_bridge_state.next_unmatched_representative ?? '(unknown)'} against the current packet/menu surface`, + `- compare the tied frontier tails ${(bridge.current_bridge_state.top_gpu_tie_class ?? []).join(', ') || '(none)'} on the next finite window`, + `- retain ${strongestCompleted?.continuation ?? '(unknown)'} as the strongest completed structured tail baseline`, + '', + 'Artifacts:', + `- Bridge JSON: ${bridgeJsonPath}`, + `- Bridge note: ${bridgeMarkdownPath}`, + `- GPU manifest: ${gpuManifestPath ?? '(missing)'}`, + `- Candidate files copied: ${copiedCandidateFiles.length}`, + '', + 'Boundary:', + '- This bundle is a workspace handoff for exact follow-up. It does not certify the problem or upgrade canonical theorem claims by itself.', + '', + ].join('\n'), + ); + + if (bridgeMarkdown) { + writeText(path.join(handoffDir, 'SEARCH_THEOREM_BRIDGE.md'), bridgeMarkdown); + } + writeJson(path.join(handoffDir, 'SEARCH_THEOREM_BRIDGE.json'), bridge); + if (gpuManifest) { + writeJson(path.join(handoffDir, 'GPU_MANIFEST.json'), gpuManifest); + } + + return { + ok: true, + handoff, + handoffDir, + handoffJsonPath, + handoffMarkdownPath, + }; +} + +function buildP848ExactFollowupPacket(problem, action, dispatchSnapshot, handoffResult, results, execution, runDir, resultsPath) { + const followupDir = path.join(runDir, 'exact-followup'); + ensureDir(followupDir); + + const summary = results?.summary ?? null; + const recommendedNextMoves = []; + if (summary?.allCandidateAchievesMaximum === true && summary?.allExampleCliquesMatchCandidateClass === true) { + recommendedNextMoves.push('Extend the exact small-N interval farther while the residue-class candidate continues to match the exact maximum.'); + } else { + recommendedNextMoves.push('Inspect the first row where the candidate fails to achieve the exact maximum or the example clique leaves the tracked residue classes.'); + } + recommendedNextMoves.push( + `Keep ${handoffResult.handoff?.exactFocus?.nextUnmatchedRepresentative ?? '(unknown)'} as the next shared-prefix pressure point for theorem/search coordination.`, + ); + + const packet = { + schema: 'erdos.number_theory.p848_exact_followup/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + activeRoute: dispatchSnapshot.activeRoute ?? null, + source: 'exact_followup_launch', + backend: { + kind: action.backendKind ?? 'exact_small_n', + readyInterval: action.readyInterval ?? null, + latestDoneInterval: action.latestDoneInterval ?? null, + min: action.min ?? null, + max: action.max ?? null, + scriptPath: action.scriptPath ?? null, + endpointMonotonicity: Boolean(action.endpointMonotonicity), + commandLine: formatCommandLine('node', [ + action.scriptPath, + '--min', + String(action.min), + '--max', + String(action.max), + ...(action.endpointMonotonicity ? ['--endpoint-monotonicity'] : []), + '--json-output', + resultsPath, + ]), + }, + handoff: { + dir: handoffResult.handoffDir ?? null, + jsonPath: handoffResult.handoffJsonPath ?? null, + markdownPath: handoffResult.handoffMarkdownPath ?? null, + exactFocus: handoffResult.handoff?.exactFocus ?? null, + recommendedContinuations: handoffResult.handoff?.recommendedContinuations ?? [], + }, + execution: { + ok: Boolean(execution?.ok), + stdout: execution?.stdout ?? null, + stderr: execution?.stderr ?? null, + }, + resultsPath, + resultsSummary: summary, + recommendedNextMoves, + honestyBoundary: 'This packet records one exact follow-up run plus its handoff context. It does not certify the full problem or promote theorem claims beyond the covered interval.', + }; + + const followupJsonPath = path.join(followupDir, 'EXACT_FOLLOWUP.json'); + const followupMarkdownPath = path.join(followupDir, 'EXACT_FOLLOWUP.md'); + writeJson(followupJsonPath, packet); + writeText( + followupMarkdownPath, + [ + '# Problem 848 Exact Follow-Up', + '', + `- Problem: ${problem.displayName}`, + `- Active route: ${dispatchSnapshot.activeRoute ?? '(none)'}`, + `- Backend: ${packet.backend.kind}`, + `- Interval: ${action.min}..${action.max}`, + `- Ready interval: ${action.readyInterval?.range ?? '(unknown)'}`, + `- Latest done interval: ${action.latestDoneInterval?.range ?? '(unknown)'}`, + `- Handoff bundle: ${handoffResult.handoffDir ?? '(missing)'}`, + `- Results JSON: ${resultsPath}`, + '', + 'Results summary:', + `- Candidate achieves maximum throughout interval: ${summary?.allCandidateAchievesMaximum ? 'yes' : 'no'}`, + `- Example cliques stay in tracked residue classes: ${summary?.allExampleCliquesMatchCandidateClass ? 'yes' : 'no'}`, + `- Rows scanned: ${summary?.rows ?? '(unknown)'}`, + '', + 'Next moves:', + ...recommendedNextMoves.map((move) => `- ${move}`), + '', + 'Boundary:', + '- This packet records one exact follow-up run plus its handoff context. It does not certify the full problem or upgrade canonical theorem claims beyond the covered interval.', + '', + ].join('\n'), + ); + + return { + ok: true, + packet, + followupDir, + followupJsonPath, + followupMarkdownPath, + }; +} + +function buildP848ExactRolloutPacket(problem, action, dispatchSnapshot, childRuns, bridgeRefresh, runDir) { + const rolloutDir = path.join(runDir, 'exact-rollout'); + ensureDir(rolloutDir); + + const completedRuns = childRuns.filter((childRun) => childRun.ok); + const failedRun = childRuns.find((childRun) => !childRun.ok) ?? null; + const completedInterval = completedRuns.length > 0 + ? `${completedRuns[0].min}..${completedRuns[completedRuns.length - 1].max}` + : null; + const recommendedNextMoves = []; + if (failedRun) { + recommendedNextMoves.push(`Inspect the failed chunk ${failedRun.interval} before widening the exact rollout further.`); + } else { + recommendedNextMoves.push('Advance the next contiguous exact rollout block while the exact-small-N backend remains stable.'); + } + recommendedNextMoves.push( + `Refresh the theorem/search bridge after exact promotion so the canonical 848 north-star stays aligned with the latest verified interval.`, + ); + + const packet = { + schema: 'erdos.number_theory.p848_exact_followup_rollout/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + activeRoute: dispatchSnapshot.activeRoute ?? null, + source: 'exact_followup_rollout', + requestedChunkCount: action.chunkCount ?? 0, + completedChunkCount: completedRuns.length, + chunkSize: action.chunkSize ?? null, + requestedInterval: action.min !== null && action.max !== null ? `${action.min}..${action.max}` : null, + completedInterval, + rolloutIntervals: (action.rolloutIntervals ?? []).map((interval) => ({ + index: interval.index, + min: interval.min, + max: interval.max, + interval: interval.interval, + })), + childRuns: childRuns.map((childRun) => ({ + index: childRun.index, + interval: childRun.interval, + min: childRun.min, + max: childRun.max, + ok: childRun.ok, + runId: childRun.runId ?? null, + runDir: childRun.runDir ?? null, + resultsSummary: childRun.resultsSummary ?? null, + error: childRun.error ?? null, + exactPromotion: childRun.exactPromotion ?? null, + })), + failedChunk: failedRun + ? { + index: failedRun.index, + interval: failedRun.interval, + error: failedRun.error ?? null, + } + : null, + bridgeRefresh: bridgeRefresh + ? { + ok: Boolean(bridgeRefresh.ok), + executionMode: bridgeRefresh.executionMode ?? null, + executionSource: bridgeRefresh.executionSource ?? null, + refreshCommand: bridgeRefresh.refreshCommand ?? null, + } + : null, + recommendedNextMoves, + honestyBoundary: 'This packet records a bounded exact rollout over contiguous intervals. It does not certify the full problem or upgrade theorem claims beyond the promoted exact base.', + }; + + const rolloutJsonPath = path.join(rolloutDir, 'EXACT_ROLLOUT.json'); + const rolloutMarkdownPath = path.join(rolloutDir, 'EXACT_ROLLOUT.md'); + writeJson(rolloutJsonPath, packet); + writeText( + rolloutMarkdownPath, + [ + '# Problem 848 Exact Rollout', + '', + `- Problem: ${problem.displayName}`, + `- Active route: ${dispatchSnapshot.activeRoute ?? '(none)'}`, + `- Requested chunks: ${action.chunkCount ?? 0}`, + `- Completed chunks: ${completedRuns.length}`, + `- Chunk size: ${action.chunkSize ?? '(unknown)'}`, + `- Requested interval: ${packet.requestedInterval ?? '(unknown)'}`, + `- Completed interval: ${completedInterval ?? '(none)'}`, + '', + 'Child runs:', + ...childRuns.map((childRun) => `- chunk ${childRun.index}: ${childRun.interval} [${childRun.ok ? 'ok' : 'failed'}]${childRun.runId ? ` (${childRun.runId})` : ''}`), + '', + 'Next moves:', + ...recommendedNextMoves.map((move) => `- ${move}`), + '', + 'Boundary:', + '- This packet records a bounded exact rollout over contiguous intervals. It does not certify the full problem or upgrade theorem claims beyond the promoted exact base.', + '', + ].join('\n'), + ); + + return { + ok: !failedRun, + packet, + rolloutDir, + rolloutJsonPath, + rolloutMarkdownPath, + }; +} + +function writeDispatchRunBundle(problem, dispatchSnapshot, action, payload, workspaceRoot = getWorkspaceRoot(), options = {}) { + const runId = options.runId ?? `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = options.runDir ?? getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + + const runRecord = { + runId, + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + cluster: problem.cluster, + actionId: action.actionId, + actionTitle: action.title, + actionKind: action.kind, + actionMode: action.mode ?? null, + actionSource: action.source ?? null, + actionReason: action.reason ?? null, + commandLine: payload.commandLine ?? action.commandLine ?? null, + currentRoute: dispatchSnapshot.activeRoute ?? null, + summary: dispatchSnapshot.summary, + artifacts: { + runPath: path.join(runDir, 'RUN.json'), + dispatchPath: path.join(runDir, 'DISPATCH.json'), + resultPath: path.join(runDir, 'RESULT.json'), + runSummaryPath: path.join(runDir, 'RUN_SUMMARY.md'), + logPath: path.join(runDir, 'RUN_LOG.txt'), + }, + }; + + writeJson(path.join(runDir, 'RUN.json'), runRecord); + writeJson(path.join(runDir, 'DISPATCH.json'), dispatchSnapshot); + writeJson(path.join(runDir, 'RESULT.json'), payload); + writeText(path.join(runDir, 'RUN_LOG.txt'), `${payload.stdout ?? payload.stderr ?? ''}\n`); + writeText( + path.join(runDir, 'RUN_SUMMARY.md'), + [ + '# Number-Theory Frontier Dispatch Run', + '', + `- Problem: ${problem.displayName}`, + `- Action: ${action.actionId}`, + `- Title: ${action.title}`, + `- Kind: ${action.kind}`, + `- Mode: ${action.mode ?? '(none)'}`, + `- Source: ${action.source ?? '(none)'}`, + `- Command: ${payload.commandLine ?? action.commandLine ?? '(none)'}`, + `- OK: ${payload.ok ? 'yes' : 'no'}`, + `- Route: ${dispatchSnapshot.activeRoute ?? '(none)'}`, + '', + 'Dispatch summary:', + `- ${dispatchSnapshot.summary}`, + '', + 'Outputs:', + '- RUN.json', + '- DISPATCH.json', + '- RESULT.json', + '- RUN_LOG.txt', + '', + 'Boundary:', + '- This is a workspace run artifact. It does not upgrade canonical theorem claims by itself.', + '', + ].join('\n'), + ); + + return { runId, runDir, runRecord }; +} + +export function runNumberTheoryFleetDispatch(problem, options = {}, workspaceRoot = getWorkspaceRoot()) { + const snapshot = getNumberTheoryFleetDispatchSnapshot(problem, options, workspaceRoot); + if (!snapshot.available) { + return { + ok: false, + error: snapshot.error ?? 'Fleet dispatch is unavailable.', + snapshot, + fleetRun: null, + }; + } + + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__fleet_${snapshot.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const memberResults = snapshot.members.map((member) => { + if (!member.available) { + return { + remoteId: member.remoteId, + status: 'skipped', + ok: false, + error: member.actionReason ?? member.dispatchError ?? 'member unavailable', + sessionId: null, + assignment: member.assignment ?? null, + }; + } + + let profileOverride = null; + if (snapshot.actionId === 'gpu_profile_sweep' && member.assignment) { + const preparedProfile = prepareP848RemoteProfileOverride(member.action, member.assignment, workspaceRoot, { + fleetId: snapshot.fleetId, + launchId: runId, + }); + if (!preparedProfile.ok) { + return { + remoteId: member.remoteId, + status: 'failed', + ok: false, + error: preparedProfile.error ?? 'failed to prepare remote profile override', + sessionId: null, + assignment: member.assignment ?? null, + profileOverride: preparedProfile, + }; + } + profileOverride = preparedProfile; + } + + const result = runNumberTheoryDispatch(problem, { + actionId: snapshot.actionId, + detach: true, + reviewAfterHours: snapshot.reviewAfterHours ?? null, + remoteId: member.remoteId, + profileOverride, + }, workspaceRoot); + + return { + remoteId: member.remoteId, + status: result.ok ? 'launched' : 'failed', + ok: Boolean(result.ok), + error: result.error ?? null, + sessionId: result.session?.sessionId ?? null, + sessionStatus: result.session?.status ?? null, + reviewDueAt: result.session?.reviewDueAt ?? null, + assignment: member.assignment ?? null, + profileOverride, + }; + }); + + const runBundle = writeFleetDispatchBundle(problem, snapshot, memberResults, workspaceRoot, { + runId, + runDir, + }); + const fleetRun = getNumberTheoryFleetRunSnapshot(runBundle.runId, workspaceRoot); + const launchedCount = memberResults.filter((member) => member.ok && member.sessionId).length; + const failedCount = memberResults.filter((member) => member.status === 'failed').length; + const skippedCount = memberResults.filter((member) => member.status === 'skipped').length; + + return { + ok: launchedCount > 0 && failedCount === 0, + partial: launchedCount > 0 && (failedCount > 0 || skippedCount > 0), + problemId: problem.problemId, + fleetId: snapshot.fleetId, + actionId: snapshot.actionId, + snapshot, + fleetRun, + launchedCount, + failedCount, + skippedCount, + error: launchedCount > 0 ? null : 'No fleet members launched successfully.', + }; +} + +export function runNumberTheoryDispatch(problem, options = {}, workspaceRoot = getWorkspaceRoot()) { + const dispatch = getNumberTheoryDispatchSnapshot(problem, options, workspaceRoot); + if (!dispatch.available) { + return { + ok: false, + error: dispatch.error ?? 'Dispatch is unavailable.', + dispatch, + }; + } + + const action = options.actionId + ? dispatch.actions.find((candidate) => candidate.actionId === options.actionId) ?? null + : dispatch.primaryAction; + + if (!action) { + return { + ok: false, + error: options.actionId + ? `Unknown dispatch action: ${options.actionId}` + : 'No primary dispatch action is currently available.', + dispatch, + }; + } + + if (!action.available) { + return { + ok: false, + error: `Dispatch action ${action.actionId} is not available right now.`, + dispatch, + action, + }; + } + + if (options.detach) { + if (action.actionId === 'gpu_profile_sweep' && action.source === 'ssh_remote') { + const remoteSpec = { + provider: action.remoteProvider ?? 'ssh', + instanceName: action.remoteInstanceName ?? null, + sshHost: action.remoteHost, + engineRoot: action.remoteEngineRoot, + pythonCommand: action.remotePythonCommand, + }; + const effectiveRemoteCommand = options.profileOverride?.remoteCommand ?? action.remoteCommand; + const remoteDetachSpec = { + backend: remoteSpec.provider === 'brev' ? 'remote_brev' : 'remote_ssh', + kind: 'number_theory_dispatch', + label: `${problem.displayName} ${action.actionId}`, + problemId: problem.problemId, + actionId: action.actionId, + mode: action.mode ?? null, + source: action.source ?? null, + reviewAfterHours: options.reviewAfterHours ?? null, + remoteProvider: remoteSpec.provider, + remoteInstanceName: remoteSpec.instanceName, + remoteHost: action.remoteHost, + remoteEngineRoot: action.remoteEngineRoot, + remotePythonCommand: action.remotePythonCommand, + remoteCommandLine: effectiveRemoteCommand, + detachedBy: 'number_theory_dispatch', + metadata: { + laneId: action.laneId ?? null, + profileOverride: options.profileOverride ?? null, + }, + }; + const reusableRemoteSession = findReusableFrontierDetachedSession(remoteDetachSpec, workspaceRoot); + if (reusableRemoteSession) { + return { + ok: true, + detached: true, + reusedExisting: true, + dispatch, + action, + session: reusableRemoteSession, + }; + } + const remoteSync = applyFrontierRemoteSync(workspaceRoot, { + remoteId: action.remoteInstanceName ?? action.remoteHost, + provider: remoteSpec.provider, + instanceName: remoteSpec.instanceName, + sshHost: action.remoteHost, + engineRoot: action.remoteEngineRoot, + pythonCommand: action.remotePythonCommand, + laneId: action.laneId ?? null, + }); + const localSharedPrefixCount = dispatch.currentBridgeState?.shared_prefix_failure_count ?? null; + const remoteSharedPrefixCount = remoteSync?.remoteLiveFrontier?.shared_prefix_failure_count ?? null; + const syncGap = !remoteSync.ok + ? (remoteSync.error ?? 'Remote frontier sync failed.') + : remoteSharedPrefixCount !== null && localSharedPrefixCount !== null && remoteSharedPrefixCount < localSharedPrefixCount + ? `Remote frontier sync is stale for canonical promotion (${remoteSharedPrefixCount} shared-prefix failures vs local ${localSharedPrefixCount}).` + : null; + + if (syncGap) { + return { + ok: false, + error: syncGap, + dispatch, + action, + remoteSync, + }; + } + + const remoteSession = launchFrontierDetachedSession({ + ...remoteDetachSpec, + metadata: { + ...(remoteDetachSpec.metadata ?? {}), + remoteSyncAt: remoteSync.appliedAt ?? null, + remoteSharedPrefixFailureCount: remoteSharedPrefixCount, + }, + }, workspaceRoot); + + if (!remoteSession.ok) { + return { + ok: false, + error: remoteSession.error ?? 'Failed to launch remote frontier session.', + dispatch, + action, + remoteSync, + }; + } + + return { + ok: true, + detached: true, + dispatch, + action, + remoteSync, + session: remoteSession.session, + }; + } + + const sessionCommand = getFrontierSessionCommandSpec( + buildDetachedDispatchCliArgs(problem.problemId, action.actionId, options), + workspaceRoot, + ); + const localDetachSpec = { + kind: 'number_theory_dispatch', + label: `${problem.displayName} ${action.actionId}`, + problemId: problem.problemId, + actionId: action.actionId, + mode: action.mode ?? null, + source: action.source ?? null, + reviewAfterHours: options.reviewAfterHours ?? null, + executable: sessionCommand.executable, + args: sessionCommand.args, + cwd: sessionCommand.cwd, + detachedBy: 'number_theory_dispatch', + metadata: { + exactMin: options.exactMin ?? null, + exactMax: options.exactMax ?? null, + exactChunks: options.exactChunks ?? null, + exactChunkSize: options.exactChunkSize ?? null, + baseSideMax: options.baseSideMax ?? null, + structuralMax: options.structuralMax ?? null, + structuralMin: options.structuralMin ?? null, + mixedBaseMaxRows: options.mixedBaseMaxRows ?? null, + fullMixedRowSampleLimit: options.fullMixedRowSampleLimit ?? null, + structuralLiftTopRows: options.structuralLiftTopRows ?? null, + structuralLiftFamilyLimit: options.structuralLiftFamilyLimit ?? null, + externalSourceDir: options.externalSourceDir ?? null, + commandLine: sessionCommand.commandLine, + }, + }; + const reusableLocalSession = findReusableFrontierDetachedSession(localDetachSpec, workspaceRoot); + if (reusableLocalSession) { + return { + ok: true, + detached: true, + reusedExisting: true, + dispatch, + action, + session: reusableLocalSession, + }; + } + const session = launchFrontierDetachedSession(localDetachSpec, workspaceRoot); + + return { + ok: true, + detached: true, + reusedExisting: false, + dispatch, + action, + session, + }; + } + + if (action.actionId === 'bridge_refresh') { + const refresh = refreshNumberTheoryBridge(problem); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: refresh.ok, + commandLine: refresh.resolvedCommand ?? action.commandLine, + stdout: refresh.commandOutput, + stderr: refresh.error ?? null, + bridge: refresh.bridge, + executionMode: refresh.executionMode ?? action.mode, + }, workspaceRoot); + return { + ok: refresh.ok, + dispatch, + action, + refresh, + runBundle, + }; + } + + if (action.actionId === 'claim_pass_refresh') { + const claimPassRefresh = refreshProblemClaimPass(problem); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: claimPassRefresh.ok, + commandLine: action.commandLine, + stdout: claimPassRefresh.ok ? `claim_pass_json: ${claimPassRefresh.jsonPath}` : null, + stderr: claimPassRefresh.error ?? null, + claimPass: claimPassRefresh.claimPass ?? null, + claimPassJsonPath: claimPassRefresh.jsonPath ?? null, + claimPassMarkdownPath: claimPassRefresh.markdownPath ?? null, + claimRefresh: claimPassRefresh.claimRefresh ?? null, + }, workspaceRoot); + return { + ok: claimPassRefresh.ok, + dispatch, + action, + claimPassRefresh, + runBundle, + error: claimPassRefresh.error ?? null, + }; + } + + if (action.actionId === 'formalization_work_refresh') { + const formalizationWorkRefresh = refreshProblemFormalizationWork(problem); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: formalizationWorkRefresh.ok, + commandLine: action.commandLine, + stdout: formalizationWorkRefresh.ok ? `formalization_work_json: ${formalizationWorkRefresh.jsonPath}` : null, + stderr: formalizationWorkRefresh.error ?? null, + formalizationWork: formalizationWorkRefresh.formalizationWork ?? null, + formalizationWorkJsonPath: formalizationWorkRefresh.jsonPath ?? null, + formalizationWorkMarkdownPath: formalizationWorkRefresh.markdownPath ?? null, + formalizationRefresh: formalizationWorkRefresh.formalizationRefresh ?? null, + }, workspaceRoot); + return { + ok: formalizationWorkRefresh.ok, + dispatch, + action, + formalizationWorkRefresh, + runBundle, + error: formalizationWorkRefresh.error ?? null, + }; + } + + if (action.actionId === 'formalization_refresh') { + const formalizationRefresh = refreshProblemFormalization(problem); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: formalizationRefresh.ok, + commandLine: action.commandLine, + stdout: formalizationRefresh.ok ? `formalization_json: ${formalizationRefresh.jsonPath}` : null, + stderr: formalizationRefresh.error ?? null, + formalization: formalizationRefresh.formalization ?? null, + formalizationJsonPath: formalizationRefresh.jsonPath ?? null, + formalizationMarkdownPath: formalizationRefresh.markdownPath ?? null, + claimPassRefresh: formalizationRefresh.claimPassRefresh ?? null, + }, workspaceRoot); + return { + ok: formalizationRefresh.ok, + dispatch, + action, + formalizationRefresh, + runBundle, + error: formalizationRefresh.error ?? null, + }; + } + + if (action.actionId === 'structural_verifier_audit') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--source-dir', + action.sourceDir, + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const audit = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + audit, + auditJsonPath: action.jsonPath, + auditMarkdownPath: action.markdownPath, + sourceDir: action.sourceDir, + auditStatus: audit?.status ?? null, + blockerCount: audit?.summary?.blockerCount ?? null, + warningCount: audit?.summary?.warningCount ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + audit, + auditJsonPath: action.jsonPath, + auditMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'base_side_scout') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--max', + String(action.max), + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const scout = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + scout, + scoutJsonPath: action.jsonPath, + scoutMarkdownPath: action.markdownPath, + max: action.max, + scoutStatus: scout?.status ?? null, + maxSide18ExceedsSide7: scout?.summary?.maxSide18ExceedsSide7 ?? null, + globalMaxSide18Minus7: scout?.summary?.globalMaxSide18Minus7 ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + scout, + scoutJsonPath: action.jsonPath, + scoutMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'structural_two_side_scout') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--max', + String(action.max), + '--min-structural-n', + String(action.minStructuralN), + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const structuralScout = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + structuralScout, + structuralScoutJsonPath: action.jsonPath, + structuralScoutMarkdownPath: action.markdownPath, + max: action.max, + minStructuralN: action.minStructuralN, + structuralStatus: structuralScout?.status ?? null, + unionFailureCount: structuralScout?.summary?.unionFailureCount ?? null, + allUnionChecksPass: structuralScout?.summary?.allUnionChecksPass ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + structuralScout, + structuralScoutJsonPath: action.jsonPath, + structuralScoutMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'mixed_base_failure_scout') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--structural-json', + action.structuralJsonPath, + '--max-rows', + String(action.maxRows), + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const mixedBaseScout = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + mixedBaseScout, + mixedBaseScoutJsonPath: action.jsonPath, + mixedBaseScoutMarkdownPath: action.markdownPath, + structuralJsonPath: action.structuralJsonPath, + maxRows: action.maxRows, + mixedBaseStatus: mixedBaseScout?.status ?? null, + mixedFailureCount: mixedBaseScout?.summary?.mixedFailureCount ?? null, + allAnalyzedRowsMixedPass: mixedBaseScout?.summary?.allAnalyzedRowsMixedPass ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + mixedBaseScout, + mixedBaseScoutJsonPath: action.jsonPath, + mixedBaseScoutMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'full_mixed_base_structural_verifier') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--max', + String(action.max), + '--min-structural-n', + String(action.minStructuralN), + '--row-sample-limit', + String(action.rowSampleLimit), + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const fullMixedStructuralVerifier = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + fullMixedStructuralVerifier, + fullMixedStructuralJsonPath: action.jsonPath, + fullMixedStructuralMarkdownPath: action.markdownPath, + max: action.max, + minStructuralN: action.minStructuralN, + rowSampleLimit: action.rowSampleLimit, + fullMixedStructuralStatus: fullMixedStructuralVerifier?.status ?? null, + mixedFailureCount: fullMixedStructuralVerifier?.summary?.mixedFailureCount ?? null, + allMixedChecksPass: fullMixedStructuralVerifier?.summary?.allMixedChecksPass ?? null, + threateningOutsiderCheckCount: fullMixedStructuralVerifier?.summary?.threateningOutsiderCheckCount ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + fullMixedStructuralVerifier, + fullMixedStructuralJsonPath: action.jsonPath, + fullMixedStructuralMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'structural_lift_miner') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--verifier-json', + action.verifierJsonPath, + '--top-rows', + String(action.topRows), + '--family-limit', + String(action.familyLimit), + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const structuralLiftMiner = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + structuralLiftMiner, + structuralLiftMinerJsonPath: action.jsonPath, + structuralLiftMinerMarkdownPath: action.markdownPath, + verifierJsonPath: action.verifierJsonPath, + topRows: action.topRows, + familyLimit: action.familyLimit, + structuralLiftStatus: structuralLiftMiner?.status ?? null, + minedExactRowCount: structuralLiftMiner?.summary?.minedExactRowCount ?? null, + primaryExactPrimes: structuralLiftMiner?.summary?.primaryExactPrimes ?? null, + nextTheoremLane: structuralLiftMiner?.summary?.nextTheoremLane ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + structuralLiftMiner, + structuralLiftMinerJsonPath: action.jsonPath, + structuralLiftMinerMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'matching_pattern_miner') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const args = [ + action.scriptPath, + '--verifier-json', + action.verifierJsonPath, + '--prime', + String(action.prime), + '--top-rows', + String(action.topRows), + '--pair-sample-limit', + String(action.pairSampleLimit), + '--json-output', + action.jsonPath, + '--markdown-output', + action.markdownPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const matchingPatternMiner = readJsonIfPresent(action.jsonPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + matchingPatternMiner, + matchingPatternMinerJsonPath: action.jsonPath, + matchingPatternMinerMarkdownPath: action.markdownPath, + verifierJsonPath: action.verifierJsonPath, + prime: action.prime, + topRows: action.topRows, + pairSampleLimit: action.pairSampleLimit, + matchingPatternStatus: matchingPatternMiner?.status ?? null, + witnessRowCount: matchingPatternMiner?.summary?.witnessRowCount ?? null, + minMatchingSlack: matchingPatternMiner?.summary?.minMatchingSlack ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + matchingPatternMiner, + matchingPatternMinerJsonPath: action.jsonPath, + matchingPatternMinerMarkdownPath: action.markdownPath, + runBundle, + error: execution.ok ? null : execution.stderr, + }; + } + + if (action.actionId === 'cpu_family_search' || action.actionId === 'gpu_profile_sweep') { + const remoteSpec = { + provider: action.remoteProvider ?? 'ssh', + instanceName: action.remoteInstanceName ?? null, + sshHost: action.remoteHost, + engineRoot: action.remoteEngineRoot, + pythonCommand: action.remotePythonCommand, + }; + const remoteSync = action.actionId === 'gpu_profile_sweep' && action.source === 'ssh_remote' + ? applyFrontierRemoteSync(workspaceRoot, { + remoteId: action.remoteInstanceName ?? action.remoteHost, + provider: remoteSpec.provider, + instanceName: remoteSpec.instanceName, + sshHost: action.remoteHost, + engineRoot: action.remoteEngineRoot, + pythonCommand: action.remotePythonCommand, + laneId: action.laneId ?? null, + }) + : null; + const localSharedPrefixCount = dispatch.currentBridgeState?.shared_prefix_failure_count ?? null; + const remoteSharedPrefixCount = remoteSync?.remoteLiveFrontier?.shared_prefix_failure_count ?? null; + const syncGap = remoteSync && !remoteSync.ok + ? (remoteSync.error ?? 'Remote frontier sync failed.') + : remoteSync && remoteSharedPrefixCount !== null && localSharedPrefixCount !== null && remoteSharedPrefixCount < localSharedPrefixCount + ? `Remote frontier sync is stale for canonical promotion (${remoteSharedPrefixCount} shared-prefix failures vs local ${localSharedPrefixCount}).` + : null; + + if (syncGap) { + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: false, + commandLine: action.commandLine, + stdout: null, + stderr: syncGap, + remoteSync, + integrationGap: syncGap, + }, workspaceRoot); + return { + ok: false, + dispatch, + action, + remoteSync, + integrationGap: syncGap, + runBundle, + }; + } + + const executionSpec = action.actionId === 'gpu_profile_sweep' && action.source === 'ssh_remote' && options.profileOverride?.remoteCommand + ? buildRemoteGpuExecutionSpec(remoteSpec, options.profileOverride.remoteCommand) + : { + executable: action.executable, + args: action.args, + commandLine: action.commandLine, + }; + const execution = executeExternalCommand(executionSpec.executable, executionSpec.args, repoRoot); + const remoteBundleDir = action.actionId === 'gpu_profile_sweep' && action.source === 'ssh_remote' + ? parseP848RemoteBundleDir(execution.stdout) + : null; + const mirroredBundle = remoteBundleDir + ? mirrorRemoteP848Bundle(remoteSpec, remoteBundleDir) + : null; + const remoteKnownFailurePacketCount = mirroredBundle?.manifest?.summary?.known_failure_packet_count ?? null; + const remoteBestEffectiveCleanThrough = mirroredBundle?.manifest?.summary?.best_effective_clean_through ?? null; + const localBestEffectiveCleanThrough = dispatch.currentBridgeState?.current_family_aware_leader?.effective_clean_through ?? null; + const remoteBundleFreshEnough = remoteKnownFailurePacketCount === null + || localSharedPrefixCount === null + || remoteKnownFailurePacketCount >= localSharedPrefixCount; + const remoteBundleDeepEnough = remoteBestEffectiveCleanThrough === null + || localBestEffectiveCleanThrough === null + || remoteBestEffectiveCleanThrough >= localBestEffectiveCleanThrough; + let integrationGap = null; + if (mirroredBundle && !remoteBundleFreshEnough) { + integrationGap = `Remote GPU bundle is stale for canonical promotion (${remoteKnownFailurePacketCount} known packets vs local ${localSharedPrefixCount}).`; + } else if (mirroredBundle && !remoteBundleDeepEnough) { + integrationGap = `Remote GPU bundle is shallower than the canonical bridge (${remoteBestEffectiveCleanThrough} clean-through vs local ${localBestEffectiveCleanThrough}).`; + } + const searchCompleted = execution.ok && (mirroredBundle?.ok ?? true); + const partial = searchCompleted && Boolean(integrationGap); + const bridgeRefresh = execution.ok && !integrationGap ? refreshNumberTheoryBridge(problem) : null; + const ok = searchCompleted && !integrationGap && (bridgeRefresh?.ok ?? true); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok, + partial, + commandLine: executionSpec.commandLine ?? action.commandLine, + stdout: [execution.stdout, bridgeRefresh?.commandOutput].filter(Boolean).join('\n'), + stderr: execution.stderr ?? mirroredBundle?.error ?? integrationGap ?? bridgeRefresh?.error ?? null, + executionMode: action.mode, + remoteSync, + remoteBundleDir, + mirroredBundle, + integrationGap, + bridgeRefresh, + profileOverride: options.profileOverride ?? null, + }, workspaceRoot); + return { + ok, + partial, + dispatch, + action, + remoteSync, + execution, + mirroredBundle, + integrationGap, + bridgeRefresh, + runBundle, + }; + } + + if (action.actionId === 'exact_interval_scout') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const resultsPath = path.join(runDir, 'EXACT_SMALL_N_RESULTS.json'); + const args = [ + action.scriptPath, + '--min', + String(action.min), + '--max', + String(action.max), + ...(action.endpointMonotonicity ? ['--endpoint-monotonicity'] : []), + '--json-output', + resultsPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const results = readJsonIfPresent(resultsPath); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: execution.ok, + commandLine: formatCommandLine('node', args), + stdout: execution.stdout, + stderr: execution.stderr, + resultsPath, + resultsSummary: results?.summary ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: execution.ok, + dispatch, + action, + execution, + results, + runBundle, + }; + } + + if (action.actionId === 'exact_handoff_bundle') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + const handoffResult = buildP848ExactHandoffBundle(problem, action, dispatch, runDir); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: handoffResult.ok, + commandLine: action.commandLine, + stdout: handoffResult.ok ? `exact_handoff_dir: ${handoffResult.handoffDir}` : null, + stderr: handoffResult.ok ? null : handoffResult.error, + handoff: handoffResult.handoff ?? null, + handoffDir: handoffResult.handoffDir ?? null, + handoffJsonPath: handoffResult.handoffJsonPath ?? null, + handoffMarkdownPath: handoffResult.handoffMarkdownPath ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: handoffResult.ok, + dispatch, + action, + handoff: handoffResult, + runBundle, + }; + } + + if (action.actionId === 'exact_followup_launch') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + + const handoffResult = buildP848ExactHandoffBundle(problem, action, dispatch, runDir); + if (!handoffResult.ok) { + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: false, + commandLine: action.commandLine, + stdout: null, + stderr: handoffResult.error, + handoff: null, + }, workspaceRoot, { runId, runDir }); + return { + ok: false, + dispatch, + action, + handoff: handoffResult, + runBundle, + }; + } + + const followupDir = path.join(runDir, 'exact-followup'); + ensureDir(followupDir); + const resultsPath = path.join(followupDir, 'EXACT_SMALL_N_RESULTS.json'); + const args = [ + action.scriptPath, + '--min', + String(action.min), + '--max', + String(action.max), + ...(action.endpointMonotonicity ? ['--endpoint-monotonicity'] : []), + '--json-output', + resultsPath, + ]; + const execution = executeExternalCommand('node', args, repoRoot); + const results = readJsonIfPresent(resultsPath); + const followupPacket = buildP848ExactFollowupPacket( + problem, + action, + dispatch, + handoffResult, + results, + execution, + runDir, + resultsPath, + ); + const exactPromotion = handoffResult.ok && execution.ok && followupPacket.ok + ? promoteP848ExactCoverage(workspaceRoot) + : null; + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: handoffResult.ok && execution.ok && followupPacket.ok && (exactPromotion?.ok ?? true), + commandLine: action.commandLine, + stdout: [execution.stdout, `exact_handoff_dir: ${handoffResult.handoffDir}`].filter(Boolean).join('\n'), + stderr: execution.stderr ?? exactPromotion?.error ?? null, + handoffDir: handoffResult.handoffDir ?? null, + handoffJsonPath: handoffResult.handoffJsonPath ?? null, + handoffMarkdownPath: handoffResult.handoffMarkdownPath ?? null, + exactFollowupDir: followupPacket.followupDir ?? null, + exactFollowupJsonPath: followupPacket.followupJsonPath ?? null, + exactFollowupMarkdownPath: followupPacket.followupMarkdownPath ?? null, + resultsPath, + resultsSummary: results?.summary ?? null, + exactPromotion, + }, workspaceRoot, { runId, runDir }); + return { + ok: handoffResult.ok && execution.ok && followupPacket.ok && (exactPromotion?.ok ?? true), + dispatch, + action, + handoff: handoffResult, + execution, + results, + exactFollowup: followupPacket, + exactPromotion, + runBundle, + }; + } + + if (action.actionId === 'exact_followup_rollout') { + const runId = `${new Date().toISOString().replaceAll(':', '-')}__number_theory_p${problem.problemId}__${action.actionId}`; + const runDir = getWorkspaceRunDir(runId, workspaceRoot); + ensureDir(runDir); + + const childRuns = []; + let encounteredError = null; + for (const interval of action.rolloutIntervals ?? []) { + const childResult = runNumberTheoryDispatch(problem, { + actionId: 'exact_followup_launch', + exactMin: interval.min, + exactMax: interval.max, + endpointMonotonicity: action.endpointMonotonicity, + }, workspaceRoot); + childRuns.push({ + index: interval.index, + interval: interval.interval, + min: interval.min, + max: interval.max, + ok: Boolean(childResult.ok), + runId: childResult.runBundle?.runId ?? null, + runDir: childResult.runBundle?.runDir ?? null, + resultsSummary: childResult.results?.summary ?? null, + exactPromotion: childResult.exactPromotion ?? null, + error: childResult.error ?? childResult.execution?.stderr ?? null, + }); + if (!childResult.ok) { + encounteredError = childResult.error ?? `Exact rollout failed on chunk ${interval.interval}.`; + break; + } + } + + const completedChunkCount = childRuns.filter((childRun) => childRun.ok).length; + const bridgeRefresh = completedChunkCount > 0 + ? refreshNumberTheoryBridge(problem, workspaceRoot) + : null; + const rollout = buildP848ExactRolloutPacket(problem, action, dispatch, childRuns, bridgeRefresh, runDir); + const runBundle = writeDispatchRunBundle(problem, dispatch, action, { + ok: !encounteredError && (bridgeRefresh?.ok ?? true), + commandLine: action.commandLine, + stdout: [ + ...childRuns + .filter((childRun) => childRun.ok) + .map((childRun) => `chunk ${childRun.index}: ${childRun.interval} (${childRun.runId ?? 'no-run-id'})`), + bridgeRefresh?.commandOutput, + ].filter(Boolean).join('\n'), + stderr: encounteredError ?? bridgeRefresh?.error ?? null, + rolloutDir: rollout.rolloutDir ?? null, + rolloutJsonPath: rollout.rolloutJsonPath ?? null, + rolloutMarkdownPath: rollout.rolloutMarkdownPath ?? null, + completedChunkCount, + requestedChunkCount: action.chunkCount ?? null, + childRuns, + bridgeRefresh, + rollout: rollout.packet ?? null, + }, workspaceRoot, { runId, runDir }); + return { + ok: !encounteredError && (bridgeRefresh?.ok ?? true), + partial: Boolean(encounteredError && completedChunkCount > 0), + dispatch, + action, + rollout, + childRuns, + completedChunkCount, + requestedChunkCount: action.chunkCount ?? null, + bridgeRefresh, + runBundle, + error: encounteredError ?? bridgeRefresh?.error ?? null, + }; + } + + return { + ok: false, + dispatch, + action, + error: `Unhandled dispatch action: ${action.actionId}`, + }; +} + +export function refreshNumberTheoryBridge(problem, workspaceRoot = getWorkspaceRoot()) { + const exactPromotion = String(problem?.problemId ?? '') === '848' + ? promoteP848ExactCoverage(workspaceRoot) + : null; + const refreshSpec = getSearchTheoremBridgeRefreshSpec(problem.problemId); + if (!refreshSpec) { + return { + ok: false, + problemId: problem.problemId, + error: `No bridge refresh command is registered for problem ${problem.problemId}.`, + }; + } + + try { + const stdout = execFileSync(refreshSpec.executable, refreshSpec.args, { + cwd: repoRoot, + encoding: 'utf8', + stdio: ['ignore', 'pipe', 'pipe'], + }).trim(); + + return { + ok: true, + refreshedAt: new Date().toISOString(), + refreshCommand: getSearchTheoremBridgeRefreshCommand(problem.problemId), + engineCommand: refreshSpec.engineCommand, + executionMode: refreshSpec.executionMode, + executionSource: refreshSpec.executionSource, + executionReason: refreshSpec.executionReason, + resolvedCommand: refreshSpec.resolvedCommand, + commandOutput: stdout || null, + exactPromotion, + bridge: getNumberTheoryBridgeSnapshot(problem), + }; + } catch (error) { + return { + ok: false, + refreshedAt: new Date().toISOString(), + refreshCommand: getSearchTheoremBridgeRefreshCommand(problem.problemId), + engineCommand: refreshSpec.engineCommand, + executionMode: refreshSpec.executionMode, + executionSource: refreshSpec.executionSource, + executionReason: refreshSpec.executionReason, + resolvedCommand: refreshSpec.resolvedCommand, + error: error?.stderr?.toString().trim() || error?.stdout?.toString().trim() || error?.message || 'Bridge refresh failed.', + exactPromotion, + bridge: getNumberTheoryBridgeSnapshot(problem), + }; + } +} + export function getNumberTheoryRouteSnapshot(problem, routeId) { const snapshot = buildNumberTheoryStatusSnapshot(problem); const routeDetail = findRouteDetail(snapshot.opsDetails, routeId); diff --git a/src/runtime/preflight.js b/src/runtime/preflight.js index 17b42d6..49a3704 100644 --- a/src/runtime/preflight.js +++ b/src/runtime/preflight.js @@ -16,7 +16,11 @@ import { } from './paths.js'; import { getProblemArtifactInventory } from './problem-artifacts.js'; import { getOrpStatus } from './orp.js'; +import { buildResearchStackSummary } from './research-stack.js'; import { syncState } from './state.js'; +import { buildGraphTheoryStatusSnapshot } from './graph-theory.js'; +import { buildNumberTheoryStatusSnapshot } from './number-theory.js'; +import { buildSunflowerStatusSnapshot } from './sunflower.js'; function checkpointPath(workspaceRoot) { return getWorkspaceCheckpointIndexPath(workspaceRoot); @@ -30,6 +34,18 @@ export function buildPreflightReport(options = {}, workspaceRoot = getWorkspaceR const inventory = problem ? getProblemArtifactInventory(problem) : null; const orp = getOrpStatus(workspaceRoot); const git = gitSummary(workspaceRoot); + const clusterSnapshot = !problem + ? null + : problem.cluster === 'sunflower' + ? buildSunflowerStatusSnapshot(problem) + : problem.cluster === 'number-theory' + ? buildNumberTheoryStatusSnapshot(problem) + : problem.cluster === 'graph-theory' + ? buildGraphTheoryStatusSnapshot(problem) + : null; + const researchStack = problem && inventory + ? buildResearchStackSummary(problem, inventory, orp, clusterSnapshot) + : null; const checks = { erdosRuntime: { @@ -111,6 +127,7 @@ export function buildPreflightReport(options = {}, workspaceRoot = getWorkspaceR activeAgent: config.preferredAgent, currentFrontier: state.currentFrontier, nextHonestMove: state.nextHonestMove, + researchStack, checks, }; diff --git a/src/runtime/problem-artifacts.js b/src/runtime/problem-artifacts.js index 1db74a1..43d9226 100644 --- a/src/runtime/problem-artifacts.js +++ b/src/runtime/problem-artifacts.js @@ -75,12 +75,12 @@ export function getProblemArtifactInventory(problem) { const snapshot = loadActiveUpstreamSnapshot(); const upstreamRecord = snapshot?.index?.by_number?.[problem.problemId] ?? null; const canonicalArtifacts = DOSSIER_FILES.map(([label, key, destinationName]) => { - const filePath = problem[key]; + const filePath = problem[key] ?? path.join(problem.problemDir, label); return { label, path: filePath, destinationName, - exists: fs.existsSync(filePath), + exists: Boolean(filePath) && fs.existsSync(filePath), }; }); const starterArtifacts = STARTER_LOOP_FILES.map(([label, destinationName]) => { diff --git a/src/runtime/state.js b/src/runtime/state.js index f6c2c19..25b127f 100644 --- a/src/runtime/state.js +++ b/src/runtime/state.js @@ -38,6 +38,7 @@ function defaultState(config, workspaceRoot) { checkpointFocus: null, nextHonestMove: 'Select or bootstrap an Erdős problem to begin.', packArtifacts: null, + frontierLoop: null, activeTicketId: null, activeAtomId: null, lastCheckpointSyncAt: null, @@ -113,6 +114,16 @@ function renderStateMarkdown(state) { - Checkpoint Template: ${state.packArtifacts?.checkpointTemplatePath || '(none)'} - Report Template: ${state.packArtifacts?.reportTemplatePath || '(none)'} +## Frontier Loop + +- Suggested: ${state.frontierLoop?.suggested ? 'yes' : 'no'} +- Mode: ${state.frontierLoop?.mode || '(inactive)'} +- Summary: ${state.frontierLoop?.summary || '(none)'} +- Entry Command: ${state.frontierLoop?.primaryCommand || '(none)'} +- Refresh Command: ${state.frontierLoop?.refreshCommand || '(none)'} +- Activation Command: ${state.frontierLoop?.activationCommand || '(none)'} +- GPU Upgrade Command: ${state.frontierLoop?.upgradeCommand || '(none)'} + ## Next Honest Move - ${state.nextHonestMove} @@ -244,6 +255,7 @@ function deriveProblemSummary(problem) { checkpointTemplatePath: snapshot.checkpointTemplatePath, reportTemplatePath: snapshot.reportTemplatePath, }, + frontierLoop: snapshot.frontierLoop, activeTicketId: snapshot.activeTicketDetail?.ticket_id ?? null, activeAtomId: snapshot.firstReadyAtom?.atom_id ?? null, questionLedger: snapshot.questionLedger, @@ -362,6 +374,7 @@ export function syncState(workspaceRoot = getWorkspaceRoot()) { checkpointFocus: summary.checkpointFocus, nextHonestMove: summary.nextHonestMove, packArtifacts: summary.packArtifacts, + frontierLoop: summary.frontierLoop, activeTicketId: summary.activeTicketId, activeAtomId: summary.activeAtomId, lastCheckpointSyncAt: existing.lastCheckpointSyncAt ?? null, diff --git a/src/runtime/sunflower.js b/src/runtime/sunflower.js index ece3421..b96bac8 100644 --- a/src/runtime/sunflower.js +++ b/src/runtime/sunflower.js @@ -9,6 +9,14 @@ import { getWorkspaceComputeRegistryDir, getWorkspaceRunDir, } from './paths.js'; +import { + getProblemClaimLoopSnapshot, + getProblemClaimPassSnapshot, + getProblemFormalizationSnapshot, + getProblemFormalizationWorkSnapshot, + getProblemTaskListSnapshot, + getProblemTheoremLoopSnapshot, +} from './theorem-loop.js'; const CLAIM_LEVEL_PRIORITY = { Exact: 4, @@ -632,6 +640,12 @@ export function buildSunflowerStatusSnapshot(problem) { const routeHistoryPath = getSunflowerRouteHistoryPath(problem.problemId); const checkpointTemplatePath = getSunflowerCheckpointTemplatePath(problem.problemId); const reportTemplatePath = getSunflowerReportTemplatePath(problem.problemId); + const theoremLoop = getProblemTheoremLoopSnapshot(problem); + const claimLoop = getProblemClaimLoopSnapshot(problem); + const claimPass = getProblemClaimPassSnapshot(problem); + const formalization = getProblemFormalizationSnapshot(problem); + const formalizationWork = getProblemFormalizationWorkSnapshot(problem); + const taskList = getProblemTaskListSnapshot(problem); const firstReadyAtom = atomicBoard?.readyQueue?.[0] ?? null; const activeRouteDetail = findRouteDetail(opsDetails, routeState.activeRoute ?? atomicBoard?.activeRoute); @@ -685,6 +699,12 @@ export function buildSunflowerStatusSnapshot(problem) { frontierNotePath: fs.existsSync(frontierNotePath) ? frontierNotePath : null, routeHistoryPresent: fs.existsSync(routeHistoryPath), routeHistoryPath: fs.existsSync(routeHistoryPath) ? routeHistoryPath : null, + theoremLoop, + claimLoop, + claimPass, + formalization, + formalizationWork, + taskList, checkpointTemplatePresent: fs.existsSync(checkpointTemplatePath), checkpointTemplatePath: fs.existsSync(checkpointTemplatePath) ? checkpointTemplatePath : null, reportTemplatePresent: fs.existsSync(reportTemplatePath), diff --git a/test/cli.test.js b/test/cli.test.js index bee1cdf..5ce4406 100644 --- a/test/cli.test.js +++ b/test/cli.test.js @@ -4,13 +4,16 @@ import { execFileSync } from 'node:child_process'; import fs from 'node:fs'; import os from 'node:os'; import path from 'node:path'; +import { getFrontierResearchModesForSnapshot } from '../src/runtime/frontier.js'; const cli = '/Volumes/Code_2TB/code/erdos-problems/src/cli/index.js'; +const repoRoot = path.dirname(path.dirname(path.dirname(cli))); function runCli(args, options = {}) { return execFileSync('node', [cli, ...args], { encoding: 'utf8', cwd: options.cwd, + maxBuffer: options.maxBuffer ?? 128 * 1024 * 1024, }); } @@ -93,6 +96,1900 @@ test('problem artifacts can emit json for agents with pack context and compute p assert.equal(payload.computePackets[0].label, 'm8_exactness_cube_and_certificate_v0'); }); +test('problem artifacts include the search/theorem bridge for 848', () => { + const output = runCli(['problem', 'artifacts', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal( + payload.packProblemArtifacts.some((artifact) => artifact.relativePath === 'SEARCH_THEOREM_BRIDGE.md'), + true, + ); + assert.equal( + payload.packProblemArtifacts.some((artifact) => artifact.relativePath === 'SEARCH_THEOREM_BRIDGE.json'), + true, + ); +}); + +test('problem theorem-loop exposes the bridge-backed theorem surface for 848', () => { + const output = runCli(['problem', 'theorem-loop', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.theoremLoopMode, 'bridge_backed'); + assert.equal(payload.sourceKind, 'search_theorem_bridge'); + assert.equal(Array.isArray(payload.theoremHooks), true); + assert.equal(payload.theoremHooks.length > 0, true); + assert.equal(Array.isArray(payload.theoremAgenda), true); + assert.equal(payload.theoremAgenda.length > 0, true); + assert.equal(payload.theoremAgenda.some((item) => item.item_id === 'explain_next_unmatched_alignment'), true); + assert.equal(payload.commands.sourceRefresh, 'erdos number-theory bridge-refresh 848'); +}); + +test('problem claim-loop exposes the generalized bridge-backed claim surface for 848', () => { + const output = runCli(['problem', 'claim-loop', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.claimLoopMode, 'bridge_backed'); + assert.equal(payload.sourceKind, 'theorem_loop_plus_bridge'); + assert.equal(Array.isArray(payload.featureExtractors), true); + assert.equal(payload.featureExtractors.some((item) => item.extractor_id === 'search_theorem_bridge_state'), true); + assert.equal(Array.isArray(payload.claimGenerators), true); + assert.equal(payload.claimGenerators.some((item) => item.generator_id === 'p848_repair_obstruction_claims'), true); + assert.equal(Array.isArray(payload.claimFalsifiers), true); + assert.equal(payload.claimFalsifiers.some((item) => item.falsifier_id === 'exact_interval_counterexample_scan'), true); + assert.equal(Array.isArray(payload.verifierAdapters), true); + assert.equal(payload.verifierAdapters.some((item) => item.adapter_id === 'p848_family_repair_surface'), true); + assert.equal(Array.isArray(payload.candidateClaims), true); + assert.equal(payload.candidateClaims.some((item) => item.claim_id === 'p848_next_unmatched_alignment_claim'), true); +}); + +test('problem theorem-loop exposes a baseline theorem surface for number-theory starter problem 1', () => { + const output = runCli(['problem', 'theorem-loop', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '1'); + assert.equal(payload.theoremLoopMode, 'baseline'); + assert.equal(payload.sourceKind, 'pack_route_state'); + assert.equal(payload.currentState.currentClaimSurface, 'route_scaffolding'); + assert.equal(Array.isArray(payload.theoremHooks), true); + assert.equal(payload.theoremHooks.length > 0, true); + assert.equal(Array.isArray(payload.theoremAgenda), true); + assert.equal(payload.theoremAgenda.length > 0, true); + assert.equal(payload.theoremAgenda.some((item) => item.item_id === 'promote_ready_atom'), true); +}); + +test('problem claim-loop exposes a generalized baseline claim surface for number-theory starter problem 1', () => { + const output = runCli(['problem', 'claim-loop', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '1'); + assert.equal(payload.claimLoopMode, 'baseline'); + assert.equal(payload.sourceKind, 'theorem_loop_only'); + assert.equal(Array.isArray(payload.featureExtractors), true); + assert.equal(payload.featureExtractors.some((item) => item.extractor_id === 'pack_route_state'), true); + assert.equal(Array.isArray(payload.claimGenerators), true); + assert.equal(payload.claimGenerators.some((item) => item.generator_id === 'baseline_route_claims'), true); + assert.equal(Array.isArray(payload.claimFalsifiers), true); + assert.equal(payload.claimFalsifiers.some((item) => item.falsifier_id === 'artifact_boundary_check'), true); + assert.equal(Array.isArray(payload.verifierAdapters), true); + assert.equal(payload.verifierAdapters.some((item) => item.adapter_id === 'canonical_artifact_reader'), true); +}); + +test('problem claim-loop-refresh writes canonical claim-loop artifacts', () => { + const output = runCli(['problem', 'claim-loop-refresh', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '1'); + assert.match(payload.jsonPath, /packs\/number-theory\/problems\/1\/CLAIM_LOOP\.json$/); + assert.match(payload.markdownPath, /packs\/number-theory\/problems\/1\/CLAIM_LOOP\.md$/); + assert.equal(fs.existsSync(payload.jsonPath), true); + assert.equal(fs.existsSync(payload.markdownPath), true); +}); + +test('problem claim-pass exposes the bridge-backed verdict surface for 848', () => { + const output = runCli(['problem', 'claim-pass', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.claimPassMode, 'bridge_backed'); + assert.equal(payload.sourceKind, 'claim_loop_plus_bridge'); + assert.equal(Array.isArray(payload.hookAssessments), true); + assert.equal(payload.hookAssessments.some((item) => item.hook_id === 'next_unmatched_equals_282_failure' && item.verdict === 'supported'), true); + assert.equal(Array.isArray(payload.claimAssessments), true); + assert.equal(payload.claimAssessments.some((item) => item.claim_id === 'p848_next_unmatched_alignment_claim' && item.verdict === 'supported'), true); + assert.equal(payload.claimAssessments.some((item) => item.claim_id === 'choose_next_finite_gap_move' && item.verdict === 'actionable'), true); + assert.equal(Array.isArray(payload.recommendations), true); + assert.equal(payload.recommendations.some((item) => item.recommendation_id === 'formalize_282_alignment'), true); +}); + +test('problem claim-pass exposes a generalized baseline verdict surface for number-theory starter problem 1', () => { + const output = runCli(['problem', 'claim-pass', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '1'); + assert.equal(payload.claimPassMode, 'baseline'); + assert.equal(payload.sourceKind, 'claim_loop_only'); + assert.equal(Array.isArray(payload.hookAssessments), true); + assert.equal(payload.hookAssessments.some((item) => item.hook_id === 'active_route_recorded' && item.verdict === 'supported'), true); + assert.equal(Array.isArray(payload.claimAssessments), true); + assert.equal(payload.claimAssessments.some((item) => item.claim_id === 'promote_ready_atom' && item.verdict === 'actionable'), true); +}); + +test('problem claim-pass-refresh writes canonical claim-pass artifacts', () => { + const output = runCli(['problem', 'claim-pass-refresh', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '1'); + assert.match(payload.jsonPath, /packs\/number-theory\/problems\/1\/CLAIM_PASS\.json$/); + assert.match(payload.markdownPath, /packs\/number-theory\/problems\/1\/CLAIM_PASS\.md$/); + assert.equal(fs.existsSync(payload.jsonPath), true); + assert.equal(fs.existsSync(payload.markdownPath), true); +}); + +test('problem formalization exposes the bridge-backed theorem packet for 848', () => { + const output = runCli(['problem', 'formalization', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.formalizationMode, 'bridge_backed'); + assert.equal(payload.sourceKind, 'claim_pass_plus_bridge'); + assert.equal(payload.currentTarget.focusId, 'formalize_282_alignment'); + assert.match(payload.currentTarget.statement, /137720141/); + assert.match(payload.currentTarget.statement, /282/); + assert.match(payload.currentTarget.statement, /Checked finite-menu statement/); + assert.equal(Array.isArray(payload.currentTarget.proofObligations), true); + assert.equal(payload.currentTarget.proofObligations.some((item) => item.obligationId === 'define_shared_prefix_obstruction_class'), true); + assert.equal(payload.currentTarget.proofObligations.some((item) => item.obligationId === 'explain_282_first_failure_mechanism' && item.status === 'done'), true); + assert.equal(payload.currentTarget.proofObligations.some((item) => item.obligationId === 'lift_132_activation_schema_beyond_finite_menu' && item.status === 'ready'), true); + assert.equal(payload.currentTarget.promotionCriteria.some((item) => item.criterionId === 'finite_menu_mechanism_checked' && item.status === 'done'), true); + assert.equal(payload.currentTarget.evidenceBasis.some((item) => item.includes('p848_132_activation_row_certificate_checker_v1')), true); + assert.equal(Array.isArray(payload.currentTarget.falsifierChecks), true); + assert.equal(payload.currentTarget.falsifierChecks.some((item) => item.checkId === 'bridge_next_unmatched_stability'), true); +}); + +test('problem formalization-refresh writes canonical formalization artifacts', () => { + const output = runCli(['problem', 'formalization-refresh', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '1'); + assert.match(payload.jsonPath, /packs\/number-theory\/problems\/1\/FORMALIZATION\.json$/); + assert.match(payload.markdownPath, /packs\/number-theory\/problems\/1\/FORMALIZATION\.md$/); + assert.equal(fs.existsSync(payload.jsonPath), true); + assert.equal(fs.existsSync(payload.markdownPath), true); +}); + +test('problem formalization-work exposes the bridge-backed theorem work packet for 848', () => { + const output = runCli(['problem', 'formalization-work', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.formalizationWorkMode, 'bridge_backed'); + assert.match(payload.formalizationWorkSvgPath, /packs\/number-theory\/problems\/848\/FORMALIZATION_WORK\.svg$/); + assert.equal(payload.formalizationWorkSvgPresent, true); + assert.equal(payload.currentWork.focusId, 'lift_132_activation_schema_beyond_finite_menu'); + assert.equal(payload.currentWork.packetData.representative, 137720141); + assert.equal(payload.currentWork.packetData.tupleKey, '4, 23^2, 7^2, 9, 17^2, 11^2'); + assert.equal(payload.currentWork.packetData.tupleRowCrtDerivation.combinedResidue, 137720141); + assert.equal(payload.currentWork.packetData.tupleRowCrtDerivation.combinedModulus, 32631532164); + assert.equal(payload.currentWork.packetData.tupleRowCrtDerivation.projectedResidueModuloWitness, 504); + assert.equal(payload.currentWork.packetData.tupleRowCrtDerivation.firstStableProjectionAnchor, 132); + assert.equal(payload.currentWork.packetData.tupleRowCrtDerivation.steps.some((step) => step.anchor === 132 && step.residueModWitness === 504), true); + assert.equal(Array.isArray(payload.currentWork.packetData.tupleRowActivationSequence), true); + assert.equal(payload.currentWork.packetData.tupleRowActivationSequence.some((step) => step.anchor === 82 && step.matchingTrackedAnchors.length === 0), true); + assert.equal(payload.currentWork.packetData.tupleRowActivationSequence.some((step) => step.anchor === 132 && step.uniqueTrackedMatch === 282), true); + assert.equal(payload.currentWork.packetData.tupleRowActivationBoundary.pre132HasNoTrackedMatch, true); + assert.equal(payload.currentWork.packetData.tupleRowActivationBoundary.activationIsUnique282, true); + assert.equal(payload.currentWork.packetData.tupleRowActivationBoundary.preservationKeepsUnique282, true); + assert.equal(payload.currentWork.packetData.menuActivationSurvey.rowsWith132TargetActivationCount, 17); + assert.equal(payload.currentWork.packetData.menuActivationSurvey.targetActivationRows.length, 17); + assert.equal(payload.currentWork.packetData.menuActivationSurvey.rowsWith132TargetActivationByFailingAnchor['282'], 1); + assert.equal(payload.currentWork.packetData.menuActivationSurvey.rowsWith132TargetActivationByWitness['841'], 1); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.schemaId, 'p848_finite_menu_132_target_activation_schema_v1'); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.scope.certifiedRowCount, 17); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.scope.universalClaim, false); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.hypotheses.length, 6); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.falsifierBoundary.length, 5); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.rowCertificates.length, 17); + assert.equal(payload.currentWork.packetData.activationLemmaSchema.currentBoundaryInstance.activationBoundary.activationIsUnique282, true); + assert.equal(payload.currentWork.packetData.activationLemmaCheck.status, 'passed'); + assert.equal(payload.currentWork.packetData.activationLemmaCheck.checkedRowCount, 17); + assert.equal(payload.currentWork.packetData.activationLemmaCheck.failCount, 0); + assert.equal(payload.currentWork.packetData.tupleRowLift132Proof.status, 'proved_from_tuple_row_crt'); + assert.equal(payload.currentWork.packetData.tupleRowLift132Proof.liftParameter, 147); + assert.equal(payload.currentWork.packetData.tupleRowLift132Proof.liftedResidueModuloWitness, 504); + assert.equal(payload.currentWork.packetData.tupleRowLift132Proof.failCount, 0); + assert.equal(payload.currentWork.packetData.activationSchemaLiftDecision.verdict, 'finite_menu_certificate_not_universal_yet'); + assert.equal(payload.currentWork.packetData.activationSchemaLiftDecision.nextTheoremPass, 'formalize_top_repair_class_mechanism'); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.status, 'symbolic_crt_hypothesis_packet_ready'); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.checkedRowCount, 17); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.failCount, 0); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.scope.universalClaim, false); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.symbolicHypotheses.length, 6); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.symbolicHypotheses.some((row) => row.hypothesisId === 'S4_anchor_132_unique_target'), true); + assert.equal(payload.currentWork.packetData.activationSymbolicLiftCandidate.finiteEvidence.rowSummaries.some((row) => row.failingAnchor === 282 && row.residueAt132 === 504), true); + assert.equal(payload.currentWork.packetData.activationDomainClosureAssessment.status, 'broad_domain_closure_not_supported_yet'); + assert.equal(payload.currentWork.packetData.activationDomainClosureAssessment.broadClosureVerdict.failingAnchorCounts['832'], 3); + assert.equal(payload.currentWork.packetData.activationDomainClosureAssessment.broadClosureVerdict.witnessCounts['529'], 4); + assert.equal(payload.currentWork.packetData.activationDomainClosureAssessment.recommendedClosureLane.targetGroupId, 'anchor_832_witness_529'); + assert.equal(payload.currentWork.packetData.activationDomainClosureAssessment.narrowedClosureCandidates.some((row) => row.candidateId === 'p848_782_1232_strict_exchange_closure'), true); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.status, 'finite_group_closure_certified_symbolic_domain_split'); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.checkedRowCount, 3); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.failCount, 0); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.targetFailureResidue, 316); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.symbolicDomainDecision.verdict, 'single_profile_symbolic_domain_falsified_by_profile_split'); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.profileGroups.length, 2); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.recommendedSuccessor.targetProfileId, 'pre132_7_1_32_224_57_229_82_412'); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.zeroLiftPreservation.allRowsAnchor182ZeroLift, true); + assert.equal(payload.currentWork.packetData.anchorWitnessDomainClosurePacket.rowProofs.every((row) => row.status === 'passed' && row.anchor182LiftParameter === 0), true); + assert.equal(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.status, 'finite_profile_sublane_resolved_as_zero_lift_duplicate'); + assert.equal(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.checkedRowCount, 2); + assert.equal(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.failCount, 0); + assert.equal(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.symbolicDomainDecision.verdict, 'profile_sublane_not_a_new_symbolic_family'); + assert.deepEqual(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.familyIndices, [270, 271]); + assert.equal(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.checks.sameTuplePrefixThrough132, true); + assert.equal(payload.currentWork.packetData.anchorWitnessProfileSublanePacket.checks.anchor182ZeroLiftForEveryRow, true); + assert.deepEqual(payload.currentWork.packetData.topRepairClassMechanism.tieClass, [432, 782, 832]); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.sharedMetrics.repairedKnownPackets, 26); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.sharedMetrics.repairedPredictedFamilies, 242); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.sharedMetrics.sameRepairedPredictedFamilies, true); + assert.deepEqual(payload.currentWork.packetData.topRepairClassMechanism.nearestContrasts.map((row) => row.continuation).slice(0, 3), [332, 382, 1232]); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.commonMissedPredictedRepresentatives.includes(210290957), true); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.commonMissedPredictedRepresentatives.includes(1229502607), true); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.status, 'finite_menu_plus2_replay_certified'); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.predictedFamilyCount, 255); + assert.deepEqual(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.topTieCounts.map((row) => row.repairedPredictedFamilyCount), [242, 242, 242]); + assert.deepEqual(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.primaryContrastCounts.map((row) => row.repairedPredictedFamilyCount), [240, 240, 240]); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.topTieSharedMissedPredictedRows.length, 9); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.pairwiseDeltas.length, 9); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.pairwiseDeltas.every((row) => row.netExtraRepairsForTop === 2), true); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.verifiedAgainstBridge.allPairwiseNetPlus2, true); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.strictDominancePairs.some((row) => row.topContinuation === 782 && row.contrastContinuation === 1232 && row.repairedByTopMissedByContrast.length === 2), true); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.mod50LaneSignature.status, 'finite_menu_mod50_lane_signature_certified'); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.mod50LaneSignature.checkedRowCount, 74); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.mod50LaneSignature.failCount, 0); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.mod50LaneSignature.continuationLaneIndices['782'], 15); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.mod50LaneSignature.continuationLaneIndices['1232'], 24); + assert.equal(payload.currentWork.packetData.topRepairClassMechanism.separationAnalysis.mod50LaneSignature.strictDominanceRows.length, 2); + assert.equal(payload.currentWork.packetData.mod50LaneSymbolicSchema.status, 'symbolic_bad_lane_schema_ready'); + assert.equal(payload.currentWork.packetData.mod50LaneSymbolicSchema.checkedRowCount, 74); + assert.equal(payload.currentWork.packetData.mod50LaneSymbolicSchema.failCount, 0); + assert.equal(payload.currentWork.packetData.mod50LaneSymbolicSchema.scope.universalDivisibilityClaim, true); + assert.equal(payload.currentWork.packetData.mod50LaneSymbolicSchema.scope.universalSquarefreeRepairClaim, false); + assert.equal(payload.currentWork.packetData.mod50LaneSymbolicSchema.strict782Vs1232Instances.length, 2); + assert.equal(payload.currentWork.packetData.strict7821232HandoffPacket.status, 'finite_strict_handoff_certified_not_gap_closure'); + assert.equal(payload.currentWork.packetData.strict7821232HandoffPacket.checkedRowCount, 2); + assert.equal(payload.currentWork.packetData.strict7821232HandoffPacket.failCount, 0); + assert.equal(payload.currentWork.packetData.strict7821232HandoffPacket.netExtraRepairsForTop, 2); + assert.equal(payload.currentWork.packetData.strict7821232HandoffPacket.topLaneIndex, 15); + assert.equal(payload.currentWork.packetData.strict7821232HandoffPacket.contrastLaneIndex, 24); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('promoted into lemma schema')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('row certificates replay successfully')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('proved from tuple-row CRT equations')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('activation schema lift decision is explicit')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('symbolic CRT hypothesis packet')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('broad domain-closure overclaim is ruled out')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('anchor_832_witness_529 closure lane has been executed')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('single-profile symbolic closure over anchor_832_witness_529 is falsified')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('lift parameter 0 at anchor 182')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('pre132_7_1_32_224_57_229_82_412 sublane is closed')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('top repair-class mechanism packet')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('finite-menu +2 repaired-predicted-family separation is discharged')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('common missed-family replay is explicit')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('mod-50 lane-index congruences')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('mod-50 bad-lane congruence has been generalized')), true); + assert.equal(payload.currentWork.dischargedWork.some((item) => item.includes('strict 782 > 1232 handoff is connected')), true); + const latestVerifiedMax = Number(payload.currentState.latestVerifiedInterval.split('..')[1]); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.status, 'active'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.canonicalSurface, 'FORMALIZATION_WORK.currentWork'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.requestedActiveAtom.obligationId, 'D2_p13_matching_lower_bound'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C1_same_side_base_clique.status, 'proved_by_mod25_identity'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C1_same_side_base_clique.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C2_two_cliques_plus_cross_edges.status, 'proved_by_c1_partition_decomposition'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C2_two_cliques_plus_cross_edges.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C3_missing_cross_graph_definition.status, 'proved_by_definition'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C3_missing_cross_graph_definition.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C4_clique_to_vertex_cover_duality.status, 'proved_by_clique_vertex_cover_complement'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C4_clique_to_vertex_cover_duality.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C5_konig_matching_reduction.status, 'proved_by_konig_theorem'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C5_konig_matching_reduction.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C6_mixed_clique_matching_formula.status, 'proved_by_vertex_cover_konig_composition'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.C6_mixed_clique_matching_formula.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.status, 'bounded_matching_saturation_extraction_certified'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.scope.boundedRowCount, 1733); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.primeSummaries.some((item) => item.p === 13 && item.minMatchingSlack === 19), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.primeSummaries.some((item) => item.p === 17 && item.minMatchingSlack === 95), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.status, 'bounded_split_core_witness_certified'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.scope.splitProfileCount, 3); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.profileSummary.every((item) => item.commonCoreMeetsMaxRequiredBound), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.profileSummary.every((item) => item.commonMatchingPairExportComplete), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.profileSummary.every((item) => item.commonMatchingPairs.length === item.commonMatchingPairCount), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.proofChecks.some((item) => item.checkId === 'split_common_core_pairs_exported' && item.passed), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.status, 'bounded_split_core_witness_certified'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.failCount, 0); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.scope.splitProfileCount, 2); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.profileSummary.every((item) => item.commonCoreMeetsMaxRequiredBound), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.profileSummary.every((item) => item.commonMatchingPairExportComplete), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.profileSummary.every((item) => item.commonMatchingPairs.length === item.commonMatchingPairCount), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.proofChecks.some((item) => item.checkId === 'split_common_core_pairs_exported' && item.passed), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.candidateId, 'p848_D2_p13_matching_lower_bound_candidate_v1'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.scope.threatRowCount, 1285); + assert.deepEqual(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.extractedTarget.requiredMatchingLowerBoundRange, [26, 90]); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.extractedTarget.minMatchingSlack, 19); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.matchingPatternArtifact.status, 'matching_pattern_witness_packet_ready'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.matchingPatternArtifact.targetPrime, 13); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.matchingPatternArtifacts.some((item) => item.targetPrime === 17 && item.witnessRowCount === 12), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.matchingPatternEvidence.witnessRowCount > 0, true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.matchingPatternEvidence.allReconstructedMatchesAgree, true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.matchingPatternEvidence.allWitnessesSaturateSmallerSide, true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.matchingPatternEvidence.patternSummary.splitProfiles.length > 0, true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.splitCoreWitnessPacket.status, 'bounded_split_core_witness_certified'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtomEvidence.splitCoreWitnessPacket.symbolicSubgoals.length, 3); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'C1_same_side_base_clique'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'C2_two_cliques_plus_cross_edges'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'C3_missing_cross_graph_definition'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'C4_clique_to_vertex_cover_duality'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'C5_konig_matching_reduction'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'C6_mixed_clique_matching_formula'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'D1_residue_block_matching_injection'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'D2_p13_split_core_witness_extraction'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.dischargedAtoms.some((item) => item.obligationId === 'D3_p17_split_core_witness_extraction'), true); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.activeAtom.obligationId, 'D2_p13_matching_lower_bound'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.targetAtom.obligationId, 'D4_matching_bound_implies_sMaxMixed_bound'); + assert.equal(payload.currentWork.packetData.structuralLiftAtomicSurface.referenceBacklog.role, 'non_canonical_reference_backlog'); + assert.equal(payload.currentWork.proofObligations.some((item) => item.obligationId === 'D1_residue_block_matching_injection' && item.status === 'done'), true); + assert.equal(payload.currentWork.proofObligations.some((item) => item.obligationId === 'D2_p13_matching_lower_bound' && item.status === 'in_progress'), true); + assert.equal(payload.currentWork.proofObligations.some((item) => item.obligationId === 'D3_p17_matching_lower_bound' && item.status === 'ready'), true); + assert.equal(payload.currentWork.proofObligations.some((item) => item.obligationId === 'D4_matching_bound_implies_sMaxMixed_bound' && item.status === 'blocked_by_D2_D3'), true); + assert.equal(payload.currentWork.remainingGaps[0].includes('D2_p13_matching_lower_bound'), true); + assert.equal(payload.currentWork.remainingGaps.some((gap) => gap.includes(`post-${latestVerifiedMax} verification lane`)), true); + assert.equal(payload.currentWork.mechanismAssessment.competingHypotheses.some((row) => row.hypothesisId === 'one_off_modular_coincidence' && row.status === 'disfavored_by_menu_survey'), true); + assert.equal(payload.currentWork.packetData.witnessSquareModulus, 841); + assert.equal(payload.currentWork.packetData.representativeResidueModuloWitness, 504); + assert.equal(payload.currentWork.packetData.firstFailingRepresentative, 137720141); + assert.equal(payload.currentWork.packetData.witnessFirstOccurrence.firstRepresentative, 137720141); + assert.equal(payload.currentWork.packetData.witnessFirstOccurrence.earlierZeroResidueCount, 0); + assert.equal(payload.currentWork.mechanismAssessment.verdict, 'controlled_congruence_candidate'); + assert.equal(payload.currentWork.mechanismAssessment.caveats.some((item) => item.includes('row itself traverses all residue classes modulo 841')), true); + assert.equal(payload.currentWork.mechanismAssessment.competingHypotheses.some((row) => row.hypothesisId === 'controlled_congruence_interaction' && row.status === 'favored'), true); + assert.equal(payload.currentWork.mechanismAssessment.competingHypotheses.some((row) => row.hypothesisId === 'shared_prefix_row_alone_forces_841' && row.status === 'not_supported'), true); + assert.equal(Array.isArray(payload.currentWork.packetData.priorRowsModuloWitness), true); + assert.equal(payload.currentWork.packetData.sameTupleCount, 1); + assert.equal(payload.currentWork.packetData.rowProgressionModuloWitness.gcdModulusWitness, 1); + assert.equal(payload.currentWork.packetData.rowProgressionModuloWitness.traversesAllWitnessResidues, true); + assert.equal(payload.currentWork.packetData.anchorCongruenceTable.some((row) => row.anchor === 282 && row.matchesRepresentativeResidue === true && row.requiredNResidueForFailure === 504), true); + assert.equal(payload.currentWork.packetData.rowProgressionAnchorTable.some((row) => row.anchor === 282 && row.rowIndexForWitness === 0 && row.witnessOccursAtCurrentRepresentative === true), true); + assert.equal(payload.currentWork.packetData.rowProgressionAnchorTable.some((row) => row.anchor === 232 && row.rowIndexForWitness === null && row.solvableAlongRowProgression === false), true); + assert.equal(payload.currentWork.packetData.rowProgressionAnchorTable.some((row) => row.anchor === 332 && row.rowIndexForWitness === 67), true); + assert.equal(payload.currentWork.packetData.rowStartDerivation282.normalizedEquation, 't ≡ 0 (mod 841)'); + assert.equal(payload.currentWork.packetData.rowStartDerivation282.representativeAlreadyOnWitnessClass, true); + assert.equal(payload.currentWork.packetData.unsolvableContrast232.solvable, false); + assert.match(payload.currentWork.packetData.unsolvableContrast232.divisibilityFailure, /29 does not divide 811/); + assert.equal(payload.currentWork.packetData.nextSameRowWitnessFor282, 27443256270065); + assert.equal(payload.currentWork.packetData.repairResidues.some((row) => row.anchor === 282 && row.residueModuloWitness === 0 && row.squarefree === false), true); +}); + +test('problem formalization-work-check certifies the 848 activation lemma rows', () => { + const output = runCli(['problem', 'formalization-work-check', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.status, 'passed'); + assert.equal(payload.summary.checkCount, 18); + assert.equal(payload.summary.checkedRowCount, 1984); + assert.equal(payload.summary.failCount, 0); + assert.equal(payload.checks[0].checkerId, 'p848_132_activation_row_certificate_checker_v1'); + assert.equal(payload.checks[0].rowChecks.every((row) => row.status === 'passed'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_132_lift_crt_checker_v1' && check.status === 'proved_from_tuple_row_crt'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_132_activation_symbolic_lift_candidate_checker_v1' && check.status === 'symbolic_crt_hypothesis_packet_ready'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_832_529_anchor_witness_domain_closure_checker_v1' && check.status === 'finite_group_closure_certified_symbolic_domain_split'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_832_529_pre132_profile_sublane_checker_v1' && check.status === 'finite_profile_sublane_resolved_as_zero_lift_duplicate'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_top_repair_plus2_family_menu_replay_checker_v1' && check.status === 'finite_menu_plus2_replay_certified'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_mod50_lane_bad_family_signature_checker_v1' && check.status === 'finite_menu_mod50_lane_signature_certified'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_mod50_bad_lane_symbolic_schema_checker_v1' && check.status === 'symbolic_bad_lane_schema_ready'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_782_1232_strict_handoff_checker_v1' && check.status === 'finite_strict_handoff_certified_not_gap_closure'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_C1_same_side_base_clique_checker_v1' && check.status === 'proved_by_mod25_identity'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_C2_two_cliques_plus_cross_edges_checker_v1' && check.status === 'proved_by_c1_partition_decomposition'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_C3_missing_cross_graph_definition_checker_v1' && check.status === 'proved_by_definition'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_C4_clique_to_vertex_cover_duality_checker_v1' && check.status === 'proved_by_clique_vertex_cover_complement'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_C5_konig_matching_reduction_checker_v1' && check.status === 'proved_by_konig_theorem'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_C6_mixed_clique_matching_formula_checker_v1' && check.status === 'proved_by_vertex_cover_konig_composition'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_D1_matching_saturation_bound_checker_v1' && check.status === 'bounded_matching_saturation_extraction_certified'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_D2_p13_split_core_witness_checker_v1' && check.status === 'bounded_split_core_witness_certified'), true); + assert.equal(payload.checks.some((check) => check.checkerId === 'p848_D3_p17_split_core_witness_checker_v1' && check.status === 'bounded_split_core_witness_certified'), true); +}); + +test('problem formalization-work-refresh writes canonical formalization-work artifacts', () => { + const output = runCli(['problem', 'formalization-work-refresh', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '1'); + assert.match(payload.jsonPath, /packs\/number-theory\/problems\/1\/FORMALIZATION_WORK\.json$/); + assert.match(payload.markdownPath, /packs\/number-theory\/problems\/1\/FORMALIZATION_WORK\.md$/); + assert.match(payload.svgPath, /packs\/number-theory\/problems\/1\/FORMALIZATION_WORK\.svg$/); + assert.equal(fs.existsSync(payload.jsonPath), true); + assert.equal(fs.existsSync(payload.markdownPath), true); + assert.equal(fs.existsSync(payload.svgPath), true); +}); + +test('problem task-list exposes the canonical research loop for 848', () => { + const output = runCli(['problem', 'task-list', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.problemId, '848'); + assert.equal(payload.taskListMode, 'bridge_backed'); + assert.equal(payload.executionRule.stance, 'concrete_execution'); + assert.equal(payload.executionRule.granularBreakdownMode.modeId, 'granular-breakdown'); + assert.match(payload.executionRule.granularBreakdownMode.fullBreakdownCommand, /orp mode breakdown granular-breakdown/); + assert.match(payload.executionRule.granularBreakdownMode.nudgeCommand, /orp mode nudge granular-breakdown/); + assert.equal(payload.granularBreakdownMode.status, 'core_loop_enabled'); + assert.equal(payload.granularBreakdownMode.modeId, 'granular-breakdown'); + assert.match(payload.granularBreakdownMode.commands.fullBreakdown, /--topic/); + assert.match(payload.granularBreakdownMode.commands.fullBreakdown, /D2_p13_matching_lower_bound/); + assert.match(payload.granularBreakdownMode.commands.nudge, /orp mode nudge granular-breakdown --json/); + assert.equal(payload.granularBreakdownMode.outputContract.includes('Atomic Obligations'), true); + assert.equal(payload.orpModeOverlays.status, 'core_loop_palette_enabled'); + assert.equal(payload.orpModeOverlays.defaultModeId, 'granular-breakdown'); + assert.match(payload.orpModeOverlays.selectionRule, /do not run every mode by default/); + assert.equal(payload.orpModeOverlays.sourceCommand, 'orp mode list --json'); + assert.equal(payload.orpModeOverlays.overlays.length, 5); + const overlayModeIds = payload.orpModeOverlays.overlays.map((item) => item.modeId); + assert.equal(overlayModeIds.includes('granular-breakdown'), true); + assert.equal(overlayModeIds.includes('ruthless-simplification'), true); + assert.equal(overlayModeIds.includes('systems-constellation'), true); + assert.equal(overlayModeIds.includes('bold-concept-generation'), true); + assert.equal(overlayModeIds.includes('sleek-minimal-progressive'), true); + assert.equal( + payload.orpModeOverlays.overlays.some((item) => item.modeId === 'systems-constellation' && item.useWhen.includes('frontier-engine')), + true, + ); + assert.equal( + payload.orpModeOverlays.overlays.some((item) => item.modeId === 'bold-concept-generation' && item.loopPlacement.includes('falsifier')), + true, + ); + assert.equal(payload.agentFlow.schema, 'erdos.problem_agent_flow/1'); + assert.equal(payload.agentFlow.status, 'ready'); + assert.equal(payload.agentFlow.audience, 'agent'); + assert.equal(payload.agentFlow.problemId, '848'); + assert.equal( + [ + 'start_singleton_p13_profile', + 'promote_d2_p13_all_n_handoff', + 'attack_d2_p13_row_universe_stratification_lift', + 'prove_d2_p13_slack_dominance_symbolic_lift', + 'prove_d2_p13_non_tight_side_count_slack_floor_lift', + 'attack_weakest_p13_side_count_floor_atom', + 'prove_weakest_p13_structural_margin_atom', + 'prove_weakest_p13_dmax_bound_atom', + 'attack_weakest_p13_dmax_growth_atom', + 'prove_weakest_p13_dmax_q2_progression_atom', + 'prove_weakest_p13_dmax_q3_progression_atom', + 'prove_weakest_p13_dmax_q5_progression_atom', + 'prove_weakest_p13_dmax_q7_progression_atom', + 'prove_weakest_p13_dmax_q11_progression_atom', + 'prove_weakest_p13_dmax_q19_progression_atom', + 'prove_weakest_p13_dmax_q23_progression_atom', + 'prove_weakest_p13_dmax_q31_progression_atom', + 'prove_weakest_p13_dmax_q251_progression_atom', + 'prove_weakest_p13_dmax_tail_recombination_atom', + 'prove_weakest_p13_dmax_tail_q17_progression_atom', + 'prove_weakest_p13_dmax_tail_q19_plus_progression_atom', + 'prove_weakest_p13_dmax_tail_q11_minus_progression_atom', + 'prove_weakest_p13_dmax_tail_q23_plus_progression_atom', + 'prove_weakest_p13_dmax_tail_q31_minus_progression_atom', + 'prove_weakest_p13_dmax_tail_q251_minus_progression_atom', + 'prove_weakest_p13_dmax_tail_q29_progression_atom', + 'prove_weakest_p13_dmax_tail_q37_progression_atom', + 'prove_weakest_p13_dmax_tail_q41_progression_atom', + 'prove_weakest_p13_dmax_tail_q43_progression_atom', + 'prove_weakest_p13_dmax_tail_q47_progression_atom', + 'prove_weakest_p13_dmax_tail_q53_progression_atom', + 'prove_weakest_p13_dmax_tail_q59_progression_atom', + 'prove_weakest_p13_dmax_tail_q61_progression_atom', + 'prove_weakest_p13_dmax_tail_q67_progression_atom', + 'prove_weakest_p13_dmax_tail_q71_progression_atom', + 'prove_weakest_p13_dmax_tail_q73_progression_atom', + 'prove_weakest_p13_dmax_tail_q79_progression_atom', + 'prove_weakest_p13_dmax_tail_q83_progression_atom', + 'prove_weakest_p13_dmax_tail_q89_progression_atom', + 'prove_weakest_p13_dmax_tail_q97_progression_atom', + 'prove_weakest_p13_dmax_tail_q101_progression_atom', + 'prove_weakest_p13_dmax_tail_q103_progression_atom', + 'prove_weakest_p13_dmax_tail_q107_progression_atom', + 'prove_weakest_p13_dmax_tail_q109_progression_atom', + 'prove_weakest_p13_dmax_tail_q113_progression_atom', + 'prove_weakest_p13_dmax_tail_q127_progression_atom', + 'prove_weakest_p13_dmax_tail_q131_progression_atom', + 'prove_weakest_p13_dmax_tail_q137_progression_atom', + 'prove_weakest_p13_dmax_tail_q139_progression_atom', + 'prove_weakest_p13_dmax_tail_q149_progression_atom', + 'prove_weakest_p13_dmax_tail_q151_progression_atom', + 'prove_weakest_p13_dmax_tail_q157_progression_atom', + 'prove_weakest_p13_dmax_tail_q163_progression_atom', + 'prove_weakest_p13_dmax_tail_q167_progression_atom', + 'prove_weakest_p13_dmax_tail_q173_progression_atom', + 'prove_weakest_p13_dmax_tail_q179_progression_atom', + 'prove_weakest_p13_dmax_tail_q181_progression_atom', + 'prove_weakest_p13_dmax_tail_q191_progression_atom', + 'prove_weakest_p13_dmax_tail_q193_progression_atom', + 'prove_weakest_p13_dmax_tail_q197_progression_atom', + 'prove_weakest_p13_dmax_tail_q199_progression_atom', + 'prove_weakest_p13_dmax_tail_q211_progression_atom', + 'prove_weakest_p13_dmax_tail_q223_progression_atom', + 'prove_weakest_p13_dmax_tail_q227_progression_atom', + 'prove_weakest_p13_dmax_tail_q229_progression_atom', + 'prove_weakest_p13_dmax_tail_q233_progression_atom', + 'prove_weakest_p13_dmax_tail_q239_progression_atom', + 'prove_weakest_p13_dmax_tail_q241_progression_atom', + 'prove_weakest_p13_dmax_tail_q257_progression_atom', + 'prove_weakest_p13_dmax_tail_q263_progression_atom', + 'prove_weakest_p13_dmax_tail_q269_progression_atom', + 'prove_weakest_p13_dmax_tail_q271_progression_atom', + 'prove_weakest_p13_dmax_tail_q277_progression_atom', + 'prove_weakest_p13_dmax_tail_q281_progression_atom', + 'prove_weakest_p13_dmax_tail_q283_progression_atom', + 'prove_weakest_p13_dmax_tail_q293_progression_atom', + 'prove_weakest_p13_dmax_tail_q307_progression_atom', + 'prove_weakest_p13_dmax_tail_q311_progression_atom', + 'prove_weakest_p13_dmax_tail_q313_progression_atom', + 'prove_weakest_p13_dmax_tail_q317_progression_atom', + 'prove_weakest_p13_dmax_tail_q331_progression_atom', + 'prove_weakest_p13_dmax_tail_q337_progression_atom', + 'prove_weakest_p13_dmax_tail_q347_progression_atom', + 'prove_weakest_p13_dmax_tail_q349_progression_atom', + 'prove_weakest_p13_dmax_tail_q353_progression_atom', + 'prove_weakest_p13_dmax_tail_q359_progression_atom', + 'prove_weakest_p13_dmax_tail_q367_progression_atom', + 'prove_weakest_p13_dmax_tail_q373_progression_atom', + 'prove_weakest_p13_dmax_tail_q379_progression_atom', + 'prove_weakest_p13_dmax_tail_q383_progression_atom', + 'prove_weakest_p13_dmax_tail_q389_progression_atom', + 'prove_weakest_p13_dmax_tail_q397_progression_atom', + 'prove_weakest_p13_dmax_tail_q401_progression_atom', + 'prove_weakest_p13_dmax_tail_q409_progression_atom', + 'prove_weakest_p13_dmax_tail_q419_progression_atom', + 'prove_weakest_p13_dmax_tail_q421_progression_atom', + 'prove_weakest_p13_dmax_tail_q431_progression_atom', + 'prove_weakest_p13_dmax_tail_q433_progression_atom', + 'prove_weakest_p13_dmax_tail_q439_progression_atom', + 'prove_weakest_p13_dmax_tail_q443_progression_atom', + 'prove_weakest_p13_dmax_tail_q449_progression_atom', + 'prove_weakest_p13_dmax_tail_q457_progression_atom', + 'prove_weakest_p13_dmax_tail_q461_progression_atom', + 'prove_weakest_p13_dmax_tail_q463_progression_atom', + 'prove_weakest_p13_dmax_tail_q467_progression_atom', + 'prove_weakest_p13_dmax_tail_q479_progression_atom', + 'prove_weakest_p13_dmax_tail_q487_progression_atom', + 'prove_weakest_p13_dmax_tail_q491_progression_atom', + 'prove_weakest_p13_dmax_tail_q499_progression_atom', + 'prove_weakest_p13_dmax_tail_q503_progression_atom', + 'prove_weakest_p13_dmax_tail_q509_progression_atom', + 'prove_weakest_p13_dmax_tail_q521_progression_atom', + 'prove_weakest_p13_dmax_tail_q523_progression_atom', + 'prove_weakest_p13_dmax_tail_q541_progression_atom', + 'prove_weakest_p13_dmax_tail_q547_progression_atom', + 'prove_weakest_p13_dmax_tail_q557_progression_atom', + 'prove_weakest_p13_dmax_tail_q563_progression_atom', + 'prove_weakest_p13_dmax_tail_q569_progression_atom', + 'prove_weakest_p13_dmax_tail_q571_progression_atom', + 'prove_weakest_p13_dmax_tail_q577_progression_atom', + 'prove_weakest_p13_dmax_tail_q587_progression_atom', + 'prove_p13_dmax_tail_q_ge_587_parametric_zero_floor_lift', + 'prove_p13_side18_residual_dynamic_margin_atom', + 'prove_p13_side18_residual_dynamic_margin_symbolic_lift', + 'prove_p13_dynamic_margin_exact_mixed_symbolic_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift', + ].includes(payload.agentFlow.primaryNextAction.stepId), + true, + ); + assert.equal(payload.agentFlow.primaryNextAction.source, 'split_core_atomization_plan'); + assert.match(payload.agentFlow.primaryNextAction.task, /singleton p13 split|D2 p13 lane|Stratify the p=13|slack-dominated|strictBaseThreshold|side-count floor atom|structural margin lemma|moving-term atom|dMax growth atom|q=2 dMax progression|q=3 dMax progression|q=5 dMax progression|q=7 dMax progression|q=11 dMax progression|q=19 dMax progression|q=23 dMax progression|q=31 dMax progression|q=251 dMax progression|dMax tail\/recombination atom|dMax tail q=17 progression atom|dMax tail plus-side q=19 progression atom|dMax tail minus-side q=11 progression atom|dMax tail plus-side q=23 progression atom|dMax tail minus-side q=31 progression atom|dMax tail minus-side q=251 progression atom|dMax tail q=29 progression atom|dMax tail q=37 progression atom|dMax tail q=41 progression atom|dMax tail q=43 progression atom|dMax tail q=47 progression atom|dMax tail q=53 progression atom|dMax tail q=59 progression atom|dMax tail q=61 progression atom|dMax tail q=67 progression atom|dMax tail q=71 progression atom|dMax tail q=73 progression atom|dMax tail q=79 progression atom|dMax tail q=83 progression atom|dMax tail q=89 progression atom|dMax tail q=97 progression atom|dMax tail q=101 progression atom|dMax tail q=103 progression atom|dMax tail q=107 progression atom|dMax tail q=109 progression atom|dMax tail q=113 progression atom|dMax tail q=127 progression atom|dMax tail q=131 progression atom|dMax tail q=137 progression atom|dMax tail q=139 progression atom|dMax tail q=149 progression atom|dMax tail q=151 progression atom|dMax tail q=157 progression atom|dMax tail q=163 progression atom|dMax tail q=167 progression atom|dMax tail q=173 progression atom|dMax tail q=179 progression atom|dMax tail q=181 progression atom|dMax tail q=191 progression atom|dMax tail q=193 progression atom|dMax tail q=197 progression atom|dMax tail q=199 progression atom|dMax tail q=211 progression atom|dMax tail q=223 progression atom|dMax tail q=227 progression atom|dMax tail q=229 progression atom|dMax tail q=233 progression atom|dMax tail q=239 progression atom|dMax tail q=241 progression atom|dMax tail q=257 progression atom|dMax tail q=263 progression atom|dMax tail q=269 progression atom|dMax tail q=271 progression atom|dMax tail q=277 progression atom|dMax tail q=281 progression atom|dMax tail q=283 progression atom|dMax tail q=293 progression atom|dMax tail q=307 progression atom|dMax tail q=311 progression atom|dMax tail q=313 progression atom|dMax tail q=317 progression atom|dMax tail q=331 progression atom|dMax tail q=337 progression atom|dMax tail q=347 progression atom|dMax tail q=349 progression atom|dMax tail q=353 progression atom|dMax tail q=359 progression atom|dMax tail q=367 progression atom|dMax tail q=373 progression atom|dMax tail q=379 progression atom|dMax tail q=383 progression atom|dMax tail q=389 progression atom|dMax tail q=397 progression atom|dMax tail q=401 progression atom|dMax tail q=409 progression atom|dMax tail q=419 progression atom|dMax tail q=421 progression atom|dMax tail q=431 progression atom|dMax tail q=433 progression atom|dMax tail q=439 progression atom|dMax tail q=443 progression atom|dMax tail q=449 progression atom|dMax tail q=457 progression atom|dMax tail q=461 progression atom|dMax tail q=463 progression atom|dMax tail q=467 progression atom|dMax tail q=479 progression atom|dMax tail q=487 progression atom|dMax tail q=491 progression atom|dMax tail q=499 progression atom|dMax tail q=503 progression atom|dMax tail q=509 progression atom|dMax tail q=521 progression atom|dMax tail q=523 progression atom|dMax tail q=541 progression atom|dMax tail q=547 progression atom|dMax tail q=557 progression atom|dMax tail q=563 progression atom|dMax tail q=569 progression atom|dMax tail q=571 progression atom|dMax tail q=577 progression atom|dMax tail q=587 progression atom|q>=587 tail atom|residual dynamic margin atom|exact mixed-margin successor atom|exact mixed-margin symbolic atom|matching-injection atom|parametric exact mixed matching-injection lift|finite augmenting-path menu|direct delta -1089 successor|direct delta -39 successor|residue-parametric delta-selection lift|residue direct-selector lift|selected cross-squarefree lift|selected cross-squarefree exception menu|selected cross-squarefree exception finite-window lift|right-compatibility escape lift|small-prime CRT escape selector|p=7 endpoint cross-squarefree fallback|period-shifted endpoint-menu|squarefree sieve|p7-shift q17 residual|q17 residual cross-bad fallback|q17 residual p13-expanded fallback|q17 residual window-relaxed fallback/); + if (payload.agentFlow.primaryNextAction.stepId === 'start_singleton_p13_profile') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2.3_persist_outP2=99_out25=14_smaller=side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/D2_3_persist_outP2_99_out25_14_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'promote_d2_p13_all_n_handoff') { + assert.equal(payload.agentFlow.primaryNextAction.packetId, 'D2_p13_matching_lower_bound'); + assert.match(payload.agentFlow.primaryNextAction.manifestJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/MANIFEST\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'attack_d2_p13_row_universe_stratification_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_row_universe_stratification_lift'); + assert.equal(payload.agentFlow.primaryNextAction.packetId, 'D2_p13_row_universe_split_coverage'); + assert.match(payload.agentFlow.primaryNextAction.manifestJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/MANIFEST\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_d2_p13_slack_dominance_symbolic_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_slack_dominance_symbolic_lift'); + assert.equal(payload.agentFlow.primaryNextAction.packetId, 'D2_p13_row_universe_split_coverage'); + assert.match(payload.agentFlow.primaryNextAction.manifestJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/MANIFEST\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_d2_p13_non_tight_side_count_slack_floor_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_non_tight_side_count_slack_floor_lift'); + assert.equal(payload.agentFlow.primaryNextAction.packetId, 'D2_p13_row_universe_split_coverage'); + assert.match(payload.agentFlow.primaryNextAction.manifestJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/MANIFEST\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'attack_weakest_p13_side_count_floor_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_structural_margin_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'attack_weakest_p13_dmax_growth_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q2_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q3_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q5_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q7_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q11_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q19_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q23_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q31_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_q251_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_recombination_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q17_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q19_plus_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q11_minus_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q23_plus_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q31_minus_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q251_minus_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q29_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q37_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q41_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q43_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q47_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q53_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q59_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q61_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q67_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q71_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q73_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q79_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q83_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q89_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q97_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q101_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q103_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q107_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q109_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q113_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q127_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q131_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q137_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q139_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q149_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q151_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q157_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q163_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q167_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q173_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q179_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q181_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q191_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q193_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q197_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q199_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q211_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q223_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q227_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q229_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q233_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q239_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q241_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q257_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q263_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q269_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q271_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q277_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q281_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q283_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q293_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q307_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q311_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q313_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q317_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q331_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q337_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q347_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q349_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q353_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q359_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q367_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q373_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q379_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q383_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q389_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q397_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q401_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q409_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q419_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q421_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q431_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q433_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q439_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q443_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q449_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q457_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q461_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q463_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q467_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q479_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q487_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q491_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q499_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q503_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q509_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q521_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q523_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q541_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q547_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q557_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q563_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q569_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q571_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q577_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_weakest_p13_dmax_tail_q587_progression_atom') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_side18_residual_dynamic_margin_atom') { + assert.equal( + [ + 'D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18', + 'D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323', + ].includes(payload.agentFlow.primaryNextAction.packetAtomId), + true, + ); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_side18_residual_dynamic_margin_symbolic_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_symbolic_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else if (payload.agentFlow.primaryNextAction.stepId === 'prove_p13_dynamic_margin_exact_mixed_matching_injection') { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } else { + assert.equal(payload.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7'); + assert.match(payload.agentFlow.primaryNextAction.packetJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + } + assert.equal(payload.agentFlow.primaryNextAction.command, null); + assert.equal(payload.agentFlow.modePolicy.defaultAction, 'execute_primary_next_action'); + assert.equal(payload.agentFlow.modePolicy.doNotRunEveryMode, true); + assert.match(payload.agentFlow.modePolicy.granularBreakdown.fullBreakdownCommand, /D2_p13_matching_lower_bound/); + assert.match(payload.agentFlow.modePolicy.granularBreakdown.nudgeCommand, /orp mode nudge granular-breakdown --json/); + assert.equal(payload.agentFlow.modePolicy.situationalOverlays.length, 4); + assert.equal(payload.agentFlow.modePolicy.situationalOverlays.some((item) => item.modeId === 'systems-constellation'), true); + assert.equal(payload.agentFlow.executionLoop.some((item) => item.includes('primaryNextAction')), true); + assert.equal(payload.agentFlow.guardrails.some((item) => item.includes('paid or remote compute')), true); + assert.equal(payload.agentFlow.writeback.refreshCommand, 'erdos problem task-list-refresh 848'); + assert.match(payload.executionRule.repetitionProtocol, /10 times or 100 times/); + assert.equal(Array.isArray(payload.loopTemplate), true); + assert.equal(payload.loopTemplate.some((item) => item.stepId === 'freeze_current_state'), true); + assert.equal(payload.loopTemplate.some((item) => item.stepId === 'apply_granular_breakdown'), true); + assert.equal(payload.loopTemplate.some((item) => item.stepId === 'refresh_and_rerank'), true); + assert.equal(Array.isArray(payload.currentTasks), true); + assert.equal(payload.currentTasks.some((item) => item.taskId === 'apply_granular_breakdown'), true); + assert.equal(payload.currentTasks.some((item) => item.taskId === 'execute_current_work_packet'), true); + assert.equal(Array.isArray(payload.completedAnchors), true); + assert.equal(payload.completedAnchors.length > 0, true); + assert.equal(Array.isArray(payload.nextNeededSteps), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'formalization_work'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'exact_breakpoint_certificate'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'finite_gap_strategy'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'external_structural_verifier_audit'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'structural_base_side_scout'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'structural_two_side_scout'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'mixed_base_failure_scout'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'full_mixed_base_structural_verifier'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'structural_lift_miner'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'split_core_atomization_plan'), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'structural_lift_checklist'), false); + const latestVerifiedMax = Number(payload.currentState.latestVerifiedInterval.split('..')[1]); + assert.equal(payload.finiteGapStrategy.status, 'ready'); + assert.equal(payload.finiteGapStrategy.verdict, 'exact_endpoint_rollout_is_not_a_sole_all_N_closure_strategy'); + assert.equal(payload.finiteGapStrategy.operationalThreshold.raw, '2.64 x 10^17'); + assert.equal(payload.finiteGapStrategy.endpointCertificate.interval, `1..${latestVerifiedMax}`); + assert.match(payload.finiteGapStrategy.projectedEndpointChecksToOperationalThresholdLabel, /,/); + assert.equal(payload.splitCoreAtomizationPlan.status, 'active'); + assert.equal(payload.splitCoreAtomizationPlan.scope.splitAtomCount, 5); + assert.equal(payload.splitCoreAtomizationPlan.scope.d2SplitCount, 3); + assert.equal(payload.splitCoreAtomizationPlan.scope.d3SplitCount, 2); + assert.equal(payload.splitCoreAtomizationPlan.packetManifest.packetCount, 5); + assert.match(payload.splitCoreAtomizationPlan.packetManifest.directoryPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS$/); + assert.equal(payload.splitCoreAtomizationPlan.packetManifest.firstPacketToAttack, 'D2.3_persist_outP2=99_out25=14_smaller=side7'); + assert.equal(payload.splitCoreAtomizationPlan.mostConfusingPart.firstPlaceToAttack, 'D2.3_persist_outP2=99_out25=14_smaller=side7'); + assert.equal(payload.splitCoreAtomizationPlan.splitAtoms.every((atom) => atom.commonMatchingPairExportComplete), true); + assert.equal(payload.splitCoreAtomizationPlan.splitAtoms.every((atom) => atom.commonMatchingPairs.length === atom.commonMatchingPairCount), true); + assert.equal(payload.splitCoreAtomizationPlan.splitAtoms.every((atom) => Boolean(atom.packetArtifact?.jsonPath)), true); + assert.equal(payload.splitCoreAtomizationPlan.splitAtoms.every((atom) => Boolean(atom.packetArtifact?.markdownPath)), true); + assert.equal(payload.splitCoreAtomizationPlan.masterLayers.some((layer) => layer.layerId === 'A2_full_common_core_pair_export' && layer.status === 'done'), true); + assert.equal(payload.splitCoreAtomizationPlan.masterLayers.some((layer) => layer.layerId === 'A3_vertex_presence_atoms' && layer.status === 'next'), true); + assert.equal(payload.splitCoreAtomizationPlan.masterLayers.some((layer) => layer.layerId === 'A5_congruence_persistence_atoms'), true); + assert.equal(payload.splitCoreAtomizationPlan.adjacentAtomizedLayers.some((layer) => layer.layerId === 'B2_vertex_formula_extraction'), true); + assert.equal(payload.splitCoreAtomizationPlan.recommendedImmediateTasks[0].taskId, 'implement_full_common_core_pair_export'); + assert.equal(payload.splitCoreAtomizationPlan.recommendedImmediateTasks[0].status, 'done'); + assert.equal(payload.splitCoreAtomizationPlan.recommendedImmediateTasks.some((task) => task.taskId === 'emit_split_atom_packets' && task.status === 'done'), true); + assert.equal(payload.structuralVerifierAudit.status, 'blocked'); + assert.equal(payload.structuralVerifierAudit.blockerIds.includes('sawhney_handoff_not_claimed_at_1e7'), true); + assert.equal(payload.structuralVerifierAudit.blockerIds.includes('base_exchange_mask_covers_both_principal_sides'), true); + assert.equal(payload.baseSideScout.status, 'counterexample_to_global_7_side_domination_found'); + assert.equal(payload.baseSideScout.summary.maxSide18ExceedsSide7, true); + assert.equal(payload.baseSideScout.firstNWithSide18MaxExceedingSide7.N, 143); + assert.equal(payload.structuralTwoSideScout.status, 'side_specific_bounds_pass_but_union_bound_fails'); + assert.equal(payload.structuralTwoSideScout.summary.allSide7ChecksPass, true); + assert.equal(payload.structuralTwoSideScout.summary.allSide18ChecksPass, true); + assert.equal(payload.structuralTwoSideScout.summary.allUnionChecksPass, false); + assert.equal(payload.mixedBaseFailureScout.status, 'sampled_union_failures_repaired_by_mixed_base_clique'); + assert.equal(payload.mixedBaseFailureScout.summary.allAnalyzedRowsMixedPass, true); + assert.equal(payload.mixedBaseFailureScout.summary.mixedFailureCount, 0); + assert.equal(payload.fullMixedBaseStructuralVerifier.status, 'bounded_full_mixed_base_structural_verifier_certified'); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.allMixedChecksPass, true); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.mixedFailureCount, 0); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.threatLiftMiningRowCount, 1733); + assert.equal(payload.structuralLiftMiner.status, 'structural_lift_obligation_packet_ready'); + assert.equal(payload.structuralLiftMiner.summary.coverageComplete, true); + assert.equal(payload.structuralLiftMiner.summary.threatMiningRowCount, 1733); + assert.equal(payload.structuralLiftMiner.summary.minThreatMatchingSlack, 19); + assert.equal(payload.structuralLiftMiner.summary.primaryExactPrimes.includes(13), true); + assert.equal(payload.structuralLiftChecklist.status, 'active'); + assert.equal(payload.structuralLiftChecklist.currentFocus.targetStepId, 'D4_matching_bound_implies_sMaxMixed_bound'); + assert.equal(payload.structuralLiftChecklist.currentFocus.firstActionableStepId, 'D2_p13_matching_lower_bound'); + assert.equal(payload.currentTasks.some((item) => item.taskId === 'discharge_first_remaining_gap' && item.task.includes('D2_p13_matching_lower_bound')), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'formalization_work' && item.task.includes('D2_p13_matching_lower_bound')), true); + assert.equal(payload.nextNeededSteps.some((item) => item.source === 'formalization_work' && item.task.includes(`post-${latestVerifiedMax} verification lane`)), true); + const regimesText = fs.readFileSync(path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'VERIFICATION_REGIMES.md'), 'utf8'); + assert.match(regimesText, new RegExp(`Regime A: exact interval \`1\\.\\.${latestVerifiedMax}\``)); + assert.match(regimesText, new RegExp(`directly beyond \`${latestVerifiedMax}\``)); + const exactResults = JSON.parse(fs.readFileSync(path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', `EXACT_SMALL_N_1_${latestVerifiedMax}_RESULTS.json`), 'utf8')); + assert.equal(exactResults.results.length, latestVerifiedMax); + assert.equal(exactResults.results[0].N, 1); + assert.equal(exactResults.results.at(-1).N, latestVerifiedMax); + assert.equal(exactResults.results.every((row, index) => row.N === index + 1), true); + assert.equal(exactResults.mergeAudit?.outputRowCount, latestVerifiedMax); + assert.equal(exactResults.mergeAudit?.conflictingDuplicateCount, 0); + const breakpointScout = JSON.parse(fs.readFileSync(path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'EXACT_BREAKPOINT_SCOUT.json'), 'utf8')); + assert.equal(breakpointScout.summary.interval, `1..${latestVerifiedMax}`); + assert.equal(breakpointScout.summary.rowCount, latestVerifiedMax); + assert.equal(breakpointScout.summary.duplicateCount, 0); + assert.equal(breakpointScout.boundary.claimLevel, 'scout_not_proof'); + const breakpointCertificate = JSON.parse(fs.readFileSync(path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'EXACT_BREAKPOINT_CERTIFICATE.json'), 'utf8')); + assert.equal(breakpointCertificate.summary.interval, `1..${latestVerifiedMax}`); + assert.equal(breakpointCertificate.status, 'certified_from_endpoint_monotonicity'); + assert.equal(breakpointCertificate.summary.allEndpointChecksCertified, true); + assert.equal(breakpointCertificate.lemma.name, 'candidate_size_plateau_endpoint_monotonicity'); + assert.match(payload.sources.exactBreakpointScoutJsonPath, /packs\/number-theory\/problems\/848\/EXACT_BREAKPOINT_SCOUT\.json$/); + assert.match(payload.sources.exactBreakpointCertificateJsonPath, /packs\/number-theory\/problems\/848\/EXACT_BREAKPOINT_CERTIFICATE\.json$/); + assert.match(payload.sources.externalStructuralVerifierAuditJsonPath, /packs\/number-theory\/problems\/848\/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT\.json$/); + assert.match(payload.sources.baseSideScoutJsonPath, /packs\/number-theory\/problems\/848\/BASE_SIDE_SCOUT\.json$/); + assert.match(payload.sources.structuralTwoSideScoutJsonPath, /packs\/number-theory\/problems\/848\/STRUCTURAL_TWO_SIDE_SCOUT\.json$/); + assert.match(payload.sources.mixedBaseFailureScoutJsonPath, /packs\/number-theory\/problems\/848\/MIXED_BASE_FAILURE_SCOUT\.json$/); + assert.match(payload.sources.fullMixedBaseStructuralVerifierJsonPath, /packs\/number-theory\/problems\/848\/FULL_MIXED_BASE_STRUCTURAL_VERIFIER\.json$/); + assert.match(payload.commands.taskList, /erdos problem task-list 848/); + assert.match(payload.commands.taskListRefresh, /erdos problem task-list-refresh 848/); + assert.match(payload.commands.orpModeList, /orp mode list --json/); + assert.match(payload.commands.granularBreakdown, /orp mode breakdown granular-breakdown/); + assert.match(payload.commands.granularNudge, /orp mode nudge granular-breakdown/); +}); + +test('problem task-list-refresh emits 848 split atom packet files', () => { + const output = runCli(['problem', 'task-list-refresh', '848', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '848'); + assert.equal(payload.splitAtomPacketWrite.ok, true); + assert.equal(payload.splitAtomPacketWrite.packetCount, 5); + assert.equal(payload.splitAtomPacketWrite.successorPacketCount, 29); + assert.match(payload.splitAtomPacketWrite.manifestJsonPath, /packs\/number-theory\/problems\/848\/SPLIT_ATOM_PACKETS\/MANIFEST\.json$/); + assert.equal(fs.existsSync(payload.splitAtomPacketWrite.manifestJsonPath), true); + const manifest = JSON.parse(fs.readFileSync(payload.splitAtomPacketWrite.manifestJsonPath, 'utf8')); + assert.equal(manifest.schema, 'erdos.p848_split_atom_packet_manifest/1'); + assert.equal(manifest.packetCount, 5); + assert.equal(manifest.successorPacketCount, 29); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.laneId, 'D2_p13_matching_lower_bound'); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.status, 'prime_lane_handoff_candidate_with_open_all_n_gaps'); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.readySplitPacketCount, 3); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.splitPacketCount, 3); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.verifiedSuccessorFamilyCount, 29); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.totalRefinementConditionCount, 29); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.promotesAllNClaim, false); + assert.equal(manifest.firstPrimeLaneHandoffCandidate.theoremCandidate.openAllNHandoffGaps[0].gapId, 'row_universe_split_coverage'); + assert.equal(manifest.firstPacketToAttack.vertexPresenceRefinementConditionCount, 10); + assert.equal(manifest.firstPacketToAttack.edgeObstructionCertificateStatus, 'literal_edge_obstruction_certificate_verified'); + assert.equal(manifest.firstPacketToAttack.edgeObstructionResidueSummary.mod25ClassCount, 1); + assert.equal(manifest.firstPacketToAttack.edgeCongruencePersistenceStatus, 'literal_constant_edge_persistence_verified'); + assert.equal(manifest.firstPacketToAttack.matchingKEnvelopeCertificateStatus, 'literal_matching_sampled_k_envelope_verified'); + assert.equal(manifest.firstPacketToAttack.splitDischargeReadinessStatus, 'split_discharge_readiness_candidate'); + assert.equal(manifest.successorPackets.every((packet) => packet.symbolicVertexFamilyLemmaStatus === 'symbolic_vertex_family_lemma_verified'), true); + assert.equal(manifest.firstPacketToAttack.atomId, 'D2.3_persist_outP2=99_out25=14_smaller=side7'); + assert.equal(manifest.firstSuccessorPacketToAttack.successorAtomId, 'D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1'); + assert.equal(manifest.packets.every((packet) => fs.existsSync(packet.jsonPath)), true); + assert.equal(manifest.packets.every((packet) => fs.existsSync(packet.markdownPath)), true); + assert.equal(manifest.successorPackets.every((packet) => fs.existsSync(packet.jsonPath)), true); + assert.equal(manifest.successorPackets.every((packet) => fs.existsSync(packet.markdownPath)), true); + const firstPacket = JSON.parse(fs.readFileSync(manifest.firstPacketToAttack.jsonPath, 'utf8')); + assert.equal(firstPacket.schema, 'erdos.p848_split_atom_packet/1'); + assert.equal(firstPacket.atomId, 'D2.3_persist_outP2=99_out25=14_smaller=side7'); + assert.equal(firstPacket.matchingCore.commonMatchingPairs.length, firstPacket.matchingCore.commonMatchingPairCount); + assert.equal(firstPacket.edgeObstructionAtoms.length, firstPacket.matchingCore.commonMatchingPairCount); + assert.equal(firstPacket.edgeObstructionCertificate.status, 'literal_edge_obstruction_certificate_verified'); + assert.equal(firstPacket.edgeObstructionCertificate.edgeAtomCount, 108); + assert.equal(firstPacket.edgeObstructionCertificate.squarefreeEdgeAtomCount, 108); + assert.equal(firstPacket.edgeObstructionCertificate.nonSquarefreeEdgeAtomCount, 0); + assert.equal(firstPacket.edgeObstructionCertificate.residueSummary.mod25ClassCount, 1); + assert.equal(firstPacket.edgeObstructionCertificate.residueSummary.primeResidueClassCount > 0, true); + assert.equal(firstPacket.edgeObstructionCertificate.firstEdgeCertificates.length > 0, true); + assert.equal(firstPacket.edgeCongruencePersistence.status, 'literal_constant_edge_persistence_verified'); + assert.equal(firstPacket.edgeCongruencePersistence.proofKind, 'constant_pair_squarefree_invariant'); + assert.equal(firstPacket.edgeCongruencePersistence.edgeAtomCount, 108); + assert.equal(firstPacket.edgeCongruencePersistence.verifiedEdgeAtomCount, 108); + assert.equal(firstPacket.edgeCongruencePersistence.failedEdgeAtomCount, 0); + assert.equal(firstPacket.edgeCongruencePersistence.dependsOnSampledN, false); + assert.equal(firstPacket.edgeCongruencePersistence.proofFamilies[0].status, 'congruence_persistence_family_verified'); + assert.equal(firstPacket.matchingDisjointness.status, 'bounded_disjointness_certified'); + assert.equal(firstPacket.kEnvelope.status, 'bounded_core_meets_sampled_K_envelope'); + assert.equal(firstPacket.matchingKEnvelopeCertificate.status, 'literal_matching_sampled_k_envelope_verified'); + assert.equal(firstPacket.matchingKEnvelopeCertificate.matchingProof.status, 'literal_matching_disjointness_verified'); + assert.equal(firstPacket.matchingKEnvelopeCertificate.kEnvelopeProof.status, 'sampled_k_envelope_dominated_by_literal_core'); + assert.equal(firstPacket.matchingKEnvelopeCertificate.kEnvelopeProof.inequality, '108 >= 88'); + assert.equal(firstPacket.matchingKEnvelopeCertificate.kEnvelopeProof.boundedSlackAgainstMaxK, 20); + assert.equal(firstPacket.splitDischargeReadiness.status, 'split_discharge_readiness_candidate'); + assert.equal(firstPacket.splitDischargeReadiness.theoremCandidate.status, 'candidate_with_open_all_n_handoff_gaps'); + assert.equal(firstPacket.splitDischargeReadiness.blockingChecks.length, 0); + assert.equal(firstPacket.splitDischargeReadiness.openAllNHandoffGaps.length, 3); + assert.equal(firstPacket.splitDischargeReadiness.lowerLayerChecks.every((check) => !check.status.includes('blocked')), true); + assert.equal(firstPacket.vertexPresenceSummary.witnessRowCount, 1); + assert.equal(firstPacket.vertexPresenceSummary.needsSharperSplitOrParametricWitnessCount > 0, true); + assert.equal(firstPacket.vertexPresenceAtoms.some((atom) => atom.status === 'needs_sharper_split_or_parametric_presence_witness'), true); + assert.equal(firstPacket.vertexPresenceRefinement.status, 'literal_core_requires_sharper_square_witness_split'); + assert.equal(firstPacket.vertexPresenceRefinement.deterministicMove, 'emit_successor_atoms_by_square_witness_residue'); + assert.equal(firstPacket.vertexPresenceRefinement.unstableAtomCount, 212); + assert.equal(firstPacket.vertexPresenceRefinement.coveredUnstableAtomCount, 212); + assert.equal(firstPacket.vertexPresenceRefinement.uncoveredUnstableAtomCount, 0); + const outMod4Condition = firstPacket.vertexPresenceRefinement.conditions.find((condition) => ( + condition.square === 4 && condition.requiredOutsiderResidueModSquare === 1 + )); + assert.equal(outMod4Condition.atomCount, 145); + assert.equal(outMod4Condition.currentSplitCompatibility.compatibleWithCurrentSplit, true); + assert.equal(outMod4Condition.successorSplitKey, 'outP2=99|out25=14|smaller=side7|out4=1'); + const outMod9Condition = firstPacket.vertexPresenceRefinement.conditions.find((condition) => ( + condition.square === 9 && condition.requiredOutsiderResidueModSquare === 7 + )); + assert.equal(outMod9Condition.atomCount, 49); + assert.equal(outMod9Condition.currentSplitCompatibility.compatibleWithCurrentSplit, true); + assert.equal(outMod9Condition.successorSplitKey, 'outP2=99|out25=14|smaller=side7|out9=7'); + const firstSuccessor = JSON.parse(fs.readFileSync(manifest.firstSuccessorPacketToAttack.jsonPath, 'utf8')); + assert.equal(firstSuccessor.schema, 'erdos.p848_split_atom_successor_packet/1'); + assert.equal(firstSuccessor.conditionId, 'square_4_outsider_1'); + assert.equal(firstSuccessor.status, 'candidate_successor_obligation_verified'); + assert.equal(firstSuccessor.parentAtomId, 'D2.1_persist_outP2=70_out25=9_smaller=side7'); + assert.equal(firstSuccessor.splitRefinement.successorSplitKey, 'outP2=70|out25=9|smaller=side7|out4=1'); + assert.equal(firstSuccessor.checks.affectedAtomCount, 145); + assert.equal(firstSuccessor.checks.stabilizedAtomCount, 145); + assert.equal(firstSuccessor.checks.failedAtomCount, 0); + assert.equal(firstSuccessor.symbolicVertexFamilyLemma.status, 'symbolic_vertex_family_lemma_verified'); + assert.equal(firstSuccessor.symbolicVertexFamilyLemma.vertexResidueModSquare, 3); + assert.equal(firstSuccessor.symbolicVertexFamilyLemma.verifiedAtomCount, 145); + assert.equal(firstSuccessor.symbolicVertexFamilyLemma.failedAtomCount, 0); + const secondSuccessor = JSON.parse(fs.readFileSync(manifest.successorPackets[1].jsonPath, 'utf8')); + assert.equal(secondSuccessor.conditionId, 'square_9_outsider_8'); + assert.equal(secondSuccessor.status, 'candidate_successor_obligation_verified'); + assert.equal(secondSuccessor.parentAtomId, 'D2.1_persist_outP2=70_out25=9_smaller=side7'); + assert.equal(secondSuccessor.checks.affectedAtomCount, 48); + assert.equal(secondSuccessor.checks.stabilizedAtomCount, 48); + assert.equal(secondSuccessor.symbolicVertexFamilyLemma.status, 'symbolic_vertex_family_lemma_verified'); + assert.equal(secondSuccessor.symbolicVertexFamilyLemma.vertexResidueModSquare, 1); + assert.equal(secondSuccessor.symbolicVertexFamilyLemma.verifiedAtomCount, 48); + assert.equal(secondSuccessor.symbolicVertexFamilyLemma.failedAtomCount, 0); + const lastSuccessor = JSON.parse(fs.readFileSync(manifest.successorPackets.at(-1).jsonPath, 'utf8')); + assert.equal(lastSuccessor.conditionId, 'square_7921_outsider_1789'); + assert.equal(lastSuccessor.status, 'candidate_successor_obligation_verified'); + assert.equal(lastSuccessor.checks.affectedAtomCount, 1); + assert.equal(lastSuccessor.symbolicVertexFamilyLemma.status, 'symbolic_vertex_family_lemma_verified'); + assert.equal(lastSuccessor.symbolicVertexFamilyLemma.verifiedAtomCount, 1); + assert.equal( + [ + 'gap_1', + 'emit_singleton_edge_obstruction_certificate', + 'promote_singleton_edge_congruence_persistence', + 'promote_singleton_matching_disjointness_and_k_envelope', + 'assemble_singleton_split_discharge_readiness', + 'attack_next_p13_split_profile', + 'promote_d2_p13_all_n_handoff', + 'attack_d2_p13_row_universe_stratification_lift', + 'prove_d2_p13_slack_dominance_symbolic_lift', + 'prove_d2_p13_non_tight_side_count_slack_floor_lift', + 'attack_weakest_p13_side_count_floor_atom', + 'prove_weakest_p13_structural_margin_atom', + 'prove_weakest_p13_dmax_bound_atom', + 'attack_weakest_p13_dmax_growth_atom', + 'prove_weakest_p13_dmax_q2_progression_atom', + 'prove_weakest_p13_dmax_q3_progression_atom', + 'prove_weakest_p13_dmax_q5_progression_atom', + 'prove_weakest_p13_dmax_q7_progression_atom', + 'prove_weakest_p13_dmax_q11_progression_atom', + 'prove_weakest_p13_dmax_q19_progression_atom', + 'prove_weakest_p13_dmax_q23_progression_atom', + 'prove_weakest_p13_dmax_q31_progression_atom', + 'prove_weakest_p13_dmax_q251_progression_atom', + 'prove_weakest_p13_dmax_tail_recombination_atom', + 'prove_weakest_p13_dmax_tail_q17_progression_atom', + 'prove_weakest_p13_dmax_tail_q19_plus_progression_atom', + 'prove_weakest_p13_dmax_tail_q11_minus_progression_atom', + 'prove_weakest_p13_dmax_tail_q23_plus_progression_atom', + 'prove_weakest_p13_dmax_tail_q31_minus_progression_atom', + 'prove_weakest_p13_dmax_tail_q251_minus_progression_atom', + 'prove_weakest_p13_dmax_tail_q29_progression_atom', + 'prove_weakest_p13_dmax_tail_q37_progression_atom', + 'prove_weakest_p13_dmax_tail_q41_progression_atom', + 'prove_weakest_p13_dmax_tail_q43_progression_atom', + 'prove_weakest_p13_dmax_tail_q47_progression_atom', + 'prove_weakest_p13_dmax_tail_q53_progression_atom', + 'prove_weakest_p13_dmax_tail_q59_progression_atom', + 'prove_weakest_p13_dmax_tail_q61_progression_atom', + 'prove_weakest_p13_dmax_tail_q67_progression_atom', + 'prove_weakest_p13_dmax_tail_q71_progression_atom', + 'prove_weakest_p13_dmax_tail_q73_progression_atom', + 'prove_weakest_p13_dmax_tail_q79_progression_atom', + 'prove_weakest_p13_dmax_tail_q83_progression_atom', + 'prove_weakest_p13_dmax_tail_q89_progression_atom', + 'prove_weakest_p13_dmax_tail_q97_progression_atom', + 'prove_weakest_p13_dmax_tail_q101_progression_atom', + 'prove_weakest_p13_dmax_tail_q103_progression_atom', + 'prove_weakest_p13_dmax_tail_q107_progression_atom', + 'prove_weakest_p13_dmax_tail_q109_progression_atom', + 'prove_weakest_p13_dmax_tail_q113_progression_atom', + 'prove_weakest_p13_dmax_tail_q127_progression_atom', + 'prove_weakest_p13_dmax_tail_q131_progression_atom', + 'prove_weakest_p13_dmax_tail_q137_progression_atom', + 'prove_weakest_p13_dmax_tail_q139_progression_atom', + 'prove_weakest_p13_dmax_tail_q149_progression_atom', + 'prove_weakest_p13_dmax_tail_q151_progression_atom', + 'prove_weakest_p13_dmax_tail_q157_progression_atom', + 'prove_weakest_p13_dmax_tail_q163_progression_atom', + 'prove_weakest_p13_dmax_tail_q167_progression_atom', + 'prove_weakest_p13_dmax_tail_q173_progression_atom', + 'prove_weakest_p13_dmax_tail_q179_progression_atom', + 'prove_weakest_p13_dmax_tail_q181_progression_atom', + 'prove_weakest_p13_dmax_tail_q191_progression_atom', + 'prove_weakest_p13_dmax_tail_q193_progression_atom', + 'prove_weakest_p13_dmax_tail_q197_progression_atom', + 'prove_weakest_p13_dmax_tail_q199_progression_atom', + 'prove_weakest_p13_dmax_tail_q211_progression_atom', + 'prove_weakest_p13_dmax_tail_q223_progression_atom', + 'prove_weakest_p13_dmax_tail_q227_progression_atom', + 'prove_weakest_p13_dmax_tail_q229_progression_atom', + 'prove_weakest_p13_dmax_tail_q233_progression_atom', + 'prove_weakest_p13_dmax_tail_q239_progression_atom', + 'prove_weakest_p13_dmax_tail_q241_progression_atom', + 'prove_weakest_p13_dmax_tail_q257_progression_atom', + 'prove_weakest_p13_dmax_tail_q263_progression_atom', + 'prove_weakest_p13_dmax_tail_q269_progression_atom', + 'prove_weakest_p13_dmax_tail_q271_progression_atom', + 'prove_weakest_p13_dmax_tail_q277_progression_atom', + 'prove_weakest_p13_dmax_tail_q281_progression_atom', + 'prove_weakest_p13_dmax_tail_q283_progression_atom', + 'prove_weakest_p13_dmax_tail_q293_progression_atom', + 'prove_weakest_p13_dmax_tail_q307_progression_atom', + 'prove_weakest_p13_dmax_tail_q311_progression_atom', + 'prove_weakest_p13_dmax_tail_q313_progression_atom', + 'prove_weakest_p13_dmax_tail_q317_progression_atom', + 'prove_weakest_p13_dmax_tail_q331_progression_atom', + 'prove_weakest_p13_dmax_tail_q337_progression_atom', + 'prove_weakest_p13_dmax_tail_q347_progression_atom', + 'prove_weakest_p13_dmax_tail_q349_progression_atom', + 'prove_weakest_p13_dmax_tail_q353_progression_atom', + 'prove_weakest_p13_dmax_tail_q359_progression_atom', + 'prove_weakest_p13_dmax_tail_q367_progression_atom', + 'prove_weakest_p13_dmax_tail_q373_progression_atom', + 'prove_weakest_p13_dmax_tail_q379_progression_atom', + 'prove_weakest_p13_dmax_tail_q383_progression_atom', + 'prove_weakest_p13_dmax_tail_q389_progression_atom', + 'prove_weakest_p13_dmax_tail_q397_progression_atom', + 'prove_weakest_p13_dmax_tail_q401_progression_atom', + 'prove_weakest_p13_dmax_tail_q409_progression_atom', + 'prove_weakest_p13_dmax_tail_q419_progression_atom', + 'prove_weakest_p13_dmax_tail_q421_progression_atom', + 'prove_weakest_p13_dmax_tail_q431_progression_atom', + 'prove_weakest_p13_dmax_tail_q433_progression_atom', + 'prove_weakest_p13_dmax_tail_q439_progression_atom', + 'prove_weakest_p13_dmax_tail_q443_progression_atom', + 'prove_weakest_p13_dmax_tail_q449_progression_atom', + 'prove_weakest_p13_dmax_tail_q457_progression_atom', + 'prove_weakest_p13_dmax_tail_q461_progression_atom', + 'prove_weakest_p13_dmax_tail_q463_progression_atom', + 'prove_weakest_p13_dmax_tail_q467_progression_atom', + 'prove_weakest_p13_dmax_tail_q479_progression_atom', + 'prove_weakest_p13_dmax_tail_q487_progression_atom', + 'prove_weakest_p13_dmax_tail_q491_progression_atom', + 'prove_weakest_p13_dmax_tail_q499_progression_atom', + 'prove_weakest_p13_dmax_tail_q503_progression_atom', + 'prove_weakest_p13_dmax_tail_q509_progression_atom', + 'prove_weakest_p13_dmax_tail_q521_progression_atom', + 'prove_weakest_p13_dmax_tail_q523_progression_atom', + 'prove_weakest_p13_dmax_tail_q541_progression_atom', + 'prove_weakest_p13_dmax_tail_q547_progression_atom', + 'prove_weakest_p13_dmax_tail_q557_progression_atom', + 'prove_weakest_p13_dmax_tail_q563_progression_atom', + 'prove_weakest_p13_dmax_tail_q569_progression_atom', + 'prove_weakest_p13_dmax_tail_q571_progression_atom', + 'prove_weakest_p13_dmax_tail_q577_progression_atom', + 'prove_weakest_p13_dmax_tail_q587_progression_atom', + 'prove_p13_dmax_tail_q_ge_587_parametric_zero_floor_lift', + 'prove_p13_side18_residual_dynamic_margin_atom', + 'prove_p13_side18_residual_dynamic_margin_symbolic_lift', + 'prove_p13_dynamic_margin_exact_mixed_symbolic_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift', + 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift', + ].includes(payload.taskList.agentFlow.primaryNextAction.stepId), + true, + ); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.allPacketFilesPresent, true); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.allSuccessorPacketFilesPresent, true); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.verifiedSuccessorFamilyCount, 29); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.allMaterializedSuccessorFamiliesVerified, true); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13SplitDischargeReadyPacketCount, 3); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.allP13SplitDischargeReady, true); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13PrimeLaneHandoffStatus, 'prime_lane_handoff_candidate_with_open_all_n_gaps'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13PrimeLaneHandoffFirstOpenGap, 'row_universe_split_coverage'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13RowUniverseCoverageStatus, 'bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13RowUniverseCoverageScope, 'bounded_p13_threat_rows_tight_splits_plus_slack_dominated_remainder'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13RowUniverseFirstMissingAtom, 'D2_p13_slack_dominance_symbolic_lift'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13SlackDominanceLiftStatus, 'bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.p13SlackDominanceFirstOpenLemma, 'D2_p13_non_tight_side_count_slack_floor_lift'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.sideCountFloorPacketCount, 2); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.firstSideCountFloorPacketToAttack, 'D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.firstSideCountFloorStructuralMarginLemma, 'D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.packetManifest.firstSideCountFloorMovingTermSubatom, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.threatRowCount, 1285); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.tightWitnessRowCount, 12); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.boundedThreatRowsOutsideTightWitnessPacket, 1273); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.boundedThreatRowsCoveredByEmittedTightSplitStrata, 96); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.boundedThreatRowsOutsideEmittedTightSplitStrata, 1189); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.boundedThreatRowsSlackDominatedOutsideTightSplitStrata, 1189); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.currentCoverage.boundedThreatRowsNeedingAdditionalSplitPacket, 0); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.boundedStratificationAudit.splitStratumCount, 52); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.boundedStratificationAudit.emittedTightSplitCoveredRowCount, 96); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.boundedStratificationAudit.outsideTightSplitRowCount, 1189); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.boundedStratificationAudit.minEmittedTightSplitSlack, 19); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.boundedStratificationAudit.minOutsideSlack, 21); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.boundedStratificationAudit.outsideRowsNeedingAdditionalSplitPacket, 0); + assert.equal(payload.taskList.splitCoreAtomizationPlan.rowUniverseCoverage.emittedMissingAtom.atomId, 'D2_p13_slack_dominance_symbolic_lift'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.status, 'bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed'); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.boundedRowCount, 1189); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.boundedStratumCount, 49); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.targetNonTightSlackLowerBound, 20); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.observedMinNonTightSlack, 21); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.failedFormulaReplayRowCount, 0); + assert.equal(payload.taskList.splitCoreAtomizationPlan.slackDominanceSymbolicLift.firstOpenSymbolicLemma.lemmaId, 'D2_p13_non_tight_side_count_slack_floor_lift'); + assert.equal(payload.taskList.agentFlow.primaryNextAction.packetAtomId, 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323'); + assert.match(payload.taskList.agentFlow.primaryNextAction.packetJsonPath, /SIDE_COUNT_FLOOR\/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7\.json$/); + assert.equal( + [ + null, + 'literal_constant_edge_persistence_verified', + ].includes(payload.taskList.splitCoreAtomizationPlan.packetManifest.firstPacketEdgeCongruencePersistenceStatus), + true, + ); + assert.equal( + [ + null, + 'literal_matching_sampled_k_envelope_verified', + ].includes(payload.taskList.splitCoreAtomizationPlan.packetManifest.firstPacketMatchingKEnvelopeCertificateStatus), + true, + ); + assert.equal( + [ + null, + 'split_discharge_readiness_candidate', + ].includes(payload.taskList.splitCoreAtomizationPlan.packetManifest.firstPacketSplitDischargeReadinessStatus), + true, + ); +}); + +test('problem task-list-refresh writes canonical task-list artifacts', () => { + const output = runCli(['problem', 'task-list-refresh', '1', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '1'); + assert.match(payload.jsonPath, /packs\/number-theory\/problems\/1\/TASK_LIST\.json$/); + assert.match(payload.markdownPath, /packs\/number-theory\/problems\/1\/TASK_LIST\.md$/); + assert.equal(fs.existsSync(payload.jsonPath), true); + assert.equal(fs.existsSync(payload.markdownPath), true); +}); + +test('problem task-list default output gives a frictionless next-step readout', () => { + const output = runCli(['problem', 'task-list', '1']); + assert.match(output, /Highest-value next step: gap_1 \[next\]/); + assert.match(output, /Next command: erdos problem formalization-work-refresh 1/); + assert.match(output, /Mode assist: Execute the next command first; if the target feels fuzzy, run orp mode nudge granular-breakdown --json\./); + assert.match(output, /Optional overlays when useful: ruthless-simplification, systems-constellation, bold-concept-generation, sleek-minimal-progressive/); +}); + +test('problem task-list-refresh default output keeps the next action visible', () => { + const output = runCli(['problem', 'task-list-refresh', '1']); + assert.match(output, /Problem task-list refresh: complete/); + assert.match(output, /Highest-value next step: gap_1 \[next\]/); + assert.match(output, /Next command: erdos problem formalization-work-refresh 1/); + assert.match(output, /Mode assist: Execute the next command first/); +}); + +test('problem task-list-run executes repeated passes and writes loop-run artifacts', () => { + const output = runCli(['problem', 'task-list-run', '1', '--passes', '3', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.problemId, '1'); + assert.equal(payload.requestedPasses, 3); + assert.equal(payload.executedPasses >= 1, true); + assert.equal(Array.isArray(payload.passes), true); + assert.equal(payload.passes.length >= 1, true); + assert.match(payload.jsonPath, /packs\/number-theory\/problems\/1\/TASK_LOOP_RUN\.json$/); + assert.match(payload.markdownPath, /packs\/number-theory\/problems\/1\/TASK_LOOP_RUN\.md$/); + assert.equal(fs.existsSync(payload.jsonPath), true); + assert.equal(fs.existsSync(payload.markdownPath), true); + assert.equal(typeof payload.stopReason, 'string'); +}); + +test('problem task-list-run can continue after convergence while preserving the first convergence pass', () => { + const output = runCli(['problem', 'task-list-run', '1', '--passes', '4', '--no-stop-on-convergence', '--json']); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.requestedPasses, 4); + assert.equal(payload.executedPasses, 4); + assert.equal(payload.converged, true); + assert.equal(payload.convergedAtPass, 2); + assert.equal(payload.stopReason, 'requested_pass_limit_reached'); +}); + +test('frontier doctor exposes the bundled optional runtime', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-doctor-')); + const output = runCli(['frontier', 'doctor', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.bundledEnginePresent, true); + assert.equal(payload.bundledEnginePyprojectPresent, true); + assert.equal(payload.bundledEngineCliPresent, true); + assert.match(payload.bundledEngineRoot, /research\/frontier-engine$/); + assert.equal(payload.commands.setupBase, 'erdos frontier setup --base'); + assert.equal(payload.commands.setupCpu, 'erdos frontier setup --cpu'); + assert.equal(payload.commands.createBrev, 'erdos frontier create-brev --gpu-name H100 --dry-run'); + assert.equal(payload.commands.createBrevFleet, 'erdos frontier create-brev-fleet --type hyperstack_H100 --count 2 --dry-run'); + assert.equal(payload.commands.attachBrev, 'erdos frontier attach-brev --instance --apply'); + assert.equal(payload.commands.enablePaidRemote, 'erdos frontier enable-paid-remote '); + assert.equal(payload.commands.enablePaidFleet, 'erdos frontier enable-paid-fleet '); + assert.equal(payload.commands.syncSsh, 'erdos frontier sync-ssh --apply'); + assert.equal(payload.commands.syncFleet, 'erdos frontier sync-fleet --lane p848_anchor_ladder --apply'); + assert.equal(payload.managedFrontierReady, false); + assert.equal(payload.frontierLoopMode, null); + assert.equal(payload.researchModes.bridgeRefresh.available, true); + assert.equal(payload.researchModes.bridgeRefresh.mode, 'system'); + assert.equal(payload.researchModes.familySearch.available, false); + assert.equal(payload.researchModes.heavySearch.available, false); +}); + +test('frontier research modes prefer a local managed GPU before an attached paid remote by default', () => { + const modes = getFrontierResearchModesForSnapshot({ + frontierLoopOptIn: true, + managedFrontierReady: true, + gpuSearchReady: true, + selectedRemoteId: null, + remote: { + attached: true, + provider: 'brev', + instanceName: 'erdos-p848-h100', + paidRung: true, + paidEnabled: true, + gpuSearchReady: true, + }, + }); + + assert.equal(modes.heavySearch.available, true); + assert.equal(modes.heavySearch.source, 'managed_runtime'); + assert.equal(modes.heavySearch.mode, 'gpu'); +}); + +test('frontier research modes honor an explicit remote selection for a paid rung when enabled', () => { + const modes = getFrontierResearchModesForSnapshot({ + frontierLoopOptIn: true, + managedFrontierReady: true, + gpuSearchReady: true, + selectedRemoteId: 'erdos-p848-h100', + remote: { + attached: true, + provider: 'brev', + instanceName: 'erdos-p848-h100', + paidRung: true, + paidEnabled: true, + gpuSearchReady: true, + }, + }); + + assert.equal(modes.heavySearch.available, true); + assert.equal(modes.heavySearch.source, 'ssh_remote'); + assert.equal(modes.heavySearch.mode, 'gpu'); +}); + +test('cli help lists the SSH sync command for frontier-engine', () => { + const output = runCli(['help']); + assert.match(output, /erdos problem theorem-loop \[\] \[--json\]/); + assert.match(output, /erdos problem theorem-loop-refresh \[\] \[--json\]/); + assert.match(output, /erdos problem claim-loop \[\] \[--json\]/); + assert.match(output, /erdos problem claim-loop-refresh \[\] \[--json\]/); + assert.match(output, /erdos problem claim-pass \[\] \[--json\]/); + assert.match(output, /erdos problem claim-pass-refresh \[\] \[--json\]/); + assert.match(output, /erdos problem formalization \[\] \[--json\]/); + assert.match(output, /erdos problem formalization-refresh \[\] \[--json\]/); + assert.match(output, /erdos problem formalization-work \[\] \[--json\]/); + assert.match(output, /erdos problem formalization-work-refresh \[\] \[--json\]/); + assert.match(output, /erdos problem task-list \[\] \[--json\]/); + assert.match(output, /erdos problem task-list-refresh \[\] \[--json\]/); + assert.match(output, /erdos problem task-list-run \[\] \[--passes \] \[--no-stop-on-convergence\] \[--json\]/); + assert.match(output, /erdos frontier create-brev \[--gpu-name \] \[--type \] \[--provider \] \[--count \] \[--attach\] \[--enable-paid-rung\] \[--sync-lane \] \[--dry-run\] \[--apply\] \[--json\]/); + assert.match(output, /erdos frontier create-brev-fleet \[--gpu-name \] \[--type \] \[--provider \] \[--count \] \[--attach\] \[--enable-paid-rung\] \[--sync-lane \] \[--dry-run\] \[--apply\] \[--json\]/); + assert.match(output, /erdos frontier attach-brev --instance \[--remote-id \] \[--ssh-host \] \[--engine-root \] \[--python-command \] \[--enable-paid-rung\] \[--apply\] \[--json\]/); + assert.match(output, /erdos frontier enable-paid-remote \[--json\]/); + assert.match(output, /erdos frontier enable-paid-fleet \[--json\]/); + assert.match(output, /erdos frontier sync-ssh \[--remote-id \] \[--ssh-host \] \[--engine-root \] \[--python-command \] \[--lane \] \[--apply\] \[--json\]/); + assert.match(output, /erdos frontier sync-fleet \[--lane \] \[--apply\] \[--json\]/); + assert.match(output, /erdos frontier sessions \[--json\]/); + assert.match(output, /erdos frontier session \[--json\]/); + assert.match(output, /erdos frontier stop-session \[--json\]/); + assert.match(output, /erdos number-theory dispatch \[\] \[--apply\] \[--detach\] \[--review-after-hours \] \[--remote-id \] \[--external-source-dir \]/); + assert.match(output, /erdos number-theory dispatch-fleet \[\] --fleet \[--apply\] \[--review-after-hours \] \[--strategy \] \[--action \] \[--json\]/); + assert.match(output, /erdos number-theory fleet-run \[--json\]/); +}); + +test('frontier attach-brev derives an SSH host from the instance name in dry-run mode', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-attach-brev-')); + const output = runCli(['frontier', 'attach-brev', '--instance', 'h100-lab', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.remote.provider, 'brev'); + assert.equal(payload.remote.instanceName, 'h100-lab'); + assert.equal(payload.remote.sshHost, 'h100-lab'); + assert.equal( + ['/home/shadeform/frontier-engine', '~/frontier-engine'].includes(payload.remote.engineRoot), + true, + ); + assert.equal(payload.remote.pythonCommand, 'python3'); + assert.equal(payload.enablePaidRung, false); + assert.equal(payload.paidEnabled, false); +}); + +test('frontier create-brev builds a native Brev provisioning plan with attach and sync follow-up', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-create-brev-')); + const output = runCli([ + 'frontier', + 'create-brev', + 'erdos-h100', + '--gpu-name', + 'H100', + '--provider', + 'hyperstack', + '--attach', + '--sync-lane', + 'p848_anchor_ladder', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.instanceName, 'erdos-h100'); + assert.equal(payload.provider, 'brev'); + assert.equal(payload.attach, true); + assert.equal(payload.syncLane, 'p848_anchor_ladder'); + assert.equal(payload.enablePaidRung, false); + assert.equal(payload.paidEnabled, false); + assert.match(payload.plan.createCommandLine, /^brev create erdos-h100 --gpu-name H100 --provider hyperstack/); + assert.equal(payload.plan.attachCommand, 'erdos frontier attach-brev --instance erdos-h100 --apply'); + assert.equal(payload.plan.syncCommand, 'erdos frontier sync-ssh --lane p848_anchor_ladder --apply'); + assert.equal(payload.warnings.some((warning) => /H100-class hardware/.test(warning)), true); +}); + +test('frontier create-brev-fleet builds a native H100 fleet plan for parallel sweeps', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-create-brev-fleet-')); + const output = runCli([ + 'frontier', + 'create-brev-fleet', + 'erdos-h100x2', + '--type', + 'hyperstack_H100', + '--count', + '2', + '--attach', + '--sync-lane', + 'p848_anchor_ladder', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.fleetId, 'erdos-h100x2'); + assert.equal(payload.count, 2); + assert.equal(payload.provider, 'brev'); + assert.equal(payload.intendedTopology, 'parallel_independent_sweeps'); + assert.equal(payload.enablePaidRung, false); + assert.equal(payload.paidEnabled, false); + assert.equal(payload.members.length, 2); + assert.equal(payload.members[0].instanceName, 'erdos-h100x2-01'); + assert.equal(payload.members[1].instanceName, 'erdos-h100x2-02'); + assert.match(payload.members[0].createCommandLine, /^brev create erdos-h100x2-01 --type hyperstack_H100/); + assert.equal(payload.members[0].syncCommand, 'erdos frontier sync-ssh --lane p848_anchor_ladder --apply'); +}); + +test('frontier can explicitly enable paid remotes and fleets before they join the active loop', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-paid-rungs-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const configPath = path.join(workspace, '.erdos', 'config.json'); + const config = JSON.parse(fs.readFileSync(configPath, 'utf8')); + config.frontier = { + ...(config.frontier ?? {}), + remotes: { + h100_box: { + remoteId: 'h100_box', + provider: 'brev', + instanceName: 'h100_box', + sshHost: 'h100_box', + attached: true, + gpuSearchReady: true, + }, + h100x8_01: { + remoteId: 'h100x8_01', + provider: 'brev', + instanceName: 'h100x8_01', + sshHost: 'h100x8_01', + }, + h100x8_02: { + remoteId: 'h100x8_02', + provider: 'brev', + instanceName: 'h100x8_02', + sshHost: 'h100x8_02', + }, + }, + fleets: { + h100x8: { + fleetId: 'h100x8', + provider: 'brev', + count: 2, + laneId: 'p848_anchor_ladder', + intendedTopology: 'parallel_independent_sweeps', + remoteIds: ['h100x8_01', 'h100x8_02'], + }, + }, + paidRungs: { + enabledRemoteIds: [], + enabledFleetIds: [], + lastUpdatedAt: null, + }, + }; + fs.writeFileSync(configPath, JSON.stringify(config, null, 2) + '\n'); + + const enableRemote = JSON.parse(runCli(['frontier', 'enable-paid-remote', 'h100_box', '--json'], { cwd: workspace })); + assert.equal(enableRemote.ok, true); + assert.equal(enableRemote.enabled, true); + assert.equal(enableRemote.snapshot.remotes.find((remote) => remote.remoteId === 'h100_box')?.paidEnabled, true); + + const enableFleet = JSON.parse(runCli(['frontier', 'enable-paid-fleet', 'h100x8', '--json'], { cwd: workspace })); + assert.equal(enableFleet.ok, true); + const fleetSnapshot = enableFleet.snapshot.fleets.find((fleet) => fleet.fleetId === 'h100x8'); + assert.equal(fleetSnapshot?.paidEnabled, true); + assert.equal(fleetSnapshot?.members.every((member) => member.paidEnabled), true); +}); + +test('frontier fleets and sync-fleet expose configured fleet members', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-fleet-registry-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const configPath = path.join(workspace, '.erdos', 'config.json'); + const config = JSON.parse(fs.readFileSync(configPath, 'utf8')); + config.frontier = { + ...(config.frontier ?? {}), + remotes: { + h100x2_01: { + remoteId: 'h100x2_01', + provider: 'brev', + instanceName: 'h100x2_01', + sshHost: 'h100x2_01', + attached: true, + gpuSearchReady: true, + }, + h100x2_02: { + remoteId: 'h100x2_02', + provider: 'brev', + instanceName: 'h100x2_02', + sshHost: 'h100x2_02', + attached: true, + gpuSearchReady: false, + }, + }, + fleets: { + h100x2: { + fleetId: 'h100x2', + provider: 'brev', + count: 2, + laneId: 'p848_anchor_ladder', + intendedTopology: 'parallel_independent_sweeps', + remoteIds: ['h100x2_01', 'h100x2_02'], + }, + }, + }; + fs.writeFileSync(configPath, JSON.stringify(config, null, 2) + '\n'); + + const fleets = JSON.parse(runCli(['frontier', 'fleets', '--json'], { cwd: workspace })); + assert.equal(fleets.fleetCount, 1); + assert.equal(fleets.fleets[0].fleetId, 'h100x2'); + assert.equal(fleets.fleets[0].attachedCount, 2); + assert.equal(fleets.fleets[0].readyGpuCount, 1); + + const fleet = JSON.parse(runCli(['frontier', 'fleet', 'h100x2', '--json'], { cwd: workspace })); + assert.equal(fleet.fleetId, 'h100x2'); + assert.equal(fleet.members.length, 2); + + const syncPlan = JSON.parse(runCli(['frontier', 'sync-fleet', 'h100x2', '--json'], { cwd: workspace })); + assert.equal(syncPlan.available, true); + assert.equal(syncPlan.members.length, 2); + assert.equal(syncPlan.members[0].syncCommand, 'erdos frontier sync-ssh --remote-id h100x2_01 --lane p848_anchor_ladder --apply'); +}); + +test('frontier sync-ssh can target one bundled lane in dry-run mode', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-sync-')); + const output = runCli(['frontier', 'sync-ssh', '--lane', 'm8_sat_rail', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.scope.mode, 'lane'); + assert.equal(payload.scope.laneId, 'm8_sat_rail'); + assert.equal(payload.scope.error, null); + assert.equal(payload.local.experimentDirs.length, 1); + assert.match(payload.local.experimentDirs[0], /m8-sat-rail$/); +}); + +test('frontier sync-ssh narrows p848 lane sync to live latest frontier data', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-sync-p848-')); + const output = runCli(['frontier', 'sync-ssh', '--lane', 'p848_anchor_ladder', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.scope.mode, 'lane'); + assert.equal(payload.scope.laneId, 'p848_anchor_ladder'); + assert.equal(Array.isArray(payload.scope.syncEntries), true); + assert.equal( + payload.scope.syncEntries.some((entry) => /live-frontier-sync\/2026-04-05/.test(entry.localPath)), + false, + ); + const chunksEntry = payload.scope.syncEntries.find((entry) => /live_latest_chunks$/.test(entry.label)); + assert.ok(chunksEntry); + assert.equal(chunksEntry.recursive, true); + assert.match(chunksEntry.localPath, /live-frontier-sync\/latest\/chunks$/); + assert.match(chunksEntry.remoteRelativePath, /experiments\/p848-anchor-ladder\/live-frontier-sync\/latest$/); +}); + +test('frontier sync-ssh defaults to all bundled lanes in dry-run mode', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-sync-all-')); + const output = runCli(['frontier', 'sync-ssh', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.scope.mode, 'all'); + assert.equal(Array.isArray(payload.local.experimentDirs), true); + assert.equal(payload.local.experimentDirs.some((entry) => /m8-sat-rail$/.test(entry)), true); + assert.equal(payload.local.experimentDirs.some((entry) => /p848-anchor-ladder$/.test(entry)), true); +}); + +test('frontier lanes exposes bundled frontier-engine lane metadata', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-lanes-')); + const output = runCli(['frontier', 'lanes', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.available, true); + assert.equal(Array.isArray(payload.lanes), true); + assert.equal(payload.lanes.some((lane) => lane.lane_id === 'm8_sat_rail'), true); + assert.equal(payload.lanes.some((lane) => lane.lane_id === 'p848_anchor_ladder'), true); +}); + +test('frontier setup emits an explicit opt-in plan for the managed runtime', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-frontier-setup-')); + const resolvedWorkspace = fs.realpathSync(workspace); + const output = runCli(['frontier', 'setup', '--cpu', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.apply, false); + assert.equal(payload.plan.mode, 'cpu'); + assert.equal(payload.plan.frontierWorkspaceDir, path.join(resolvedWorkspace, '.erdos', 'frontier')); + assert.equal(payload.plan.managedVenvDir, path.join(resolvedWorkspace, '.erdos', 'frontier', 'venv')); + assert.equal( + payload.plan.steps.some((step) => step.label === 'install_bundled_frontier_engine'), + true, + ); + assert.equal( + payload.plan.steps.some((step) => step.label === 'install_torch_cpu'), + true, + ); + assert.equal(payload.doctor.bundledEnginePresent, true); +}); + test('cluster list shows multiple seeded clusters', () => { const output = runCli(['cluster', 'list']); assert.match(output, /sunflower: 4 problems, 2 deep-harness/); @@ -218,6 +2115,15 @@ test('sunflower status shows packaged compute lane and family context for 857', assert.match(output, /Atomic board first ready atom: T10.G3.A2/); assert.match(output, /Checkpoint packet:/); assert.match(output, /Report packet:/); + assert.match(output, /Theorem loop: baseline/); + assert.match(output, /Theorem claim surface: frontier_supported_route/); + assert.match(output, /Theorem command: erdos problem theorem-loop 857/); + assert.match(output, /Claim loop: baseline/); + assert.match(output, /Claim command: erdos problem claim-loop 857/); + assert.match(output, /Claim pass: baseline/); + assert.match(output, /Claim pass command: erdos problem claim-pass 857/); + assert.match(output, /Task list: baseline/); + assert.match(output, /Task list command: erdos problem task-list 857/); assert.match(output, /Compute lane: m8_exactness_cube_and_certificate_v0 \[ready_for_local_scout\]/); assert.match(output, /Breakthroughs engine: breakthroughs/); assert.match(output, /Dispatch action: run_local/); @@ -236,6 +2142,7 @@ test('sunflower status can emit json using the active problem', () => { assert.equal(payload.activePacket.laneId, 'm8_exactness_cube_and_certificate_v0'); assert.equal(payload.atomicBoardPresent, true); assert.equal(payload.firstReadyAtom.atomId, 'T10.G3.A2'); + assert.equal(payload.theoremLoop.theoremLoopMode, 'baseline'); }); test('sunflower status records a no-compute dossier bridge cleanly for 536', () => { @@ -263,6 +2170,13 @@ test('number-theory status shows the starter workspace for 1', () => { assert.match(output, /Active route: distinct_subset_sum_lower_bound/); assert.match(output, /Route packet present: yes/); assert.match(output, /Frontier note:/); + assert.match(output, /Theorem loop: baseline/); + assert.match(output, /Theorem claim surface: route_scaffolding/); + assert.match(output, /Theorem command: erdos problem theorem-loop 1/); + assert.match(output, /Claim pass: baseline/); + assert.match(output, /Claim pass command: erdos problem claim-pass 1/); + assert.match(output, /Task list: baseline/); + assert.match(output, /Task list command: erdos problem task-list 1/); assert.match(output, /Active ticket: N1/); assert.match(output, /Ready atoms: 1/); }); @@ -301,6 +2215,74 @@ test('number-theory status exposes the finite-check workspace for 848', () => { assert.match(output, /Route packet present: yes/); assert.match(output, /Active ticket: N848/); assert.match(output, /First ready atom: N848\.G1\.A21/); + assert.match(output, /Theorem loop: bridge_backed/); + assert.match(output, /Theorem claim surface: bridge_backed_frontier_support/); + assert.match(output, /Theorem command: erdos problem theorem-loop 848/); + assert.match(output, /Theorem refresh: erdos problem theorem-loop-refresh 848/); + assert.match(output, /Claim loop: bridge_backed/); + assert.match(output, /Claim command: erdos problem claim-loop 848/); + assert.match(output, /Claim refresh: erdos problem claim-loop-refresh 848/); + assert.match(output, /Claim pass: bridge_backed/); + assert.match(output, /Claim pass command: erdos problem claim-pass 848/); + assert.match(output, /Claim pass refresh: erdos problem claim-pass-refresh 848/); + assert.match(output, /Formalization: bridge_backed/); + assert.match(output, /Formalization command: erdos problem formalization 848/); + assert.match(output, /Formalization refresh: erdos problem formalization-refresh 848/); + assert.match(output, /Formalization work: bridge_backed/); + assert.match(output, /Formalization work command: erdos problem formalization-work 848/); + assert.match(output, /Formalization work refresh: erdos problem formalization-work-refresh 848/); + assert.match(output, /Task list: bridge_backed/); + assert.match(output, /Task list command: erdos problem task-list 848/); + assert.match(output, /Task list refresh: erdos problem task-list-refresh 848/); + assert.match(output, /Search\/theorem bridge:/); + assert.match(output, /SEARCH_THEOREM_BRIDGE\.md/); + assert.match(output, /Bridge data:/); + assert.match(output, /Bridge refresh: erdos number-theory bridge-refresh 848/); + assert.match(output, /Frontier loop: inactive/); + assert.match(output, /Frontier loop activation: erdos frontier setup --base --apply/); + assert.match(output, /Frontier loop GPU path: erdos frontier setup --cuda --torch-index-url --apply/); +}); + +test('number-theory bridge exposes the frontier-engine theorem bridge for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-bridge-848-')); + const output = runCli(['number-theory', 'bridge', '848'], { cwd: workspace }); + assert.match(output, /Erdos Problem #848 number-theory bridge/); + assert.match(output, /Bridge note: .*SEARCH_THEOREM_BRIDGE\.md/); + assert.match(output, /Bridge data: .*SEARCH_THEOREM_BRIDGE\.json/); + assert.match(output, /Frontier-engine: .*research\/frontier-engine/); + assert.match(output, /Refresh command: erdos number-theory bridge-refresh 848/); + assert.match(output, /Engine command: python3 research\/frontier-engine\/src\/frontier_engine\/cli\.py export-p848-theorem-bridge/); + assert.match(output, /Refresh mode: system/); + assert.match(output, /Resolved engine command: .*frontier_engine\/cli\.py export-p848-theorem-bridge/); + assert.match(output, /Shared-prefix failures frozen: 24/); + assert.match(output, /Next unmatched representative: 137720141/); + assert.match(output, /Current family-aware leader: 432/); + assert.match(output, /Top GPU tie class: 432, 782, 832/); +}); + +test('number-theory bridge keeps the strongest theorem-relevant GPU manifest for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-bridge-strongest-848-')); + const payload = JSON.parse(runCli(['number-theory', 'bridge', '848', '--json'], { cwd: workspace })); + const state = payload.bridgeCurrentState; + + assert.equal(state.current_family_aware_leader.continuation, 432); + assert.equal(state.current_family_aware_leader.repaired_known_packets, 26); + assert.equal(state.current_family_aware_leader.repaired_predicted_families, 242); + assert.equal(state.current_family_aware_leader.effective_clean_through >= 250075000, true); + assert.deepEqual(state.top_gpu_tie_class, [432, 782, 832]); + assert.equal(payload.bridgeGpuLeaderboard.length >= 16, true); +}); + +test('number-theory bridge-refresh runs the frontier-engine exporter for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-bridge-refresh-848-')); + const output = runCli(['number-theory', 'bridge-refresh', '848'], { cwd: workspace }); + assert.match(output, /Bridge refresh: complete/); + assert.match(output, /Refresh command: erdos number-theory bridge-refresh 848/); + assert.match(output, /Engine command: python3 research\/frontier-engine\/src\/frontier_engine\/cli\.py export-p848-theorem-bridge/); + assert.match(output, /Execution mode: system/); + assert.match(output, /Resolved engine command: .*frontier_engine\/cli\.py export-p848-theorem-bridge/); + assert.match(output, /Erdos Problem #848 number-theory bridge/); + assert.match(output, /Shared-prefix failures frozen: 24/); }); test('sunflower board prints the mirrored atomic frontier for 857', () => { @@ -670,6 +2652,9 @@ test('preflight reports ok after bootstrap and checkpoint sync', () => { const output = runCli(['preflight'], { cwd: workspace }); assert.match(output, /Verdict: ok/); assert.match(output, /Continuation policy: route/); + assert.match(output, /Research stack:/); + assert.match(output, /Canonical source: https:\/\/www\.erdosproblems\.com\/857/); + assert.match(output, /Theorem loop: erdos problem theorem-loop 857/); assert.equal(fs.existsSync(path.join(workspace, '.erdos', 'registry', 'preflight')), true); }); @@ -697,6 +2682,14 @@ test('workspace show includes research loop paths and continuation mode', () => assert.match(output, /Active seeded dossier dir:/); assert.match(output, /Continuation mode: route/); assert.match(output, /Next honest move:/); + assert.match(output, /Sunflower theorem loop: baseline/); + assert.match(output, /Sunflower theorem command: erdos problem theorem-loop 857/); + assert.match(output, /Sunflower task list: baseline/); + assert.match(output, /Sunflower task list command: erdos problem task-list 857/); + assert.match(output, /Research canonical source: https:\/\/www\.erdosproblems\.com\/857/); + assert.match(output, /Research ORP sync: erdos orp sync/); + assert.match(output, /Research writeback: erdos problem theorem-loop-refresh 857/); + assert.match(output, /Research task list refresh: erdos problem task-list-refresh 857/); assert.match(output, /Sunflower board: yes/); assert.match(output, /Sunflower board ready atoms: 1/); assert.match(output, /Sunflower first ready atom: T10.G3.A2/); @@ -709,10 +2702,819 @@ test('workspace show includes number-theory workspace context for problem 1', () assert.match(output, /Active route: distinct_subset_sum_lower_bound/); assert.match(output, /Number-theory family role: additive_number_theory_seed/); assert.match(output, /Number-theory frontier note:/); + assert.match(output, /Number-theory theorem loop: baseline/); + assert.match(output, /Number-theory theorem command: erdos problem theorem-loop 1/); + assert.match(output, /Number-theory task list: baseline/); + assert.match(output, /Number-theory task list command: erdos problem task-list 1/); assert.match(output, /Number-theory active ticket: N1/); assert.match(output, /Number-theory ready atoms: 1/); }); +test('workspace show includes inactive frontier loop guidance for problem 848 by default', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-workspace-number-theory-848-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const output = runCli(['workspace', 'show'], { cwd: workspace }); + assert.match(output, /Number-theory theorem loop: bridge_backed/); + assert.match(output, /Number-theory theorem command: erdos problem theorem-loop 848/); + assert.match(output, /Number-theory claim loop: bridge_backed/); + assert.match(output, /Number-theory claim command: erdos problem claim-loop 848/); + assert.match(output, /Number-theory claim pass: bridge_backed/); + assert.match(output, /Number-theory claim pass command: erdos problem claim-pass 848/); + assert.match(output, /Number-theory formalization: bridge_backed/); + assert.match(output, /Number-theory formalization command: erdos problem formalization 848/); + assert.match(output, /Number-theory formalization work: bridge_backed/); + assert.match(output, /Number-theory formalization work command: erdos problem formalization-work 848/); + assert.match(output, /Number-theory task list: bridge_backed/); + assert.match(output, /Number-theory task list command: erdos problem task-list 848/); + assert.match(output, /Research canonical source: https:\/\/www\.erdosproblems\.com\/848/); + assert.match(output, /Research compute entry: erdos number-theory dispatch 848/); + assert.match(output, /Research hardware doctor: erdos frontier doctor/); + assert.match(output, /Research source refresh: erdos number-theory bridge-refresh 848/); + assert.match(output, /Research claim refresh: erdos problem claim-loop-refresh 848/); + assert.match(output, /Research claim pass refresh: erdos problem claim-pass-refresh 848/); + assert.match(output, /Research formalization refresh: erdos problem formalization-refresh 848/); + assert.match(output, /Research formalization work refresh: erdos problem formalization-work-refresh 848/); + assert.match(output, /Research task list refresh: erdos problem task-list-refresh 848/); + assert.match(output, /Number-theory frontier loop: inactive/); + assert.match(output, /Number-theory frontier loop activation: erdos frontier setup --base --apply/); + assert.match(output, /Number-theory frontier loop GPU path: erdos frontier setup --cuda --torch-index-url --apply/); +}); + +test('state show includes inactive frontier loop guidance for problem 848 by default', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-state-frontier-848-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const output = runCli(['state', 'show'], { cwd: workspace }); + assert.match(output, /Frontier loop: inactive/); + assert.match(output, /Frontier loop activation: erdos frontier setup --base --apply/); + assert.match(output, /Frontier loop GPU path: erdos frontier setup --cuda --torch-index-url --apply/); + assert.match(fs.readFileSync(path.join(workspace, '.erdos', 'STATE.md'), 'utf8'), /## Frontier Loop/); + assert.match(fs.readFileSync(path.join(workspace, '.erdos', 'STATE.md'), 'utf8'), /GPU Upgrade Command:/); +}); + +test('number-theory status activates the frontier loop in cpu mode when the workspace is opted in and managed-ready', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-848-frontier-cpu-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const configPath = path.join(workspace, '.erdos', 'config.json'); + const config = JSON.parse(fs.readFileSync(configPath, 'utf8')); + config.frontier = { + ...(config.frontier ?? {}), + loopOptIn: true, + runtimeMode: 'base', + activeMode: 'cpu', + managedFrontierReady: true, + gpuSearchReady: false, + lastSetupAt: '2026-04-06T00:00:00.000Z', + lastDoctorAt: '2026-04-06T00:00:00.000Z', + }; + fs.writeFileSync(configPath, JSON.stringify(config, null, 2) + '\n'); + + const output = runCli(['number-theory', 'status', '848'], { cwd: workspace }); + assert.match(output, /Frontier loop: active \(cpu\)/); + assert.match(output, /Frontier loop summary:/); + assert.match(output, /Frontier loop entry: erdos number-theory dispatch 848/); + assert.match(output, /Frontier loop commands:/); + assert.match(output, /Frontier loop upgrade: erdos frontier setup --cuda --torch-index-url --apply/); +}); + +test('number-theory status activates the frontier loop when the workspace is opted in and GPU-ready', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-848-frontier-active-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const configPath = path.join(workspace, '.erdos', 'config.json'); + const config = JSON.parse(fs.readFileSync(configPath, 'utf8')); + config.frontier = { + ...(config.frontier ?? {}), + loopOptIn: true, + runtimeMode: 'cuda', + activeMode: 'gpu', + managedFrontierReady: true, + gpuSearchReady: true, + lastSetupAt: '2026-04-06T00:00:00.000Z', + lastDoctorAt: '2026-04-06T00:00:00.000Z', + }; + fs.writeFileSync(configPath, JSON.stringify(config, null, 2) + '\n'); + + const output = runCli(['number-theory', 'status', '848'], { cwd: workspace }); + assert.match(output, /Frontier loop: active \(gpu\)/); + assert.match(output, /Frontier loop summary:/); + assert.match(output, /Frontier loop entry: erdos number-theory dispatch 848/); + assert.match(output, /Frontier loop commands:/); +}); + +test('number-theory status keeps a paid Brev GPU rung out of the active loop until explicitly enabled', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-848-paid-rung-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const configPath = path.join(workspace, '.erdos', 'config.json'); + const config = JSON.parse(fs.readFileSync(configPath, 'utf8')); + config.frontier = { + ...(config.frontier ?? {}), + loopOptIn: true, + runtimeMode: null, + activeMode: null, + activeRemoteId: 'erdos-p848-h100', + remotes: { + 'erdos-p848-h100': { + remoteId: 'erdos-p848-h100', + provider: 'brev', + instanceName: 'erdos-p848-h100', + sshHost: 'erdos-p848-h100', + attached: true, + frontierEngineReady: true, + gpuSearchReady: true, + }, + }, + paidRungs: { + enabledRemoteIds: [], + enabledFleetIds: [], + lastUpdatedAt: null, + }, + remote: { + remoteId: 'erdos-p848-h100', + provider: 'brev', + instanceName: 'erdos-p848-h100', + sshHost: 'erdos-p848-h100', + attached: true, + frontierEngineReady: true, + gpuSearchReady: true, + paidEnabled: false, + }, + }; + fs.writeFileSync(configPath, JSON.stringify(config, null, 2) + '\n'); + + const output = runCli(['number-theory', 'status', '848'], { cwd: workspace }); + assert.match(output, /Frontier loop: inactive/); + assert.match(output, /Frontier loop reason: paid_rung_not_enabled/); + assert.match(output, /Frontier loop activation: erdos frontier setup --base --apply/); +}); + +test('number-theory dispatch defaults to bridge refresh and surfaces the exact scout lane on an inactive workspace', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-dispatch-848-')); + const output = runCli(['number-theory', 'dispatch', '848'], { cwd: workspace }); + assert.match(output, /Erdos Problem #848 number-theory dispatch/); + assert.match(output, /Primary action: bridge_refresh/); + assert.match(output, /Claim-pass recommendations:/); + assert.match(output, /formalize_282_alignment \[high\] theorem_formalization/); + assert.match(output, /- bridge_refresh \[primary, available, system\]/); + assert.match(output, /- formalization_work_refresh \[available, theorem\]/); + assert.match(output, /- formalization_refresh \[available, theorem\]/); + assert.match(output, /- claim_pass_refresh \[available, theorem\]/); + assert.match(output, /- exact_followup_rollout \[available, cpu\]/); + assert.match(output, /- exact_followup_launch \[available, cpu\]/); + assert.match(output, /- exact_interval_scout \[available, cpu\]/); + assert.match(output, /- structural_two_side_scout \[available, cpu\]/); + assert.match(output, /- mixed_base_failure_scout \[available, cpu\]/); + assert.match(output, /- full_mixed_base_structural_verifier \[available, cpu\]/); + assert.match(output, /- structural_lift_miner \[available, cpu\]/); + assert.match(output, /apply: erdos number-theory dispatch 848 --apply --action exact_interval_scout/); +}); + +test('number-theory dispatch apply runs the current primary action on an inactive workspace', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-dispatch-apply-848-')); + const output = runCli(['number-theory', 'dispatch', '848', '--apply'], { cwd: workspace }); + assert.match(output, /Number-theory dispatch: complete/); + assert.match(output, /Action: bridge_refresh/); + assert.match(output, /Bridge refresh: complete/); +}); + +test('number-theory dispatch can refresh claim-pass recommendations for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-claim-pass-848-')); + const output = runCli(['number-theory', 'dispatch', '848', '--apply', '--action', 'claim_pass_refresh', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'claim_pass_refresh'); + assert.match(payload.claimPassRefresh.jsonPath, /packs\/number-theory\/problems\/848\/CLAIM_PASS\.json$/); + assert.equal(fs.existsSync(payload.claimPassRefresh.jsonPath), true); + const claimPass = JSON.parse(fs.readFileSync(payload.claimPassRefresh.jsonPath, 'utf8')); + assert.equal(claimPass.problemId, '848'); + assert.equal(claimPass.summary.claims.supported >= 2, true); + assert.equal(claimPass.recommendations.some((item) => item.recommendation_id === 'formalize_282_alignment'), true); + assert.equal(claimPass.recommendations.some((item) => item.recommendation_id === 'formalize_top_repair_cluster'), true); +}); + +test('number-theory dispatch can refresh the formalization packet for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-formalization-848-')); + const output = runCli(['number-theory', 'dispatch', '848', '--apply', '--action', 'formalization_refresh', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'formalization_refresh'); + assert.match(payload.formalizationRefresh.jsonPath, /packs\/number-theory\/problems\/848\/FORMALIZATION\.json$/); + assert.equal(fs.existsSync(payload.formalizationRefresh.jsonPath), true); + const formalization = JSON.parse(fs.readFileSync(payload.formalizationRefresh.jsonPath, 'utf8')); + assert.equal(formalization.problemId, '848'); + assert.equal(formalization.currentTarget.focusId, 'formalize_282_alignment'); +}); + +test('number-theory dispatch can refresh the formalization work packet for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-formalization-work-848-')); + const output = runCli(['number-theory', 'dispatch', '848', '--apply', '--action', 'formalization_work_refresh', '--json'], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'formalization_work_refresh'); + assert.match(payload.formalizationWorkRefresh.jsonPath, /packs\/number-theory\/problems\/848\/FORMALIZATION_WORK\.json$/); + assert.equal(fs.existsSync(payload.formalizationWorkRefresh.jsonPath), true); + const formalizationWork = JSON.parse(fs.readFileSync(payload.formalizationWorkRefresh.jsonPath, 'utf8')); + assert.equal(formalizationWork.problemId, '848'); + assert.equal(formalizationWork.currentWork.focusId, 'lift_132_activation_schema_beyond_finite_menu'); + assert.equal(formalizationWork.currentWork.packetData.tupleRowCrtDerivation.projectedResidueModuloWitness, 504); + assert.equal(formalizationWork.currentWork.packetData.witnessSquareModulus, 841); + assert.equal(formalizationWork.currentWork.packetData.witnessFirstOccurrence.firstRepresentative, 137720141); + assert.equal(formalizationWork.currentWork.packetData.representativeResidueModuloWitness, 504); + assert.equal(formalizationWork.currentWork.mechanismAssessment.verdict, 'controlled_congruence_candidate'); + assert.equal(formalizationWork.currentWork.packetData.rowProgressionModuloWitness.traversesAllWitnessResidues, true); + assert.equal(formalizationWork.currentWork.packetData.rowProgressionAnchorTable.some((row) => row.anchor === 282 && row.rowIndexForWitness === 0), true); + assert.equal(formalizationWork.currentWork.packetData.rowStartDerivation282.normalizedEquation, 't ≡ 0 (mod 841)'); + assert.equal(formalizationWork.currentWork.packetData.unsolvableContrast232.solvable, false); + assert.equal(formalizationWork.currentWork.packetData.nextSameRowWitnessFor282, 27443256270065); + assert.equal(fs.existsSync(payload.formalizationWorkRefresh.svgPath), true); +}); + +test('number-theory dispatch audits external structural verifier blockers for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-structural-audit-848-')); + const sourceDir = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-848-external-source-')); + const problemDir = path.join(sourceDir, '848'); + fs.mkdirSync(problemDir, { recursive: true }); + fs.writeFileSync(path.join(sourceDir, 'README.md'), [ + '# External 848 verifier', + '', + 'Problem 848 solved for all N by checking N <= 10^7 and using Sawhney for N > 10^7.', + '', + ].join('\n')); + fs.writeFileSync(path.join(problemDir, 'proof.md'), [ + '# Proof', + '', + 'Sawhney handles N > 10^7 after the finite verifier.', + '', + 's_max^(p)(N) + max(V_p, V_p) + d_max^(p)(N) + R_{>p}(N) < M(N)', + '', + ].join('\n')); + fs.writeFileSync(path.join(problemDir, 'erdos848_verifier_v5.cpp'), [ + 'bool is_base_residue(int x) { const int r = x % 25; return r == 7 || r == 18; }', + 'void build_base_masks(long long x, long long m_max) {', + ' const long long b = 7LL * x + 1;', + ' const long long max_val = x * (7LL + 25LL * (m_max - 1)) + 1;', + '}', + '', + ].join('\n')); + + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'structural_verifier_audit', + '--external-source-dir', + sourceDir, + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'structural_verifier_audit'); + assert.equal(payload.structuralVerifierAudit.status, 'blocked'); + assert.equal(payload.structuralVerifierAudit.summary.blockerCount, 2); + assert.equal(payload.structuralVerifierAudit.summary.baseSevenMaskPresent, true); + assert.equal(payload.structuralVerifierAudit.summary.baseEighteenMaskPresent, false); + assert.equal(fs.existsSync(payload.structuralVerifierAudit.jsonPath), true); + assert.equal(fs.existsSync(payload.structuralVerifierAudit.markdownPath), true); + const audit = JSON.parse(fs.readFileSync(payload.structuralVerifierAudit.jsonPath, 'utf8')); + assert.equal(audit.checks.some((check) => check.checkId === 'sawhney_handoff_not_claimed_at_1e7' && check.status === 'failed'), true); + assert.equal(audit.checks.some((check) => check.checkId === 'base_exchange_mask_covers_both_principal_sides' && check.status === 'failed'), true); +}); + +test('number-theory dispatch runs the base-side scout for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-base-side-scout-848-')); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'base_side_scout', + '--base-side-max', + '200', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'base_side_scout'); + assert.equal(payload.baseSideScout.status, 'counterexample_to_global_7_side_domination_found'); + assert.equal(payload.baseSideScout.summary.interval, '1..200'); + assert.equal(payload.baseSideScout.summary.maxSide18ExceedsSide7, true); + assert.equal(payload.baseSideScout.firstNWithSide18MaxExceedingSide7.N, 143); + assert.equal(fs.existsSync(payload.baseSideScout.jsonPath), true); + assert.equal(fs.existsSync(payload.baseSideScout.markdownPath), true); +}); + +test('number-theory dispatch runs the two-sided structural scout for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-two-side-structural-848-')); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'structural_two_side_scout', + '--structural-min', + '1', + '--structural-max', + '1000', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'structural_two_side_scout'); + assert.equal(payload.structuralTwoSideScout.summary.assessedRange, '1..1000'); + assert.equal(payload.structuralTwoSideScout.summary.allUnionChecksPass, false); + assert.equal(payload.structuralTwoSideScout.summary.unionFailureCount > 0, true); + assert.equal(fs.existsSync(payload.structuralTwoSideScout.jsonPath), true); + assert.equal(fs.existsSync(payload.structuralTwoSideScout.markdownPath), true); +}); + +test('number-theory dispatch runs the mixed-base failure scout for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-mixed-base-scout-848-')); + runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'structural_two_side_scout', + '--structural-min', + '7307', + '--structural-max', + '7600', + '--json', + ], { cwd: workspace }); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'mixed_base_failure_scout', + '--mixed-base-max-rows', + '8', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'mixed_base_failure_scout'); + assert.equal(payload.mixedBaseFailureScout.summary.analyzedRowCount > 0, true); + assert.equal(payload.mixedBaseFailureScout.summary.allAnalyzedRowsMixedPass, true); + assert.equal(payload.mixedBaseFailureScout.summary.mixedFailureCount, 0); + assert.equal(fs.existsSync(payload.mixedBaseFailureScout.jsonPath), true); + assert.equal(fs.existsSync(payload.mixedBaseFailureScout.markdownPath), true); +}); + +test('number-theory dispatch runs the full mixed-base structural verifier for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-full-mixed-structural-848-')); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'full_mixed_base_structural_verifier', + '--structural-min', + '7307', + '--structural-max', + '7600', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'full_mixed_base_structural_verifier'); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.assessedRange, '7307..7600'); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.allMixedChecksPass, true); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.mixedFailureCount, 0); + assert.equal(payload.fullMixedBaseStructuralVerifier.summary.threateningOutsiderCheckCount > 0, true); + assert.equal(fs.existsSync(payload.fullMixedBaseStructuralVerifier.jsonPath), true); + assert.equal(fs.existsSync(payload.fullMixedBaseStructuralVerifier.markdownPath), true); +}); + +test('number-theory dispatch runs the structural lift miner for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-structural-lift-miner-848-')); + const artifactJsonPath = path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'STRUCTURAL_LIFT_MINER.json'); + const artifactMarkdownPath = path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'STRUCTURAL_LIFT_MINER.md'); + const previousJson = fs.existsSync(artifactJsonPath) ? fs.readFileSync(artifactJsonPath, 'utf8') : null; + const previousMarkdown = fs.existsSync(artifactMarkdownPath) ? fs.readFileSync(artifactMarkdownPath, 'utf8') : null; + try { + runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'full_mixed_base_structural_verifier', + '--structural-min', + '7307', + '--structural-max', + '7600', + '--json', + ], { cwd: workspace }); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'structural_lift_miner', + '--structural-lift-top-rows', + '8', + '--structural-lift-family-limit', + '8', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'structural_lift_miner'); + assert.equal(payload.structuralLiftMiner.status, 'structural_lift_obligation_packet_ready'); + assert.equal(payload.structuralLiftMiner.summary.coverageComplete, true); + assert.deepEqual(payload.structuralLiftMiner.summary.primaryExactPrimes, [13, 17]); + assert.equal(payload.structuralLiftMiner.summary.nextTheoremLane, 'formalize_cross_side_matching_bound_then_exact_prime_margin_lift'); + assert.equal(fs.existsSync(payload.structuralLiftMiner.jsonPath), true); + assert.equal(fs.existsSync(payload.structuralLiftMiner.markdownPath), true); + } finally { + if (previousJson === null) { + fs.rmSync(artifactJsonPath, { force: true }); + } else { + fs.writeFileSync(artifactJsonPath, previousJson); + } + if (previousMarkdown === null) { + fs.rmSync(artifactMarkdownPath, { force: true }); + } else { + fs.writeFileSync(artifactMarkdownPath, previousMarkdown); + } + } +}); + +test('number-theory dispatch runs the matching pattern miner for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-matching-pattern-miner-848-')); + const artifactJsonPath = path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'MATCHING_PATTERN_MINER.json'); + const artifactMarkdownPath = path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'MATCHING_PATTERN_MINER.md'); + const previousJson = fs.existsSync(artifactJsonPath) ? fs.readFileSync(artifactJsonPath, 'utf8') : null; + const previousMarkdown = fs.existsSync(artifactMarkdownPath) ? fs.readFileSync(artifactMarkdownPath, 'utf8') : null; + try { + runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'full_mixed_base_structural_verifier', + '--structural-min', + '7307', + '--structural-max', + '7600', + '--json', + ], { cwd: workspace }); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'matching_pattern_miner', + '--matching-pattern-prime', + '13', + '--matching-pattern-top-rows', + '6', + '--matching-pattern-pair-sample-limit', + '8', + '--json', + ], { cwd: workspace }); + const payload = JSON.parse(output); + assert.equal(payload.ok, true); + assert.equal(payload.action.actionId, 'matching_pattern_miner'); + assert.equal(payload.matchingPatternMiner.status, 'matching_pattern_witness_packet_ready'); + assert.equal(payload.matchingPatternMiner.parameters.targetPrime, 13); + assert.equal(payload.matchingPatternMiner.summary.witnessRowCount, 6); + assert.equal(payload.matchingPatternMiner.summary.allReconstructedMatchesAgree, true); + assert.equal(payload.matchingPatternMiner.summary.allWitnessesMeetRequiredMatchingLowerBound, true); + assert.equal(payload.matchingPatternMiner.summary.allWitnessesSaturateSmallerSide, true); + assert.equal(payload.matchingPatternMiner.summary.minMatchingSlack, 19); + assert.equal(payload.matchingPatternMiner.patternSummary.totalWitnessMatchingPairs > 0, true); + assert.equal(payload.matchingPatternMiner.patternSummary.splitProfiles.length > 0, true); + assert.equal(payload.matchingPatternMiner.patternSummary.allSplitCommonCoresMeetMaxRequiredBound, true); + assert.equal(payload.matchingPatternMiner.patternSummary.allSplitCommonCoresSaturateMinSmallerSide, true); + assert.equal(payload.matchingPatternMiner.patternSummary.splitProfiles.every((profile) => profile.commonMatchingPairExportComplete), true); + assert.equal(payload.matchingPatternMiner.patternSummary.splitProfiles.every((profile) => profile.commonMatchingPairExportedCount === profile.commonMatchingPairCount), true); + assert.equal(payload.matchingPatternMiner.symbolicUse.activeAtom, 'D2_p13_matching_lower_bound'); + assert.equal(payload.matchingPatternMiner.witnessSample[0].matchingPairSample.length > 0, true); + assert.equal(fs.existsSync(payload.matchingPatternMiner.jsonPath), true); + const artifact = JSON.parse(fs.readFileSync(payload.matchingPatternMiner.jsonPath, 'utf8')); + assert.equal(artifact.patternSummary.splitProfiles.every((profile) => profile.commonMatchingPairExportComplete), true); + assert.equal(artifact.patternSummary.splitProfiles.every((profile) => profile.commonMatchingPairs.length === profile.commonMatchingPairCount), true); + assert.equal(fs.existsSync(payload.matchingPatternMiner.markdownPath), true); + } finally { + if (previousJson === null) { + fs.rmSync(artifactJsonPath, { force: true }); + } else { + fs.writeFileSync(artifactJsonPath, previousJson); + } + if (previousMarkdown === null) { + fs.rmSync(artifactMarkdownPath, { force: true }); + } else { + fs.writeFileSync(artifactMarkdownPath, previousMarkdown); + } + } +}); + +test('number-theory dispatch can assemble an exact handoff bundle for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-exact-handoff-848-')); + const output = runCli(['number-theory', 'dispatch', '848', '--apply', '--action', 'exact_handoff_bundle'], { cwd: workspace }); + assert.match(output, /Number-theory dispatch: complete/); + assert.match(output, /Action: exact_handoff_bundle/); + assert.match(output, /Exact handoff JSON:/); + + const runsDir = path.join(workspace, '.erdos', 'runs'); + const runEntries = fs.readdirSync(runsDir); + assert.equal(runEntries.length, 1); + const runDir = path.join(runsDir, runEntries[0], 'exact-handoff'); + assert.equal(fs.existsSync(path.join(runDir, 'EXACT_HANDOFF.json')), true); + assert.equal(fs.existsSync(path.join(runDir, 'EXACT_HANDOFF.md')), true); + + const handoff = JSON.parse(fs.readFileSync(path.join(runDir, 'EXACT_HANDOFF.json'), 'utf8')); + assert.equal(handoff.problemId, '848'); + assert.equal(handoff.exactFocus.nextUnmatchedRepresentative, 137720141); +}); + +test('number-theory dispatch can launch exact follow-up from the handoff bundle for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-exact-followup-848-')); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'exact_followup_launch', + '--exact-min', + '10001', + '--exact-max', + '10002', + ], { cwd: workspace }); + + assert.match(output, /Number-theory dispatch: complete/); + assert.match(output, /Action: exact_followup_launch/); + assert.match(output, /Exact handoff dir:/); + assert.match(output, /Exact follow-up JSON:/); + assert.match(output, /Exact follow-up interval: 10001\.\.10002/); + + const runsDir = path.join(workspace, '.erdos', 'runs'); + const runEntries = fs.readdirSync(runsDir); + assert.equal(runEntries.length, 1); + const runRoot = path.join(runsDir, runEntries[0]); + const handoffPath = path.join(runRoot, 'exact-handoff', 'EXACT_HANDOFF.json'); + const followupPath = path.join(runRoot, 'exact-followup', 'EXACT_FOLLOWUP.json'); + const resultsPath = path.join(runRoot, 'exact-followup', 'EXACT_SMALL_N_RESULTS.json'); + + assert.equal(fs.existsSync(handoffPath), true); + assert.equal(fs.existsSync(followupPath), true); + assert.equal(fs.existsSync(resultsPath), true); + + const followup = JSON.parse(fs.readFileSync(followupPath, 'utf8')); + assert.equal(followup.problemId, '848'); + assert.equal(followup.backend.kind, 'exact_small_n'); + assert.equal(followup.backend.min, 10001); + assert.equal(followup.backend.max, 10002); + assert.equal(followup.resultsSummary.interval, '10001..10002'); +}); + +test('problem 848 exact scanner supports endpoint-monotonicity mode', () => { + const outputPath = path.join(os.tmpdir(), `p848-endpoint-scan-${Date.now()}.json`); + const scriptPath = path.join(repoRoot, 'packs', 'number-theory', 'problems', '848', 'compute', 'problem848_small_n_exact_scan.mjs'); + const output = execFileSync('node', [ + scriptPath, + '--min', + '17301', + '--max', + '17400', + '--endpoint-monotonicity', + '--json-output', + outputPath, + ], { encoding: 'utf8' }); + const summary = JSON.parse(output); + const payload = JSON.parse(fs.readFileSync(outputPath, 'utf8')); + assert.equal(summary.interval, '17301..17400'); + assert.equal(payload.method, 'endpoint_monotonicity_maximum_clique_scan'); + assert.equal(payload.summary.rows, 100); + assert.equal(payload.endpointMonotonicity.allEndpointChecksCertified, true); + assert.equal(payload.endpointMonotonicity.endpointCheckCount < payload.summary.rows, true); + assert.equal(payload.results.every((row) => row.inferredByEndpointMonotonicity === true), true); +}); + +test('number-theory dispatch can roll out multiple exact follow-up chunks for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-exact-rollout-848-')); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--action', + 'exact_followup_rollout', + '--exact-min', + '10001', + '--exact-chunks', + '2', + '--exact-chunk-size', + '1', + ], { cwd: workspace }); + + assert.match(output, /Number-theory dispatch: complete/); + assert.match(output, /Action: exact_followup_rollout/); + assert.match(output, /Exact rollout JSON:/); + assert.match(output, /Exact rollout completed chunks: 2\/2/); + assert.match(output, /Exact rollout covered interval: 10001\.\.10002/); + assert.match(output, /- chunk 1: 10001\.\.10001 \[ok\]/); + assert.match(output, /- chunk 2: 10002\.\.10002 \[ok\]/); + + const runsDir = path.join(workspace, '.erdos', 'runs'); + const runEntries = fs.readdirSync(runsDir); + assert.equal(runEntries.length, 3); + + const rolloutRunDir = runEntries + .map((entry) => path.join(runsDir, entry)) + .find((entry) => fs.existsSync(path.join(entry, 'exact-rollout', 'EXACT_ROLLOUT.json'))); + assert.ok(rolloutRunDir); + + const rolloutPath = path.join(rolloutRunDir, 'exact-rollout', 'EXACT_ROLLOUT.json'); + const rollout = JSON.parse(fs.readFileSync(rolloutPath, 'utf8')); + assert.equal(rollout.problemId, '848'); + assert.equal(rollout.requestedChunkCount, 2); + assert.equal(rollout.completedChunkCount, 2); + assert.equal(rollout.completedInterval, '10001..10002'); + assert.equal(rollout.childRuns.length, 2); + assert.equal(rollout.childRuns[0].interval, '10001..10001'); + assert.equal(rollout.childRuns[1].interval, '10002..10002'); +}); + +test('number-theory dispatch can detach into a supervised frontier session for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-detach-848-')); + const output = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--detach', + '--action', + 'bridge_refresh', + '--review-after-hours', + '0.001', + ], { cwd: workspace }); + + assert.match(output, /Number-theory dispatch: detached/); + assert.match(output, /Action: bridge_refresh/); + const sessionId = output.match(/Frontier session id: (.+)$/m)?.[1]?.trim(); + assert.ok(sessionId); + + const session = JSON.parse(runCli(['frontier', 'session', sessionId, '--json'], { cwd: workspace })); + assert.equal(session.problemId, '848'); + assert.equal(session.actionId, 'bridge_refresh'); + assert.equal(session.kind, 'number_theory_dispatch'); + assert.equal(Number(session.reviewAfterHours), 0.001); + + const sessions = JSON.parse(runCli(['frontier', 'sessions', '--json'], { cwd: workspace })); + assert.equal(sessions.sessions.some((entry) => entry.sessionId === sessionId), true); + + const stopResult = JSON.parse(runCli(['frontier', 'stop-session', sessionId, '--json'], { cwd: workspace })); + assert.equal(stopResult.ok, true); +}); + +test('number-theory detach reuses an equivalent running exact rollout session instead of launching a duplicate', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-detach-reuse-848-')); + const firstOutput = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--detach', + '--action', + 'exact_followup_rollout', + '--exact-min', + '12001', + '--exact-chunks', + '2', + '--exact-chunk-size', + '10', + '--review-after-hours', + '1', + ], { cwd: workspace }); + const firstSessionId = firstOutput.match(/Frontier session id: (.+)$/m)?.[1]?.trim(); + assert.ok(firstSessionId); + + const secondOutput = runCli([ + 'number-theory', + 'dispatch', + '848', + '--apply', + '--detach', + '--action', + 'exact_followup_rollout', + '--exact-min', + '12001', + '--exact-chunks', + '2', + '--exact-chunk-size', + '10', + '--review-after-hours', + '1', + ], { cwd: workspace }); + const secondSessionId = secondOutput.match(/Frontier session id: (.+)$/m)?.[1]?.trim(); + assert.equal(secondSessionId, firstSessionId); + assert.match(secondOutput, /Reused existing session: yes/); +}); + +test('number-theory dispatch-fleet previews and launches an aggregated fleet run for 848', () => { + const workspace = fs.mkdtempSync(path.join(os.tmpdir(), 'erdos-number-theory-dispatch-fleet-848-')); + runCli(['problem', 'use', '848'], { cwd: workspace }); + const configPath = path.join(workspace, '.erdos', 'config.json'); + const config = JSON.parse(fs.readFileSync(configPath, 'utf8')); + config.frontier = { + ...(config.frontier ?? {}), + loopOptIn: true, + runtimeMode: 'cuda', + activeMode: 'gpu', + managedFrontierReady: true, + gpuSearchReady: true, + remotes: { + h100x2_01: { + remoteId: 'h100x2_01', + provider: 'ssh', + attached: false, + }, + h100x2_02: { + remoteId: 'h100x2_02', + provider: 'ssh', + attached: false, + }, + }, + fleets: { + h100x2: { + fleetId: 'h100x2', + provider: 'brev', + count: 2, + laneId: 'p848_anchor_ladder', + intendedTopology: 'parallel_independent_sweeps', + remoteIds: ['h100x2_01', 'h100x2_02'], + }, + }, + }; + fs.writeFileSync(configPath, JSON.stringify(config, null, 2) + '\n'); + + const preview = JSON.parse(runCli([ + 'number-theory', + 'dispatch-fleet', + '848', + '--fleet', + 'h100x2', + '--action', + 'bridge_refresh', + '--json', + ], { cwd: workspace })); + assert.equal(preview.available, true); + assert.equal(preview.fleetId, 'h100x2'); + assert.equal(preview.members.length, 2); + assert.equal(preview.availableMemberCount, 2); + + const gpuPreview = JSON.parse(runCli([ + 'number-theory', + 'dispatch-fleet', + '848', + '--fleet', + 'h100x2', + '--action', + 'gpu_profile_sweep', + '--strategy', + 'ladder_cover_v1', + '--json', + ], { cwd: workspace })); + assert.equal(gpuPreview.strategyId, 'ladder_cover_v1'); + assert.equal(gpuPreview.members.every((member) => Boolean(member.assignment)), true); + assert.equal(gpuPreview.members[0].assignment.center > 0, true); + + const launched = JSON.parse(runCli([ + 'number-theory', + 'dispatch-fleet', + '848', + '--fleet', + 'h100x2', + '--apply', + '--action', + 'bridge_refresh', + '--json', + ], { cwd: workspace })); + assert.equal(launched.launchedCount, 2); + assert.equal(Boolean(launched.fleetRun?.runId), true); + + const fleetRun = JSON.parse(runCli([ + 'number-theory', + 'fleet-run', + launched.fleetRun.runId, + '--json', + ], { cwd: workspace })); + assert.equal(fleetRun.fleetId, 'h100x2'); + assert.equal(fleetRun.members.length, 2); +}); + test('problem show surfaces solved archival mode for 1008', () => { const output = runCli(['problem', 'show', '1008']); assert.match(output, /Archive mode: method_exemplar/); @@ -848,6 +3650,14 @@ test('graph-theory status shows the lean archive workspace for 1008', () => { assert.match(output, /Harness profile: lean_archive_workspace/); assert.match(output, /Archive mode: method_exemplar/); assert.match(output, /Problem solved: yes/); + assert.match(output, /Theorem loop: baseline/); + assert.match(output, /Theorem command: erdos problem theorem-loop 1008/); + assert.match(output, /Claim loop: baseline/); + assert.match(output, /Claim command: erdos problem claim-loop 1008/); + assert.match(output, /Claim pass: baseline/); + assert.match(output, /Claim pass command: erdos problem claim-pass 1008/); + assert.match(output, /Task list: baseline/); + assert.match(output, /Task list command: erdos problem task-list 1008/); assert.match(output, /First ready atom: G1008.G1.A1/); }); From 6cc14aebd233223030add1ec22cc2fb270745a75 Mon Sep 17 00:00:00 2001 From: Cody Mitchell Date: Tue, 14 Apr 2026 10:58:26 -0500 Subject: [PATCH 2/4] Add frontier and theorem loop artifacts --- .../problems/1008/CLAIM_LOOP.json | 157 + .../graph-theory/problems/1008/CLAIM_LOOP.md | 53 + .../problems/1008/CLAIM_PASS.json | 119 + .../graph-theory/problems/1008/CLAIM_PASS.md | 54 + .../problems/1008/FORMALIZATION.json | 194 + .../problems/1008/FORMALIZATION.md | 86 + .../problems/1008/FORMALIZATION_WORK.json | 64 + .../problems/1008/FORMALIZATION_WORK.md | 61 + .../problems/1008/FORMALIZATION_WORK.svg | 1 + .../graph-theory/problems/1008/TASK_LIST.json | 215 + packs/graph-theory/problems/1008/TASK_LIST.md | 85 + .../problems/1008/THEOREM_LOOP.json | 74 + .../problems/1008/THEOREM_LOOP.md | 46 + .../number-theory/problems/1/CLAIM_LOOP.json | 171 + packs/number-theory/problems/1/CLAIM_LOOP.md | 55 + .../number-theory/problems/1/CLAIM_PASS.json | 119 + packs/number-theory/problems/1/CLAIM_PASS.md | 54 + .../problems/1/FORMALIZATION.json | 194 + .../number-theory/problems/1/FORMALIZATION.md | 86 + .../problems/1/FORMALIZATION_WORK.json | 65 + .../problems/1/FORMALIZATION_WORK.md | 61 + .../problems/1/FORMALIZATION_WORK.svg | 1 + packs/number-theory/problems/1/TASK_LIST.json | 445 + packs/number-theory/problems/1/TASK_LIST.md | 142 + .../problems/1/TASK_LOOP_RUN.json | 120 + .../number-theory/problems/1/TASK_LOOP_RUN.md | 20 + .../problems/1/THEOREM_LOOP.json | 74 + .../number-theory/problems/1/THEOREM_LOOP.md | 46 + .../problems/848/BASE_SIDE_SCOUT.json | 4145 + .../problems/848/BASE_SIDE_SCOUT.md | 22 + .../problems/848/CLAIM_LOOP.json | 297 + .../number-theory/problems/848/CLAIM_LOOP.md | 69 + .../problems/848/CLAIM_PASS.json | 204 + .../number-theory/problems/848/CLAIM_PASS.md | 64 + .../problems/848/ENDPOINT_MENU_ABSTRACTION.md | 75 + .../848/EXACT_BREAKPOINT_CERTIFICATE.json | 19486 ++++ .../problems/848/EXACT_BREAKPOINT_SCOUT.json | 35710 ++++++++ .../EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json | 130 + .../848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md | 55 + .../problems/848/FORMALIZATION.json | 311 + .../problems/848/FORMALIZATION.md | 101 + .../problems/848/FORMALIZATION_WORK.json | 58279 ++++++++++++ .../problems/848/FORMALIZATION_WORK.md | 235 + .../problems/848/FORMALIZATION_WORK.svg | 1 + .../FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json | 75235 ++++++++++++++++ .../FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md | 37 + .../problems/848/MATCHING_PATTERN_MINER.json | 17177 ++++ .../problems/848/MATCHING_PATTERN_MINER.md | 61 + .../848/MATCHING_PATTERN_MINER_P17.json | 15938 ++++ .../848/MATCHING_PATTERN_MINER_P17.md | 60 + .../848/MIXED_BASE_FAILURE_SCOUT.json | 1241 + .../problems/848/MIXED_BASE_FAILURE_SCOUT.md | 20 + .../problems/848/SEARCH_THEOREM_BRIDGE.json | 530 + .../problems/848/SEARCH_THEOREM_BRIDGE.md | 60 + .../848/STRUCTURAL_LIFT_CHECKLIST.json | 379 + .../problems/848/STRUCTURAL_LIFT_CHECKLIST.md | 83 + .../problems/848/STRUCTURAL_LIFT_MINER.json | 5095 ++ .../problems/848/STRUCTURAL_LIFT_MINER.md | 68 + .../848/STRUCTURAL_TWO_SIDE_SCOUT.json | 2780 + .../problems/848/STRUCTURAL_TWO_SIDE_SCOUT.md | 34 + .../number-theory/problems/848/TASK_LIST.json | 22248 +++++ packs/number-theory/problems/848/TASK_LIST.md | 683 + .../problems/848/TASK_LOOP_RUN.json | 4548 + .../problems/848/TASK_LOOP_RUN.md | 266 + .../problems/848/THEOREM_LOOP.json | 125 + .../problems/848/THEOREM_LOOP.md | 60 + .../compute/problem848_base_side_scout.mjs | 270 + .../problem848_breakpoint_certificate.mjs | 148 + .../problem848_endpoint_menu_compiler.mjs | 1020 + .../problem848_exact_breakpoint_scout.mjs | 140 + .../problem848_external_structural_audit.mjs | 354 + ...48_full_mixed_base_structural_verifier.mjs | 933 + .../problem848_matching_pattern_miner.mjs | 570 + .../problem848_mixed_base_failure_scout.mjs | 332 + .../problem848_structural_lift_miner.mjs | 548 + .../problem848_structural_two_side_scout.mjs | 528 + packs/sunflower/problems/857/CLAIM_LOOP.json | 183 + packs/sunflower/problems/857/CLAIM_LOOP.md | 54 + packs/sunflower/problems/857/CLAIM_PASS.json | 139 + packs/sunflower/problems/857/CLAIM_PASS.md | 56 + .../sunflower/problems/857/FORMALIZATION.json | 210 + packs/sunflower/problems/857/FORMALIZATION.md | 86 + .../problems/857/FORMALIZATION_WORK.json | 64 + .../problems/857/FORMALIZATION_WORK.md | 61 + .../problems/857/FORMALIZATION_WORK.svg | 1 + .../857/MULTIPLICATIVE_REORIENTATION.md | 118 + packs/sunflower/problems/857/TASK_LIST.json | 215 + packs/sunflower/problems/857/TASK_LIST.md | 85 + .../sunflower/problems/857/THEOREM_LOOP.json | 85 + packs/sunflower/problems/857/THEOREM_LOOP.md | 48 + paper/problems/857/progress_note.typ | 353 + problems/848/FORUM_COMMENT_DRAFT.txt | 6 + research/frontier-engine/ARCHITECTURE.md | 132 + research/frontier-engine/ERDOS_ADAPTER.md | 42 + research/frontier-engine/HARDWARE.md | 55 + research/frontier-engine/NAMING.md | 45 + research/frontier-engine/README.md | 129 + research/frontier-engine/ROADMAP.md | 98 + research/frontier-engine/VISION.md | 72 + .../frontier-engine/experiments/README.md | 17 + .../m8-sat-rail/ARTIFACT_SCHEMA.md | 48 + .../m8-sat-rail/CANDIDATE_SCHEMA.md | 52 + .../experiments/m8-sat-rail/README.md | 103 + .../m8-sat-rail/SAT_BUNDLE_SCHEMA.md | 62 + .../experiments/m8-sat-rail/benchmark.json | 17 + .../reference_m8_lower_bound_45.json | 59 + .../windows_rtx4090_search_profile.json | 21 + .../p848-anchor-ladder/BUNDLE_SCHEMA.md | 70 + .../p848-anchor-ladder/FRONTIER_STATE.json | 58 + .../experiments/p848-anchor-ladder/README.md | 136 + .../batched_smoke_profile.json | 27 + .../p848-anchor-ladder/benchmark.json | 12 + .../brev_h100_search_profile.json | 34 + .../known_failure_packets.json | 39 + .../observed_continuations.json | 50 + .../windows_rtx4090_search_profile.json | 34 + .../hardware/legacy_multi_gpu_reference.json | 10 + .../hardware/windows_rtx4090.json | 11 + research/frontier-engine/pyproject.toml | 26 + .../src/frontier_engine/__init__.py | 21 + .../src/frontier_engine/artifacts.py | 57 + .../frontier_engine/benchmarks/__init__.py | 1 + .../frontier_engine/benchmarks/m8_sat_rail.py | 178 + .../src/frontier_engine/cli.py | 596 + .../src/frontier_engine/contracts.py | 70 + .../src/frontier_engine/frontier.py | 49 + .../src/frontier_engine/generator.py | 21 + .../src/frontier_engine/inventory.py | 44 + .../src/frontier_engine/lanes.py | 105 + .../src/frontier_engine/m8_backends.py | 338 + .../src/frontier_engine/m8_search.py | 139 + .../src/frontier_engine/m8_warm_start.py | 89 + .../src/frontier_engine/p848_anchor_search.py | 1084 + .../src/frontier_engine/p848_bundle.py | 85 + .../frontier_engine/p848_theorem_bridge.py | 487 + .../src/frontier_engine/p848_torch_backend.py | 334 + .../src/frontier_engine/pipeline.py | 65 + .../src/frontier_engine/plans.py | 47 + .../src/frontier_engine/rarity.py | 57 + .../src/frontier_engine/runtime.py | 78 + .../src/frontier_engine/sampler.py | 26 + .../src/frontier_engine/surrogate.py | 24 + .../src/frontier_engine/verifier.py | 81 + .../src/frontier_engine/verifier_bundle.py | 72 + src/commands/frontier.js | 1717 + src/runtime/frontier-remote.js | 267 + src/runtime/frontier-sessions.js | 1345 + src/runtime/frontier.js | 2875 + src/runtime/research-stack.js | 129 + src/runtime/theorem-loop.js | 21668 +++++ test/p848-endpoint-menu-compiler.test.js | 163 + 151 files changed, 309152 insertions(+) create mode 100644 packs/graph-theory/problems/1008/CLAIM_LOOP.json create mode 100644 packs/graph-theory/problems/1008/CLAIM_LOOP.md create mode 100644 packs/graph-theory/problems/1008/CLAIM_PASS.json create mode 100644 packs/graph-theory/problems/1008/CLAIM_PASS.md create mode 100644 packs/graph-theory/problems/1008/FORMALIZATION.json create mode 100644 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research/frontier-engine/src/frontier_engine/verifier_bundle.py create mode 100644 src/commands/frontier.js create mode 100644 src/runtime/frontier-remote.js create mode 100644 src/runtime/frontier-sessions.js create mode 100644 src/runtime/frontier.js create mode 100644 src/runtime/research-stack.js create mode 100644 src/runtime/theorem-loop.js create mode 100644 test/p848-endpoint-menu-compiler.test.js diff --git a/packs/graph-theory/problems/1008/CLAIM_LOOP.json b/packs/graph-theory/problems/1008/CLAIM_LOOP.json new file mode 100644 index 0000000..fea5d48 --- /dev/null +++ b/packs/graph-theory/problems/1008/CLAIM_LOOP.json @@ -0,0 +1,157 @@ +{ + "schema": "erdos.problem_claim_loop/1", + "generatedAt": "2026-04-10T08:11:06.262Z", + "problemId": "1008", + "displayName": "Erdos Problem #1008", + "title": "C4-Free Subgraph Density Problem", + "cluster": "graph-theory", + "sourceKind": "theorem_loop_only", + "claimLoopMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "theoremLoopMode": "baseline", + "activeRoute": "c4_free_lean_archive", + "nextHonestMove": "Record the best public/formalization hook and checkpoint the archive packet.", + "routeSummary": "Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture.", + "sourceRefresh": null + }, + "featureExtractors": [ + { + "extractor_id": "pack_route_state", + "kind": "pack_context", + "scope": "all_problems", + "status": "ready", + "note": "Reads pack route, ticket, and atom state as the baseline theorem-search context." + }, + { + "extractor_id": "theorem_loop_snapshot", + "kind": "theorem_loop", + "scope": "all_problems", + "status": "ready", + "note": "Uses the canonical theorem-loop as the current claim-surface ledger." + }, + { + "extractor_id": "cluster_graph_theory_features", + "kind": "cluster_adapter", + "scope": "graph_theory", + "status": "ready", + "note": "Exposes graph-theory archive or theorem-state context to the claim loop." + } + ], + "claimGenerators": [ + { + "generator_id": "baseline_route_claims", + "kind": "route_state", + "scope": "all_problems", + "status": "ready", + "note": "Promotes active routes, ready atoms, and next-honest-move records into candidate claims." + }, + { + "generator_id": "theorem_agenda_claims", + "kind": "agenda_projection", + "scope": "all_problems", + "status": "ready", + "note": "Turns theorem agenda items into explicit candidate claim tickets." + } + ], + "claimFalsifiers": [ + { + "falsifier_id": "theorem_loop_consistency_check", + "kind": "ledger_consistency", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims that overstate the current theorem-loop claim surface." + }, + { + "falsifier_id": "artifact_boundary_check", + "kind": "artifact_boundary", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims unsupported by canonical artifacts already present in the pack." + } + ], + "verifierAdapters": [ + { + "adapter_id": "canonical_artifact_reader", + "kind": "artifact_reader", + "scope": "all_problems", + "status": "ready", + "note": "Reads theorem-loop, route, and pack artifacts as verifier-facing evidence." + } + ], + "candidateClaims": [ + { + "claim_id": "promote_ready_atom", + "status": "ready", + "source": "theorem_agenda", + "summary": "Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint.", + "why": "Record the best public/formalization hook and checkpoint the archive packet.", + "support": [ + "active_route_recorded", + "ready_atom_present", + "frontier_note_present" + ] + }, + { + "claim_id": "tighten_active_route_claim", + "status": "ready", + "source": "theorem_agenda", + "summary": "Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit.", + "why": "Record the best public/formalization hook and checkpoint the archive packet.", + "support": [ + "active_route_recorded", + "ready_atom_present", + "frontier_note_present" + ] + } + ], + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `c4_free_lean_archive`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `G1008.G1.A1`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "theoremAgenda": [ + { + "item_id": "promote_ready_atom", + "status": "ready", + "task": "Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint.", + "why": "Record the best public/formalization hook and checkpoint the archive packet." + }, + { + "item_id": "tighten_active_route_claim", + "status": "ready", + "task": "Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit.", + "why": "Record the best public/formalization hook and checkpoint the archive packet." + } + ], + "commands": { + "problemShow": "erdos problem show 1008", + "problemArtifacts": "erdos problem artifacts 1008", + "theoremLoop": "erdos problem theorem-loop 1008", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 1008", + "claimLoop": "erdos problem claim-loop 1008", + "claimLoopRefresh": "erdos problem claim-loop-refresh 1008", + "sourceRefresh": null + }, + "sources": { + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null, + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008" + } +} diff --git a/packs/graph-theory/problems/1008/CLAIM_LOOP.md b/packs/graph-theory/problems/1008/CLAIM_LOOP.md new file mode 100644 index 0000000..35fef1c --- /dev/null +++ b/packs/graph-theory/problems/1008/CLAIM_LOOP.md @@ -0,0 +1,53 @@ +# Erdos Problem #1008 Claim Loop + +This claim loop generalizes theorem-search-verification work directly from the canonical theorem loop, even when no richer bridge is present yet. + +## Current State + +- Claim loop mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `c4_free_lean_archive`. +- Route summary: Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture. +- Next honest move: Record the best public/formalization hook and checkpoint the archive packet. + +## Feature Extractors + +- `pack_route_state`: ready | Reads pack route, ticket, and atom state as the baseline theorem-search context. +- `theorem_loop_snapshot`: ready | Uses the canonical theorem-loop as the current claim-surface ledger. +- `cluster_graph_theory_features`: ready | Exposes graph-theory archive or theorem-state context to the claim loop. + +## Claim Generators + +- `baseline_route_claims`: ready | Promotes active routes, ready atoms, and next-honest-move records into candidate claims. +- `theorem_agenda_claims`: ready | Turns theorem agenda items into explicit candidate claim tickets. + +## Claim Falsifiers + +- `theorem_loop_consistency_check`: ready | Rejects claims that overstate the current theorem-loop claim surface. +- `artifact_boundary_check`: ready | Rejects claims unsupported by canonical artifacts already present in the pack. + +## Verifier Adapters + +- `canonical_artifact_reader`: ready | Reads theorem-loop, route, and pack artifacts as verifier-facing evidence. + +## Candidate Claims + +- `promote_ready_atom`: ready | Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint. | Record the best public/formalization hook and checkpoint the archive packet. +- `tighten_active_route_claim`: ready | Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit. | Record the best public/formalization hook and checkpoint the archive packet. + +## Commands + +- Problem surface: `erdos problem show 1008` +- Problem artifacts: `erdos problem artifacts 1008` +- Theorem loop: `erdos problem theorem-loop 1008` +- Theorem refresh: `erdos problem theorem-loop-refresh 1008` +- Claim loop: `erdos problem claim-loop 1008` +- Claim refresh: `erdos problem claim-loop-refresh 1008` + +## Sources + +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md` +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008` diff --git a/packs/graph-theory/problems/1008/CLAIM_PASS.json b/packs/graph-theory/problems/1008/CLAIM_PASS.json new file mode 100644 index 0000000..b1f3b07 --- /dev/null +++ b/packs/graph-theory/problems/1008/CLAIM_PASS.json @@ -0,0 +1,119 @@ +{ + "schema": "erdos.problem_claim_pass/1", + "generatedAt": "2026-04-10T08:11:06.265Z", + "problemId": "1008", + "displayName": "Erdos Problem #1008", + "title": "C4-Free Subgraph Density Problem", + "cluster": "graph-theory", + "sourceKind": "claim_loop_only", + "claimPassMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "activeRoute": "c4_free_lean_archive", + "nextHonestMove": "Record the best public/formalization hook and checkpoint the archive packet.", + "routeSummary": "Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture.", + "latestVerifiedInterval": null, + "sourceRefresh": null + }, + "summary": { + "hooks": { + "total": 3, + "supported": 3, + "actionable": 0, + "unresolved": 0, + "broken": 0 + }, + "claims": { + "total": 2, + "supported": 0, + "actionable": 2, + "unresolved": 0, + "broken": 0 + } + }, + "hookAssessments": [ + { + "hook_id": "active_route_recorded", + "verdict": "supported", + "status": "supported", + "evidenceClass": "route_state", + "theoremReady": false, + "rationale": "The pack records an active route, currently `c4_free_lean_archive`.", + "nextAction": "promote_route_claim" + }, + { + "hook_id": "ready_atom_present", + "verdict": "supported", + "status": "supported", + "evidenceClass": "ready_atom", + "theoremReady": false, + "rationale": "The live route already has a ready atom, `G1008.G1.A1`, which can feed the theorem lane.", + "nextAction": "promote_ready_atom" + }, + { + "hook_id": "frontier_note_present", + "verdict": "supported", + "status": "supported", + "evidenceClass": "frontier_note", + "theoremReady": false, + "rationale": "The pack already carries a frontier note that can anchor theorem-facing updates.", + "nextAction": "anchor_frontier_note" + } + ], + "claimAssessments": [ + { + "claim_id": "promote_ready_atom", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint.", + "rationale": "Record the best public/formalization hook and checkpoint the archive packet.", + "nextAction": "promote_ready_atom" + }, + { + "claim_id": "tighten_active_route_claim", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit.", + "rationale": "Record the best public/formalization hook and checkpoint the archive packet.", + "nextAction": "tighten_active_route_claim" + } + ], + "recommendations": [ + { + "recommendation_id": "promote_ready_atom", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Record the best public/formalization hook and checkpoint the archive packet.", + "command": "erdos problem formalization 1008" + } + ], + "commands": { + "problemShow": "erdos problem show 1008", + "problemArtifacts": "erdos problem artifacts 1008", + "theoremLoop": "erdos problem theorem-loop 1008", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 1008", + "claimLoop": "erdos problem claim-loop 1008", + "claimLoopRefresh": "erdos problem claim-loop-refresh 1008", + "claimPass": "erdos problem claim-pass 1008", + "claimPassRefresh": "erdos problem claim-pass-refresh 1008", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/SEARCH_THEOREM_BRIDGE.md", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/INTERVAL_WORK_QUEUE.yaml" + } +} diff --git a/packs/graph-theory/problems/1008/CLAIM_PASS.md b/packs/graph-theory/problems/1008/CLAIM_PASS.md new file mode 100644 index 0000000..c17d65c --- /dev/null +++ b/packs/graph-theory/problems/1008/CLAIM_PASS.md @@ -0,0 +1,54 @@ +# Erdos Problem #1008 Claim Pass + +This claim pass evaluates theorem-search claims against the canonical claim loop and pack-level evidence. + +## Current State + +- Claim pass mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `c4_free_lean_archive`. +- Route summary: Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture. +- Next honest move: Record the best public/formalization hook and checkpoint the archive packet. +- Latest verified interval: `(none)` + +## Summary + +- Hook assessments: supported `3`, unresolved `0`, broken `0`. +- Claim assessments: supported `0`, actionable `2`, unresolved `0`, broken `0`. + +## Hook Assessments + +- `active_route_recorded`: supported | The pack records an active route, currently `c4_free_lean_archive`. +- `ready_atom_present`: supported | The live route already has a ready atom, `G1008.G1.A1`, which can feed the theorem lane. +- `frontier_note_present`: supported | The pack already carries a frontier note that can anchor theorem-facing updates. + +## Claim Assessments + +- `promote_ready_atom`: actionable | Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint. | Record the best public/formalization hook and checkpoint the archive packet. +- `tighten_active_route_claim`: actionable | Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit. | Record the best public/formalization hook and checkpoint the archive packet. + +## Recommendations + +- `promote_ready_atom`: medium | theorem_formalization | Record the best public/formalization hook and checkpoint the archive packet. | erdos problem formalization 1008 + +## Commands + +- Problem surface: `erdos problem show 1008` +- Problem artifacts: `erdos problem artifacts 1008` +- Theorem loop: `erdos problem theorem-loop 1008` +- Claim loop: `erdos problem claim-loop 1008` +- Claim pass: `erdos problem claim-pass 1008` +- Claim pass refresh: `erdos problem claim-pass-refresh 1008` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/SEARCH_THEOREM_BRIDGE.md` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/graph-theory/problems/1008/FORMALIZATION.json b/packs/graph-theory/problems/1008/FORMALIZATION.json new file mode 100644 index 0000000..d057cac --- /dev/null +++ b/packs/graph-theory/problems/1008/FORMALIZATION.json @@ -0,0 +1,194 @@ +{ + "schema": "erdos.problem_formalization/1", + "generatedAt": "2026-04-10T08:11:06.269Z", + "problemId": "1008", + "displayName": "Erdos Problem #1008", + "title": "C4-Free Subgraph Density Problem", + "cluster": "graph-theory", + "sourceKind": "claim_pass_only", + "formalizationMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "activeRoute": "c4_free_lean_archive", + "routeSummary": "Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture.", + "nextHonestMove": "Record the best public/formalization hook and checkpoint the archive packet.", + "latestVerifiedInterval": null, + "sourceRefresh": null + }, + "currentTarget": { + "formalizationId": "graph-theory_1008_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "status": "ready", + "lane": "theorem_formalization", + "sourceRecommendationId": "promote_ready_atom", + "summary": "Record the best public/formalization hook and checkpoint the archive packet.", + "statement": "Candidate formalization target: Record the best public/formalization hook and checkpoint the archive packet.", + "whyThisExists": "This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria.", + "whyNow": "Record the best public/formalization hook and checkpoint the archive packet.", + "evidenceBasis": [ + "Current claim surface: route_scaffolding.", + "Active route: c4_free_lean_archive.", + "No canonical verified interval is currently frozen." + ], + "proofObligations": [ + { + "obligationId": "state_claim_honestly", + "status": "ready", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "This keeps the formalization target narrower than the current evidence boundary.", + "dischargeWith": "Write a claim statement that is no stronger than the active claim-pass support surface." + }, + { + "obligationId": "freeze_support_artifacts", + "status": "ready", + "task": "List the exact canonical artifacts that support the claim and the artifacts that could still falsify it.", + "why": "The theorem lane should point at stable evidence, not drifting interpretation.", + "dischargeWith": "Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet." + }, + { + "obligationId": "define_promotion_boundary", + "status": "ready", + "task": "Promote the target only when its support survives the current claim-pass falsifiers.", + "why": "This prevents formalization packets from silently outrunning the rest of the loop.", + "dischargeWith": "Record explicit promotion criteria tied to current falsifiers." + } + ], + "falsifierChecks": [ + { + "checkId": "claim_pass_survival", + "status": "ready", + "task": "A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported.", + "why": "If the recommendation itself no longer survives refresh, the formalization target is stale.", + "command": "erdos problem claim-pass-refresh 1008" + }, + { + "checkId": "artifact_boundary_check", + "status": "ready", + "task": "A canonical artifact boundary check shows the statement is stronger than the current pack evidence.", + "why": "The packet should fail early if it is stronger than what the pack actually certifies.", + "command": "erdos problem theorem-loop 1008" + } + ], + "promotionCriteria": [ + { + "criterionId": "top_recommendation_survives", + "status": "ready", + "task": "The current target remains the top theorem-formalization recommendation after refresh." + }, + { + "criterionId": "statement_stays_narrow", + "status": "ready", + "task": "The candidate statement is narrower than or equal to the current claim-pass support surface." + }, + { + "criterionId": "obligations_are_actionable", + "status": "ready", + "task": "The remaining proof obligations are explicit enough to guide search or exact follow-up." + } + ], + "supportingCommands": [ + "erdos problem theorem-loop 1008", + "erdos problem claim-pass 1008", + "erdos problem claim-pass-refresh 1008" + ] + }, + "summary": { + "proofObligations": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "falsifierChecks": { + "total": 2, + "ready": 2, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "promotionCriteria": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + } + }, + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `c4_free_lean_archive`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `G1008.G1.A1`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "claimAssessments": [ + { + "claim_id": "promote_ready_atom", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint.", + "rationale": "Record the best public/formalization hook and checkpoint the archive packet.", + "nextAction": "promote_ready_atom" + }, + { + "claim_id": "tighten_active_route_claim", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit.", + "rationale": "Record the best public/formalization hook and checkpoint the archive packet.", + "nextAction": "tighten_active_route_claim" + } + ], + "recommendationLedger": [ + { + "recommendation_id": "promote_ready_atom", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Record the best public/formalization hook and checkpoint the archive packet.", + "command": "erdos problem formalization 1008" + } + ], + "commands": { + "problemShow": "erdos problem show 1008", + "problemArtifacts": "erdos problem artifacts 1008", + "theoremLoop": "erdos problem theorem-loop 1008", + "claimLoop": "erdos problem claim-loop 1008", + "claimPass": "erdos problem claim-pass 1008", + "formalization": "erdos problem formalization 1008", + "formalizationRefresh": "erdos problem formalization-refresh 1008", + "formalizationWork": "erdos problem formalization-work 1008", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 1008", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.md", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null + } +} diff --git a/packs/graph-theory/problems/1008/FORMALIZATION.md b/packs/graph-theory/problems/1008/FORMALIZATION.md new file mode 100644 index 0000000..0f3b486 --- /dev/null +++ b/packs/graph-theory/problems/1008/FORMALIZATION.md @@ -0,0 +1,86 @@ +# Erdos Problem #1008 Formalization + +This formalization packet promotes the current claim-pass recommendation into a concrete theorem-facing proof obligation anchored in canonical pack evidence. + +## Current State + +- Formalization mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `c4_free_lean_archive`. +- Route summary: Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture. +- Next honest move: Record the best public/formalization hook and checkpoint the archive packet. +- Latest verified interval: `(none)` + +## Current Target + +- Formalization id: `graph-theory_1008_promote_ready_atom_v1`. +- Focus id: `promote_ready_atom`. +- Title: Promote Ready Atom +- Status: `ready`. +- Lane: `theorem_formalization`. +- Summary: Record the best public/formalization hook and checkpoint the archive packet. +- Candidate statement: Candidate formalization target: Record the best public/formalization hook and checkpoint the archive packet. +- Proof obligations: ready `3` / total `3`. +- Falsifier checks: ready `2` / total `2`. +- Promotion criteria: ready `3` / total `3`. + +## Why This Exists + +This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria. + +## Why Now + +Record the best public/formalization hook and checkpoint the archive packet. + +## Evidence Basis + +- Current claim surface: route_scaffolding. +- Active route: c4_free_lean_archive. +- No canonical verified interval is currently frozen. + +## Proof Obligations + +- `state_claim_honestly`: ready | State the candidate theorem-facing claim in pack language without overstating current support. | This keeps the formalization target narrower than the current evidence boundary. | discharge: Write a claim statement that is no stronger than the active claim-pass support surface. +- `freeze_support_artifacts`: ready | List the exact canonical artifacts that support the claim and the artifacts that could still falsify it. | The theorem lane should point at stable evidence, not drifting interpretation. | discharge: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. +- `define_promotion_boundary`: ready | Promote the target only when its support survives the current claim-pass falsifiers. | This prevents formalization packets from silently outrunning the rest of the loop. | discharge: Record explicit promotion criteria tied to current falsifiers. + +## Falsifier Checks + +- `claim_pass_survival`: ready | A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported. | If the recommendation itself no longer survives refresh, the formalization target is stale. | command: erdos problem claim-pass-refresh 1008 +- `artifact_boundary_check`: ready | A canonical artifact boundary check shows the statement is stronger than the current pack evidence. | The packet should fail early if it is stronger than what the pack actually certifies. | command: erdos problem theorem-loop 1008 + +## Promotion Criteria + +- `top_recommendation_survives`: ready | The current target remains the top theorem-formalization recommendation after refresh. +- `statement_stays_narrow`: ready | The candidate statement is narrower than or equal to the current claim-pass support surface. +- `obligations_are_actionable`: ready | The remaining proof obligations are explicit enough to guide search or exact follow-up. + +## Supporting Commands + +- `erdos problem theorem-loop 1008` +- `erdos problem claim-pass 1008` +- `erdos problem claim-pass-refresh 1008` + +## Commands + +- Problem surface: `erdos problem show 1008` +- Problem artifacts: `erdos problem artifacts 1008` +- Theorem loop: `erdos problem theorem-loop 1008` +- Claim loop: `erdos problem claim-loop 1008` +- Claim pass: `erdos problem claim-pass 1008` +- Formalization: `erdos problem formalization 1008` +- Formalization refresh: `erdos problem formalization-refresh 1008` +- Formalization work: `erdos problem formalization-work 1008` +- Formalization work refresh: `erdos problem formalization-work-refresh 1008` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.md` diff --git a/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json b/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json new file mode 100644 index 0000000..37c41c1 --- /dev/null +++ b/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json @@ -0,0 +1,64 @@ +{ + "schema": "erdos.problem_formalization_work/1", + "generatedAt": "2026-04-10T08:11:06.272Z", + "problemId": "1008", + "displayName": "Erdos Problem #1008", + "title": "C4-Free Subgraph Density Problem", + "cluster": "graph-theory", + "sourceKind": "claim_pass_only", + "formalizationWorkMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "activeRoute": "c4_free_lean_archive", + "routeSummary": "Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture.", + "nextHonestMove": "Record the best public/formalization hook and checkpoint the archive packet.", + "latestVerifiedInterval": null + }, + "currentWork": { + "workId": "graph-theory_1008_state_claim_honestly_v1", + "focusFormalizationId": "graph-theory_1008_promote_ready_atom_v1", + "focusId": "state_claim_honestly", + "title": "State Claim Honestly", + "status": "ready", + "summary": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "This keeps the formalization target narrower than the current evidence boundary.", + "workingDefinition": [ + "Candidate formalization target: Record the best public/formalization hook and checkpoint the archive packet." + ], + "currentEvidence": [ + "Current claim surface: route_scaffolding.", + "Active route: c4_free_lean_archive.", + "No canonical verified interval is currently frozen." + ], + "dischargedWork": [], + "remainingGaps": [ + "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.", + "define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers." + ], + "nextCommands": [ + "erdos problem formalization-refresh 1008", + "erdos problem formalization 1008" + ] + }, + "commands": { + "problemShow": "erdos problem show 1008", + "problemArtifacts": "erdos problem artifacts 1008", + "formalization": "erdos problem formalization 1008", + "formalizationRefresh": "erdos problem formalization-refresh 1008", + "formalizationWork": "erdos problem formalization-work 1008", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 1008", + "claimPass": "erdos problem claim-pass 1008", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json", + "formalizationWorkMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.md", + "formalizationWorkSvgPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.svg", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json", + "legacyBridgeJsonPath": null + } +} diff --git a/packs/graph-theory/problems/1008/FORMALIZATION_WORK.md b/packs/graph-theory/problems/1008/FORMALIZATION_WORK.md new file mode 100644 index 0000000..6edde9c --- /dev/null +++ b/packs/graph-theory/problems/1008/FORMALIZATION_WORK.md @@ -0,0 +1,61 @@ +# Erdos Problem #1008 Formalization Work + +This packet turns the current formalization target into one concrete work unit that can be discharged, falsified, or narrowed without losing the surrounding theorem-search context. + +## Current State + +- Formalization work mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `c4_free_lean_archive`. +- Route summary: Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture. +- Next honest move: Record the best public/formalization hook and checkpoint the archive packet. +- Latest verified interval: `(none)` + +## Current Work + +- Work id: `graph-theory_1008_state_claim_honestly_v1`. +- Focus formalization id: `graph-theory_1008_promote_ready_atom_v1`. +- Focus id: `state_claim_honestly`. +- Title: State Claim Honestly +- Status: `ready`. +- Summary: State the candidate theorem-facing claim in pack language without overstating current support. +- Why: This keeps the formalization target narrower than the current evidence boundary. + +## Working Definition + +- Candidate formalization target: Record the best public/formalization hook and checkpoint the archive packet. + +## Current Evidence + +- Current claim surface: route_scaffolding. +- Active route: c4_free_lean_archive. +- No canonical verified interval is currently frozen. + +## Discharged Work + + +## Remaining Gaps + +- state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. +- define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers. + +## Commands + +- Problem surface: `erdos problem show 1008` +- Problem artifacts: `erdos problem artifacts 1008` +- Formalization: `erdos problem formalization 1008` +- Formalization refresh: `erdos problem formalization-refresh 1008` +- Formalization work: `erdos problem formalization-work 1008` +- Formalization work refresh: `erdos problem formalization-work-refresh 1008` +- Claim pass: `erdos problem claim-pass 1008` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json` +- formalizationWorkMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.md` +- formalizationWorkSvgPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.svg` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json` diff --git a/packs/graph-theory/problems/1008/FORMALIZATION_WORK.svg b/packs/graph-theory/problems/1008/FORMALIZATION_WORK.svg new file mode 100644 index 0000000..d730784 --- /dev/null +++ b/packs/graph-theory/problems/1008/FORMALIZATION_WORK.svg @@ -0,0 +1 @@ +Erdos Problem #1008 formalization work diagramGeneric visual summary of the current formalization-work packet.Erdos Problem #1008 Formalization WorkState Claim HonestlyStatus: ready | Route: c4_free_lean_archiveWorking DefinitionCurrent Evidence• Candidate formalization target: Record the best• public/formalization hook and checkpoint the• archive packet.• Current claim surface: route_scaffolding.• Active route: c4_free_lean_archive.• No canonical verified interval is currently• frozen.Canonical files: /Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json and /Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.md \ No newline at end of file diff --git a/packs/graph-theory/problems/1008/TASK_LIST.json b/packs/graph-theory/problems/1008/TASK_LIST.json new file mode 100644 index 0000000..3b6a7b0 --- /dev/null +++ b/packs/graph-theory/problems/1008/TASK_LIST.json @@ -0,0 +1,215 @@ +{ + "schema": "erdos.problem_task_list/1", + "generatedAt": "2026-04-10T08:11:06.280Z", + "problemId": "1008", + "displayName": "Erdos Problem #1008", + "title": "C4-Free Subgraph Density Problem", + "cluster": "graph-theory", + "sourceKind": "claim_pass_only", + "taskListMode": "baseline", + "currentState": { + "activeRoute": "c4_free_lean_archive", + "currentClaimSurface": "route_scaffolding", + "routeSummary": "Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture.", + "nextHonestMove": "Record the best public/formalization hook and checkpoint the archive packet.", + "latestVerifiedInterval": null + }, + "executionRule": { + "stance": "concrete_execution", + "summary": "Treat the task list as a concrete research loop for problem 1008: execute the highest-value task itself, not wrapper prose about the task.", + "afterEachCompletion": [ + "Cross off the completed task.", + "Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary.", + "Invent the next highest-value step from the updated evidence rather than following a stale fixed script.", + "Append that next step to the task list and refresh the canonical task-list artifacts." + ], + "repetitionProtocol": "To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass.", + "lowStressLongHorizonNote": "This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan." + }, + "loopTemplate": [ + { + "stepId": "freeze_current_state", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `c4_free_lean_archive`, claim surface `route_scaffolding`, and active theorem packet before widening the search.", + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 1008" + }, + { + "stepId": "audit_theorem_surfaces", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 1008" + }, + { + "stepId": "verify_canonical_inputs", + "title": "Verify canonical pack inputs against the latest route and verifier artifacts", + "task": "Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.", + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos problem theorem-loop-refresh 1008" + }, + { + "stepId": "verify_primary_structural_hook", + "title": "Verify the current highest-value structural hook remains canonical", + "task": "Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.", + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 1008" + }, + { + "stepId": "verify_verifier_boundary", + "title": "Verify the current verifier boundary and next target", + "task": "Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.", + "completionRule": "The verifier-facing boundary remains explicit even without a dedicated interval queue.", + "command": "erdos problem formalization 1008" + }, + { + "stepId": "execute_current_work_packet", + "title": "State Claim Honestly", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work 1008" + }, + { + "stepId": "refresh_and_rerank", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 1008" + } + ], + "currentObjective": { + "formalizationId": "graph-theory_1008_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "activeWorkId": "graph-theory_1008_state_claim_honestly_v1", + "activeWorkTitle": "State Claim Honestly", + "activeWorkStatus": "ready" + }, + "currentTasks": [ + { + "taskId": "freeze_current_state", + "status": "ready", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `c4_free_lean_archive`, claim surface `route_scaffolding`, and active theorem packet before widening the search.", + "why": null, + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 1008" + }, + { + "taskId": "audit_theorem_surfaces", + "status": "ready", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "why": null, + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 1008" + }, + { + "taskId": "verify_canonical_inputs", + "status": "ready", + "title": "Verify canonical pack inputs against the latest route and verifier artifacts", + "task": "Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.", + "why": null, + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos problem theorem-loop-refresh 1008" + }, + { + "taskId": "verify_primary_structural_hook", + "status": "ready", + "title": "Verify the current highest-value structural hook remains canonical", + "task": "Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.", + "why": null, + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 1008" + }, + { + "taskId": "verify_verifier_boundary", + "status": "ready", + "title": "Verify the current verifier boundary and next target", + "task": "Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.", + "why": null, + "completionRule": "The verifier-facing boundary remains explicit even without a dedicated interval queue.", + "command": "erdos problem formalization 1008" + }, + { + "taskId": "execute_current_work_packet", + "status": "ready", + "title": "State Claim Honestly", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "Record the best public/formalization hook and checkpoint the archive packet.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work 1008" + }, + { + "taskId": "discharge_first_remaining_gap", + "status": "ready", + "title": "Discharge the first remaining gap in the active theorem packet", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "why": "This is the sharpest unresolved statement already named by the active theorem-work packet.", + "completionRule": "The first remaining gap is either resolved or replaced by a more precise successor gap.", + "command": "erdos problem formalization-work-refresh 1008" + }, + { + "taskId": "refresh_and_rerank", + "status": "ready", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "why": null, + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 1008" + } + ], + "completedAnchors": [], + "nextNeededSteps": [ + { + "stepId": "gap_1", + "status": "next", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 1008" + }, + { + "stepId": "gap_2", + "status": "next", + "task": "freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 1008" + }, + { + "stepId": "gap_3", + "status": "next", + "task": "define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 1008" + }, + { + "stepId": "promote_ready_atom", + "status": "medium", + "task": "Record the best public/formalization hook and checkpoint the archive packet.", + "source": "theorem_formalization", + "command": "erdos problem formalization 1008" + } + ], + "commands": { + "problemShow": "erdos problem show 1008", + "problemArtifacts": "erdos problem artifacts 1008", + "taskList": "erdos problem task-list 1008", + "taskListRefresh": "erdos problem task-list-refresh 1008", + "theoremLoop": "erdos problem theorem-loop 1008", + "claimPass": "erdos problem claim-pass 1008", + "formalization": "erdos problem formalization 1008", + "formalizationWork": "erdos problem formalization-work 1008", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008", + "taskListJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/TASK_LIST.json", + "taskListMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/TASK_LIST.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.json", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.json", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/INTERVAL_WORK_QUEUE.yaml", + "legacyBridgeJsonPath": null + } +} diff --git a/packs/graph-theory/problems/1008/TASK_LIST.md b/packs/graph-theory/problems/1008/TASK_LIST.md new file mode 100644 index 0000000..c9b67e5 --- /dev/null +++ b/packs/graph-theory/problems/1008/TASK_LIST.md @@ -0,0 +1,85 @@ +# Erdos Problem #1008 Task List + +This task list is the canonical research-loop surface for the problem. It gives one reusable execution rule, one templated loop, the current active tasks, and the next steps discovered from the current theorem/search/verifier state. + +## Current State + +- Task list mode: `baseline`. +- Active route: `c4_free_lean_archive`. +- Current claim surface: `route_scaffolding`. +- Route summary: Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture. +- Next honest move: Record the best public/formalization hook and checkpoint the archive packet. +- Latest verified interval: `(none)` + +## Execution Rule + +- Stance: `concrete_execution` +- Summary: Treat the task list as a concrete research loop for problem 1008: execute the highest-value task itself, not wrapper prose about the task. +- After each completed step: Cross off the completed task. +- After each completed step: Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary. +- After each completed step: Invent the next highest-value step from the updated evidence rather than following a stale fixed script. +- After each completed step: Append that next step to the task list and refresh the canonical task-list artifacts. +- Repetition protocol: To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass. +- Long-horizon note: This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan. + +## Template Loop + +- `freeze_current_state`: Freeze the current north star and active theorem packet | Freeze the current route `c4_free_lean_archive`, claim surface `route_scaffolding`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 1008` +- `audit_theorem_surfaces`: Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 1008` +- `verify_canonical_inputs`: Verify canonical pack inputs against the latest route and verifier artifacts | Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos problem theorem-loop-refresh 1008` +- `verify_primary_structural_hook`: Verify the current highest-value structural hook remains canonical | Verify that the strongest supported structural hook still survives across the theorem and claim surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 1008` +- `verify_verifier_boundary`: Verify the current verifier boundary and next target | Verify that the current verifier boundary and next target are stated honestly across the pack surfaces. | completion: The verifier-facing boundary remains explicit even without a dedicated interval queue. | command: `erdos problem formalization 1008` +- `execute_current_work_packet`: State Claim Honestly | State the candidate theorem-facing claim in pack language without overstating current support. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | command: `erdos problem formalization-work 1008` +- `refresh_and_rerank`: Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 1008` + +## Current Objective + +- Formalization id: `graph-theory_1008_promote_ready_atom_v1` +- Focus id: `promote_ready_atom` +- Title: Promote Ready Atom +- Active work id: `graph-theory_1008_state_claim_honestly_v1` +- Active work title: State Claim Honestly +- Active work status: `ready` + +## Current Tasks + +- `freeze_current_state` [ready] Freeze the current north star and active theorem packet | Freeze the current route `c4_free_lean_archive`, claim surface `route_scaffolding`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 1008` +- `audit_theorem_surfaces` [ready] Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 1008` +- `verify_canonical_inputs` [ready] Verify canonical pack inputs against the latest route and verifier artifacts | Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos problem theorem-loop-refresh 1008` +- `verify_primary_structural_hook` [ready] Verify the current highest-value structural hook remains canonical | Verify that the strongest supported structural hook still survives across the theorem and claim surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 1008` +- `verify_verifier_boundary` [ready] Verify the current verifier boundary and next target | Verify that the current verifier boundary and next target are stated honestly across the pack surfaces. | completion: The verifier-facing boundary remains explicit even without a dedicated interval queue. | command: `erdos problem formalization 1008` +- `execute_current_work_packet` [ready] State Claim Honestly | State the candidate theorem-facing claim in pack language without overstating current support. | Record the best public/formalization hook and checkpoint the archive packet. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | command: `erdos problem formalization-work 1008` +- `discharge_first_remaining_gap` [ready] Discharge the first remaining gap in the active theorem packet | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | This is the sharpest unresolved statement already named by the active theorem-work packet. | completion: The first remaining gap is either resolved or replaced by a more precise successor gap. | command: `erdos problem formalization-work-refresh 1008` +- `refresh_and_rerank` [ready] Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 1008` + +## Completed Anchors + + +## Next Needed Steps + +- `gap_1` [next] state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | source: formalization_work | command: `erdos problem formalization-work-refresh 1008` +- `gap_2` [next] freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. | source: formalization_work | command: `erdos problem formalization-work-refresh 1008` +- `gap_3` [next] define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers. | source: formalization_work | command: `erdos problem formalization-work-refresh 1008` +- `promote_ready_atom` [medium] Record the best public/formalization hook and checkpoint the archive packet. | source: theorem_formalization | command: `erdos problem formalization 1008` + +## Commands + +- Problem surface: `erdos problem show 1008` +- Problem artifacts: `erdos problem artifacts 1008` +- Task list: `erdos problem task-list 1008` +- Task list refresh: `erdos problem task-list-refresh 1008` +- Theorem loop: `erdos problem theorem-loop 1008` +- Claim pass: `erdos problem claim-pass 1008` +- Formalization: `erdos problem formalization 1008` +- Formalization work: `erdos problem formalization-work 1008` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008` +- taskListJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/TASK_LIST.json` +- taskListMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/TASK_LIST.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/CLAIM_PASS.json` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION.json` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FORMALIZATION_WORK.json` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/graph-theory/problems/1008/THEOREM_LOOP.json b/packs/graph-theory/problems/1008/THEOREM_LOOP.json new file mode 100644 index 0000000..79bc7e1 --- /dev/null +++ b/packs/graph-theory/problems/1008/THEOREM_LOOP.json @@ -0,0 +1,74 @@ +{ + "schema": "erdos.problem_theorem_loop/1", + "generatedAt": "2026-04-10T08:11:06.260Z", + "problemId": "1008", + "displayName": "Erdos Problem #1008", + "title": "C4-Free Subgraph Density Problem", + "cluster": "graph-theory", + "sourceKind": "pack_route_state", + "theoremLoopMode": "baseline", + "activeRoute": "c4_free_lean_archive", + "theoremModule": null, + "currentState": { + "siteStatus": "solved", + "repoStatus": "historical", + "openProblem": false, + "routeBreakthrough": false, + "problemSolved": false, + "currentClaimSurface": "route_scaffolding", + "routeSummary": "Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture.", + "nextHonestMove": "Record the best public/formalization hook and checkpoint the archive packet." + }, + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `c4_free_lean_archive`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `G1008.G1.A1`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "theoremAgenda": [ + { + "item_id": "promote_ready_atom", + "status": "ready", + "task": "Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint.", + "why": "Record the best public/formalization hook and checkpoint the archive packet." + }, + { + "item_id": "tighten_active_route_claim", + "status": "ready", + "task": "Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit.", + "why": "Record the best public/formalization hook and checkpoint the archive packet." + } + ], + "currentBridgeState": null, + "commands": { + "problemShow": "erdos problem show 1008", + "problemArtifacts": "erdos problem artifacts 1008", + "theoremLoop": "erdos problem theorem-loop 1008", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 1008", + "clusterStatus": "erdos graph-theory status 1008", + "clusterFrontier": "erdos graph-theory frontier 1008", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md", + "contextPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/context.yaml", + "routePacketPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/ROUTE_PACKET.yaml", + "frontierNotePath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FRONTIER_NOTE.md", + "opsDetailsPath": "/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/OPS_DETAILS.yaml", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null + } +} diff --git a/packs/graph-theory/problems/1008/THEOREM_LOOP.md b/packs/graph-theory/problems/1008/THEOREM_LOOP.md new file mode 100644 index 0000000..d058ca1 --- /dev/null +++ b/packs/graph-theory/problems/1008/THEOREM_LOOP.md @@ -0,0 +1,46 @@ +# Erdos Problem #1008 Theorem Loop + +This note is the generic theorem-loop surface for the problem pack. It keeps theorem-facing route state visible even when no richer search bridge exists yet. + +## Current State + +- Theorem loop mode: `baseline`. +- Active route: `c4_free_lean_archive`. +- Current claim surface: `route_scaffolding`. +- Repo status: `historical`; site status: `solved`. +- Route breakthrough: `no`. +- Problem solved: `no`. +- Open problem: `no`. +- Theorem module: `(none)`. +- Route summary: Keep the solved `C_4`-free density record explicit and preserve the Lean-facing archive posture. +- Next honest move: Record the best public/formalization hook and checkpoint the archive packet. + +## Theorem Hooks + +- `active_route_recorded`: supported | The pack records an active route, currently `c4_free_lean_archive`. +- `ready_atom_present`: supported | The live route already has a ready atom, `G1008.G1.A1`, which can feed the theorem lane. +- `frontier_note_present`: supported | The pack already carries a frontier note that can anchor theorem-facing updates. + +## Theorem Agenda + +- `promote_ready_atom`: ready | Turn ready atom `G1008.G1.A1` into the next theorem-facing checkpoint. | Record the best public/formalization hook and checkpoint the archive packet. +- `tighten_active_route_claim`: ready | Compress the active route `c4_free_lean_archive` into the next honest theorem-facing claim unit. | Record the best public/formalization hook and checkpoint the archive packet. + +## Commands + +- Problem surface: `erdos problem show 1008` +- Canonical theorem loop: `erdos problem theorem-loop 1008` +- Refresh theorem loop: `erdos problem theorem-loop-refresh 1008` +- Problem artifacts: `erdos problem artifacts 1008` +- Cluster status: `erdos graph-theory status 1008` +- Cluster frontier: `erdos graph-theory frontier 1008` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/THEOREM_LOOP.md` +- contextPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/context.yaml` +- routePacketPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/ROUTE_PACKET.yaml` +- frontierNotePath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/FRONTIER_NOTE.md` +- opsDetailsPath: `/Volumes/Code_2TB/code/erdos-problems/packs/graph-theory/problems/1008/OPS_DETAILS.yaml` diff --git a/packs/number-theory/problems/1/CLAIM_LOOP.json b/packs/number-theory/problems/1/CLAIM_LOOP.json new file mode 100644 index 0000000..d153230 --- /dev/null +++ b/packs/number-theory/problems/1/CLAIM_LOOP.json @@ -0,0 +1,171 @@ +{ + "schema": "erdos.problem_claim_loop/1", + "generatedAt": "2026-04-14T11:46:21.670Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "cluster": "number-theory", + "sourceKind": "theorem_loop_only", + "claimLoopMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "theoremLoopMode": "baseline", + "activeRoute": "distinct_subset_sum_lower_bound", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "sourceRefresh": null + }, + "featureExtractors": [ + { + "extractor_id": "pack_route_state", + "kind": "pack_context", + "scope": "all_problems", + "status": "ready", + "note": "Reads pack route, ticket, and atom state as the baseline theorem-search context." + }, + { + "extractor_id": "theorem_loop_snapshot", + "kind": "theorem_loop", + "scope": "all_problems", + "status": "ready", + "note": "Uses the canonical theorem-loop as the current claim-surface ledger." + }, + { + "extractor_id": "cluster_number_theory_features", + "kind": "cluster_adapter", + "scope": "number_theory", + "status": "ready", + "note": "Exposes number-theory specific finite-gap and verifier-facing metadata." + } + ], + "claimGenerators": [ + { + "generator_id": "baseline_route_claims", + "kind": "route_state", + "scope": "all_problems", + "status": "ready", + "note": "Promotes active routes, ready atoms, and next-honest-move records into candidate claims." + }, + { + "generator_id": "theorem_agenda_claims", + "kind": "agenda_projection", + "scope": "all_problems", + "status": "ready", + "note": "Turns theorem agenda items into explicit candidate claim tickets." + } + ], + "claimFalsifiers": [ + { + "falsifier_id": "theorem_loop_consistency_check", + "kind": "ledger_consistency", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims that overstate the current theorem-loop claim surface." + }, + { + "falsifier_id": "artifact_boundary_check", + "kind": "artifact_boundary", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims unsupported by canonical artifacts already present in the pack." + }, + { + "falsifier_id": "exact_interval_counterexample_scan", + "kind": "exact_verifier", + "scope": "number_theory", + "status": "ready", + "note": "Uses bounded exact interval checks to kill false local claims quickly." + } + ], + "verifierAdapters": [ + { + "adapter_id": "canonical_artifact_reader", + "kind": "artifact_reader", + "scope": "all_problems", + "status": "ready", + "note": "Reads theorem-loop, route, and pack artifacts as verifier-facing evidence." + }, + { + "adapter_id": "exact_small_n", + "kind": "exact_verifier", + "scope": "number_theory", + "status": "ready", + "note": "Bounded exact verifier for finite interval certification." + } + ], + "candidateClaims": [ + { + "claim_id": "promote_ready_atom", + "status": "ready", + "source": "theorem_agenda", + "summary": "Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "support": [ + "active_route_recorded", + "ready_atom_present", + "frontier_note_present" + ] + }, + { + "claim_id": "tighten_active_route_claim", + "status": "ready", + "source": "theorem_agenda", + "summary": "Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "support": [ + "active_route_recorded", + "ready_atom_present", + "frontier_note_present" + ] + } + ], + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `distinct_subset_sum_lower_bound`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `N1.G1.A1`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "theoremAgenda": [ + { + "item_id": "promote_ready_atom", + "status": "ready", + "task": "Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress." + }, + { + "item_id": "tighten_active_route_claim", + "status": "ready", + "task": "Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress." + } + ], + "commands": { + "problemShow": "erdos problem show 1", + "problemArtifacts": "erdos problem artifacts 1", + "theoremLoop": "erdos problem theorem-loop 1", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 1", + "claimLoop": "erdos problem claim-loop 1", + "claimLoopRefresh": "erdos problem claim-loop-refresh 1", + "sourceRefresh": null + }, + "sources": { + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null, + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1" + } +} diff --git a/packs/number-theory/problems/1/CLAIM_LOOP.md b/packs/number-theory/problems/1/CLAIM_LOOP.md new file mode 100644 index 0000000..cfb2abf --- /dev/null +++ b/packs/number-theory/problems/1/CLAIM_LOOP.md @@ -0,0 +1,55 @@ +# Erdos Problem #1 Claim Loop + +This claim loop generalizes theorem-search-verification work directly from the canonical theorem loop, even when no richer bridge is present yet. + +## Current State + +- Claim loop mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `distinct_subset_sum_lower_bound`. +- Route summary: Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums. +- Next honest move: Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Feature Extractors + +- `pack_route_state`: ready | Reads pack route, ticket, and atom state as the baseline theorem-search context. +- `theorem_loop_snapshot`: ready | Uses the canonical theorem-loop as the current claim-surface ledger. +- `cluster_number_theory_features`: ready | Exposes number-theory specific finite-gap and verifier-facing metadata. + +## Claim Generators + +- `baseline_route_claims`: ready | Promotes active routes, ready atoms, and next-honest-move records into candidate claims. +- `theorem_agenda_claims`: ready | Turns theorem agenda items into explicit candidate claim tickets. + +## Claim Falsifiers + +- `theorem_loop_consistency_check`: ready | Rejects claims that overstate the current theorem-loop claim surface. +- `artifact_boundary_check`: ready | Rejects claims unsupported by canonical artifacts already present in the pack. +- `exact_interval_counterexample_scan`: ready | Uses bounded exact interval checks to kill false local claims quickly. + +## Verifier Adapters + +- `canonical_artifact_reader`: ready | Reads theorem-loop, route, and pack artifacts as verifier-facing evidence. +- `exact_small_n`: ready | Bounded exact verifier for finite interval certification. + +## Candidate Claims + +- `promote_ready_atom`: ready | Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint. | Record the first reduction and checkpoint it without overclaiming theorem progress. +- `tighten_active_route_claim`: ready | Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit. | Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Commands + +- Problem surface: `erdos problem show 1` +- Problem artifacts: `erdos problem artifacts 1` +- Theorem loop: `erdos problem theorem-loop 1` +- Theorem refresh: `erdos problem theorem-loop-refresh 1` +- Claim loop: `erdos problem claim-loop 1` +- Claim refresh: `erdos problem claim-loop-refresh 1` + +## Sources + +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md` +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1` diff --git a/packs/number-theory/problems/1/CLAIM_PASS.json b/packs/number-theory/problems/1/CLAIM_PASS.json new file mode 100644 index 0000000..e60e715 --- /dev/null +++ b/packs/number-theory/problems/1/CLAIM_PASS.json @@ -0,0 +1,119 @@ +{ + "schema": "erdos.problem_claim_pass/1", + "generatedAt": "2026-04-14T11:46:21.685Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "cluster": "number-theory", + "sourceKind": "claim_loop_only", + "claimPassMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "activeRoute": "distinct_subset_sum_lower_bound", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "latestVerifiedInterval": null, + "sourceRefresh": null + }, + "summary": { + "hooks": { + "total": 3, + "supported": 3, + "actionable": 0, + "unresolved": 0, + "broken": 0 + }, + "claims": { + "total": 2, + "supported": 0, + "actionable": 2, + "unresolved": 0, + "broken": 0 + } + }, + "hookAssessments": [ + { + "hook_id": "active_route_recorded", + "verdict": "supported", + "status": "supported", + "evidenceClass": "route_state", + "theoremReady": false, + "rationale": "The pack records an active route, currently `distinct_subset_sum_lower_bound`.", + "nextAction": "promote_route_claim" + }, + { + "hook_id": "ready_atom_present", + "verdict": "supported", + "status": "supported", + "evidenceClass": "ready_atom", + "theoremReady": false, + "rationale": "The live route already has a ready atom, `N1.G1.A1`, which can feed the theorem lane.", + "nextAction": "promote_ready_atom" + }, + { + "hook_id": "frontier_note_present", + "verdict": "supported", + "status": "supported", + "evidenceClass": "frontier_note", + "theoremReady": false, + "rationale": "The pack already carries a frontier note that can anchor theorem-facing updates.", + "nextAction": "anchor_frontier_note" + } + ], + "claimAssessments": [ + { + "claim_id": "promote_ready_atom", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint.", + "rationale": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "nextAction": "promote_ready_atom" + }, + { + "claim_id": "tighten_active_route_claim", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit.", + "rationale": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "nextAction": "tighten_active_route_claim" + } + ], + "recommendations": [ + { + "recommendation_id": "promote_ready_atom", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "command": "erdos problem formalization 1" + } + ], + "commands": { + "problemShow": "erdos problem show 1", + "problemArtifacts": "erdos problem artifacts 1", + "theoremLoop": "erdos problem theorem-loop 1", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 1", + "claimLoop": "erdos problem claim-loop 1", + "claimLoopRefresh": "erdos problem claim-loop-refresh 1", + "claimPass": "erdos problem claim-pass 1", + "claimPassRefresh": "erdos problem claim-pass-refresh 1", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/SEARCH_THEOREM_BRIDGE.md", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/INTERVAL_WORK_QUEUE.yaml" + } +} diff --git a/packs/number-theory/problems/1/CLAIM_PASS.md b/packs/number-theory/problems/1/CLAIM_PASS.md new file mode 100644 index 0000000..743e280 --- /dev/null +++ b/packs/number-theory/problems/1/CLAIM_PASS.md @@ -0,0 +1,54 @@ +# Erdos Problem #1 Claim Pass + +This claim pass evaluates theorem-search claims against the canonical claim loop and pack-level evidence. + +## Current State + +- Claim pass mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `distinct_subset_sum_lower_bound`. +- Route summary: Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums. +- Next honest move: Record the first reduction and checkpoint it without overclaiming theorem progress. +- Latest verified interval: `(none)` + +## Summary + +- Hook assessments: supported `3`, unresolved `0`, broken `0`. +- Claim assessments: supported `0`, actionable `2`, unresolved `0`, broken `0`. + +## Hook Assessments + +- `active_route_recorded`: supported | The pack records an active route, currently `distinct_subset_sum_lower_bound`. +- `ready_atom_present`: supported | The live route already has a ready atom, `N1.G1.A1`, which can feed the theorem lane. +- `frontier_note_present`: supported | The pack already carries a frontier note that can anchor theorem-facing updates. + +## Claim Assessments + +- `promote_ready_atom`: actionable | Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint. | Record the first reduction and checkpoint it without overclaiming theorem progress. +- `tighten_active_route_claim`: actionable | Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit. | Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Recommendations + +- `promote_ready_atom`: medium | theorem_formalization | Record the first reduction and checkpoint it without overclaiming theorem progress. | erdos problem formalization 1 + +## Commands + +- Problem surface: `erdos problem show 1` +- Problem artifacts: `erdos problem artifacts 1` +- Theorem loop: `erdos problem theorem-loop 1` +- Claim loop: `erdos problem claim-loop 1` +- Claim pass: `erdos problem claim-pass 1` +- Claim pass refresh: `erdos problem claim-pass-refresh 1` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/SEARCH_THEOREM_BRIDGE.md` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/number-theory/problems/1/FORMALIZATION.json b/packs/number-theory/problems/1/FORMALIZATION.json new file mode 100644 index 0000000..58f6bfe --- /dev/null +++ b/packs/number-theory/problems/1/FORMALIZATION.json @@ -0,0 +1,194 @@ +{ + "schema": "erdos.problem_formalization/1", + "generatedAt": "2026-04-14T11:46:21.717Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "cluster": "number-theory", + "sourceKind": "claim_pass_only", + "formalizationMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "activeRoute": "distinct_subset_sum_lower_bound", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "latestVerifiedInterval": null, + "sourceRefresh": null + }, + "currentTarget": { + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "status": "ready", + "lane": "theorem_formalization", + "sourceRecommendationId": "promote_ready_atom", + "summary": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "statement": "Candidate formalization target: Record the first reduction and checkpoint it without overclaiming theorem progress.", + "whyThisExists": "This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria.", + "whyNow": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "evidenceBasis": [ + "Current claim surface: route_scaffolding.", + "Active route: distinct_subset_sum_lower_bound.", + "No canonical verified interval is currently frozen." + ], + "proofObligations": [ + { + "obligationId": "state_claim_honestly", + "status": "ready", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "This keeps the formalization target narrower than the current evidence boundary.", + "dischargeWith": "Write a claim statement that is no stronger than the active claim-pass support surface." + }, + { + "obligationId": "freeze_support_artifacts", + "status": "ready", + "task": "List the exact canonical artifacts that support the claim and the artifacts that could still falsify it.", + "why": "The theorem lane should point at stable evidence, not drifting interpretation.", + "dischargeWith": "Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet." + }, + { + "obligationId": "define_promotion_boundary", + "status": "ready", + "task": "Promote the target only when its support survives the current claim-pass falsifiers.", + "why": "This prevents formalization packets from silently outrunning the rest of the loop.", + "dischargeWith": "Record explicit promotion criteria tied to current falsifiers." + } + ], + "falsifierChecks": [ + { + "checkId": "claim_pass_survival", + "status": "ready", + "task": "A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported.", + "why": "If the recommendation itself no longer survives refresh, the formalization target is stale.", + "command": "erdos problem claim-pass-refresh 1" + }, + { + "checkId": "artifact_boundary_check", + "status": "ready", + "task": "A canonical artifact boundary check shows the statement is stronger than the current pack evidence.", + "why": "The packet should fail early if it is stronger than what the pack actually certifies.", + "command": "erdos problem theorem-loop 1" + } + ], + "promotionCriteria": [ + { + "criterionId": "top_recommendation_survives", + "status": "ready", + "task": "The current target remains the top theorem-formalization recommendation after refresh." + }, + { + "criterionId": "statement_stays_narrow", + "status": "ready", + "task": "The candidate statement is narrower than or equal to the current claim-pass support surface." + }, + { + "criterionId": "obligations_are_actionable", + "status": "ready", + "task": "The remaining proof obligations are explicit enough to guide search or exact follow-up." + } + ], + "supportingCommands": [ + "erdos problem theorem-loop 1", + "erdos problem claim-pass 1", + "erdos problem claim-pass-refresh 1" + ] + }, + "summary": { + "proofObligations": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "falsifierChecks": { + "total": 2, + "ready": 2, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "promotionCriteria": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + } + }, + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `distinct_subset_sum_lower_bound`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `N1.G1.A1`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "claimAssessments": [ + { + "claim_id": "promote_ready_atom", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint.", + "rationale": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "nextAction": "promote_ready_atom" + }, + { + "claim_id": "tighten_active_route_claim", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit.", + "rationale": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "nextAction": "tighten_active_route_claim" + } + ], + "recommendationLedger": [ + { + "recommendation_id": "promote_ready_atom", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "command": "erdos problem formalization 1" + } + ], + "commands": { + "problemShow": "erdos problem show 1", + "problemArtifacts": "erdos problem artifacts 1", + "theoremLoop": "erdos problem theorem-loop 1", + "claimLoop": "erdos problem claim-loop 1", + "claimPass": "erdos problem claim-pass 1", + "formalization": "erdos problem formalization 1", + "formalizationRefresh": "erdos problem formalization-refresh 1", + "formalizationWork": "erdos problem formalization-work 1", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 1", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.md", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null + } +} diff --git a/packs/number-theory/problems/1/FORMALIZATION.md b/packs/number-theory/problems/1/FORMALIZATION.md new file mode 100644 index 0000000..1796bfe --- /dev/null +++ b/packs/number-theory/problems/1/FORMALIZATION.md @@ -0,0 +1,86 @@ +# Erdos Problem #1 Formalization + +This formalization packet promotes the current claim-pass recommendation into a concrete theorem-facing proof obligation anchored in canonical pack evidence. + +## Current State + +- Formalization mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `distinct_subset_sum_lower_bound`. +- Route summary: Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums. +- Next honest move: Record the first reduction and checkpoint it without overclaiming theorem progress. +- Latest verified interval: `(none)` + +## Current Target + +- Formalization id: `number-theory_1_promote_ready_atom_v1`. +- Focus id: `promote_ready_atom`. +- Title: Promote Ready Atom +- Status: `ready`. +- Lane: `theorem_formalization`. +- Summary: Record the first reduction and checkpoint it without overclaiming theorem progress. +- Candidate statement: Candidate formalization target: Record the first reduction and checkpoint it without overclaiming theorem progress. +- Proof obligations: ready `3` / total `3`. +- Falsifier checks: ready `2` / total `2`. +- Promotion criteria: ready `3` / total `3`. + +## Why This Exists + +This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria. + +## Why Now + +Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Evidence Basis + +- Current claim surface: route_scaffolding. +- Active route: distinct_subset_sum_lower_bound. +- No canonical verified interval is currently frozen. + +## Proof Obligations + +- `state_claim_honestly`: ready | State the candidate theorem-facing claim in pack language without overstating current support. | This keeps the formalization target narrower than the current evidence boundary. | discharge: Write a claim statement that is no stronger than the active claim-pass support surface. +- `freeze_support_artifacts`: ready | List the exact canonical artifacts that support the claim and the artifacts that could still falsify it. | The theorem lane should point at stable evidence, not drifting interpretation. | discharge: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. +- `define_promotion_boundary`: ready | Promote the target only when its support survives the current claim-pass falsifiers. | This prevents formalization packets from silently outrunning the rest of the loop. | discharge: Record explicit promotion criteria tied to current falsifiers. + +## Falsifier Checks + +- `claim_pass_survival`: ready | A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported. | If the recommendation itself no longer survives refresh, the formalization target is stale. | command: erdos problem claim-pass-refresh 1 +- `artifact_boundary_check`: ready | A canonical artifact boundary check shows the statement is stronger than the current pack evidence. | The packet should fail early if it is stronger than what the pack actually certifies. | command: erdos problem theorem-loop 1 + +## Promotion Criteria + +- `top_recommendation_survives`: ready | The current target remains the top theorem-formalization recommendation after refresh. +- `statement_stays_narrow`: ready | The candidate statement is narrower than or equal to the current claim-pass support surface. +- `obligations_are_actionable`: ready | The remaining proof obligations are explicit enough to guide search or exact follow-up. + +## Supporting Commands + +- `erdos problem theorem-loop 1` +- `erdos problem claim-pass 1` +- `erdos problem claim-pass-refresh 1` + +## Commands + +- Problem surface: `erdos problem show 1` +- Problem artifacts: `erdos problem artifacts 1` +- Theorem loop: `erdos problem theorem-loop 1` +- Claim loop: `erdos problem claim-loop 1` +- Claim pass: `erdos problem claim-pass 1` +- Formalization: `erdos problem formalization 1` +- Formalization refresh: `erdos problem formalization-refresh 1` +- Formalization work: `erdos problem formalization-work 1` +- Formalization work refresh: `erdos problem formalization-work-refresh 1` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.md` diff --git a/packs/number-theory/problems/1/FORMALIZATION_WORK.json b/packs/number-theory/problems/1/FORMALIZATION_WORK.json new file mode 100644 index 0000000..1b91e5b --- /dev/null +++ b/packs/number-theory/problems/1/FORMALIZATION_WORK.json @@ -0,0 +1,65 @@ +{ + "schema": "erdos.problem_formalization_work/1", + "generatedAt": "2026-04-14T11:46:21.751Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "cluster": "number-theory", + "sourceKind": "claim_pass_only", + "formalizationWorkMode": "baseline", + "currentClaimSurface": "route_scaffolding", + "currentState": { + "activeRoute": "distinct_subset_sum_lower_bound", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "latestVerifiedInterval": null + }, + "currentWork": { + "workId": "number-theory_1_state_claim_honestly_v1", + "focusFormalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "state_claim_honestly", + "title": "State Claim Honestly", + "status": "ready", + "summary": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "This keeps the formalization target narrower than the current evidence boundary.", + "workingDefinition": [ + "Candidate formalization target: Record the first reduction and checkpoint it without overclaiming theorem progress." + ], + "currentEvidence": [ + "Current claim surface: route_scaffolding.", + "Active route: distinct_subset_sum_lower_bound.", + "No canonical verified interval is currently frozen." + ], + "dischargedWork": [], + "remainingGaps": [ + "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.", + "define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers." + ], + "nextCommands": [ + "erdos problem formalization-refresh 1", + "erdos problem formalization 1" + ] + }, + "commands": { + "problemShow": "erdos problem show 1", + "problemArtifacts": "erdos problem artifacts 1", + "formalization": "erdos problem formalization 1", + "formalizationRefresh": "erdos problem formalization-refresh 1", + "formalizationWork": "erdos problem formalization-work 1", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 1", + "formalizationWorkCheck": "erdos problem formalization-work-check 1", + "claimPass": "erdos problem claim-pass 1", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.json", + "formalizationWorkMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.md", + "formalizationWorkSvgPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.svg", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json", + "legacyBridgeJsonPath": null + } +} diff --git a/packs/number-theory/problems/1/FORMALIZATION_WORK.md b/packs/number-theory/problems/1/FORMALIZATION_WORK.md new file mode 100644 index 0000000..f337a22 --- /dev/null +++ b/packs/number-theory/problems/1/FORMALIZATION_WORK.md @@ -0,0 +1,61 @@ +# Erdos Problem #1 Formalization Work + +This packet turns the current formalization target into one concrete work unit that can be discharged, falsified, or narrowed without losing the surrounding theorem-search context. + +## Current State + +- Formalization work mode: `baseline`. +- Current claim surface: `route_scaffolding`. +- Active route: `distinct_subset_sum_lower_bound`. +- Route summary: Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums. +- Next honest move: Record the first reduction and checkpoint it without overclaiming theorem progress. +- Latest verified interval: `(none)` + +## Current Work + +- Work id: `number-theory_1_state_claim_honestly_v1`. +- Focus formalization id: `number-theory_1_promote_ready_atom_v1`. +- Focus id: `state_claim_honestly`. +- Title: State Claim Honestly +- Status: `ready`. +- Summary: State the candidate theorem-facing claim in pack language without overstating current support. +- Why: This keeps the formalization target narrower than the current evidence boundary. + +## Working Definition + +- Candidate formalization target: Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Current Evidence + +- Current claim surface: route_scaffolding. +- Active route: distinct_subset_sum_lower_bound. +- No canonical verified interval is currently frozen. + +## Discharged Work + + +## Remaining Gaps + +- state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. +- define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers. + +## Commands + +- Problem surface: `erdos problem show 1` +- Problem artifacts: `erdos problem artifacts 1` +- Formalization: `erdos problem formalization 1` +- Formalization refresh: `erdos problem formalization-refresh 1` +- Formalization work: `erdos problem formalization-work 1` +- Formalization work refresh: `erdos problem formalization-work-refresh 1` +- Claim pass: `erdos problem claim-pass 1` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.json` +- formalizationWorkMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.md` +- formalizationWorkSvgPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.svg` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json` diff --git a/packs/number-theory/problems/1/FORMALIZATION_WORK.svg b/packs/number-theory/problems/1/FORMALIZATION_WORK.svg new file mode 100644 index 0000000..28ad667 --- /dev/null +++ b/packs/number-theory/problems/1/FORMALIZATION_WORK.svg @@ -0,0 +1 @@ +Erdos Problem #1 formalization work diagramGeneric visual summary of the current formalization-work packet.Erdos Problem #1 Formalization WorkState Claim HonestlyStatus: ready | Route: distinct_subset_sum_lower_boundWorking DefinitionCurrent Evidence• Candidate formalization target: Record the first• reduction and checkpoint it without overclaiming• theorem progress.• Current claim surface: route_scaffolding.• Active route: distinct_subset_sum_lower_bound.• No canonical verified interval is currently• frozen.Canonical files: /Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.json and /Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.md \ No newline at end of file diff --git a/packs/number-theory/problems/1/TASK_LIST.json b/packs/number-theory/problems/1/TASK_LIST.json new file mode 100644 index 0000000..f3afd22 --- /dev/null +++ b/packs/number-theory/problems/1/TASK_LIST.json @@ -0,0 +1,445 @@ +{ + "schema": "erdos.problem_task_list/1", + "generatedAt": "2026-04-14T11:46:21.807Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "cluster": "number-theory", + "sourceKind": "claim_pass_only", + "taskListMode": "baseline", + "currentState": { + "activeRoute": "distinct_subset_sum_lower_bound", + "currentClaimSurface": "route_scaffolding", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "latestVerifiedInterval": null + }, + "finiteGapStrategy": null, + "granularBreakdownMode": { + "status": "core_loop_enabled", + "modeId": "granular-breakdown", + "label": "ORP Granular Breakdown", + "topic": "problem 1 | State Claim Honestly", + "activationPhrase": "Break it down until it can move.", + "invocationRule": "Use the full breakdown before executing a complex theorem/search packet; use the nudge card whenever the agent or user is confused, the target feels too broad, or the next action is not deterministic.", + "commands": { + "fullBreakdown": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json", + "nudge": "orp mode nudge granular-breakdown --json", + "unscopedBreakdown": "orp mode breakdown granular-breakdown --json" + }, + "outputContract": [ + "Broad Frame", + "Boundary", + "Major Lanes", + "Subclaims", + "Atomic Obligations", + "Dependency Ladder", + "Active Target", + "Durable Checklist", + "Next Verification" + ], + "loopIntegration": [ + "Run the full breakdown after the theorem/search surfaces are audited and before executing the current work packet.", + "Write operationally important decompositions into TASK_LIST, FORMALIZATION_WORK, or a dedicated checklist artifact rather than leaving them in chat.", + "Use the nudge card for quick reorientation when a step becomes blurry during implementation.", + "Compress the breakdown back into one active target and one verification command before continuing." + ], + "durableArtifactRule": "If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state." + }, + "orpModeOverlays": { + "status": "core_loop_palette_enabled", + "sourceCommand": "orp mode list --json", + "defaultModeId": "granular-breakdown", + "selectionRule": "Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default.", + "alwaysDurableWhenOperational": true, + "overlays": [ + { + "modeId": "granular-breakdown", + "label": "Granular Breakdown", + "role": "core_decomposition_loop", + "useWhen": "The work is broad, confusing, theorem-heavy, or needs a durable dependency ladder before execution.", + "command": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json", + "nudgeCommand": "orp mode nudge granular-breakdown --json", + "loopPlacement": "Before execute_current_work_packet and whenever the active target becomes fuzzy.", + "outputExpectation": "Boundary, lanes, subclaims, atomic obligations, dependency ladder, active target, durable checklist, and next verification." + }, + { + "modeId": "ruthless-simplification", + "label": "Ruthless Simplification", + "role": "compression_and_signal_filter", + "useWhen": "A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision.", + "command": "orp mode nudge ruthless-simplification --json", + "nudgeCommand": "orp mode nudge ruthless-simplification --json", + "loopPlacement": "After granular decomposition, before committing a plan to TASK_LIST, and before final summaries.", + "outputExpectation": "One core sentence, one surviving move, and a list of noise to delete or defer." + }, + { + "modeId": "systems-constellation", + "label": "Systems Constellation", + "role": "dependency_and_downstream_effects", + "useWhen": "A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow.", + "command": "orp mode nudge systems-constellation --json", + "nudgeCommand": "orp mode nudge systems-constellation --json", + "loopPlacement": "Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow.", + "outputExpectation": "Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision." + }, + { + "modeId": "bold-concept-generation", + "label": "Bold Concept Generation", + "role": "candidate_generation_when_stuck", + "useWhen": "The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions.", + "command": "orp mode nudge bold-concept-generation --json", + "nudgeCommand": "orp mode nudge bold-concept-generation --json", + "loopPlacement": "After a falsifier, before launching broad compute, or when inventing the next symbolic construction.", + "outputExpectation": "Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment." + }, + { + "modeId": "sleek-minimal-progressive", + "label": "Sleek Minimal Progressive", + "role": "fresh_lens_and_low_friction_motion", + "useWhen": "The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up.", + "command": "orp mode nudge sleek-minimal-progressive --json", + "nudgeCommand": "orp mode nudge sleek-minimal-progressive --json", + "loopPlacement": "When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation.", + "outputExpectation": "One subtraction, one tasteful surprise, and one concrete next move that keeps momentum." + } + ] + }, + "agentFlow": { + "schema": "erdos.problem_agent_flow/1", + "status": "ready", + "audience": "agent", + "problemId": "1", + "purpose": "Give agents one compact execution contract without forcing humans or agents through every task-list section.", + "operatingRule": "Read this object first; execute the primary next action unless a guardrail blocks it or the task list is stale.", + "primaryNextAction": { + "source": "formalization_work", + "stepId": "gap_1", + "status": "next", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work-refresh 1", + "completionRule": null, + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": null, + "manifestMarkdownPath": null + }, + "modePolicy": { + "defaultAction": "execute_primary_next_action", + "doNotRunEveryMode": true, + "selectionRule": "Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default.", + "granularBreakdown": { + "modeId": "granular-breakdown", + "useWhen": "Use when the primary action is broad, fuzzy, theorem-heavy, or has unclear dependencies.", + "fullBreakdownCommand": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json", + "nudgeCommand": "orp mode nudge granular-breakdown --json", + "compressionRule": "After any breakdown, compress back to one active target and one verification command." + }, + "situationalOverlays": [ + { + "modeId": "ruthless-simplification", + "role": "compression_and_signal_filter", + "useWhen": "A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision.", + "command": "orp mode nudge ruthless-simplification --json", + "loopPlacement": "After granular decomposition, before committing a plan to TASK_LIST, and before final summaries.", + "outputExpectation": "One core sentence, one surviving move, and a list of noise to delete or defer." + }, + { + "modeId": "systems-constellation", + "role": "dependency_and_downstream_effects", + "useWhen": "A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow.", + "command": "orp mode nudge systems-constellation --json", + "loopPlacement": "Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow.", + "outputExpectation": "Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision." + }, + { + "modeId": "bold-concept-generation", + "role": "candidate_generation_when_stuck", + "useWhen": "The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions.", + "command": "orp mode nudge bold-concept-generation --json", + "loopPlacement": "After a falsifier, before launching broad compute, or when inventing the next symbolic construction.", + "outputExpectation": "Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment." + }, + { + "modeId": "sleek-minimal-progressive", + "role": "fresh_lens_and_low_friction_motion", + "useWhen": "The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up.", + "command": "orp mode nudge sleek-minimal-progressive --json", + "loopPlacement": "When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation.", + "outputExpectation": "One subtraction, one tasteful surprise, and one concrete next move that keeps momentum." + } + ] + }, + "executionLoop": [ + "Load agentFlow.primaryNextAction.", + "If the action is clear, execute its command or implement the named task directly.", + "If the action is fuzzy, run the granular nudge or full breakdown, then compress to one target and one command.", + "Use at most one additional ORP overlay when it clearly reduces friction for the current decision.", + "Refresh the canonical task list after material progress and continue from the regenerated agentFlow." + ], + "guardrails": [ + "Do not run paid or remote compute unless the frontier configuration explicitly enables that paid rung.", + "Prefer local/free compute before opt-in paid compute.", + "Do not treat bounded search evidence as an all-N proof without a theorem-facing handoff.", + "Do not run every ORP mode by default.", + "Persist operationally important changes into canonical artifacts rather than chat-only state." + ], + "writeback": { + "refreshCommand": "erdos problem task-list-refresh 1", + "taskListCommand": "erdos problem task-list 1", + "durableArtifactRule": "If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state." + } + }, + "splitCoreAtomizationPlan": null, + "structuralVerifierAudit": null, + "baseSideScout": null, + "structuralTwoSideScout": null, + "mixedBaseFailureScout": null, + "fullMixedBaseStructuralVerifier": null, + "structuralLiftMiner": null, + "structuralLiftChecklist": null, + "executionRule": { + "stance": "concrete_execution", + "summary": "Treat the task list as a concrete research loop for problem 1: execute the highest-value task itself, not wrapper prose about the task.", + "afterEachCompletion": [ + "Cross off the completed task.", + "Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary.", + "Use ORP granular breakdown when the next step is broad or confusing: orp mode nudge granular-breakdown --json", + "Use the smallest relevant ORP mode overlay when it simplifies the work: simplification for bloat, systems for cross-surface consequences, bold generation for new candidates, and sleek-progressive for clearer handoff shape.", + "Invent the next highest-value step from the updated evidence rather than following a stale fixed script.", + "Append that next step to the task list and refresh the canonical task-list artifacts." + ], + "granularBreakdownMode": { + "modeId": "granular-breakdown", + "status": "core_loop_enabled", + "fullBreakdownCommand": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json", + "nudgeCommand": "orp mode nudge granular-breakdown --json" + }, + "repetitionProtocol": "To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass.", + "lowStressLongHorizonNote": "This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan." + }, + "loopTemplate": [ + { + "stepId": "freeze_current_state", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search.", + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 1" + }, + { + "stepId": "audit_theorem_surfaces", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 1" + }, + { + "stepId": "verify_canonical_inputs", + "title": "Verify canonical pack inputs against the latest route and verifier artifacts", + "task": "Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.", + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos problem theorem-loop-refresh 1" + }, + { + "stepId": "verify_primary_structural_hook", + "title": "Verify the current highest-value structural hook remains canonical", + "task": "Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.", + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 1" + }, + { + "stepId": "verify_verifier_boundary", + "title": "Verify the current verifier boundary and next target", + "task": "Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.", + "completionRule": "The verifier-facing boundary remains explicit even without a dedicated interval queue.", + "command": "erdos number-theory dispatch 1" + }, + { + "stepId": "apply_granular_breakdown", + "title": "Apply ORP granular breakdown before execution", + "task": "Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command.", + "completionRule": "The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification.", + "command": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json" + }, + { + "stepId": "execute_current_work_packet", + "title": "State Claim Honestly", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work 1" + }, + { + "stepId": "refresh_and_rerank", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 1" + } + ], + "currentObjective": { + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "activeWorkId": "number-theory_1_state_claim_honestly_v1", + "activeWorkTitle": "State Claim Honestly", + "activeWorkStatus": "ready" + }, + "currentTasks": [ + { + "taskId": "freeze_current_state", + "status": "ready", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search.", + "why": null, + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 1" + }, + { + "taskId": "audit_theorem_surfaces", + "status": "ready", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "why": null, + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 1" + }, + { + "taskId": "verify_canonical_inputs", + "status": "ready", + "title": "Verify canonical pack inputs against the latest route and verifier artifacts", + "task": "Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.", + "why": null, + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos problem theorem-loop-refresh 1" + }, + { + "taskId": "verify_primary_structural_hook", + "status": "ready", + "title": "Verify the current highest-value structural hook remains canonical", + "task": "Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.", + "why": null, + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 1" + }, + { + "taskId": "verify_verifier_boundary", + "status": "ready", + "title": "Verify the current verifier boundary and next target", + "task": "Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.", + "why": null, + "completionRule": "The verifier-facing boundary remains explicit even without a dedicated interval queue.", + "command": "erdos number-theory dispatch 1" + }, + { + "taskId": "apply_granular_breakdown", + "status": "ready", + "title": "Apply ORP granular breakdown before execution", + "task": "Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command.", + "why": null, + "completionRule": "The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification.", + "command": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json" + }, + { + "taskId": "execute_current_work_packet", + "status": "ready", + "title": "State Claim Honestly", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work 1" + }, + { + "taskId": "discharge_first_remaining_gap", + "status": "ready", + "title": "Discharge the first remaining gap in the active theorem packet", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "why": "This is the sharpest unresolved statement already named by the active theorem-work packet.", + "completionRule": "The first remaining gap is either resolved or replaced by a more precise successor gap.", + "command": "erdos problem formalization-work-refresh 1" + }, + { + "taskId": "refresh_and_rerank", + "status": "ready", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "why": null, + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 1" + } + ], + "completedAnchors": [], + "nextNeededSteps": [ + { + "stepId": "gap_1", + "status": "next", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 1" + }, + { + "stepId": "gap_2", + "status": "next", + "task": "freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 1" + }, + { + "stepId": "gap_3", + "status": "next", + "task": "define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 1" + }, + { + "stepId": "promote_ready_atom", + "status": "medium", + "task": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "source": "theorem_formalization", + "command": "erdos problem formalization 1" + } + ], + "commands": { + "problemShow": "erdos problem show 1", + "problemArtifacts": "erdos problem artifacts 1", + "taskList": "erdos problem task-list 1", + "taskListRefresh": "erdos problem task-list-refresh 1", + "taskListRun": "erdos problem task-list-run 1 --passes 10", + "orpModeList": "orp mode list --json", + "granularBreakdown": "orp mode breakdown granular-breakdown --topic \"problem 1 | State Claim Honestly\" --json", + "granularNudge": "orp mode nudge granular-breakdown --json", + "theoremLoop": "erdos problem theorem-loop 1", + "claimPass": "erdos problem claim-pass 1", + "formalization": "erdos problem formalization 1", + "formalizationWork": "erdos problem formalization-work 1", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1", + "taskListJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LIST.json", + "taskListMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LIST.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.json", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.json", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.json", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/INTERVAL_WORK_QUEUE.yaml", + "exactBreakpointScoutJsonPath": null, + "exactBreakpointCertificateJsonPath": null, + "externalStructuralVerifierAuditJsonPath": null, + "externalStructuralVerifierAuditMarkdownPath": null, + "baseSideScoutJsonPath": null, + "baseSideScoutMarkdownPath": null, + "structuralTwoSideScoutJsonPath": null, + "structuralTwoSideScoutMarkdownPath": null, + "mixedBaseFailureScoutJsonPath": null, + "mixedBaseFailureScoutMarkdownPath": null, + "fullMixedBaseStructuralVerifierJsonPath": null, + "fullMixedBaseStructuralVerifierMarkdownPath": null, + "structuralLiftMinerJsonPath": null, + "structuralLiftMinerMarkdownPath": null, + "structuralLiftChecklistJsonPath": null, + "structuralLiftChecklistMarkdownPath": null, + "legacyBridgeJsonPath": null + } +} diff --git a/packs/number-theory/problems/1/TASK_LIST.md b/packs/number-theory/problems/1/TASK_LIST.md new file mode 100644 index 0000000..60ee383 --- /dev/null +++ b/packs/number-theory/problems/1/TASK_LIST.md @@ -0,0 +1,142 @@ +# Erdos Problem #1 Task List + +This task list is the canonical research-loop surface for the problem. It gives one reusable execution rule, one templated loop, the current active tasks, and the next steps discovered from the current theorem/search/verifier state. + +## Current State + +- Task list mode: `baseline`. +- Active route: `distinct_subset_sum_lower_bound`. +- Current claim surface: `route_scaffolding`. +- Route summary: Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums. +- Next honest move: Record the first reduction and checkpoint it without overclaiming theorem progress. +- Latest verified interval: `(none)` + +## Execution Rule + +- Stance: `concrete_execution` +- Summary: Treat the task list as a concrete research loop for problem 1: execute the highest-value task itself, not wrapper prose about the task. +- After each completed step: Cross off the completed task. +- After each completed step: Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary. +- After each completed step: Use ORP granular breakdown when the next step is broad or confusing: orp mode nudge granular-breakdown --json +- After each completed step: Use the smallest relevant ORP mode overlay when it simplifies the work: simplification for bloat, systems for cross-surface consequences, bold generation for new candidates, and sleek-progressive for clearer handoff shape. +- After each completed step: Invent the next highest-value step from the updated evidence rather than following a stale fixed script. +- After each completed step: Append that next step to the task list and refresh the canonical task-list artifacts. +- Repetition protocol: To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass. +- Long-horizon note: This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan. + +## ORP Granular Breakdown + +- Status: `core_loop_enabled` +- Mode id: `granular-breakdown` +- Topic: problem 1 | State Claim Honestly +- Activation phrase: Break it down until it can move. +- Invocation rule: Use the full breakdown before executing a complex theorem/search packet; use the nudge card whenever the agent or user is confused, the target feels too broad, or the next action is not deterministic. +- Full breakdown: `orp mode breakdown granular-breakdown --topic "problem 1 | State Claim Honestly" --json` +- Nudge: `orp mode nudge granular-breakdown --json` +- Loop integration: Run the full breakdown after the theorem/search surfaces are audited and before executing the current work packet. +- Loop integration: Write operationally important decompositions into TASK_LIST, FORMALIZATION_WORK, or a dedicated checklist artifact rather than leaving them in chat. +- Loop integration: Use the nudge card for quick reorientation when a step becomes blurry during implementation. +- Loop integration: Compress the breakdown back into one active target and one verification command before continuing. +- Durable artifact rule: If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state. + +## ORP Mode Overlay Palette + +- Status: `core_loop_palette_enabled` +- Source command: `orp mode list --json` +- Default mode id: `granular-breakdown` +- Selection rule: Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default. +- Durable when operational: `yes` +- Overlay `granular-breakdown` (core_decomposition_loop): The work is broad, confusing, theorem-heavy, or needs a durable dependency ladder before execution. | placement: Before execute_current_work_packet and whenever the active target becomes fuzzy. | command: `orp mode breakdown granular-breakdown --topic "problem 1 | State Claim Honestly" --json` | output: Boundary, lanes, subclaims, atomic obligations, dependency ladder, active target, durable checklist, and next verification. +- Overlay `ruthless-simplification` (compression_and_signal_filter): A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision. | placement: After granular decomposition, before committing a plan to TASK_LIST, and before final summaries. | command: `orp mode nudge ruthless-simplification --json` | output: One core sentence, one surviving move, and a list of noise to delete or defer. +- Overlay `systems-constellation` (dependency_and_downstream_effects): A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow. | placement: Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow. | command: `orp mode nudge systems-constellation --json` | output: Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision. +- Overlay `bold-concept-generation` (candidate_generation_when_stuck): The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions. | placement: After a falsifier, before launching broad compute, or when inventing the next symbolic construction. | command: `orp mode nudge bold-concept-generation --json` | output: Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment. +- Overlay `sleek-minimal-progressive` (fresh_lens_and_low_friction_motion): The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up. | placement: When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation. | command: `orp mode nudge sleek-minimal-progressive --json` | output: One subtraction, one tasteful surprise, and one concrete next move that keeps momentum. + +## Agent Flow + +- Status: `ready` +- Audience: `agent` +- Operating rule: Read this object first; execute the primary next action unless a guardrail blocks it or the task list is stale. +- Primary next action: `gap_1` [next] state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- Primary command: `erdos problem formalization-work-refresh 1` +- Default agent action: `execute_primary_next_action` +- Mode selection: Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default. +- Granular nudge: `orp mode nudge granular-breakdown --json` +- Situational overlay `ruthless-simplification`: A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision. | command: `orp mode nudge ruthless-simplification --json` +- Situational overlay `systems-constellation`: A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow. | command: `orp mode nudge systems-constellation --json` +- Situational overlay `bold-concept-generation`: The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions. | command: `orp mode nudge bold-concept-generation --json` +- Situational overlay `sleek-minimal-progressive`: The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up. | command: `orp mode nudge sleek-minimal-progressive --json` +- Agent guardrail: Do not run paid or remote compute unless the frontier configuration explicitly enables that paid rung. +- Agent guardrail: Prefer local/free compute before opt-in paid compute. +- Agent guardrail: Do not treat bounded search evidence as an all-N proof without a theorem-facing handoff. +- Agent guardrail: Do not run every ORP mode by default. +- Agent guardrail: Persist operationally important changes into canonical artifacts rather than chat-only state. +- Refresh after material progress: `erdos problem task-list-refresh 1` + +## Template Loop + +- `freeze_current_state`: Freeze the current north star and active theorem packet | Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 1` +- `audit_theorem_surfaces`: Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 1` +- `verify_canonical_inputs`: Verify canonical pack inputs against the latest route and verifier artifacts | Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos problem theorem-loop-refresh 1` +- `verify_primary_structural_hook`: Verify the current highest-value structural hook remains canonical | Verify that the strongest supported structural hook still survives across the theorem and claim surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 1` +- `verify_verifier_boundary`: Verify the current verifier boundary and next target | Verify that the current verifier boundary and next target are stated honestly across the pack surfaces. | completion: The verifier-facing boundary remains explicit even without a dedicated interval queue. | command: `erdos number-theory dispatch 1` +- `apply_granular_breakdown`: Apply ORP granular breakdown before execution | Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command. | completion: The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification. | command: `orp mode breakdown granular-breakdown --topic "problem 1 | State Claim Honestly" --json` +- `execute_current_work_packet`: State Claim Honestly | State the candidate theorem-facing claim in pack language without overstating current support. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | command: `erdos problem formalization-work 1` +- `refresh_and_rerank`: Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 1` + +## Current Objective + +- Formalization id: `number-theory_1_promote_ready_atom_v1` +- Focus id: `promote_ready_atom` +- Title: Promote Ready Atom +- Active work id: `number-theory_1_state_claim_honestly_v1` +- Active work title: State Claim Honestly +- Active work status: `ready` + +## Current Tasks + +- `freeze_current_state` [ready] Freeze the current north star and active theorem packet | Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 1` +- `audit_theorem_surfaces` [ready] Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 1` +- `verify_canonical_inputs` [ready] Verify canonical pack inputs against the latest route and verifier artifacts | Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos problem theorem-loop-refresh 1` +- `verify_primary_structural_hook` [ready] Verify the current highest-value structural hook remains canonical | Verify that the strongest supported structural hook still survives across the theorem and claim surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 1` +- `verify_verifier_boundary` [ready] Verify the current verifier boundary and next target | Verify that the current verifier boundary and next target are stated honestly across the pack surfaces. | completion: The verifier-facing boundary remains explicit even without a dedicated interval queue. | command: `erdos number-theory dispatch 1` +- `apply_granular_breakdown` [ready] Apply ORP granular breakdown before execution | Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command. | completion: The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification. | command: `orp mode breakdown granular-breakdown --topic "problem 1 | State Claim Honestly" --json` +- `execute_current_work_packet` [ready] State Claim Honestly | State the candidate theorem-facing claim in pack language without overstating current support. | Record the first reduction and checkpoint it without overclaiming theorem progress. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | command: `erdos problem formalization-work 1` +- `discharge_first_remaining_gap` [ready] Discharge the first remaining gap in the active theorem packet | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | This is the sharpest unresolved statement already named by the active theorem-work packet. | completion: The first remaining gap is either resolved or replaced by a more precise successor gap. | command: `erdos problem formalization-work-refresh 1` +- `refresh_and_rerank` [ready] Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 1` + +## Completed Anchors + + +## Next Needed Steps + +- `gap_1` [next] state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | source: formalization_work | command: `erdos problem formalization-work-refresh 1` +- `gap_2` [next] freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. | source: formalization_work | command: `erdos problem formalization-work-refresh 1` +- `gap_3` [next] define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers. | source: formalization_work | command: `erdos problem formalization-work-refresh 1` +- `promote_ready_atom` [medium] Record the first reduction and checkpoint it without overclaiming theorem progress. | source: theorem_formalization | command: `erdos problem formalization 1` + +## Commands + +- Problem surface: `erdos problem show 1` +- Problem artifacts: `erdos problem artifacts 1` +- Task list: `erdos problem task-list 1` +- Task list refresh: `erdos problem task-list-refresh 1` +- Task list run: `erdos problem task-list-run 1 --passes 10` +- ORP mode list: `orp mode list --json` +- ORP granular breakdown: `orp mode breakdown granular-breakdown --topic "problem 1 | State Claim Honestly" --json` +- ORP granular nudge: `orp mode nudge granular-breakdown --json` +- Theorem loop: `erdos problem theorem-loop 1` +- Claim pass: `erdos problem claim-pass 1` +- Formalization: `erdos problem formalization 1` +- Formalization work: `erdos problem formalization-work 1` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1` +- taskListJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LIST.json` +- taskListMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LIST.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/CLAIM_PASS.json` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION.json` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FORMALIZATION_WORK.json` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/number-theory/problems/1/TASK_LOOP_RUN.json b/packs/number-theory/problems/1/TASK_LOOP_RUN.json new file mode 100644 index 0000000..2be2db5 --- /dev/null +++ b/packs/number-theory/problems/1/TASK_LOOP_RUN.json @@ -0,0 +1,120 @@ +{ + "ok": true, + "schema": "erdos.problem_task_loop_run/1", + "generatedAt": "2026-04-14T11:46:21.821Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "requestedPasses": 4, + "executedPasses": 4, + "stopOnConvergence": false, + "stopReason": "requested_pass_limit_reached", + "converged": true, + "convergedAtPass": 2, + "currentState": { + "activeRoute": "distinct_subset_sum_lower_bound", + "currentClaimSurface": "route_scaffolding", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress.", + "latestVerifiedInterval": null + }, + "currentObjective": { + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "activeWorkId": "number-theory_1_state_claim_honestly_v1", + "activeWorkTitle": "State Claim Honestly", + "activeWorkStatus": "ready" + }, + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work-refresh 1" + }, + "passes": [ + { + "passNumber": 1, + "changed": true, + "activeRoute": "distinct_subset_sum_lower_bound", + "latestVerifiedInterval": null, + "currentClaimSurface": "route_scaffolding", + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "activeWorkId": "number-theory_1_state_claim_honestly_v1", + "activeWorkStatus": "ready", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work-refresh 1" + }, + "fingerprint": "{\"activeRoute\":\"distinct_subset_sum_lower_bound\",\"currentClaimSurface\":\"route_scaffolding\",\"nextHonestMove\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"latestVerifiedInterval\":null,\"currentObjective\":{\"formalizationId\":\"number-theory_1_promote_ready_atom_v1\",\"focusId\":\"promote_ready_atom\",\"activeWorkId\":\"number-theory_1_state_claim_honestly_v1\",\"activeWorkStatus\":\"ready\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical pack inputs against the latest route and verifier artifacts\",\"task\":\"Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the current highest-value structural hook remains canonical\",\"task\":\"Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current verifier boundary and next target\",\"task\":\"Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.\"},{\"taskId\":\"apply_granular_breakdown\",\"status\":\"ready\",\"title\":\"Apply ORP granular breakdown before execution\",\"task\":\"Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"ready\",\"title\":\"State Claim Honestly\",\"task\":\"State the candidate theorem-facing claim in pack language without overstating current support.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_3\",\"status\":\"next\",\"task\":\"define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.\",\"source\":\"formalization_work\"},{\"stepId\":\"promote_ready_atom\",\"status\":\"medium\",\"task\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 2, + "changed": false, + "activeRoute": "distinct_subset_sum_lower_bound", + "latestVerifiedInterval": null, + "currentClaimSurface": "route_scaffolding", + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "activeWorkId": "number-theory_1_state_claim_honestly_v1", + "activeWorkStatus": "ready", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work-refresh 1" + }, + "fingerprint": "{\"activeRoute\":\"distinct_subset_sum_lower_bound\",\"currentClaimSurface\":\"route_scaffolding\",\"nextHonestMove\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"latestVerifiedInterval\":null,\"currentObjective\":{\"formalizationId\":\"number-theory_1_promote_ready_atom_v1\",\"focusId\":\"promote_ready_atom\",\"activeWorkId\":\"number-theory_1_state_claim_honestly_v1\",\"activeWorkStatus\":\"ready\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical pack inputs against the latest route and verifier artifacts\",\"task\":\"Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the current highest-value structural hook remains canonical\",\"task\":\"Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current verifier boundary and next target\",\"task\":\"Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.\"},{\"taskId\":\"apply_granular_breakdown\",\"status\":\"ready\",\"title\":\"Apply ORP granular breakdown before execution\",\"task\":\"Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"ready\",\"title\":\"State Claim Honestly\",\"task\":\"State the candidate theorem-facing claim in pack language without overstating current support.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_3\",\"status\":\"next\",\"task\":\"define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.\",\"source\":\"formalization_work\"},{\"stepId\":\"promote_ready_atom\",\"status\":\"medium\",\"task\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 3, + "changed": false, + "activeRoute": "distinct_subset_sum_lower_bound", + "latestVerifiedInterval": null, + "currentClaimSurface": "route_scaffolding", + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "activeWorkId": "number-theory_1_state_claim_honestly_v1", + "activeWorkStatus": "ready", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work-refresh 1" + }, + "fingerprint": "{\"activeRoute\":\"distinct_subset_sum_lower_bound\",\"currentClaimSurface\":\"route_scaffolding\",\"nextHonestMove\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"latestVerifiedInterval\":null,\"currentObjective\":{\"formalizationId\":\"number-theory_1_promote_ready_atom_v1\",\"focusId\":\"promote_ready_atom\",\"activeWorkId\":\"number-theory_1_state_claim_honestly_v1\",\"activeWorkStatus\":\"ready\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical pack inputs against the latest route and verifier artifacts\",\"task\":\"Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the current highest-value structural hook remains canonical\",\"task\":\"Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current verifier boundary and next target\",\"task\":\"Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.\"},{\"taskId\":\"apply_granular_breakdown\",\"status\":\"ready\",\"title\":\"Apply ORP granular breakdown before execution\",\"task\":\"Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"ready\",\"title\":\"State Claim Honestly\",\"task\":\"State the candidate theorem-facing claim in pack language without overstating current support.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_3\",\"status\":\"next\",\"task\":\"define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.\",\"source\":\"formalization_work\"},{\"stepId\":\"promote_ready_atom\",\"status\":\"medium\",\"task\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 4, + "changed": false, + "activeRoute": "distinct_subset_sum_lower_bound", + "latestVerifiedInterval": null, + "currentClaimSurface": "route_scaffolding", + "formalizationId": "number-theory_1_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "activeWorkId": "number-theory_1_state_claim_honestly_v1", + "activeWorkStatus": "ready", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work-refresh 1" + }, + "fingerprint": "{\"activeRoute\":\"distinct_subset_sum_lower_bound\",\"currentClaimSurface\":\"route_scaffolding\",\"nextHonestMove\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"latestVerifiedInterval\":null,\"currentObjective\":{\"formalizationId\":\"number-theory_1_promote_ready_atom_v1\",\"focusId\":\"promote_ready_atom\",\"activeWorkId\":\"number-theory_1_state_claim_honestly_v1\",\"activeWorkStatus\":\"ready\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `distinct_subset_sum_lower_bound`, claim surface `route_scaffolding`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical pack inputs against the latest route and verifier artifacts\",\"task\":\"Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the current highest-value structural hook remains canonical\",\"task\":\"Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current verifier boundary and next target\",\"task\":\"Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.\"},{\"taskId\":\"apply_granular_breakdown\",\"status\":\"ready\",\"title\":\"Apply ORP granular breakdown before execution\",\"task\":\"Run ORP granular breakdown on the active topic `problem 1 | State Claim Honestly` and compress it into one active target plus one verification command.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"ready\",\"title\":\"State Claim Honestly\",\"task\":\"State the candidate theorem-facing claim in pack language without overstating current support.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_3\",\"status\":\"next\",\"task\":\"define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.\",\"source\":\"formalization_work\"},{\"stepId\":\"promote_ready_atom\",\"status\":\"medium\",\"task\":\"Record the first reduction and checkpoint it without overclaiming theorem progress.\",\"source\":\"theorem_formalization\"}]}" + } + ], + "commands": { + "taskList": "erdos problem task-list 1", + "taskListRefresh": "erdos problem task-list-refresh 1", + "rerun": "erdos problem task-list-run 1 --passes 4" + }, + "sources": { + "taskListJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LIST.json", + "taskListMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LIST.md", + "taskLoopRunJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LOOP_RUN.json", + "taskLoopRunMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/TASK_LOOP_RUN.md" + } +} diff --git a/packs/number-theory/problems/1/TASK_LOOP_RUN.md b/packs/number-theory/problems/1/TASK_LOOP_RUN.md new file mode 100644 index 0000000..5c36587 --- /dev/null +++ b/packs/number-theory/problems/1/TASK_LOOP_RUN.md @@ -0,0 +1,20 @@ +# Erdos Problem #1 Task Loop Run + +- Problem id: `1` +- Requested passes: `4` +- Executed passes: `4` +- Stop reason: `requested_pass_limit_reached` +- Converged: `yes` +- Converged at pass: `2` +- Active route: `distinct_subset_sum_lower_bound` +- Current claim surface: `route_scaffolding` +- Latest verified interval: `(none)` +- Highest-value next step: `gap_1` | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- Highest-value command: `erdos problem formalization-work-refresh 1` + +## Passes + +- Pass 1: changed=`yes` | active work=`number-theory_1_state_claim_honestly_v1` | next=`gap_1` | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- Pass 2: changed=`no` | active work=`number-theory_1_state_claim_honestly_v1` | next=`gap_1` | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- Pass 3: changed=`no` | active work=`number-theory_1_state_claim_honestly_v1` | next=`gap_1` | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- Pass 4: changed=`no` | active work=`number-theory_1_state_claim_honestly_v1` | next=`gap_1` | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. diff --git a/packs/number-theory/problems/1/THEOREM_LOOP.json b/packs/number-theory/problems/1/THEOREM_LOOP.json new file mode 100644 index 0000000..1733aeb --- /dev/null +++ b/packs/number-theory/problems/1/THEOREM_LOOP.json @@ -0,0 +1,74 @@ +{ + "schema": "erdos.problem_theorem_loop/1", + "generatedAt": "2026-04-14T11:46:21.656Z", + "problemId": "1", + "displayName": "Erdos Problem #1", + "title": "Erdos Problem #1", + "cluster": "number-theory", + "sourceKind": "pack_route_state", + "theoremLoopMode": "baseline", + "activeRoute": "distinct_subset_sum_lower_bound", + "theoremModule": null, + "currentState": { + "siteStatus": "open", + "repoStatus": "cataloged", + "openProblem": true, + "routeBreakthrough": false, + "problemSolved": false, + "currentClaimSurface": "route_scaffolding", + "routeSummary": "Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums.", + "nextHonestMove": "Record the first reduction and checkpoint it without overclaiming theorem progress." + }, + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `distinct_subset_sum_lower_bound`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `N1.G1.A1`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "theoremAgenda": [ + { + "item_id": "promote_ready_atom", + "status": "ready", + "task": "Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress." + }, + { + "item_id": "tighten_active_route_claim", + "status": "ready", + "task": "Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit.", + "why": "Record the first reduction and checkpoint it without overclaiming theorem progress." + } + ], + "currentBridgeState": null, + "commands": { + "problemShow": "erdos problem show 1", + "problemArtifacts": "erdos problem artifacts 1", + "theoremLoop": "erdos problem theorem-loop 1", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 1", + "clusterStatus": "erdos number-theory status 1", + "clusterFrontier": "erdos number-theory frontier 1", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md", + "contextPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/context.yaml", + "routePacketPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/ROUTE_PACKET.yaml", + "frontierNotePath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FRONTIER_NOTE.md", + "opsDetailsPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/OPS_DETAILS.yaml", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null + } +} diff --git a/packs/number-theory/problems/1/THEOREM_LOOP.md b/packs/number-theory/problems/1/THEOREM_LOOP.md new file mode 100644 index 0000000..5ee2a74 --- /dev/null +++ b/packs/number-theory/problems/1/THEOREM_LOOP.md @@ -0,0 +1,46 @@ +# Erdos Problem #1 Theorem Loop + +This note is the generic theorem-loop surface for the problem pack. It keeps theorem-facing route state visible even when no richer search bridge exists yet. + +## Current State + +- Theorem loop mode: `baseline`. +- Active route: `distinct_subset_sum_lower_bound`. +- Current claim surface: `route_scaffolding`. +- Repo status: `cataloged`; site status: `open`. +- Route breakthrough: `no`. +- Problem solved: `no`. +- Open problem: `yes`. +- Theorem module: `(none)`. +- Route summary: Keep the problem centered on the exponential-growth lower-bound route implied by distinct subset sums. +- Next honest move: Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Theorem Hooks + +- `active_route_recorded`: supported | The pack records an active route, currently `distinct_subset_sum_lower_bound`. +- `ready_atom_present`: supported | The live route already has a ready atom, `N1.G1.A1`, which can feed the theorem lane. +- `frontier_note_present`: supported | The pack already carries a frontier note that can anchor theorem-facing updates. + +## Theorem Agenda + +- `promote_ready_atom`: ready | Turn ready atom `N1.G1.A1` into the next theorem-facing checkpoint. | Record the first reduction and checkpoint it without overclaiming theorem progress. +- `tighten_active_route_claim`: ready | Compress the active route `distinct_subset_sum_lower_bound` into the next honest theorem-facing claim unit. | Record the first reduction and checkpoint it without overclaiming theorem progress. + +## Commands + +- Problem surface: `erdos problem show 1` +- Canonical theorem loop: `erdos problem theorem-loop 1` +- Refresh theorem loop: `erdos problem theorem-loop-refresh 1` +- Problem artifacts: `erdos problem artifacts 1` +- Cluster status: `erdos number-theory status 1` +- Cluster frontier: `erdos number-theory frontier 1` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/THEOREM_LOOP.md` +- contextPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/context.yaml` +- routePacketPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/ROUTE_PACKET.yaml` +- frontierNotePath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/FRONTIER_NOTE.md` +- opsDetailsPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/1/OPS_DETAILS.yaml` diff --git a/packs/number-theory/problems/848/BASE_SIDE_SCOUT.json b/packs/number-theory/problems/848/BASE_SIDE_SCOUT.json new file mode 100644 index 0000000..9534015 --- /dev/null +++ b/packs/number-theory/problems/848/BASE_SIDE_SCOUT.json @@ -0,0 +1,4145 @@ +{ + "schema": "erdos.number_theory.p848_base_side_scout/1", + "generatedAt": "2026-04-11T20:36:43.797Z", + 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"side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 167, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 117, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 117, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 168, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 169, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 170, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 171, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 172, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 173, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 174, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 175, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 176, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 177, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 178, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 179, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + 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"maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 183, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 184, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, 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"maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 188, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 189, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 190, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 191, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 192, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 2, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 0, + "delta7Minus18": 2 + } + }, + { + "N": 193, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 194, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 195, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 196, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 197, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 198, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 199, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + }, + { + "N": 200, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 38, + "maxSide18Outsider": 41, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 41, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 2, + "side18": 1, + "delta7Minus18": 1 + } + } + ], + "boundary": { + "claimLevel": "bounded_scout_not_proof", + "note": "This scout compares principal-base compatibility counts on a finite interval only. It does not prove all-N base-side domination.", + "nextUse": "A one-sided 7 mod 25 base mask is not safe on this bounded scout; a two-sided structural verifier is needed." + } +} diff --git a/packs/number-theory/problems/848/BASE_SIDE_SCOUT.md b/packs/number-theory/problems/848/BASE_SIDE_SCOUT.md new file mode 100644 index 0000000..7deeaa8 --- /dev/null +++ b/packs/number-theory/problems/848/BASE_SIDE_SCOUT.md @@ -0,0 +1,22 @@ +# Problem 848 Base-Side Scout + +- Generated: 2026-04-11T20:36:43.797Z +- Method: `bounded_base_side_compatibility_scout` +- Status: `counterexample_to_global_7_side_domination_found` +- Interval: `1..200` +- Outsiders checked: `5` +- Global max side18-minus-side7: `1` +- Max per-outsider side18-minus-side7: `1` + +## Strongest Rows + +- Strongest global side-18 row: `{"N":143,"maxSide7":2,"maxSide18":3,"maxSide7Outsider":41,"maxSide18Outsider":117,"maxSide18Minus7":1,"maxPerOutsider18Minus7":1,"maxPerOutsider7Minus18":1,"perOutsider18Winner":{"outsider":117,"side7":2,"side18":3,"delta18Minus7":1},"perOutsider7Winner":{"outsider":38,"side7":1,"side18":0,"delta7Minus18":1}}` +- Strongest per-outsider side-18 row: `{"N":143,"maxSide7":2,"maxSide18":3,"maxSide7Outsider":41,"maxSide18Outsider":117,"maxSide18Minus7":1,"maxPerOutsider18Minus7":1,"maxPerOutsider7Minus18":1,"perOutsider18Winner":{"outsider":117,"side7":2,"side18":3,"delta18Minus7":1},"perOutsider7Winner":{"outsider":38,"side7":1,"side18":0,"delta7Minus18":1}}` +- First global side-18 exceedance: `{"N":143,"maxSide7":2,"maxSide18":3,"maxSide7Outsider":41,"maxSide18Outsider":117,"maxSide18Minus7":1,"maxPerOutsider18Minus7":1,"maxPerOutsider7Minus18":1,"perOutsider18Winner":{"outsider":117,"side7":2,"side18":3,"delta18Minus7":1},"perOutsider7Winner":{"outsider":38,"side7":1,"side18":0,"delta7Minus18":1}}` +- First per-outsider side-18 exceedance: `{"N":143,"maxSide7":2,"maxSide18":3,"maxSide7Outsider":41,"maxSide18Outsider":117,"maxSide18Minus7":1,"maxPerOutsider18Minus7":1,"maxPerOutsider7Minus18":1,"perOutsider18Winner":{"outsider":117,"side7":2,"side18":3,"delta18Minus7":1},"perOutsider7Winner":{"outsider":38,"side7":1,"side18":0,"delta7Minus18":1}}` + +## Boundary + +- Claim level: `bounded_scout_not_proof` +- This scout compares principal-base compatibility counts on a finite interval only. It does not prove all-N base-side domination. +- Next use: A one-sided 7 mod 25 base mask is not safe on this bounded scout; a two-sided structural verifier is needed. diff --git a/packs/number-theory/problems/848/CLAIM_LOOP.json b/packs/number-theory/problems/848/CLAIM_LOOP.json new file mode 100644 index 0000000..7ae2b01 --- /dev/null +++ b/packs/number-theory/problems/848/CLAIM_LOOP.json @@ -0,0 +1,297 @@ +{ + "schema": "erdos.problem_claim_loop/1", + "generatedAt": "2026-04-14T11:45:57.618Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "cluster": "number-theory", + "sourceKind": "theorem_loop_plus_bridge", + "claimLoopMode": "bridge_backed", + "currentClaimSurface": "bridge_backed_frontier_support", + "currentState": { + "theoremLoopMode": "bridge_backed", + "activeRoute": "finite_check_gap_closure", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `40500` or switch method class.", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "featureExtractors": [ + { + "extractor_id": "pack_route_state", + "kind": "pack_context", + "scope": "all_problems", + "status": "ready", + "note": "Reads pack route, ticket, and atom state as the baseline theorem-search context." + }, + { + "extractor_id": "theorem_loop_snapshot", + "kind": "theorem_loop", + "scope": "all_problems", + "status": "ready", + "note": "Uses the canonical theorem-loop as the current claim-surface ledger." + }, + { + "extractor_id": "search_theorem_bridge_state", + "kind": "search_bridge", + "scope": "bridge_backed_problems", + "status": "ready", + "note": "Imports structured bridge state, packet ledgers, and search-side claim hooks." + }, + { + "extractor_id": "cluster_number_theory_features", + "kind": "cluster_adapter", + "scope": "number_theory", + "status": "ready", + "note": "Exposes number-theory specific finite-gap and verifier-facing metadata." + } + ], + "claimGenerators": [ + { + "generator_id": "baseline_route_claims", + "kind": "route_state", + "scope": "all_problems", + "status": "ready", + "note": "Promotes active routes, ready atoms, and next-honest-move records into candidate claims." + }, + { + "generator_id": "theorem_agenda_claims", + "kind": "agenda_projection", + "scope": "all_problems", + "status": "ready", + "note": "Turns theorem agenda items into explicit candidate claim tickets." + }, + { + "generator_id": "search_bridge_claims", + "kind": "bridge_pattern_projection", + "scope": "bridge_backed_problems", + "status": "ready", + "note": "Projects bridge-backed structural hooks into concrete claim candidates." + }, + { + "generator_id": "p848_repair_obstruction_claims", + "kind": "problem_adapter", + "scope": "problem_848", + "status": "ready", + "note": "Builds obstruction-alignment and repair-class candidate claims from the live packet ledger." + } + ], + "claimFalsifiers": [ + { + "falsifier_id": "theorem_loop_consistency_check", + "kind": "ledger_consistency", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims that overstate the current theorem-loop claim surface." + }, + { + "falsifier_id": "artifact_boundary_check", + "kind": "artifact_boundary", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims unsupported by canonical artifacts already present in the pack." + }, + { + "falsifier_id": "exact_interval_counterexample_scan", + "kind": "exact_verifier", + "scope": "number_theory", + "status": "ready", + "note": "Uses bounded exact interval checks to kill false local claims quickly." + }, + { + "falsifier_id": "bridge_packet_replay", + "kind": "search_bridge_replay", + "scope": "bridge_backed_problems", + "status": "ready", + "note": "Replays current bridge packets and tracked tails against candidate claims." + } + ], + "verifierAdapters": [ + { + "adapter_id": "canonical_artifact_reader", + "kind": "artifact_reader", + "scope": "all_problems", + "status": "ready", + "note": "Reads theorem-loop, route, and pack artifacts as verifier-facing evidence." + }, + { + "adapter_id": "exact_small_n", + "kind": "exact_verifier", + "scope": "number_theory", + "status": "ready", + "note": "Bounded exact verifier for finite interval certification." + }, + { + "adapter_id": "search_theorem_bridge", + "kind": "bridge_verifier", + "scope": "bridge_backed_problems", + "status": "ready", + "note": "Supplies live search-side packet and leaderboard evidence to the claim loop." + }, + { + "adapter_id": "p848_family_repair_surface", + "kind": "problem_adapter", + "scope": "problem_848", + "status": "ready", + "note": "Evaluates candidate claims against tracked-tail repair surfaces and shared-prefix packets." + } + ], + "candidateClaims": [ + { + "claim_id": "choose_next_finite_gap_move", + "status": "ready", + "source": "theorem_agenda", + "summary": "Choose the next finite-gap closure move and keep the theorem-facing claim surface honest.", + "why": "Decide whether to extend exact verified coverage beyond `40500` or switch method class.", + "support": [ + "next_unmatched_equals_282_failure", + "completed_tail_vs_search_leader_split", + "repair_pool_not_closed", + "top_repair_class_cluster" + ] + }, + { + "claim_id": "explain_next_unmatched_alignment", + "status": "ready", + "source": "theorem_agenda", + "summary": "Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`.", + "why": "If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class.", + "support": [ + "next_unmatched_equals_282_failure", + "completed_tail_vs_search_leader_split", + "repair_pool_not_closed", + "top_repair_class_cluster" + ] + }, + { + "claim_id": "explain_completed_vs_search_leader_split", + "status": "ready", + "source": "theorem_agenda", + "summary": "Explain why completed structured tail `332` differs from current family-aware leader `432`.", + "why": "That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class.", + "support": [ + "next_unmatched_equals_282_failure", + "completed_tail_vs_search_leader_split", + "repair_pool_not_closed", + "top_repair_class_cluster" + ] + }, + { + "claim_id": "model_repair_pool_growth", + "status": "ready", + "source": "theorem_agenda", + "summary": "Model the repaired square-modulus pool as a growing family rather than treating it as already closed.", + "why": "Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure.", + "support": [ + "next_unmatched_equals_282_failure", + "completed_tail_vs_search_leader_split", + "repair_pool_not_closed", + "top_repair_class_cluster" + ] + }, + { + "claim_id": "characterize_top_repair_cluster", + "status": "ready", + "source": "theorem_agenda", + "summary": "Characterize what the top repair cluster `432, 782, 832` shares structurally.", + "why": "If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction.", + "support": [ + "next_unmatched_equals_282_failure", + "completed_tail_vs_search_leader_split", + "repair_pool_not_closed", + "top_repair_class_cluster" + ] + }, + { + "claim_id": "p848_next_unmatched_alignment_claim", + "status": "ready", + "source": "search_bridge", + "summary": "Shared-prefix representative 137720141 aligns structurally with the first failure of tail 282.", + "why": "If this survives falsification, it upgrades a numerical coincidence into an obstruction-class candidate.", + "support": [ + "next_unmatched_equals_282_failure" + ] + }, + { + "claim_id": "p848_top_repair_cluster_claim", + "status": "ready", + "source": "search_bridge", + "summary": "Top repair class 432, 782, 832 shares a common repair mechanism.", + "why": "A shared mechanism would compress the search frontier into a reusable lemma candidate.", + "support": [ + "top_repair_class_cluster" + ] + } + ], + "theoremHooks": [ + { + "hook_id": "next_unmatched_equals_282_failure", + "status": "supported", + "note": "" + }, + { + "hook_id": "completed_tail_vs_search_leader_split", + "status": "supported", + "note": "" + }, + { + "hook_id": "repair_pool_not_closed", + "status": "supported", + "note": "" + }, + { + "hook_id": "top_repair_class_cluster", + "status": "supported", + "note": "" + } + ], + "theoremAgenda": [ + { + "item_id": "choose_next_finite_gap_move", + "status": "ready", + "task": "Choose the next finite-gap closure move and keep the theorem-facing claim surface honest.", + "why": "Decide whether to extend exact verified coverage beyond `40500` or switch method class." + }, + { + "item_id": "explain_next_unmatched_alignment", + "status": "ready", + "task": "Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`.", + "why": "If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class." + }, + { + "item_id": "explain_completed_vs_search_leader_split", + "status": "ready", + "task": "Explain why completed structured tail `332` differs from current family-aware leader `432`.", + "why": "That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class." + }, + { + "item_id": "model_repair_pool_growth", + "status": "ready", + "task": "Model the repaired square-modulus pool as a growing family rather than treating it as already closed.", + "why": "Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure." + }, + { + "item_id": "characterize_top_repair_cluster", + "status": "ready", + "task": "Characterize what the top repair cluster `432, 782, 832` shares structurally.", + "why": "If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction." + } + ], + "commands": { + "problemShow": "erdos problem show 848", + "problemArtifacts": "erdos problem artifacts 848", + "theoremLoop": "erdos problem theorem-loop 848", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 848", + "claimLoop": "erdos problem claim-loop 848", + "claimLoopRefresh": "erdos problem claim-loop-refresh 848", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "sources": { + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md", + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848" + } +} diff --git a/packs/number-theory/problems/848/CLAIM_LOOP.md b/packs/number-theory/problems/848/CLAIM_LOOP.md new file mode 100644 index 0000000..8f876af --- /dev/null +++ b/packs/number-theory/problems/848/CLAIM_LOOP.md @@ -0,0 +1,69 @@ +# Erdos Problem #848 Claim Loop + +This claim loop generalizes theorem-search-verification work using the theorem loop plus richer bridge-backed search evidence. + +## Current State + +- Claim loop mode: `bridge_backed`. +- Current claim surface: `bridge_backed_frontier_support`. +- Active route: `finite_check_gap_closure`. +- Route summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. +- Next honest move: Decide whether to extend exact verified coverage beyond `40500` or switch method class. + +## Feature Extractors + +- `pack_route_state`: ready | Reads pack route, ticket, and atom state as the baseline theorem-search context. +- `theorem_loop_snapshot`: ready | Uses the canonical theorem-loop as the current claim-surface ledger. +- `search_theorem_bridge_state`: ready | Imports structured bridge state, packet ledgers, and search-side claim hooks. +- `cluster_number_theory_features`: ready | Exposes number-theory specific finite-gap and verifier-facing metadata. + +## Claim Generators + +- `baseline_route_claims`: ready | Promotes active routes, ready atoms, and next-honest-move records into candidate claims. +- `theorem_agenda_claims`: ready | Turns theorem agenda items into explicit candidate claim tickets. +- `search_bridge_claims`: ready | Projects bridge-backed structural hooks into concrete claim candidates. +- `p848_repair_obstruction_claims`: ready | Builds obstruction-alignment and repair-class candidate claims from the live packet ledger. + +## Claim Falsifiers + +- `theorem_loop_consistency_check`: ready | Rejects claims that overstate the current theorem-loop claim surface. +- `artifact_boundary_check`: ready | Rejects claims unsupported by canonical artifacts already present in the pack. +- `exact_interval_counterexample_scan`: ready | Uses bounded exact interval checks to kill false local claims quickly. +- `bridge_packet_replay`: ready | Replays current bridge packets and tracked tails against candidate claims. + +## Verifier Adapters + +- `canonical_artifact_reader`: ready | Reads theorem-loop, route, and pack artifacts as verifier-facing evidence. +- `exact_small_n`: ready | Bounded exact verifier for finite interval certification. +- `search_theorem_bridge`: ready | Supplies live search-side packet and leaderboard evidence to the claim loop. +- `p848_family_repair_surface`: ready | Evaluates candidate claims against tracked-tail repair surfaces and shared-prefix packets. + +## Candidate Claims + +- `choose_next_finite_gap_move`: ready | Choose the next finite-gap closure move and keep the theorem-facing claim surface honest. | Decide whether to extend exact verified coverage beyond `40500` or switch method class. +- `explain_next_unmatched_alignment`: ready | Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`. | If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class. +- `explain_completed_vs_search_leader_split`: ready | Explain why completed structured tail `332` differs from current family-aware leader `432`. | That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class. +- `model_repair_pool_growth`: ready | Model the repaired square-modulus pool as a growing family rather than treating it as already closed. | Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure. +- `characterize_top_repair_cluster`: ready | Characterize what the top repair cluster `432, 782, 832` shares structurally. | If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction. +- `p848_next_unmatched_alignment_claim`: ready | Shared-prefix representative 137720141 aligns structurally with the first failure of tail 282. | If this survives falsification, it upgrades a numerical coincidence into an obstruction-class candidate. +- `p848_top_repair_cluster_claim`: ready | Top repair class 432, 782, 832 shares a common repair mechanism. | A shared mechanism would compress the search frontier into a reusable lemma candidate. + +## Commands + +- Problem surface: `erdos problem show 848` +- Problem artifacts: `erdos problem artifacts 848` +- Theorem loop: `erdos problem theorem-loop 848` +- Theorem refresh: `erdos problem theorem-loop-refresh 848` +- Claim loop: `erdos problem claim-loop 848` +- Claim refresh: `erdos problem claim-loop-refresh 848` +- Source refresh: `erdos number-theory bridge-refresh 848` + +## Sources + +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md` +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848` diff --git a/packs/number-theory/problems/848/CLAIM_PASS.json b/packs/number-theory/problems/848/CLAIM_PASS.json new file mode 100644 index 0000000..20e7593 --- /dev/null +++ b/packs/number-theory/problems/848/CLAIM_PASS.json @@ -0,0 +1,204 @@ +{ + "schema": "erdos.problem_claim_pass/1", + "generatedAt": "2026-04-14T11:45:57.664Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "cluster": "number-theory", + "sourceKind": "claim_loop_plus_bridge", + "claimPassMode": "bridge_backed", + "currentClaimSurface": "bridge_backed_frontier_support", + "currentState": { + "activeRoute": "finite_check_gap_closure", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `40500` or switch method class.", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "latestVerifiedInterval": "1..40500", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "summary": { + "hooks": { + "total": 4, + "supported": 4, + "actionable": 0, + "unresolved": 0, + "broken": 0 + }, + "claims": { + "total": 7, + "supported": 2, + "actionable": 5, + "unresolved": 0, + "broken": 0 + } + }, + "hookAssessments": [ + { + "hook_id": "next_unmatched_equals_282_failure", + "verdict": "supported", + "status": "supported", + "evidenceClass": "search_bridge_alignment", + "theoremReady": false, + "rationale": "Shared-prefix representative 137720141 matches tracked tail 282 first failure 137720141.", + "nextAction": "formalize_alignment_mechanism" + }, + { + "hook_id": "completed_tail_vs_search_leader_split", + "verdict": "supported", + "status": "supported", + "evidenceClass": "search_bridge_split", + "theoremReady": false, + "rationale": "Completed structured tail 332 differs from family-aware leader 432 on the live bridge.", + "nextAction": "explain_search_leader_split" + }, + { + "hook_id": "repair_pool_not_closed", + "verdict": "supported", + "status": "supported", + "evidenceClass": "bridge_packet_growth", + "theoremReady": false, + "rationale": "Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.", + "nextAction": "model_repair_pool_growth" + }, + { + "hook_id": "top_repair_class_cluster", + "verdict": "supported", + "status": "supported", + "evidenceClass": "gpu_leaderboard_cluster", + "theoremReady": false, + "rationale": "Tie class 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.", + "nextAction": "formalize_repair_cluster_mechanism" + } + ], + "claimAssessments": [ + { + "claim_id": "choose_next_finite_gap_move", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Choose the next finite-gap closure move and keep the theorem-facing claim surface honest.", + "rationale": "The current canonical exact base is 1..40500; the next interval is still open.", + "nextAction": "decide_post_40500_verification_lane" + }, + { + "claim_id": "explain_next_unmatched_alignment", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`.", + "rationale": "If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class.", + "nextAction": "formalize_alignment_mechanism" + }, + { + "claim_id": "explain_completed_vs_search_leader_split", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Explain why completed structured tail `332` differs from current family-aware leader `432`.", + "rationale": "That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class.", + "nextAction": "explain_search_leader_split" + }, + { + "claim_id": "model_repair_pool_growth", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Model the repaired square-modulus pool as a growing family rather than treating it as already closed.", + "rationale": "Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure.", + "nextAction": "model_repair_pool_growth" + }, + { + "claim_id": "characterize_top_repair_cluster", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Characterize what the top repair cluster `432, 782, 832` shares structurally.", + "rationale": "If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction.", + "nextAction": "formalize_repair_cluster_mechanism" + }, + { + "claim_id": "p848_next_unmatched_alignment_claim", + "source": "search_bridge", + "verdict": "supported", + "evidenceClass": "search_bridge_alignment", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Shared-prefix representative 137720141 aligns structurally with the first failure of tail 282.", + "rationale": "The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.", + "nextAction": "formalize_alignment_mechanism" + }, + { + "claim_id": "p848_top_repair_cluster_claim", + "source": "search_bridge", + "verdict": "supported", + "evidenceClass": "gpu_leaderboard_cluster", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Top repair class 432, 782, 832 shares a common repair mechanism.", + "rationale": "Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.", + "nextAction": "formalize_repair_cluster_mechanism" + } + ], + "recommendations": [ + { + "recommendation_id": "formalize_282_alignment", + "priority": "high", + "lane": "theorem_formalization", + "reason": "The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.", + "command": "erdos problem formalization 848" + }, + { + "recommendation_id": "formalize_top_repair_cluster", + "priority": "high", + "lane": "theorem_formalization", + "reason": "Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.", + "command": "erdos problem formalization 848" + }, + { + "recommendation_id": "decide_post_40500_verification_lane", + "priority": "high", + "lane": "exact_verifier", + "reason": "The canonical exact base currently ends at 1..40500. The next verification move is still open.", + "command": "erdos number-theory dispatch 848" + }, + { + "recommendation_id": "model_repair_pool_growth", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.", + "command": "erdos problem formalization 848" + } + ], + "commands": { + "problemShow": "erdos problem show 848", + "problemArtifacts": "erdos problem artifacts 848", + "theoremLoop": "erdos problem theorem-loop 848", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 848", + "claimLoop": "erdos problem claim-loop 848", + "claimLoopRefresh": "erdos problem claim-loop-refresh 848", + "claimPass": "erdos problem claim-pass 848", + "claimPassRefresh": "erdos problem claim-pass-refresh 848", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml" + } +} diff --git a/packs/number-theory/problems/848/CLAIM_PASS.md b/packs/number-theory/problems/848/CLAIM_PASS.md new file mode 100644 index 0000000..ba1d035 --- /dev/null +++ b/packs/number-theory/problems/848/CLAIM_PASS.md @@ -0,0 +1,64 @@ +# Erdos Problem #848 Claim Pass + +This claim pass evaluates theorem-search claims against the canonical claim loop plus bridge-backed search evidence. + +## Current State + +- Claim pass mode: `bridge_backed`. +- Current claim surface: `bridge_backed_frontier_support`. +- Active route: `finite_check_gap_closure`. +- Route summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. +- Next honest move: Decide whether to extend exact verified coverage beyond `40500` or switch method class. +- Latest verified interval: `1..40500` + +## Summary + +- Hook assessments: supported `4`, unresolved `0`, broken `0`. +- Claim assessments: supported `2`, actionable `5`, unresolved `0`, broken `0`. + +## Hook Assessments + +- `next_unmatched_equals_282_failure`: supported | Shared-prefix representative 137720141 matches tracked tail 282 first failure 137720141. +- `completed_tail_vs_search_leader_split`: supported | Completed structured tail 332 differs from family-aware leader 432 on the live bridge. +- `repair_pool_not_closed`: supported | Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849. +- `top_repair_class_cluster`: supported | Tie class 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000. + +## Claim Assessments + +- `choose_next_finite_gap_move`: actionable | Choose the next finite-gap closure move and keep the theorem-facing claim surface honest. | The current canonical exact base is 1..40500; the next interval is still open. +- `explain_next_unmatched_alignment`: actionable | Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`. | If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class. +- `explain_completed_vs_search_leader_split`: actionable | Explain why completed structured tail `332` differs from current family-aware leader `432`. | That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class. +- `model_repair_pool_growth`: actionable | Model the repaired square-modulus pool as a growing family rather than treating it as already closed. | Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure. +- `characterize_top_repair_cluster`: actionable | Characterize what the top repair cluster `432, 782, 832` shares structurally. | If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction. +- `p848_next_unmatched_alignment_claim`: supported | Shared-prefix representative 137720141 aligns structurally with the first failure of tail 282. | The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141. +- `p848_top_repair_cluster_claim`: supported | Top repair class 432, 782, 832 shares a common repair mechanism. | Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000. + +## Recommendations + +- `formalize_282_alignment`: high | theorem_formalization | The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141. | erdos problem formalization 848 +- `formalize_top_repair_cluster`: high | theorem_formalization | Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000. | erdos problem formalization 848 +- `decide_post_40500_verification_lane`: high | exact_verifier | The canonical exact base currently ends at 1..40500. The next verification move is still open. | erdos number-theory dispatch 848 +- `model_repair_pool_growth`: medium | theorem_formalization | Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849. | erdos problem formalization 848 + +## Commands + +- Problem surface: `erdos problem show 848` +- Problem artifacts: `erdos problem artifacts 848` +- Theorem loop: `erdos problem theorem-loop 848` +- Claim loop: `erdos problem claim-loop 848` +- Claim pass: `erdos problem claim-pass 848` +- Claim pass refresh: `erdos problem claim-pass-refresh 848` +- Source refresh: `erdos number-theory bridge-refresh 848` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/number-theory/problems/848/ENDPOINT_MENU_ABSTRACTION.md b/packs/number-theory/problems/848/ENDPOINT_MENU_ABSTRACTION.md new file mode 100644 index 0000000..4a9de06 --- /dev/null +++ b/packs/number-theory/problems/848/ENDPOINT_MENU_ABSTRACTION.md @@ -0,0 +1,75 @@ +# Problem 848 Endpoint Menu Abstraction + +This note records the current atomic breakdown for the active q17 residual window-relaxed fallback-menu target. + +## Boundary + +- Scope: side18-compatible endpoint selection for the q17 residual class `left == 5882 mod 11025` and outsider `6323`. +- Active atom: `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323`. +- This layer only proves or falsifies endpoint availability and cross-squarefree hitting. +- This layer does not by itself prove collision-free matching, D2/D3 promotion, or the final all-N handoff. + +## Simplified Object + +For each menu prime `p`, choose `k_p(left)` modulo `p^2` so that: + +```text +p^2 | 6323 * (left - 14 - 25*k_p(left)) + 1 +right_p(left) = left - 14 - 25*k_p(left) +``` + +Then `right_p(left) == 18 mod 25`, and the outsider-compatibility congruence is automatic. The remaining question is whether at least one available endpoint has squarefree `left * right_p(left) + 1`. + +## Current Compiler + +- Script: `packs/number-theory/problems/848/compute/problem848_endpoint_menu_compiler.mjs` +- Test: `test/p848-endpoint-menu-compiler.test.js` +- Seed profile: `output/p848-endpoint-menu-seed.md` +- Broad fast profile: `output/p848-endpoint-menu-27932207-40000000-fast.md` +- First expanded repair profile: `output/p848-endpoint-menu-first-full-miss-expanded-exact.md` +- P67 broad fast profile: `output/p848-endpoint-menu-27932207-40000000-p67-fast.md` +- P67 first full-miss exact profile: `output/p848-endpoint-menu-p67-first-full-miss-expanded-exact.md` +- Broad window grid profile: `output/p848-endpoint-menu-window-grid-27932207-40000000-fast.md` +- First full-miss window grid profile: `output/p848-endpoint-menu-window-grid-34414907-fast.md` +- Canonical window grid packet: `packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.md` +- Canonical first window-miss packet: `packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.md` +- Canonical first window-miss exact grid packet: `packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.md` +- Canonical window-legality audit: `packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.md` + +## Atomic Layers + +- `E0_formula_compile`: Derive each affine `k_p(left)` rule modulo `p^2`. +- `E1_window_availability`: Decide whether each prime is always inside the 25000-window or only conditionally available. +- `E2_square_obstruction`: For each endpoint, classify the first square divisor of `left * right + 1` when one is found. +- `E3_primary_menu_hitting`: Test whether `{23,31}` alone covers the residual rows. +- `E4_fallback_menu_hitting`: Test whether `{23,31,37,41,61}` covers the residual rows. +- `E5_repair_prime_discovery`: When the fallback menu misses, search the next menu primes and record the first deterministic repair. +- `E6_symbolic_hitting_lift`: Convert bounded endpoint profiles into residue-class lemmas instead of extending the row staircase. +- `E7_matching_handoff`: Feed the selected endpoint lemma back into the side-count/matching proof without claiming this compiler proves matching by itself. + +## Current Evidence + +- The known predecessor-blocked seed `left=27932207` is covered by the 25000-window primary menu `{23,31}`. +- Over `27932207..40000000`, fast screening finds the first primary miss at `left=27965282`. +- At `left=27965282`, prime `37` is a within-window fallback candidate. +- The first fast-screen full-menu miss for `{23,31,37,41,61}` appears at `left=28792157`. +- At `left=28792157`, the within-window primary/fallback candidates `23`, `31`, `37`, and `47` are killed by `2^2`; `41`, `61`, `43`, `53`, `59`, `71`, `73`, and `79` are not all simultaneously useful because of window availability or obstruction. +- Prime `67` repairs `left=28792157` with `k=679`, `delta=-16989`, `right=28775168`, `right == 18 mod 25`, and exact squarefree certification in the local exact artifact. +- A broad fast profile with primary menu `{23,31,37,41,61,67}` and fallback `{71,73,79,83,89,97}` covers `1089/1095` rows over `27932207..40000000`; its first full-menu miss is `left=34414907`. +- Therefore `67` is a genuine repair stratum, but it is not the whole symbolic endpoint selector. +- At `left=34414907`, the only within-window endpoints in the expanded exact profile are `23` and `31`, and both are killed by `2^2`. +- At the same row, primes such as `37`, `61`, `67`, `73`, `79`, `89`, `109`, and `113` have exact-squarefree endpoint products but are outside the 25000-window. +- The next obstruction is therefore primarily a window-availability problem, not evidence that squarefree endpoints disappear. +- The exact two-window grid for `left=34414907` proves that window `28500` selects the p67 endpoint exactly squarefree, with delta `-28489`. +- A broad fast window grid over `27932207..40000000` with primary `{23,31,37,41,61,67}` and fallback `{71,73,79,83,89,97,101,103,107,109,113}` first covers every observed residual row at window `28500`. +- In that broad grid, window `25000` covers `1091/1095` rows with first full-menu miss `34414907`; window `28500` screens `1095/1095`. +- The window-legality audit currently finds `25000` as inherited task/seed-window language, while the proof packets still separate endpoint selection from collision-free matching. + +## Next Highest-Value Move + +1. Prove or falsify `28500` endpoint-window legality before extending the row staircase. +2. Promote `p67` and the next repair primes into availability/obstruction strata instead of treating them as one-off rows. +3. If `28500` is legal, compose the p67 repair into the symbolic endpoint selector; if `25000` is structural, route `34414907` into replacement/augmentation. +4. Run the compiler on those strata rather than scanning every q-prime staircase row. +5. If the p67-expanded miss has its own clean within-window repair after a legitimate theorem-side transformation, emit that repair as a new atom and repeat at the stratum level. +6. Once the repair menu stabilizes, prove the menu hitting lemma as a finite residue-class cover and hand it back to the dynamic-margin theorem packet. diff --git a/packs/number-theory/problems/848/EXACT_BREAKPOINT_CERTIFICATE.json b/packs/number-theory/problems/848/EXACT_BREAKPOINT_CERTIFICATE.json new file mode 100644 index 0000000..ab71398 --- /dev/null +++ b/packs/number-theory/problems/848/EXACT_BREAKPOINT_CERTIFICATE.json @@ -0,0 +1,19486 @@ +{ + "generatedAt": "2026-04-11T02:57:10.497Z", + "method": "candidate_plateau_endpoint_monotonicity", + "problemId": "848", + "sourceResultsPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/EXACT_SMALL_N_1_40500_RESULTS.json", + "status": "certified_from_endpoint_monotonicity", + "summary": { + "interval": "1..40500", + "rowCount": 40500, + "endpointCheckCount": 1621, + "compressionRatio": 24.98457742134485, + "allRowsAlreadyExact": true, + "allEndpointChecksCertified": true, + "plateauLengthFrequency": { + "6": 1, + "19": 1, + "25": 1619 + } + }, + "lemma": { + "name": "candidate_size_plateau_endpoint_monotonicity", + "statement": "For a candidate-size plateau [L,R], if the exact verifier proves omega(G_R) equals the constant candidate size C, then every N in [L,R] has omega(G_N)=C.", + "proofSketch": [ + "The graph G_N is an induced subgraph of G_R for every N <= R, so omega(G_N) <= omega(G_R).", + "The candidate residue class has constant size C throughout the plateau, so omega(G_N) >= C for every N in [L,R].", + "The endpoint exact check gives omega(G_R)=C, hence C <= omega(G_N) <= C throughout the plateau." + ], + "scopeBoundary": "This certificate compresses exact checks inside the certified interval. It does not certify any endpoint that has not itself been exactly checked." + }, + "endpointChecks": [ + { + "startN": 1, + "endN": 6, + "length": 6, + "candidateSize": 0, + "endpointN": 6, + "endpointMaxCliqueSize": 0, + "endpointCandidateSize": 0, + "endpointCertified": true, + "inferredRows": 6, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 7, + "endN": 31, + "length": 25, + "candidateSize": 1, + "endpointN": 31, + "endpointMaxCliqueSize": 1, + "endpointCandidateSize": 1, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 32, + "endN": 56, + "length": 25, + "candidateSize": 2, + "endpointN": 56, + "endpointMaxCliqueSize": 2, + "endpointCandidateSize": 2, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 57, + "endN": 81, + "length": 25, + "candidateSize": 3, + "endpointN": 81, + "endpointMaxCliqueSize": 3, + "endpointCandidateSize": 3, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 82, + "endN": 106, + "length": 25, + "candidateSize": 4, + "endpointN": 106, + "endpointMaxCliqueSize": 4, + "endpointCandidateSize": 4, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 107, + "endN": 131, + "length": 25, + "candidateSize": 5, + "endpointN": 131, + "endpointMaxCliqueSize": 5, + "endpointCandidateSize": 5, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 132, + "endN": 156, + "length": 25, + "candidateSize": 6, + "endpointN": 156, + "endpointMaxCliqueSize": 6, + "endpointCandidateSize": 6, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 157, + "endN": 181, + "length": 25, + "candidateSize": 7, + "endpointN": 181, + "endpointMaxCliqueSize": 7, + "endpointCandidateSize": 7, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 182, + "endN": 206, + "length": 25, + "candidateSize": 8, + "endpointN": 206, + "endpointMaxCliqueSize": 8, + "endpointCandidateSize": 8, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 207, + "endN": 231, + "length": 25, + "candidateSize": 9, + "endpointN": 231, + "endpointMaxCliqueSize": 9, + "endpointCandidateSize": 9, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 232, + "endN": 256, + "length": 25, + "candidateSize": 10, + "endpointN": 256, + "endpointMaxCliqueSize": 10, + "endpointCandidateSize": 10, + "endpointCertified": true, + "inferredRows": 25, + "candidateClassAtEnd": "7_or_18_mod_25" + }, + { + "startN": 257, + "endN": 281, + "length": 25, + "candidateSize": 11, + "endpointN": 281, + 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It does not prove coverage between unchecked rows or replace a Regime B monotonicity/breakpoint lemma.", + "nextUse": "Use the plateau and breakpoint pattern to propose a structured-breakpoint certificate with an explicit monotonicity justification." + } +} diff --git a/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json b/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json new file mode 100644 index 0000000..813665f --- /dev/null +++ b/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json @@ -0,0 +1,130 @@ +{ + "schema": "erdos.number_theory.p848_external_structural_verifier_audit/1", + "generatedAt": "2026-04-11T20:36:37.541Z", + "problemId": "848", + "sourceDir": "/var/folders/n8/r4w8t2xx4_nfhwggsk2n0hlh0000gn/T/erdos-848-external-source-zKb0jJ", + "sourceAvailable": true, + "status": "blocked", + "conclusion": "The external verifier is useful as an idea source, but it is blocked from canonical promotion.", + "summary": { + "sourceFileCount": 3, + "markdownFileCount": 2, + "cppFileCount": 1, + "certificateLikeFileCount": 0, + "blockerCount": 2, + "warningCount": 1, + "supportCount": 3, + "baseSevenMaskPresent": true, + "baseEighteenMaskPresent": false, + "baseResidueBothPresent": true, + "claimsTenMillionSawhneyHandoff": true + }, + "checks": [ + { + "checkId": "external_source_tree_available", + "status": "passed", + "severity": "support", + "summary": "Audited 3 files under /var/folders/n8/r4w8t2xx4_nfhwggsk2n0hlh0000gn/T/erdos-848-external-source-zKb0jJ.", + "evidence": [ + { + "file": ".", + "line": null, + "text": "/var/folders/n8/r4w8t2xx4_nfhwggsk2n0hlh0000gn/T/erdos-848-external-source-zKb0jJ" + } + ], + "recommendation": "Keep this source tree pinned by URL and commit before any promotion." + }, + { + "checkId": "sawhney_handoff_not_claimed_at_1e7", + "status": "failed", + "severity": "blocker", + "summary": "The external writeup appears to claim that Sawhney handles N > 10^7.", + "evidence": [ + { + "file": "848/proof.md", + "line": 3, + "text": "Sawhney handles N > 10^7 after the finite verifier." + }, + { + "file": "README.md", + "line": 3, + "text": "Problem 848 solved for all N by checking N <= 10^7 and using Sawhney for N > 10^7." + } + ], + "recommendation": "Replace the 10^7 handoff with a repo-audited explicit threshold or mark the claim external-only." + }, + { + "checkId": "base_exchange_mask_covers_both_principal_sides", + "status": "failed", + "severity": "blocker", + "summary": "The verifier appears to build base-exchange masks for the 7 mod 25 side without a parallel 18 mod 25 mask.", + "evidence": [ + { + "file": "848/erdos848_verifier_v5.cpp", + "line": 1, + "text": "bool is_base_residue(int x) { const int r = x % 25; return r == 7 || r == 18; }" + }, + { + "file": "848/erdos848_verifier_v5.cpp", + "line": 3, + "text": "const long long b = 7LL * x + 1;" + }, + { + "file": "848/erdos848_verifier_v5.cpp", + "line": 4, + "text": "const long long max_val = x * (7LL + 25LL * (m_max - 1)) + 1;" + } + ], + "recommendation": "Either add a separate 18 mod 25 mask audit, or supply a proof that the 7-side mask dominates the 18-side case for every outsider and N." + }, + { + "checkId": "both_base_residues_are_excluded_from_outsider_pool", + "status": "passed", + "severity": "support", + "summary": "The verifier source explicitly recognizes both 7 and 18 mod 25 as principal base residues.", + "evidence": [ + { + "file": "848/erdos848_verifier_v5.cpp", + "line": 1, + "text": "bool is_base_residue(int x) { const int r = x % 25; return r == 7 || r == 18; }" + } + ], + "recommendation": "Keep outsider-pool exclusion separate from base-exchange mask coverage; both are required for promotion." + }, + { + "checkId": "outsider_clique_inequality_is_documented", + "status": "passed", + "severity": "support", + "summary": "The external writeup documents an outsider-clique style inequality.", + "evidence": [ + { + "file": "848/proof.md", + "line": 5, + "text": "s_max^(p)(N) + max(V_p, V_p) + d_max^(p)(N) + R_{>p}(N) < M(N)" + } + ], + "recommendation": "Treat this as a structural idea source until the inequality is ported into repo-owned definitions and tests." + }, + { + "checkId": "finite_certificate_surface_present", + "status": "warning", + "severity": "warning", + "summary": "The scan did not find a complete verifier/certificate/writeup surface.", + "evidence": [ + { + "file": "848/erdos848_verifier_v5.cpp", + "line": null, + "text": "verifier source" + } + ], + "recommendation": "Require a repo-owned certificate schema before importing any interval coverage." + } + ], + "nextActions": [ + "Keep the external computation in EXTERNAL_VERIFICATION_LEDGER as blocked, not promoted.", + "Patch or independently reimplement the structural verifier with both base sides covered.", + "Replace the false 10^7 Sawhney handoff with a repo-audited explicit threshold before any all-N claim.", + "Port only the outsider-clique inequality shape into a repo-owned structural verifier lane." + ], + "honestyBoundary": "This audit only evaluates structural import readiness. It does not certify the external computation or solve Problem 848." +} diff --git a/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md b/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md new file mode 100644 index 0000000..ea60641 --- /dev/null +++ b/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md @@ -0,0 +1,55 @@ +# Problem 848 External Structural Verifier Audit + +- Generated: 2026-04-11T20:36:37.541Z +- Source dir: `/var/folders/n8/r4w8t2xx4_nfhwggsk2n0hlh0000gn/T/erdos-848-external-source-zKb0jJ` +- Status: `blocked` +- Conclusion: The external verifier is useful as an idea source, but it is blocked from canonical promotion. + +## Summary + +- sourceFileCount: `3` +- markdownFileCount: `2` +- cppFileCount: `1` +- certificateLikeFileCount: `0` +- blockerCount: `2` +- warningCount: `1` +- supportCount: `3` +- baseSevenMaskPresent: `true` +- baseEighteenMaskPresent: `false` +- baseResidueBothPresent: `true` +- claimsTenMillionSawhneyHandoff: `true` + +## Checks + +- `external_source_tree_available` [passed/support] Audited 3 files under /var/folders/n8/r4w8t2xx4_nfhwggsk2n0hlh0000gn/T/erdos-848-external-source-zKb0jJ. +- Recommendation: Keep this source tree pinned by URL and commit before any promotion. +- Evidence: `.` /var/folders/n8/r4w8t2xx4_nfhwggsk2n0hlh0000gn/T/erdos-848-external-source-zKb0jJ +- `sawhney_handoff_not_claimed_at_1e7` [failed/blocker] The external writeup appears to claim that Sawhney handles N > 10^7. +- Recommendation: Replace the 10^7 handoff with a repo-audited explicit threshold or mark the claim external-only. +- Evidence: `848/proof.md:3` Sawhney handles N > 10^7 after the finite verifier. +- Evidence: `README.md:3` Problem 848 solved for all N by checking N <= 10^7 and using Sawhney for N > 10^7. +- `base_exchange_mask_covers_both_principal_sides` [failed/blocker] The verifier appears to build base-exchange masks for the 7 mod 25 side without a parallel 18 mod 25 mask. +- Recommendation: Either add a separate 18 mod 25 mask audit, or supply a proof that the 7-side mask dominates the 18-side case for every outsider and N. +- Evidence: `848/erdos848_verifier_v5.cpp:1` bool is_base_residue(int x) { const int r = x % 25; return r == 7 || r == 18; } +- Evidence: `848/erdos848_verifier_v5.cpp:3` const long long b = 7LL * x + 1; +- Evidence: `848/erdos848_verifier_v5.cpp:4` const long long max_val = x * (7LL + 25LL * (m_max - 1)) + 1; +- `both_base_residues_are_excluded_from_outsider_pool` [passed/support] The verifier source explicitly recognizes both 7 and 18 mod 25 as principal base residues. +- Recommendation: Keep outsider-pool exclusion separate from base-exchange mask coverage; both are required for promotion. +- Evidence: `848/erdos848_verifier_v5.cpp:1` bool is_base_residue(int x) { const int r = x % 25; return r == 7 || r == 18; } +- `outsider_clique_inequality_is_documented` [passed/support] The external writeup documents an outsider-clique style inequality. +- Recommendation: Treat this as a structural idea source until the inequality is ported into repo-owned definitions and tests. +- Evidence: `848/proof.md:5` s_max^(p)(N) + max(V_p, V_p) + d_max^(p)(N) + R_{>p}(N) < M(N) +- `finite_certificate_surface_present` [warning/warning] The scan did not find a complete verifier/certificate/writeup surface. +- Recommendation: Require a repo-owned certificate schema before importing any interval coverage. +- Evidence: `848/erdos848_verifier_v5.cpp` verifier source + +## Next Actions + +- Keep the external computation in EXTERNAL_VERIFICATION_LEDGER as blocked, not promoted. +- Patch or independently reimplement the structural verifier with both base sides covered. +- Replace the false 10^7 Sawhney handoff with a repo-audited explicit threshold before any all-N claim. +- Port only the outsider-clique inequality shape into a repo-owned structural verifier lane. + +## Boundary + +- This audit only evaluates structural import readiness. It does not certify the external computation or solve Problem 848. diff --git a/packs/number-theory/problems/848/FORMALIZATION.json b/packs/number-theory/problems/848/FORMALIZATION.json new file mode 100644 index 0000000..a5fc2f6 --- /dev/null +++ b/packs/number-theory/problems/848/FORMALIZATION.json @@ -0,0 +1,311 @@ +{ + "schema": "erdos.problem_formalization/1", + "generatedAt": "2026-04-14T11:45:59.647Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "cluster": "number-theory", + "sourceKind": "claim_pass_plus_bridge", + "formalizationMode": "bridge_backed", + "currentClaimSurface": "bridge_backed_frontier_support", + "currentState": { + "activeRoute": "finite_check_gap_closure", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `40500` or switch method class.", + "latestVerifiedInterval": "1..40500", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "currentTarget": { + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "title": "Formalize the 282 Obstruction Alignment", + "status": "in_progress", + "lane": "theorem_formalization", + "sourceRecommendationId": "formalize_282_alignment", + "sourceClaimId": "p848_next_unmatched_alignment_claim", + "sourceHookId": "next_unmatched_equals_282_failure", + "summary": "The live 137720141 / 282 obstruction packet is checked at finite-menu scope; the remaining theorem work is the narrower symbolic-lift boundary.", + "statement": "Checked finite-menu statement: the shared-prefix obstruction represented at n=137720141 aligns with continuation tail 282 through the 841 witness class, with the 132-row lift and activation certificates replayed; a universal symbolic lift remains separate.", + "whyThisExists": "This packet exists to bridge the gap between search evidence and proof. Without it, the loop only says the alignment is suggestive; with it, the theorem lane gets an explicit object to prove, falsify, or narrow.", + "whyNow": "The canonical bridge freezes next unmatched representative 137720141, and the claim pass already marks its equality with the first failure of tail 282 as supported.", + "evidenceBasis": [ + "The canonical bridge records next unmatched representative 137720141.", + "The tracked-tail matrix records continuation 282 failing first at 137720141.", + "The current family menu already contains representative 137720141 with tuple key 4, 23^2, 7^2, 9, 17^2, 11^2 and tuple rows 7->4/1, 32->529/281, 57->49/6, 82->9/8, 132->289/81, 182->121/119.", + "On that family-menu row, only continuation 282 fails among the tracked tails, and it does so via witness modulus 841.", + "The strongest completed structured tail remains 332, so this packet isolates the 282 obstruction mechanism rather than conflating it with the current family-aware leader 432.", + "The finite exact base is already certified through 1..40500, so the open work is structural rather than basic interval bookkeeping.", + "Formalization-work checker p848_132_activation_row_certificate_checker_v1 replayed 17 activation rows with 0 failures.", + "Formalization-work checker p848_132_lift_crt_checker_v1 proved the 132-row lift with k=147 and residue 504 mod 841.", + "The top repair-class side packet is also checked: +2 finite-menu replay plus 74 mod-50 lane exchange rows pass." + ], + "proofObligations": [ + { + "obligationId": "define_shared_prefix_obstruction_class", + "status": "done", + "task": "Define the shared-prefix obstruction class precisely enough that the representative n=137720141 and the 282 continuation can be discussed in the same language.", + "why": "Without a shared obstruction language, the current equality is still only a numerical coincidence.", + "dischargeWith": "Use the family-menu row language: shared-prefix tuple rows plus representative/modulus/residue plus tracked-tail repair rows." + }, + { + "obligationId": "explain_282_first_failure_mechanism", + "status": "done", + "task": "Explain why the 282 continuation first fails on that obstruction class rather than merely sharing the same first failing n by accident.", + "why": "This is the core mechanism claim that would upgrade the bridge fact into a theorem-facing lemma candidate.", + "dischargeWith": "Use the checked packet: p848_132_activation_row_certificate_checker_v1 plus p848_132_lift_crt_checker_v1 certify the finite-menu mechanism, while keeping the universal lift out of scope." + }, + { + "obligationId": "separate_alignment_from_leaderboard_artifacts", + "status": "done", + "task": "Separate this obstruction-alignment claim from unrelated leaderboard behavior of 432, 782, and 832 so the statement stays narrow and honest.", + "why": "The 282 packet should not inherit unsupported claims from the current repair-class leaderboard.", + "dischargeWith": "Freeze the local repair boundary: 282 fails on this class while 157, 232, 332, 382, 432, 782, 832 remain squarefree." + }, + { + "obligationId": "freeze_alignment_falsifier_boundary", + "status": "done", + "task": "Record what extra bridge or exact evidence would count as a genuine falsifier of the alignment mechanism.", + "why": "A theorem packet is more trustworthy when it names its own failure modes.", + "dischargeWith": "Bind the packet to the explicit falsifier boundary: a lower representative in the 841 witness class, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment." + }, + { + "obligationId": "lift_132_activation_schema_beyond_finite_menu", + "status": "ready", + "task": "Decide whether the checked finite-menu 132 activation schema can be lifted into a symbolic CRT lemma beyond the current family menu.", + "why": "This is now the honest successor to the discharged 282 mechanism packet: the mechanism is checked finitely, but the universal theorem should not inherit it without a symbolic lift.", + "dischargeWith": "Prove parameterized tuple-row CRT hypotheses that force pre-132 misses, unique 132 target activation, and 182 preservation beyond the current finite menu." + } + ], + "falsifierChecks": [ + { + "checkId": "bridge_next_unmatched_stability", + "status": "ready", + "task": "A refreshed bridge no longer lists 137720141 as the next unmatched representative.", + "why": "If the bridge frontier moves, the current packet may no longer be pointing at the right obstruction.", + "command": "erdos number-theory bridge-refresh 848" + }, + { + "checkId": "tracked_tail_282_stability", + "status": "ready", + "task": "A refreshed tracked-tail matrix no longer gives continuation 282 first failure 137720141.", + "why": "The packet is only interesting if the 282-tail boundary stays synchronized with the shared-prefix representative.", + "command": "erdos problem claim-pass-refresh 848" + }, + { + "checkId": "obstruction_class_mismatch", + "status": "ready", + "task": "Packet replay or family-menu analysis shows that the shared-prefix representative and the 282 failure belong to different obstruction classes.", + "why": "This would directly break the mechanism-level interpretation of the alignment.", + "command": "erdos number-theory dispatch 848 --apply --action cpu_family_search" + } + ], + "promotionCriteria": [ + { + "criterionId": "alignment_hook_survives", + "status": "done", + "task": "The next_unmatched_equals_282_failure hook stays supported after refresh." + }, + { + "criterionId": "statement_is_mechanism_level", + "status": "done", + "task": "The candidate statement is expressed as an obstruction-class alignment, not as a full theorem of closure." + }, + { + "criterionId": "mechanism_is_testable", + "status": "done", + "task": "The packet identifies at least one mechanism-level explanation to test, not just a repeated equality of two numbers." + }, + { + "criterionId": "finite_menu_mechanism_checked", + "status": "done", + "task": "The finite-menu 282 mechanism is checked by activation-row and CRT-lift replay certificates." + } + ], + "supportingCommands": [ + "erdos number-theory bridge-refresh 848", + "erdos problem claim-pass-refresh 848", + "erdos problem formalization-work 848", + "erdos number-theory dispatch 848 --apply --action cpu_family_search", + "erdos number-theory dispatch 848 --apply --action exact_followup_rollout" + ] + }, + "summary": { + "proofObligations": { + "total": 5, + "ready": 1, + "inProgress": 0, + "blocked": 0, + "done": 4 + }, + "falsifierChecks": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "promotionCriteria": { + "total": 4, + "ready": 0, + "inProgress": 0, + "blocked": 0, + "done": 4 + } + }, + "theoremHooks": [ + { + "hook_id": "next_unmatched_equals_282_failure", + "status": "supported", + "note": "" + }, + { + "hook_id": "completed_tail_vs_search_leader_split", + "status": "supported", + "note": "" + }, + { + "hook_id": "repair_pool_not_closed", + "status": "supported", + "note": "" + }, + { + "hook_id": "top_repair_class_cluster", + "status": "supported", + "note": "" + } + ], + "claimAssessments": [ + { + "claim_id": "choose_next_finite_gap_move", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Choose the next finite-gap closure move and keep the theorem-facing claim surface honest.", + "rationale": "The current canonical exact base is 1..40500; the next interval is still open.", + "nextAction": "decide_post_40500_verification_lane" + }, + { + "claim_id": "explain_next_unmatched_alignment", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`.", + "rationale": "If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class.", + "nextAction": "formalize_alignment_mechanism" + }, + { + "claim_id": "explain_completed_vs_search_leader_split", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Explain why completed structured tail `332` differs from current family-aware leader `432`.", + "rationale": "That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class.", + "nextAction": "explain_search_leader_split" + }, + { + "claim_id": "model_repair_pool_growth", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Model the repaired square-modulus pool as a growing family rather than treating it as already closed.", + "rationale": "Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure.", + "nextAction": "model_repair_pool_growth" + }, + { + "claim_id": "characterize_top_repair_cluster", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Characterize what the top repair cluster `432, 782, 832` shares structurally.", + "rationale": "If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction.", + "nextAction": "formalize_repair_cluster_mechanism" + }, + { + "claim_id": "p848_next_unmatched_alignment_claim", + "source": "search_bridge", + "verdict": "supported", + "evidenceClass": "search_bridge_alignment", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Shared-prefix representative 137720141 aligns structurally with the first failure of tail 282.", + "rationale": "The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.", + "nextAction": "formalize_alignment_mechanism" + }, + { + "claim_id": "p848_top_repair_cluster_claim", + "source": "search_bridge", + "verdict": "supported", + "evidenceClass": "gpu_leaderboard_cluster", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Top repair class 432, 782, 832 shares a common repair mechanism.", + "rationale": "Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.", + "nextAction": "formalize_repair_cluster_mechanism" + } + ], + "recommendationLedger": [ + { + "recommendation_id": "formalize_282_alignment", + "priority": "high", + "lane": "theorem_formalization", + "reason": "The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.", + "command": "erdos problem formalization 848" + }, + { + "recommendation_id": "formalize_top_repair_cluster", + "priority": "high", + "lane": "theorem_formalization", + "reason": "Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.", + "command": "erdos problem formalization 848" + }, + { + "recommendation_id": "decide_post_40500_verification_lane", + "priority": "high", + "lane": "exact_verifier", + "reason": "The canonical exact base currently ends at 1..40500. The next verification move is still open.", + "command": "erdos number-theory dispatch 848" + }, + { + "recommendation_id": "model_repair_pool_growth", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.", + "command": "erdos problem formalization 848" + } + ], + "commands": { + "problemShow": "erdos problem show 848", + "problemArtifacts": "erdos problem artifacts 848", + "theoremLoop": "erdos problem theorem-loop 848", + "claimLoop": "erdos problem claim-loop 848", + "claimPass": "erdos problem claim-pass 848", + "formalization": "erdos problem formalization 848", + "formalizationRefresh": "erdos problem formalization-refresh 848", + "formalizationWork": "erdos problem formalization-work 848", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 848", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md" + } +} diff --git a/packs/number-theory/problems/848/FORMALIZATION.md b/packs/number-theory/problems/848/FORMALIZATION.md new file mode 100644 index 0000000..dd4129c --- /dev/null +++ b/packs/number-theory/problems/848/FORMALIZATION.md @@ -0,0 +1,101 @@ +# Erdos Problem #848 Formalization + +This formalization packet promotes the current claim-pass recommendation into a concrete theorem-facing proof obligation anchored in canonical bridge evidence. + +## Current State + +- Formalization mode: `bridge_backed`. +- Current claim surface: `bridge_backed_frontier_support`. +- Active route: `finite_check_gap_closure`. +- Route summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. +- Next honest move: Decide whether to extend exact verified coverage beyond `40500` or switch method class. +- Latest verified interval: `1..40500` + +## Current Target + +- Formalization id: `p848_282_alignment_formalization_v1`. +- Focus id: `formalize_282_alignment`. +- Title: Formalize the 282 Obstruction Alignment +- Status: `in_progress`. +- Lane: `theorem_formalization`. +- Summary: The live 137720141 / 282 obstruction packet is checked at finite-menu scope; the remaining theorem work is the narrower symbolic-lift boundary. +- Candidate statement: Checked finite-menu statement: the shared-prefix obstruction represented at n=137720141 aligns with continuation tail 282 through the 841 witness class, with the 132-row lift and activation certificates replayed; a universal symbolic lift remains separate. +- Proof obligations: ready `1` / total `5`. +- Falsifier checks: ready `3` / total `3`. +- Promotion criteria: ready `0` / total `4`. + +## Why This Exists + +This packet exists to bridge the gap between search evidence and proof. Without it, the loop only says the alignment is suggestive; with it, the theorem lane gets an explicit object to prove, falsify, or narrow. + +## Why Now + +The canonical bridge freezes next unmatched representative 137720141, and the claim pass already marks its equality with the first failure of tail 282 as supported. + +## Evidence Basis + +- The canonical bridge records next unmatched representative 137720141. +- The tracked-tail matrix records continuation 282 failing first at 137720141. +- The current family menu already contains representative 137720141 with tuple key 4, 23^2, 7^2, 9, 17^2, 11^2 and tuple rows 7->4/1, 32->529/281, 57->49/6, 82->9/8, 132->289/81, 182->121/119. +- On that family-menu row, only continuation 282 fails among the tracked tails, and it does so via witness modulus 841. +- The strongest completed structured tail remains 332, so this packet isolates the 282 obstruction mechanism rather than conflating it with the current family-aware leader 432. +- The finite exact base is already certified through 1..40500, so the open work is structural rather than basic interval bookkeeping. +- Formalization-work checker p848_132_activation_row_certificate_checker_v1 replayed 17 activation rows with 0 failures. +- Formalization-work checker p848_132_lift_crt_checker_v1 proved the 132-row lift with k=147 and residue 504 mod 841. +- The top repair-class side packet is also checked: +2 finite-menu replay plus 74 mod-50 lane exchange rows pass. + +## Proof Obligations + +- `define_shared_prefix_obstruction_class`: done | Define the shared-prefix obstruction class precisely enough that the representative n=137720141 and the 282 continuation can be discussed in the same language. | Without a shared obstruction language, the current equality is still only a numerical coincidence. | discharge: Use the family-menu row language: shared-prefix tuple rows plus representative/modulus/residue plus tracked-tail repair rows. +- `explain_282_first_failure_mechanism`: done | Explain why the 282 continuation first fails on that obstruction class rather than merely sharing the same first failing n by accident. | This is the core mechanism claim that would upgrade the bridge fact into a theorem-facing lemma candidate. | discharge: Use the checked packet: p848_132_activation_row_certificate_checker_v1 plus p848_132_lift_crt_checker_v1 certify the finite-menu mechanism, while keeping the universal lift out of scope. +- `separate_alignment_from_leaderboard_artifacts`: done | Separate this obstruction-alignment claim from unrelated leaderboard behavior of 432, 782, and 832 so the statement stays narrow and honest. | The 282 packet should not inherit unsupported claims from the current repair-class leaderboard. | discharge: Freeze the local repair boundary: 282 fails on this class while 157, 232, 332, 382, 432, 782, 832 remain squarefree. +- `freeze_alignment_falsifier_boundary`: done | Record what extra bridge or exact evidence would count as a genuine falsifier of the alignment mechanism. | A theorem packet is more trustworthy when it names its own failure modes. | discharge: Bind the packet to the explicit falsifier boundary: a lower representative in the 841 witness class, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment. +- `lift_132_activation_schema_beyond_finite_menu`: ready | Decide whether the checked finite-menu 132 activation schema can be lifted into a symbolic CRT lemma beyond the current family menu. | This is now the honest successor to the discharged 282 mechanism packet: the mechanism is checked finitely, but the universal theorem should not inherit it without a symbolic lift. | discharge: Prove parameterized tuple-row CRT hypotheses that force pre-132 misses, unique 132 target activation, and 182 preservation beyond the current finite menu. + +## Falsifier Checks + +- `bridge_next_unmatched_stability`: ready | A refreshed bridge no longer lists 137720141 as the next unmatched representative. | If the bridge frontier moves, the current packet may no longer be pointing at the right obstruction. | command: erdos number-theory bridge-refresh 848 +- `tracked_tail_282_stability`: ready | A refreshed tracked-tail matrix no longer gives continuation 282 first failure 137720141. | The packet is only interesting if the 282-tail boundary stays synchronized with the shared-prefix representative. | command: erdos problem claim-pass-refresh 848 +- `obstruction_class_mismatch`: ready | Packet replay or family-menu analysis shows that the shared-prefix representative and the 282 failure belong to different obstruction classes. | This would directly break the mechanism-level interpretation of the alignment. | command: erdos number-theory dispatch 848 --apply --action cpu_family_search + +## Promotion Criteria + +- `alignment_hook_survives`: done | The next_unmatched_equals_282_failure hook stays supported after refresh. +- `statement_is_mechanism_level`: done | The candidate statement is expressed as an obstruction-class alignment, not as a full theorem of closure. +- `mechanism_is_testable`: done | The packet identifies at least one mechanism-level explanation to test, not just a repeated equality of two numbers. +- `finite_menu_mechanism_checked`: done | The finite-menu 282 mechanism is checked by activation-row and CRT-lift replay certificates. + +## Supporting Commands + +- `erdos number-theory bridge-refresh 848` +- `erdos problem claim-pass-refresh 848` +- `erdos problem formalization-work 848` +- `erdos number-theory dispatch 848 --apply --action cpu_family_search` +- `erdos number-theory dispatch 848 --apply --action exact_followup_rollout` + +## Commands + +- Problem surface: `erdos problem show 848` +- Problem artifacts: `erdos problem artifacts 848` +- Theorem loop: `erdos problem theorem-loop 848` +- Claim loop: `erdos problem claim-loop 848` +- Claim pass: `erdos problem claim-pass 848` +- Formalization: `erdos problem formalization 848` +- Formalization refresh: `erdos problem formalization-refresh 848` +- Formalization work: `erdos problem formalization-work 848` +- Formalization work refresh: `erdos problem formalization-work-refresh 848` +- Source refresh: `erdos number-theory bridge-refresh 848` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md` diff --git a/packs/number-theory/problems/848/FORMALIZATION_WORK.json b/packs/number-theory/problems/848/FORMALIZATION_WORK.json new file mode 100644 index 0000000..b5dcec1 --- /dev/null +++ b/packs/number-theory/problems/848/FORMALIZATION_WORK.json @@ -0,0 +1,58279 @@ +{ + "schema": "erdos.problem_formalization_work/1", + "generatedAt": "2026-04-14T11:46:03.768Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "cluster": "number-theory", + "sourceKind": "claim_pass_plus_bridge", + "formalizationWorkMode": "bridge_backed", + "currentClaimSurface": "bridge_backed_frontier_support", + "currentState": { + "activeRoute": "finite_check_gap_closure", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `40500` or switch method class.", + "latestVerifiedInterval": "1..40500" + }, + "currentWork": { + "workId": "p848_282_first_failure_mechanism_packet_v1", + "focusFormalizationId": "p848_282_alignment_formalization_v1", + "focusId": "lift_132_activation_schema_beyond_finite_menu", + "title": "Explain the 282 First-Failure Mechanism", + "status": "in_progress", + "summary": "Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.", + "why": "Once the shared-prefix class is named, the next theorem step is to explain why continuation 282, and not the neighboring tracked tails, is the one that first acquires a square witness there.", + "workingDefinition": [ + "A 282 first-failure mechanism is the first shared-prefix class where the 282 repair row becomes non-squarefree while the neighboring tracked repair rows remain squarefree.", + "On the live boundary class, the six defining tuple moduli are 4, 529, 49, 9, 289, 121 and the extra 282 witness is 841.", + "The witness 841 is not one of the six tuple-row moduli, so the failure appears as an extra repair witness intersecting the shared-prefix class.", + "The representative itself sits in residue class 504 modulo 841." + ], + "currentEvidence": [ + "Among the current family-menu rows where continuation 282 is non-squarefree, the earliest representative is 137720141.", + "At representative 137720141, 282*n+1 = 38837079763 = 841 * 46179643.", + "Modulo 841, the 282 repair row is exactly 0 while the neighboring tracked rows remain nonzero.", + "Neighbor residues mod 841: 157->75, 232->30, 332->811, 382->781, 432->751, 782->541, 832->511.", + "The first family-menu occurrence of witness 841 on tail 282 is representative 137720141, with 0 earlier rows giving residue 0 mod 841.", + "Solving the tuple-row CRT gives n ≡ 137720141 (mod 32631532164), and projecting that class modulo 841 gives 504.", + "The tuple-row CRT projection stabilizes at residue 504 mod 841 once anchor 132 is added.", + "The last earlier 282 rows before the first failure stay nonzero mod 841: 127484267->736, 127682743->736, 136702637->457.", + "Among the tracked repair anchors, the representative residue class modulo 841 matches only anchors 282.", + "Some tracked anchors cannot fail via modulus 841 at all because gcd(anchor, 841) > 1: 232.", + "The boundary row progression does not itself force witness 841: gcd(modulus, 841) = 1, so the progression visits every residue class mod 841.", + "Within that row progression, the representative sits exactly at the witness-start index for tracked anchor(s) 282.", + "Substituting the row formula into 282*n+1 ≡ 0 (mod 841) gives 543*t ≡ 0 (mod 841); since gcd(543, 841) = 1, this reduces to t ≡ 0 (mod 841).", + "The contrasting 232 equation 232*t ≡ 811 (mod 841) is impossible because 29 does not divide 811.", + "The next number in the same shared-prefix progression where tail 282 hits witness 841 is 27443256270065.", + "At the family-menu level, the earliest representative in residue class 504 mod 841 is 137720141 at row index 25; the 25 earlier menu rows all miss the 282 witness residue class.", + "The packet has an explicit falsifier boundary: it breaks if a refreshed menu finds an earlier representative with residue 504 mod 841, if continuation 282 first fails through a different witness, or if bridge refresh breaks the 137720141 <-> 282 alignment.", + "Top repair-class packet seeded from bridge leaderboard: 432, 782, 832 tie at 242 repaired predicted families; nearest contrasts are 332->240, 382->240, 1232->240, 882->236.", + "The top tie shares common early missed predicted representatives: 210290957, 287180657, 517124182, 525631657, 1229502607.", + "The current finite menu has 255 predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence.", + "The replayed top-tie common missed rows now include 9 predicted family rows, so the common-miss boundary is no longer just an eight-row bridge summary.", + "The strictest finite-menu contrast certificate is 782 vs 1232.", + "The mod-50 lane signature checks 74 exchange rows using continuation = 32 + 50*m and passes all of them.", + "The finite mod-50 exchange packet is now backed by a reusable divisibility schema over 74 checked witness instances.", + "The strict 782 > 1232 handoff is certified on the current finite menu: 782 repairs exactly two predicted rows that 1232 misses, 1232 repairs no predicted row that 782 misses, and both strict rows are explained by the symbolic mod-50 bad-lane schema.", + "The symbolic 132-lift candidate checks 17 finite-menu certificate rows and promotes them into parameterized CRT hypotheses without claiming universal scope.", + "Domain-closure assessment rejects a broad 17-row universal lift for now and recommends anchor_832_witness_529 as the next narrow closure lane.", + "Every current finite-menu occurrence of anchor_832_witness_529 replays from raw tuple-row CRT data: pre-132 prefixes are clear, anchor 132 uniquely activates tracked tail 832, and anchor 182 preserves residue 316 mod 529.", + "The recommended anchor_832_witness_529 lane is not one clean symbolic profile yet: it splits into 2 pre-132 profiles, with successor pre132_7_1_32_224_57_229_82_412.", + "In the certified rows, the anchor-132 CRT prefix already satisfies the anchor-182 tuple row, so adding anchor 182 uses lift parameter 0 and cannot move the witness residue modulo 529.", + "Rows 270, 271 are a finite duplicate final-anchor variant over the same CRT prefix through anchor 132, not evidence for a separate broad symbolic family.", + "Structural atom C1 is discharged by the mod-25 same-side base identity: 7^2+1 and 18^2+1 are both 0 mod 25.", + "Structural atom C2 is discharged: after partitioning compatible base vertices into B7 and B18 sides, C1 makes both sides cliques and only cross edges remain unconstrained.", + "Structural atom C3 is discharged: H_{x,N} is now explicitly the bipartite graph of missing B7-by-B18 cross edges.", + "The C-graph reduction packet is discharged through C6: mixed-base clique size is now the two-side total minus a maximum matching in H_{x,N}.", + "The bounded D1 extraction is discharged on current verifier rows: all 1733 exact mixed-base threatening-outsider rows meet the required matching lower bound and saturate the smaller compatible side.", + "The active D2 p=13 candidate is now backed by 1285 bounded threatening-outsider rows; K(N,x) ranges 26..90 and the minimum matching slack is 19.", + "The D2 split-core witness packet reduces the tight p=13 sample to 3 residue/smaller-side subgoals; each split common core meets the sampled max K(N,x).", + "The D3 p=17 split-core witness packet reduces the tight p=17 sample to 2 residue/smaller-side subgoals with minimum sampled slack 95.", + "The structural lift miner is now feeding the existing atomic theorem lane: active atom D2_p13_matching_lower_bound targets D4_matching_bound_implies_sMaxMixed_bound from 64 mined exact rows." + ], + "dischargedWork": [ + "The family-menu boundary agrees with the tracked-tail boundary: the earliest 282-failing family row is also representative 137720141.", + "The extra witness has been isolated: 841 belongs to the 282 repair row, not to the six defining tuple moduli of the shared-prefix class.", + "The witness boundary is locally frozen: no earlier family-menu row gives tail 282 residue 0 modulo 841.", + "The representative residue is structurally derived: the tuple-row CRT projects the shared-prefix obstruction class to 504 mod 841.", + "The congruence boundary is isolated: residue class 504 mod 841 is the failure class for tracked tail 282 and no other tracked coprime tail.", + "The row-index boundary is isolated: within the shared-prefix row progression, tracked anchor 282 is the only tracked anchor whose 841 witness class starts at row index 0.", + "The row-start derivation is explicit: the boundary representative already lies on the 282 witness class modulo 841, so the row equation reduces to t ≡ 0 (mod 841).", + "The menu-level first-occurrence boundary is isolated: 137720141 is the first family-menu representative in the 282 witness class 504 mod 841, so no earlier menu row can fail via witness 841 on that same congruence class.", + "The mechanism falsifier boundary is explicit: a lower representative in residue class 504 mod 841, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment would all break this packet.", + "The 132-row lift is explicit: adding the 132 row forces the tuple-row CRT class from residue 400 mod 841 to the boundary residue 504 mod 841 via k ≡ 147 (mod 289).", + "The activation boundary is explicit: before anchor 132 no tuple-row CRT step lands on any tracked failure residue mod 841, anchor 132 creates the unique tracked 282 match at residue 504, and anchor 182 preserves that same unique match.", + "The 132-activation pattern is reusable on the current finite menu: 17 failing witness rows first activate their own failing tracked tail at anchor 132.", + "The finite-menu 132-activation pattern has been promoted into lemma schema p848_finite_menu_132_target_activation_schema_v1 with hypotheses, conclusion, falsifier boundary, and 17 row certificates.", + "The 17 finite-menu 132-activation row certificates replay successfully in checker p848_132_activation_row_certificate_checker_v1.", + "The 132-row lift to residue 504 mod 841 is proved from tuple-row CRT equations by checker p848_132_lift_crt_checker_v1.", + "The activation schema lift decision is explicit: finite_menu_certificate_not_universal_yet; next theorem pass is formalize_top_repair_class_mechanism.", + "The checked 132 activation schema has been lifted into symbolic CRT hypothesis packet p848_132_activation_symbolic_lift_candidate_v1; the next obligation is domain closure, not merely packet construction.", + "The broad domain-closure overclaim is ruled out at the current evidence boundary: The finite symbolic-lift survey splits across 8 failing anchors and 12 witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem.", + "The recommended anchor_832_witness_529 closure lane has been executed at finite repeated-group scope: 3 raw rows pass checker p848_832_529_anchor_witness_domain_closure_checker_v1.", + "The single-profile symbolic closure over anchor_832_witness_529 is falsified by the finite evidence split into 2 pre-132 residue profiles.", + "The anchor_832_witness_529 anchor-182 preservation step is explained: every checked row has lift parameter 0 at anchor 182.", + "The repeated pre132_7_1_32_224_57_229_82_412 sublane is closed as a finite duplicate final-anchor variant, not a new symbolic family.", + "Structural atom C1_same_side_base_clique is discharged: same-side principal base residues force a 25 divisor of u*v+1, so each same-side component is a clique.", + "Structural atom C2_two_cliques_plus_cross_edges is discharged by checker p848_C2_two_cliques_plus_cross_edges_checker_v1: the mixed-base graph is two cliques plus arbitrary cross edges.", + "Structural atom C3_missing_cross_graph_definition is discharged by checker p848_C3_missing_cross_graph_definition_checker_v1: H_{x,N} records exactly the missing cross edges between the two clique sides.", + "Structural atom C4_clique_to_vertex_cover_duality is discharged by checker p848_C4_clique_to_vertex_cover_duality_checker_v1: clique complements are exactly vertex covers of H_{x,N}.", + "Structural atom C5_konig_matching_reduction is discharged by checker p848_C5_konig_matching_reduction_checker_v1: Konig's theorem applies because H_{x,N} is finite bipartite.", + "Structural atom C6_mixed_clique_matching_formula is discharged by checker p848_C6_mixed_clique_matching_formula_checker_v1: sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).", + "Structural atom D1_residue_block_matching_injection is discharged at bounded extraction scope by checker p848_D1_matching_saturation_bound_checker_v1: every current exact mixed-base threatening outsider meets K(N,x) and saturates the smaller compatible side.", + "D2 split-core witness extraction is discharged at bounded pattern scope by checker p848_D2_p13_split_core_witness_checker_v1: each p=13 split common core reaches the sampled K(N,x) target.", + "D3 split-core witness extraction is discharged at bounded pattern scope by checker p848_D3_p17_split_core_witness_checker_v1: each p=17 split common core reaches the sampled K(N,x) target.", + "The top repair-class mechanism packet p848_top_repair_class_mechanism_packet_v1 is seeded with shared metrics, nearest contrasts, common missed-family boundary, and falsifier conditions.", + "The finite-menu +2 repaired-predicted-family separation is discharged: 432->242, 782->242, 832->242 versus 332->240, 382->240, 1232->240.", + "The common missed-family replay is explicit: 9 top-tie shared missed predicted family rows were replayed directly from the family menu.", + "The finite-menu +2 separation has been lifted into mod-50 lane-index congruences: 74 exchange rows all pass the bad-m-class certificate.", + "The mod-50 bad-lane congruence has been generalized into symbolic schema p848_mod50_bad_lane_symbolic_schema_v1; 74 finite witness instances replay with 0 failures.", + "The strict 782 > 1232 handoff is connected to the symbolic mod-50 schema by checker p848_782_1232_strict_handoff_checker_v1; it is certified as finite-menu guidance, not all-N closure.", + "The 182 row preserves the boundary residue: the 132-lifted class already satisfies 137720141 ≡ 119 (mod 121), so the final anchor adds no further correction modulo 841." + ], + "remainingGaps": [ + "Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "Advance the same atomic packet toward target D4_matching_bound_implies_sMaxMixed_bound: If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "Decide and run the next post-40500 verification lane using local CPU and opt-in local 4090 compute only." + ], + "proofObligations": [ + { + "obligationId": "D1_residue_block_matching_injection", + "status": "done", + "task": "Extract the current residue-block matching target from all bounded exact mixed-base threatening-outsider rows: K(N,x) = |L| + |R| - strictBaseThreshold + 1, and the recorded matching saturates the smaller compatible side in every current row.", + "statement": "Extract the current residue-block matching target from all bounded exact mixed-base threatening-outsider rows: K(N,x) = |L| + |R| - strictBaseThreshold + 1, and the recorded matching saturates the smaller compatible side in every current row.", + "dependsOn": [ + "C6_mixed_clique_matching_formula" + ], + "proofType": "bounded_matching_saturation_extraction", + "falsifierBoundary": "A refreshed exact mixed-base threatening-outsider row has matching below K(N,x), disagrees with the C6 formula replay, or fails the smaller-side saturation pattern. This bounded extraction is not yet the all-N symbolic matching proof.", + "dischargedBy": "p848_D1_matching_saturation_bound_checker_v1", + "dischargeWith": "All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row." + }, + { + "obligationId": "D2_p13_matching_lower_bound", + "status": "in_progress", + "task": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "statement": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=13 family row fails the claimed lower bound.", + "dischargedBy": null, + "dischargeWith": "Prove the active atom D2_p13_matching_lower_bound at its stated scope, then refresh FORMALIZATION_WORK so the next dependency is selected from the updated evidence." + }, + { + "obligationId": "D3_p17_matching_lower_bound", + "status": "ready", + "task": "For p=17 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "statement": "For p=17 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=17 family row fails the claimed lower bound.", + "dischargedBy": null, + "dischargeWith": null + }, + { + "obligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "status": "blocked_by_D2_D3", + "task": "If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "statement": "If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "dependsOn": [ + "C6_mixed_clique_matching_formula", + "D2_p13_matching_lower_bound", + "D3_p17_matching_lower_bound" + ], + "proofType": "inequality_substitution", + "falsifierBoundary": "The matching lower bound is substituted with the wrong inequality direction.", + "dischargedBy": null, + "dischargeWith": null + } + ], + "mechanismAssessment": { + "verdict": "controlled_congruence_candidate", + "confidence": "medium", + "rationale": [ + "Witness 841 first appears for tail 282 at representative 137720141, with 0 earlier zero-residue hits modulo 841.", + "Representative residue class 504 mod 841 matches tracked failure equations only for anchor(s) 282.", + "At least one tracked anchor cannot fail through modulus 841 at all because gcd(anchor, 841) > 1: 232.", + "The boundary tuple key appears exactly once in the current family menu, so this packet is not mixing multiple identical tuple rows.", + "Along the shared-prefix row progression itself, the witness 841 occurs at row index 0 only for tracked anchor(s) 282.", + "Other tracked anchors hit the same witness only later along the row progression: 332->t=67, 782->t=164, 432->t=318, 832->t=379, 382->t=592, 157->t=610.", + "Some tracked anchors never hit witness 841 along this row progression at all: 232.", + "At the family-menu level, representative residue 504 mod 841 first appears at representative 137720141 (row index 25), with 0 earlier menu rows on the same residue class.", + "The 132 row is the first tuple-row lift that forces residue 504 mod 841: 264*k ≡ 82 (mod 289), so k ≡ 147 and the CRT class lifts to 137720141.", + "Before anchor 132, no tuple-row CRT step lands on any tracked failure residue modulo 841; anchor 132 is the first step whose projected residue 504 uniquely matches tracked tail 282.", + "The 182 row preserves that residue: 137720141 ≡ 119 (mod 121), so the final CRT class keeps residue 504 mod 841.", + "Anchor 182 preserves the same unique tracked match: the projected residue stays on tail 282's failure class and does not activate any neighboring tracked tail.", + "This is not a one-row phenomenon in the current menu: 17 failing witness rows have the same first-target-activation-at-132 shape across tracked tails 157, 232, 282, 332, 382, 432, 782, 832.", + "The finite-menu 132-activation schema is now explicit with 17 row certificates, six hypotheses, and five falsifier classes.", + "The dedicated activation checker replayed 17 row certificates from raw tuple-row CRT projections with 0 failures.", + "The 132-row lift is proved directly from the tuple-row CRT equation: 264*k ≡ 82 (mod 289) with k = 147.", + "The symbolic-lift decision is explicit: keep the 132 schema finite-menu certified for now and route the next theorem pass to formalize_top_repair_class_mechanism.", + "The top repair-class mechanism packet is seeded: 432, 782, 832 share repaired-known=26, repaired-predicted=242, and clean-through=250075000.", + "The +2 top repair separation is certified by raw family-menu replay: top tails miss 13 predicted families each, while primary contrasts 332, 382, 1232 miss 15 each.", + "The cleanest pairwise handoff is 782>1232: the top tail repairs two predicted rows that the contrast misses and loses no predicted row back.", + "The mod-50 symbolic signature is now explicit: each pairwise exchange row solves a bad lane-index congruence for c = 32 + 50*m, and the repaired continuation misses that bad m-class.", + "The mod-50 bad-lane rule is now a symbolic divisibility schema checked on 74 witness instances; it is universal for a named witness congruence but not a full squarefree repair theorem.", + "The strict 782 > 1232 handoff is finite-menu certified: 782 repairs 2 predicted rows that 1232 misses, with no predicted row lost back.", + "The 132 activation lift is now parameterized as symbolic CRT hypotheses S1_pairwise_crt_compatibility, S2_same_witness_projection, S3_pre_132_clear, S4_anchor_132_unique_target, S5_anchor_182_preserves_target, S6_no_scope_promotion_without_domain_closure.", + "anchor_832_witness_529 is now replay-certified over 3 raw family-menu rows; the symbolic decision is single_profile_symbolic_domain_falsified_by_profile_split.", + "The anchor_832_witness_529 preservation mechanism is a zero-lift at anchor 182: anchor 132 already satisfies the final tuple row, so the witness residue stays fixed.", + "pre132_7_1_32_224_57_229_82_412 is resolved as a finite final-anchor duplicate: rows 270, 271 share the CRT prefix through anchor 132 and differ only by zero-lift anchor-182 variants." + ], + "caveats": [ + "The shared-prefix row progression is coprime to 841, so the row itself traverses all residue classes modulo 841; the 841 hit is not forced by the row alone.", + "The activation-pattern survey is over the current finite family menu, so it supports reusability inside the live search surface but does not by itself prove a universal obstruction-family theorem.", + "The activation lemma schema is a finite-menu certificate schema until its CRT hypotheses are lifted symbolically.", + "A universal lift still needs: A symbolic lift needs parameterized tuple-row CRT hypotheses plus a proof that pre-132 prefixes miss tracked failure residues and anchor 132 uniquely activates the target for the whole family.", + "The anchor_832_witness_529 lane splits into 2 pre-132 profiles, so it should be handled as profile sublanes rather than one broad symbolic family.", + "The repeated pre132_7_1_32_224_57_229_82_412 rows are a finite duplicate, so this sublane should not be promoted as independent evidence for a broad symbolic domain.", + "The mod-50 schema proves a bad-lane divisibility equivalence for a named witness Q; it still needs a separate control argument before it can close a squarefree finite-gap theorem lane.", + "The strict 782 > 1232 handoff is still finite-menu evidence; it guides the next exact verifier rollout but is not an all-N coverage theorem." + ], + "competingHypotheses": [ + { + "hypothesisId": "controlled_congruence_interaction", + "status": "favored", + "note": "The shared-prefix class and the 282 repair row intersect in a distinguished witness residue class modulo 841." + }, + { + "hypothesisId": "one_off_modular_coincidence", + "status": "disfavored_by_menu_survey", + "note": "The current family menu contains 17 rows with the same first-target-activation-at-132 shape, so the one-off explanation is no longer the best finite-menu reading." + }, + { + "hypothesisId": "shared_prefix_row_alone_forces_841", + "status": "not_supported", + "note": "A stronger claim that the family-row progression itself already forces the 841 witness class." + } + ] + }, + "packetData": { + "representative": 137720141, + "tupleKey": "4, 23^2, 7^2, 9, 17^2, 11^2", + "tupleRowCrtDerivation": { + "combinedResidue": 137720141, + "combinedModulus": 32631532164, + "projectedResidueModuloWitness": 504, + "firstStableProjectionAnchor": 132, + "steps": [ + { + "anchor": 7, + "rowSquareModulus": 4, + "rowResidue": 1, + "preCombinedResidue": 0, + "preCombinedModulus": 1, + "liftParameter": 1, + "combinedResidue": 1, + "combinedModulus": 4, + "residueModWitness": 1 + }, + { + "anchor": 32, + "rowSquareModulus": 529, + "rowResidue": 281, + "preCombinedResidue": 1, + "preCombinedModulus": 4, + "liftParameter": 70, + "combinedResidue": 281, + "combinedModulus": 2116, + "residueModWitness": 281 + }, + { + "anchor": 57, + "rowSquareModulus": 49, + "rowResidue": 6, + "preCombinedResidue": 281, + "preCombinedModulus": 2116, + "liftParameter": 13, + "combinedResidue": 27789, + "combinedModulus": 103684, + "residueModWitness": 36 + }, + { + "anchor": 82, + "rowSquareModulus": 9, + "rowResidue": 8, + "preCombinedResidue": 27789, + "preCombinedModulus": 103684, + "liftParameter": 5, + "combinedResidue": 546209, + "combinedModulus": 933156, + "residueModWitness": 400 + }, + { + "anchor": 132, + "rowSquareModulus": 289, + "rowResidue": 81, + "preCombinedResidue": 546209, + "preCombinedModulus": 933156, + "liftParameter": 147, + "combinedResidue": 137720141, + "combinedModulus": 269682084, + "residueModWitness": 504 + }, + { + "anchor": 182, + "rowSquareModulus": 121, + "rowResidue": 119, + "preCombinedResidue": 137720141, + "preCombinedModulus": 269682084, + "liftParameter": 0, + "combinedResidue": 137720141, + "combinedModulus": 32631532164, + "residueModWitness": 504 + } + ] + }, + "tupleRowActivationSequence": [ + { + "anchor": 7, + "residueModWitness": 1, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 281, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 36, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 400, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 504, + "matchingTrackedAnchors": [ + 282 + ], + "uniqueTrackedMatch": 282 + }, + { + "anchor": 182, + "residueModWitness": 504, + "matchingTrackedAnchors": [ + 282 + ], + "uniqueTrackedMatch": 282 + } + ], + "tupleRowActivationBoundary": { + "pre132HasNoTrackedMatch": true, + "activationAnchor": 132, + "activationResidueModuloWitness": 504, + "activationTrackedAnchors": [ + 282 + ], + "activationIsUnique282": true, + "preservationAnchor": 182, + "preservationResidueModuloWitness": 504, + "preservationTrackedAnchors": [ + 282 + ], + "preservationKeepsUnique282": true + }, + "menuActivationSurvey": { + "totalFailingWitnessRows": 305, + "firstMatchAnchorCounts": { + "7": 79, + "32": 26, + "57": 117, + "82": 13, + "132": 41, + "182": 29 + }, + "targetAtFirstMatchCount": 216, + "rowsWith132TargetActivationCount": 17, + "rowsWith132TargetActivationByFailingAnchor": { + "157": 3, + "232": 4, + "282": 1, + "332": 1, + "382": 2, + "432": 2, + "782": 1, + "832": 3 + }, + "rowsWith132TargetActivationByWitness": { + "4": 1, + "9": 1, + "121": 1, + "169": 1, + "289": 2, + "529": 4, + "841": 1, + "1681": 1, + "1849": 1, + "3481": 1, + "4489": 2, + "66049": 1 + }, + "targetActivationRows": [ + { + "familyIndex": 25, + "representative": 137720141, + "failingAnchor": 282, + "witnessSquareModulus": 841, + "firstMatchAnchor": 132, + "firstMatchTrackedAnchors": [ + 282 + ], + "tupleKey": "4, 23^2, 7^2, 9, 17^2, 11^2", + "activationSequence": [ + { + "anchor": 7, + "residueModWitness": 1, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 281, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 36, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 400, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 504, + "matchingTrackedAnchors": [ + 282 + ], + "uniqueTrackedMatch": 282 + }, + { + "anchor": 182, + "residueModWitness": 504, + "matchingTrackedAnchors": [ + 282 + ], + "uniqueTrackedMatch": 282 + } + ] + }, + { + "familyIndex": 63, + "representative": 365477947, + "failingAnchor": 232, + "witnessSquareModulus": 121, + "firstMatchAnchor": 132, + "firstMatchTrackedAnchors": [ + 232 + ], + "tupleKey": "19^2, 9, 4, 13^2, 131^2, 23^2", + "activationSequence": [ + { + "anchor": 7, + "residueModWitness": 103, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 97, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 79, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 23, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 109, + "matchingTrackedAnchors": [ + 232 + ], + "uniqueTrackedMatch": 232 + }, + { + "anchor": 182, + "residueModWitness": 109, + "matchingTrackedAnchors": [ + 232 + ], + "uniqueTrackedMatch": 232 + } + ] + }, + { + "familyIndex": 81, + "representative": 520923103, + "failingAnchor": 382, + "witnessSquareModulus": 66049, + "firstMatchAnchor": 132, + "firstMatchTrackedAnchors": [ + 382 + ], + "tupleKey": "19^2, 9, 4, 79^2, 7^2, 29^2", + "activationSequence": [ + { + "anchor": 7, + "residueModWitness": 103, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 1186, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 4435, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 61505, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 60689, + "matchingTrackedAnchors": [ + 382 + ], + "uniqueTrackedMatch": 382 + }, + { + "anchor": 182, + "residueModWitness": 60689, + "matchingTrackedAnchors": [ + 382 + ], + "uniqueTrackedMatch": 382 + } + ] + }, + { + "familyIndex": 112, + "representative": 712418111, + "failingAnchor": 157, + "witnessSquareModulus": 4, + "firstMatchAnchor": 132, + "firstMatchTrackedAnchors": [ + 157 + ], + "tupleKey": "17^2, 13^2, 7^2, 9, 19^2, 11^2", + "activationSequence": [ + { + "anchor": 7, + "residueModWitness": 1, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 1, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 2, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 2, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 3, + "matchingTrackedAnchors": [ + 157 + ], + "uniqueTrackedMatch": 157 + }, + { + "anchor": 182, + "residueModWitness": 3, + "matchingTrackedAnchors": [ + 157 + ], + "uniqueTrackedMatch": 157 + } + ] + }, + { + "familyIndex": 112, + "representative": 712418111, + "failingAnchor": 232, + "witnessSquareModulus": 529, + "firstMatchAnchor": 132, + "firstMatchTrackedAnchors": [ + 232 + ], + "tupleKey": "17^2, 13^2, 7^2, 9, 19^2, 11^2", + "activationSequence": [ + { + "anchor": 7, + "residueModWitness": 165, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 9, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 428, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 428, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 57, + "matchingTrackedAnchors": [ + 232 + ], + "uniqueTrackedMatch": 232 + }, + { + "anchor": 182, + "residueModWitness": 57, + "matchingTrackedAnchors": [ + 232 + ], + "uniqueTrackedMatch": 232 + } + ] + }, + { + "familyIndex": 133, + 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"witnessSquareModuli": [ + 4, + 9, + 121, + 169, + 289, + 529, + 841, + 1681, + 1849, + 3481, + 4489, + 66049 + ], + "familyMenuPath": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/SIX_PREFIX_TWENTY_FOUR_FAMILY_MENU.json" + }, + "informalStatement": "For each certified finite-menu witness row in this packet, the tuple-row CRT projection has no tracked failure-residue match before anchor 132; anchor 132 is the first step whose projected residue matches the failing tracked tail; anchor 182 preserves that match on the current six-row menu.", + "hypotheses": [ + { + "hypothesisId": "H1_finite_menu_row", + "text": "The row is one of the current finite family-menu rows with a tracked repair anchor a and square witness q^2 for a*n+1." + }, + { + "hypothesisId": "H2_tuple_crt_projection", + "text": "The tuple rows are replayed in anchor order, and each CRT prefix is projected modulo the same witness q^2." + }, + { + "hypothesisId": "H3_failure_residue_formula", + "text": "For every tracked anchor b coprime to q^2, the witness failure residue is n = -b^{-1} mod q^2; non-coprime anchors are marked unsolvable for that witness." + }, + { + "hypothesisId": "H4_pre_132_clear", + "text": "No tuple-row CRT prefix before anchor 132 lands on any tracked witness-failure residue modulo q^2." + }, + { + "hypothesisId": "H5_132_unique_target_activation", + "text": "The anchor-132 CRT prefix lands on exactly one tracked witness-failure residue, and that tracked anchor is the failing repair anchor a." + }, + { + "hypothesisId": "H6_182_preservation", + "text": "The anchor-182 CRT prefix preserves the same unique tracked witness-failure match and does not activate a competing tracked anchor." + } + ], + "conclusion": { + "text": "Inside the current finite family menu, the row has a controlled 132 target-activation certificate rather than an unexplained one-row coincidence.", + "outputs": [ + "firstTrackedActivationAnchor = 132", + "firstTrackedActivationAnchorMatchesFailingAnchor = true", + "anchor182PreservesTargetActivation = true" + ] + }, + "falsifierBoundary": [ + { + "falsifierId": "pre_132_tracked_match", + "text": "A replayed row has a tracked witness-failure residue match at anchor 7, 32, 57, or 82." + }, + { + "falsifierId": "wrong_132_target", + "text": "Anchor 132 activates no tracked anchor, multiple tracked anchors, or a tracked anchor different from the failing repair anchor." + }, + { + "falsifierId": "lost_182_preservation", + "text": "Anchor 182 changes the projection so the target activation is no longer the unique tracked match." + }, + { + "falsifierId": "menu_refresh_breaks_certificate", + "text": "A refreshed finite menu changes the witness rows, tuple rows, or repair rows so the 17 row certificates no longer replay." + }, + { + "falsifierId": "scope_overclaim", + "text": "The schema is used as a universal theorem without first proving the symbolic 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"firstMatchTrackedAnchors": [ + 832 + ], + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "activationSequence": [ + { + "anchor": 7, + "residueModWitness": 1, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 32, + "residueModWitness": 224, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 57, + "residueModWitness": 229, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 82, + "residueModWitness": 412, + "matchingTrackedAnchors": [], + "uniqueTrackedMatch": null + }, + { + "anchor": 132, + "residueModWitness": 316, + "matchingTrackedAnchors": [ + 832 + ], + "uniqueTrackedMatch": 832 + }, + { + "anchor": 182, + "residueModWitness": 316, + "matchingTrackedAnchors": [ + 832 + ], + "uniqueTrackedMatch": 832 + } + ] + }, + { + "familyIndex": 271, + "representative": 1797117529, + "failingAnchor": 832, + "witnessSquareModulus": 529, + "firstMatchAnchor": 132, + "firstMatchTrackedAnchors": [ + 832 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the current finite menu to a symbolic CRT lemma for a reusable obstruction family.", + "Keep the finite-menu scope explicit until the symbolic lift is proved." + ] + }, + "activationSchemaLiftDecision": { + "decisionId": "p848_activation_schema_symbolic_lift_decision_v1", + "verdict": "finite_menu_certificate_not_universal_yet", + "safeUse": "Use the schema as a checked finite-menu lemma/certificate family for the current 848 search surface.", + "rejectedOverclaim": "Do not state a universal obstruction-family theorem from the 17-row finite-menu certificate alone.", + "reason": [ + "The current packet has a replayed certificate for all 17 finite-menu 132 target-activation rows.", + "The current 282 boundary lift is proved from its tuple-row CRT equation.", + "The packet does not yet contain symbolic hypotheses that characterize every future tuple-row family producing the same 132 activation shape." + ], + "nextTheoremPass": "formalize_top_repair_class_mechanism", + "nextTheoremPassReason": "The 282-specific mechanism is now narrow, checked, and claim-safe; the live bridge still exposes an independent high-value top cluster 432, 782, 832 with shared repaired-known and repaired-predicted counts.", + "promotionRequirement": "A symbolic lift needs parameterized tuple-row CRT hypotheses plus a proof that pre-132 prefixes miss tracked failure residues and anchor 132 uniquely activates the target for the whole family.", + "falsifierBoundary": [ + "A refreshed menu breaks one of the 17 finite row certificates.", + "A symbolic family instance satisfies the proposed hypotheses but has a pre-132 tracked match.", + "Anchor 132 activates a non-target or multiple tracked tails under the proposed symbolic hypotheses.", + "Anchor 182 fails to preserve the target activation under the proposed symbolic hypotheses." + ] + }, + "activationSymbolicLiftCandidate": { + "candidateId": "p848_132_activation_symbolic_lift_candidate_v1", + "checkerId": "p848_132_activation_symbolic_lift_candidate_checker_v1", + "source": "finite_menu_certificate_to_symbolic_crt_hypotheses", + "status": "symbolic_crt_hypothesis_packet_ready", + "checkedRowCount": 17, + "passCount": 17, + "failCount": 0, + "failedRows": [], + "scope": { + "problemId": "848", + "universalClaim": false, + "candidateOnly": true, + "finiteCertificateRows": 17, + "boundaryWitnessSquareModulus": 841 + }, + "parameterization": { + "anchorOrder": [ + 7, + 32, + 57, + 82, + 132, + 182 + ], + "trackedAnchors": [ + 157, + 232, + 282, + 332, + 382, + 432, + 782, + 832 + ], + "variables": [ + "Q: square witness modulus q^2", + "a: failing tracked repair anchor", + "M_i: square modulus introduced by tuple anchor i", + "r_i: tuple-row residue introduced by tuple anchor i", + "N_i: CRT prefix residue after anchors up to i", + "R_b(Q): tracked failure residue -b^{-1} mod Q when gcd(b, Q) = 1" + ], + "crtPrefixRecurrence": "N_i is the unique residue modulo lcm(M_7,...,M_i) satisfying all tuple rows through anchor i.", + "failureResidueFormula": "R_b(Q) = -b^{-1} mod Q for gcd(b,Q)=1; if gcd(b,Q)>1, b cannot supply a residue class modulo Q unless the divisibility condition is satisfied." + }, + "symbolicHypotheses": [ + { + "hypothesisId": "S1_pairwise_crt_compatibility", + "text": "The tuple-row moduli through anchors 7, 32, 57, 82, 132, 182 are CRT-compatible and define prefixes N_i." + }, + { + "hypothesisId": "S2_same_witness_projection", + "text": "Every prefix N_i is projected modulo the same square witness Q attached to the failing repair row a*n+1." + }, + { + "hypothesisId": "S3_pre_132_clear", + "text": "For i in {7,32,57,82}, N_i is not congruent to R_b(Q) for any tracked anchor b whose failure residue is defined." + }, + { + "hypothesisId": "S4_anchor_132_unique_target", + "text": "N_132 is congruent to R_a(Q), and N_132 is not congruent to R_b(Q) for every tracked b != a whose failure residue is defined." + }, + { + "hypothesisId": "S5_anchor_182_preserves_target", + "text": "N_182 is congruent to N_132 modulo Q, so the target activation survives the final shared-prefix anchor." + }, + { + "hypothesisId": "S6_no_scope_promotion_without_domain_closure", + "text": "A problem-level theorem may use this packet only after a separate domain-closure lemma proves S1-S5 for the intended family, not merely for the current finite menu." + } + ], + "symbolicConclusion": { + "text": "Any row satisfying S1-S5 has first tracked failure-residue activation at anchor 132, uniquely activates the failing anchor a, and preserves that activation at anchor 182.", + "proofSketch": [ + "S3 rules out every tracked activation before anchor 132.", + "S4 makes anchor 132 a unique activation of the target failing anchor.", + "S5 carries the same witness-residue class through anchor 182 without adding a competing tracked match." + ] + }, + "finiteEvidence": { + "activationCheckerId": "p848_132_activation_row_certificate_checker_v1", + 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"witnessSquareModulus": 289, + "status": "passed", + "failedChecks": [] + }, + { + "familyIndex": 270, + "failingAnchor": 832, + "witnessSquareModulus": 529, + "status": "passed", + "failedChecks": [] + }, + { + "familyIndex": 271, + "failingAnchor": 832, + "witnessSquareModulus": 529, + "status": "passed", + "failedChecks": [] + } + ] + }, + "nextProofObligations": [ + "Prove a domain-closure lemma that supplies S1-S5 for a reusable class of tuple rows instead of only the 17 current finite-menu rows.", + "Decide whether the domain-closure class should be the 282 obstruction family, the full 132-activation survey, or the stricter 782-vs-1232 exchange family.", + "Connect the symbolic activation packet to the finite-gap verifier boundary so it narrows the post-11300 exact work rather than becoming an isolated lemma." + ] + }, + "activationDomainClosureAssessment": { + "assessmentId": "p848_132_activation_domain_closure_assessment_v1", + "status": "broad_domain_closure_not_supported_yet", + "checkedRowCount": 17, + "failCount": 0, + "broadClosureVerdict": { + "verdict": "do_not_promote_broad_17_row_survey_to_universal_domain", + "reason": "The finite symbolic-lift survey splits across 8 failing anchors and 12 witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem.", + "failingAnchorCounts": { + "157": 3, + "232": 4, + "282": 1, + "332": 1, + "382": 2, + "432": 2, + "782": 1, + "832": 3 + }, + "witnessCounts": { + "4": 1, + "9": 1, + "121": 1, + "169": 1, + "289": 2, + "529": 4, + "841": 1, + "1681": 1, + "1849": 1, + "3481": 1, + "4489": 2, + "66049": 1 + } + }, + "repeatedAnchorWitnessGroups": [ + { + "groupId": "anchor_832_witness_529", + "failingAnchor": 832, + "witnessSquareModulus": 529, + "rowCount": 3, + "familyIndices": [ + 217, + 270, + 271 + ], + "representatives": [ + 1446717451, + 1797117529 + ], + "tupleKeys": [ + "11^2, 29^2, 4, 7^2, 31^2, 9", + "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "4, 53^2, 17^2, 7^2, 61^2, 9" + ] + }, + { + "groupId": "anchor_432_witness_4489", + "failingAnchor": 432, + "witnessSquareModulus": 4489, + "rowCount": 2, + "familyIndices": [ + 236, + 237 + ], + "representatives": [ + 1585191353 + ], + "tupleKeys": [ + "4, 19^2, 13^2, 7^2, 23^2, 11^2", + "9, 19^2, 13^2, 7^2, 23^2, 11^2" + ] + } + ], + "narrowedClosureCandidates": [ + { + "candidateId": "p848_282_841_boundary_instance_closure", + "priority": "high", + "rowCount": 1, + "task": "Prove the 282/841 boundary instance from the explicit CRT equations and keep it scoped as the current obstruction packet.", + "tradeoff": "Best alignment with the 282 north star, but currently only a single finite-menu row." + }, + { + "candidateId": "p848_832_529_repeated_activation_family", + "priority": "high", + "rowCount": 3, + "task": "Try to prove a reusable closure lemma for anchor 832 with witness 529.", + "tradeoff": "Best repeated symbolic-lift family in the current activation survey, but it may be less directly tied to the 282 alignment." + }, + { + "candidateId": "p848_782_1232_strict_exchange_closure", + "priority": "high", + "rowCount": 2, + "task": "Use the strict 782 > 1232 exchange rows as a small theorem-facing family for the mod-50 lane closure.", + "tradeoff": "Best bridge to the top repair-class mechanism, but it is a top-cluster theorem lane rather than the 132 activation lane itself." + } + ], + "recommendedClosureLane": { + "laneId": "repeat_anchor_witness_activation_family", + "targetGroupId": "anchor_832_witness_529", + "why": "This is the largest repeated symbolic-activation class in the 17-row survey: anchor 832 with witness 529 appears 3 times." + }, + "nextProofObligations": [ + "Do not claim a universal 17-row domain theorem until a single structural family supplies S1-S5.", + "Start with anchor_832_witness_529 and prove or falsify its CRT-domain closure.", + "After one narrow closure lane is proved, decide whether it genuinely reduces the finite gap or only explains a search-side feature." + ] + }, + "anchorWitnessDomainClosurePacket": { + "checkerId": "p848_832_529_anchor_witness_domain_closure_checker_v1", + "packetId": "p848_832_529_anchor_witness_domain_closure_packet_v1", + "source": "raw_family_menu_anchor_witness_replay", + "familyMenuPath": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/SIX_PREFIX_TWENTY_FOUR_FAMILY_MENU.json", + "status": "finite_group_closure_certified_symbolic_domain_split", + "checkedRowCount": 3, + "passCount": 3, + "failCount": 0, + "targetGroupId": "anchor_832_witness_529", + "failingAnchor": 832, + "witnessSquareModulus": 529, + "targetFailureResidue": 316, + "expectedRowCount": 3, + "rowCountMatchesAssessment": true, + "finiteScopeConclusion": "Every current finite-menu occurrence of anchor_832_witness_529 replays from raw tuple-row CRT data: pre-132 prefixes are clear, anchor 132 uniquely activates tracked tail 832, and anchor 182 preserves residue 316 mod 529.", + "symbolicDomainDecision": { + "verdict": "single_profile_symbolic_domain_falsified_by_profile_split", + "reason": "The recommended anchor/witness group splits into 2 pre-132 residue profiles, so one broad single-profile symbolic closure would overclaim the evidence.", + "profileGroupCount": 2, + "repeatedProfileId": "pre132_7_1_32_224_57_229_82_412" + }, + "zeroLiftPreservation": { + "allRowsAnchor182ZeroLift": true, + "explanation": "In the certified rows, the anchor-132 CRT prefix already satisfies the anchor-182 tuple row, so adding anchor 182 uses lift parameter 0 and cannot move the witness residue modulo 529." + }, + "profileGroups": [ + { + "profileId": "pre132_7_1_32_224_57_229_82_412", + "profile": "7->1, 32->224, 57->229, 82->412", + "rowCount": 2, + "familyIndices": [ + 270, + 271 + ], + "representatives": [ + 1797117529 + ], + "tupleKeys": [ + "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "4, 53^2, 17^2, 7^2, 61^2, 9" + ], + "anchor182RowSquareModuli": [ + 121, + 9 + ] + }, + { + "profileId": "pre132_7_69_32_22_57_22_82_521", + "profile": "7->69, 32->22, 57->22, 82->521", + "rowCount": 1, + "familyIndices": [ + 217 + ], + "representatives": [ + 1446717451 + ], + "tupleKeys": [ + "11^2, 29^2, 4, 7^2, 31^2, 9" + ], + "anchor182RowSquareModuli": [ + 9 + ] + } + ], + "rowProofs": [ + { + "familyIndex": 217, + "representative": 1446717451, + "tupleKey": "11^2, 29^2, 4, 7^2, 31^2, 9", + "failingAnchor": 832, + "witnessSquareModulus": 529, + "targetFailureResidue": 316, + "repairValue": 1203668919233, + "squareWitnesses": [ + { + "prime": 23, + "exponent": 2, + "squareModulus": 529 + } + ], + "representativeResidueModuloWitness": 316, + "pre132ProfileId": "pre132_7_69_32_22_57_22_82_521", + "pre132Profile": "7->69, 32->22, 57->22, 82->521", + "pre132Residues": [ + { + "anchor": 7, + "residueModWitness": 69, + "matchingTrackedAnchors": [] + }, + { + "anchor": 32, + "residueModWitness": 22, + "matchingTrackedAnchors": [] + }, + { + "anchor": 57, + "residueModWitness": 22, + "matchingTrackedAnchors": [] + }, + { + "anchor": 82, + "residueModWitness": 521, + "matchingTrackedAnchors": [] + } + ], + "residueAt132": 316, + "residueAt182": 316, + "anchor132LiftParameter": 72, + "anchor182LiftParameter": 0, + "anchor182RowSquareModulus": 9, + "anchor182RowResidue": 4, + "tupleRows": [ + { + "anchor": 7, + "squareModulus": 121, + "residue": 69 + }, + { + "anchor": 32, + "squareModulus": 841, + "residue": 657 + }, + { + "anchor": 57, + "squareModulus": 4, + "residue": 3 + }, + { + "anchor": 82, + "squareModulus": 49, + "residue": 46 + }, + { + "anchor": 132, + "squareModulus": 961, + "residue": 182 + }, + { + "anchor": 182, + "squareModulus": 9, + "residue": 4 + } + ], + "crtDerivation": { + "combinedResidue": 1446717451, + "combinedModulus": 172505654244, + "projectedResidueModuloWitness": 316, + "firstStableProjectionAnchor": 132, + "steps": [ + { + "anchor": 7, + "rowSquareModulus": 121, + "rowResidue": 69, + "preCombinedResidue": 0, + "preCombinedModulus": 1, + "liftParameter": 69, + "combinedResidue": 69, + "combinedModulus": 121, + "residueModWitness": 69 + }, + { + "anchor": 32, + "rowSquareModulus": 841, + "rowResidue": 657, + "preCombinedResidue": 69, + "preCombinedModulus": 121, + "liftParameter": 686, + "combinedResidue": 83075, + "combinedModulus": 101761, + "residueModWitness": 22 + }, + { + "anchor": 57, + "rowSquareModulus": 4, + "rowResidue": 3, + "preCombinedResidue": 83075, + "preCombinedModulus": 101761, + "liftParameter": 0, + "combinedResidue": 83075, + "combinedModulus": 407044, + "residueModWitness": 22 + }, + { + "anchor": 82, + "rowSquareModulus": 49, + "rowResidue": 46, + "preCombinedResidue": 83075, + "preCombinedModulus": 407044, + "liftParameter": 26, + "combinedResidue": 10666219, + "combinedModulus": 19945156, + "residueModWitness": 521 + }, + { + "anchor": 132, + "rowSquareModulus": 961, + "rowResidue": 182, + "preCombinedResidue": 10666219, + "preCombinedModulus": 19945156, + "liftParameter": 72, + "combinedResidue": 1446717451, + "combinedModulus": 19167294916, + "residueModWitness": 316 + }, + { + "anchor": 182, + "rowSquareModulus": 9, + "rowResidue": 4, + "preCombinedResidue": 1446717451, + "preCombinedModulus": 19167294916, + "liftParameter": 0, + "combinedResidue": 1446717451, + "combinedModulus": 172505654244, + "residueModWitness": 316 + } + ] + }, + "checks": { + "witnessPresentOnTargetRepair": true, + "repairValueDivisibleByWitness": true, + "representativeHitsTargetFailureResidue": true, + "rawRepresentativeMatchesCrtResidue": true, + "pre132HasNoTrackedMatch": true, + "firstTrackedMatchIs132": true, + "anchor132UniqueTarget": true, + "anchor182PreservesTarget": true, + "anchor182ZeroLift": true + }, + "status": "passed", + "failedChecks": [] + }, + { + "familyIndex": 270, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "failingAnchor": 832, + "witnessSquareModulus": 529, + "targetFailureResidue": 316, + "repairValue": 1495201784129, + "squareWitnesses": [ + { + "prime": 23, + "exponent": 2, + "squareModulus": 529 + } + ], + "representativeResidueModuloWitness": 316, + "pre132ProfileId": "pre132_7_1_32_224_57_229_82_412", + "pre132Profile": "7->1, 32->224, 57->229, 82->412", + "pre132Residues": [ + { + "anchor": 7, + "residueModWitness": 1, + "matchingTrackedAnchors": [] + }, + { + "anchor": 32, + "residueModWitness": 224, + "matchingTrackedAnchors": [] + }, + { + "anchor": 57, + "residueModWitness": 229, + "matchingTrackedAnchors": [] + }, + { + "anchor": 82, + "residueModWitness": 412, + "matchingTrackedAnchors": [] + } + ], + "residueAt132": 316, + "residueAt182": 316, + "anchor132LiftParameter": 11, + "anchor182LiftParameter": 0, + "anchor182RowSquareModulus": 121, + "anchor182RowResidue": 119, + "tupleRows": [ + { + "anchor": 7, + "squareModulus": 4, + "residue": 1 + }, + { + "anchor": 32, + "squareModulus": 2809, + "residue": 790 + }, + { + "anchor": 57, + "squareModulus": 289, + "residue": 218 + }, + { + "anchor": 82, + "squareModulus": 49, + "residue": 46 + }, + { + "anchor": 132, + "squareModulus": 3721, + "residue": 1043 + }, + { + "anchor": 182, + "squareModulus": 121, + "residue": 119 + } + ], + "crtDerivation": { + "combinedResidue": 1797117529, + "combinedModulus": 71639194432036, + "projectedResidueModuloWitness": 316, + "firstStableProjectionAnchor": 132, + "steps": [ + { + "anchor": 7, + "rowSquareModulus": 4, + "rowResidue": 1, + "preCombinedResidue": 0, + "preCombinedModulus": 1, + "liftParameter": 1, + "combinedResidue": 1, + "combinedModulus": 4, + "residueModWitness": 1 + }, + { + "anchor": 32, + "rowSquareModulus": 2809, + "rowResidue": 790, + "preCombinedResidue": 1, + "preCombinedModulus": 4, + "liftParameter": 2304, + "combinedResidue": 9217, + "combinedModulus": 11236, + "residueModWitness": 224 + }, + { + "anchor": 57, + "rowSquareModulus": 289, + "rowResidue": 218, + "preCombinedResidue": 9217, + "preCombinedModulus": 11236, + "liftParameter": 125, + "combinedResidue": 1413717, + "combinedModulus": 3247204, + "residueModWitness": 229 + }, + { + "anchor": 82, + "rowSquareModulus": 49, + "rowResidue": 46, + "preCombinedResidue": 1413717, + "preCombinedModulus": 3247204, + "liftParameter": 14, + "combinedResidue": 46874573, + "combinedModulus": 159112996, + "residueModWitness": 412 + }, + { + "anchor": 132, + "rowSquareModulus": 3721, + "rowResidue": 1043, + "preCombinedResidue": 46874573, + "preCombinedModulus": 159112996, + "liftParameter": 11, + "combinedResidue": 1797117529, + "combinedModulus": 592059458116, + "residueModWitness": 316 + }, + { + "anchor": 182, + "rowSquareModulus": 121, + "rowResidue": 119, + "preCombinedResidue": 1797117529, + "preCombinedModulus": 592059458116, + "liftParameter": 0, + "combinedResidue": 1797117529, + "combinedModulus": 71639194432036, + "residueModWitness": 316 + } + ] + }, + "checks": { + "witnessPresentOnTargetRepair": true, + "repairValueDivisibleByWitness": true, + "representativeHitsTargetFailureResidue": true, + "rawRepresentativeMatchesCrtResidue": true, + "pre132HasNoTrackedMatch": true, + "firstTrackedMatchIs132": true, + "anchor132UniqueTarget": true, + "anchor182PreservesTarget": true, + "anchor182ZeroLift": true + }, + "status": "passed", + "failedChecks": [] + }, + { + "familyIndex": 271, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 9", + "failingAnchor": 832, + "witnessSquareModulus": 529, + "targetFailureResidue": 316, + "repairValue": 1495201784129, + "squareWitnesses": [ + { + "prime": 23, + "exponent": 2, + "squareModulus": 529 + } + ], + "representativeResidueModuloWitness": 316, + "pre132ProfileId": "pre132_7_1_32_224_57_229_82_412", + "pre132Profile": "7->1, 32->224, 57->229, 82->412", + "pre132Residues": [ + { + "anchor": 7, + "residueModWitness": 1, + "matchingTrackedAnchors": [] + }, + { + "anchor": 32, + "residueModWitness": 224, + "matchingTrackedAnchors": [] + }, + { + "anchor": 57, + "residueModWitness": 229, + "matchingTrackedAnchors": [] + }, + { + "anchor": 82, + "residueModWitness": 412, + "matchingTrackedAnchors": [] + } + ], + "residueAt132": 316, + "residueAt182": 316, + "anchor132LiftParameter": 11, + "anchor182LiftParameter": 0, + "anchor182RowSquareModulus": 9, + "anchor182RowResidue": 4, + "tupleRows": [ + { + "anchor": 7, + "squareModulus": 4, + "residue": 1 + }, + { + "anchor": 32, + "squareModulus": 2809, + "residue": 790 + }, + { + "anchor": 57, + "squareModulus": 289, + "residue": 218 + }, + { + "anchor": 82, + "squareModulus": 49, + "residue": 46 + }, + { + "anchor": 132, + "squareModulus": 3721, + "residue": 1043 + }, + { + "anchor": 182, + "squareModulus": 9, + "residue": 4 + } + ], + "crtDerivation": { + "combinedResidue": 1797117529, + "combinedModulus": 5328535123044, + "projectedResidueModuloWitness": 316, + "firstStableProjectionAnchor": 132, + "steps": [ + { + "anchor": 7, + "rowSquareModulus": 4, + "rowResidue": 1, + "preCombinedResidue": 0, + "preCombinedModulus": 1, + "liftParameter": 1, + "combinedResidue": 1, + "combinedModulus": 4, + "residueModWitness": 1 + }, + { + "anchor": 32, + "rowSquareModulus": 2809, + "rowResidue": 790, + "preCombinedResidue": 1, + "preCombinedModulus": 4, + "liftParameter": 2304, + "combinedResidue": 9217, + "combinedModulus": 11236, + "residueModWitness": 224 + }, + { + "anchor": 57, + "rowSquareModulus": 289, + "rowResidue": 218, + "preCombinedResidue": 9217, + "preCombinedModulus": 11236, + "liftParameter": 125, + "combinedResidue": 1413717, + "combinedModulus": 3247204, + "residueModWitness": 229 + }, + { + "anchor": 82, + "rowSquareModulus": 49, + "rowResidue": 46, + "preCombinedResidue": 1413717, + "preCombinedModulus": 3247204, + "liftParameter": 14, + "combinedResidue": 46874573, + "combinedModulus": 159112996, + "residueModWitness": 412 + }, + { + "anchor": 132, + "rowSquareModulus": 3721, + "rowResidue": 1043, + "preCombinedResidue": 46874573, + "preCombinedModulus": 159112996, + "liftParameter": 11, + "combinedResidue": 1797117529, + "combinedModulus": 592059458116, + "residueModWitness": 316 + }, + { + "anchor": 182, + "rowSquareModulus": 9, + "rowResidue": 4, + "preCombinedResidue": 1797117529, + "preCombinedModulus": 592059458116, + "liftParameter": 0, + "combinedResidue": 1797117529, + "combinedModulus": 5328535123044, + "residueModWitness": 316 + } + ] + }, + "checks": { + "witnessPresentOnTargetRepair": true, + "repairValueDivisibleByWitness": true, + "representativeHitsTargetFailureResidue": true, + "rawRepresentativeMatchesCrtResidue": true, + "pre132HasNoTrackedMatch": true, + "firstTrackedMatchIs132": true, + "anchor132UniqueTarget": true, + "anchor182PreservesTarget": true, + "anchor182ZeroLift": true + }, + "status": "passed", + "failedChecks": [] + } + ], + "failedRows": [], + "recommendedSuccessor": { + "laneId": "repeat_pre132_profile_subfamily", + "targetProfileId": "pre132_7_1_32_224_57_229_82_412", + "task": "Prove or falsify the repeated anchor_832_witness_529 pre-132 profile sublane pre132_7_1_32_224_57_229_82_412 beyond finite rows 270, 271.", + "why": "Rows 270, 271 share the same pre-132 residues, hit 316 mod 529 at anchor 132, and have a zero-lift anchor-182 preservation step despite different final tuple moduli." + }, + "falsifierBoundary": [ + "A refreshed family menu adds another anchor_832_witness_529 row that fails any row check in this packet.", + "A refreshed family menu removes one of the certified rows 217, 270, 271 or changes its witness modulus.", + "A symbolic theorem tries to use the finite group as one broad profile despite the recorded profile split.", + "A future profile sublane instance has a nonzero anchor-182 lift or a pre-132 tracked failure-residue match." + ], + "nextProofObligations": [ + "Prove or falsify the repeated anchor_832_witness_529 pre-132 profile sublane pre132_7_1_32_224_57_229_82_412 beyond finite rows 270, 271.", + "Decide whether the repeated profile is a true symbolic family or only a finite-menu duplicate created by alternative final tuple rows.", + "If the repeated profile is finite-only, move the theorem lane to the mod-50 bad-family signature or the next local exact verifier rollout." + ] + }, + "anchorWitnessProfileSublanePacket": { + "checkerId": "p848_832_529_pre132_profile_sublane_checker_v1", + "packetId": "p848_832_529_pre132_profile_sublane_packet_v1", + "source": "anchor_witness_domain_closure_profile_replay", + "status": "finite_profile_sublane_resolved_as_zero_lift_duplicate", + "checkedRowCount": 2, + "passCount": 2, + "failCount": 0, + "parentPacketId": "p848_832_529_anchor_witness_domain_closure_packet_v1", + "targetGroupId": "anchor_832_witness_529", + "targetProfileId": "pre132_7_1_32_224_57_229_82_412", + "failingAnchor": 832, + "witnessSquareModulus": 529, + "targetFailureResidue": 316, + "familyIndices": [ + 270, + 271 + ], + "representatives": [ + 1797117529 + ], + "repairValues": [ + 1495201784129 + ], + "tupleKeys": [ + "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "4, 53^2, 17^2, 7^2, 61^2, 9" + ], + "sharedPrefixThrough132": [ + { + "anchor": 7, + "squareModulus": 4, + "residue": 1 + }, + { + "anchor": 32, + "squareModulus": 2809, + "residue": 790 + }, + { + "anchor": 57, + "squareModulus": 289, + "residue": 218 + }, + { + "anchor": 82, + "squareModulus": 49, + "residue": 46 + }, + { + "anchor": 132, + "squareModulus": 3721, + "residue": 1043 + } + ], + "finalAnchorVariants": [ + { + "familyIndex": 270, + "anchor": 182, + "squareModulus": 121, + "residue": 119, + "liftParameter": 0 + }, + { + "familyIndex": 271, + "anchor": 182, + "squareModulus": 9, + "residue": 4, + "liftParameter": 0 + } + ], + "anchor132LiftParameter": 11, + "checks": { + "repeatedProfileHasAtLeastTwoRows": true, + "sameRepresentative": true, + "sameRepairValue": true, + "sameTuplePrefixThrough132": true, + "distinctFullTupleRows": true, + "differsOnlyAtAnchor182": true, + "sameAnchor132Lift": true, + "anchor182ZeroLiftForEveryRow": true, + "allRowsAlreadyPassedParentClosure": true + }, + "failedChecks": [], + "rowProofRefs": [ + { + "familyIndex": 270, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "residueAt132": 316, + "residueAt182": 316, + "anchor182LiftParameter": 0 + }, + { + "familyIndex": 271, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 9", + "residueAt132": 316, + "residueAt182": 316, + "anchor182LiftParameter": 0 + } + ], + "conclusion": "Rows 270, 271 are a finite duplicate final-anchor variant over the same CRT prefix through anchor 132, not evidence for a separate broad symbolic family.", + "symbolicDomainDecision": { + "verdict": "profile_sublane_not_a_new_symbolic_family", + "reason": "The repeated profile rows share representative, repair value, tuple prefix through anchor 132, and anchor-132 lift; they differ only by the final anchor-182 tuple row, which is a zero-lift in both cases." + }, + "nextProofObligations": [ + "Move the theorem lane to the mod-50 bad-family signature, because the repeated 832/529 profile did not yield a new broad symbolic domain.", + "Keep the 832/529 packet as finite checked wisdom for future family-menu refreshes.", + "Run the next local exact verifier rollout only after the theorem-facing mod-50 handoff has been sharpened or falsified." + ] + }, + "mod50LaneSymbolicSchema": { + "checkerId": "p848_mod50_bad_lane_symbolic_schema_checker_v1", + "schemaId": "p848_mod50_bad_lane_symbolic_schema_v1", + "source": "mod50_lane_congruence_lift", + "status": "symbolic_bad_lane_schema_ready", + "laneBase": 32, + "laneStep": 50, + "laneFormula": "continuation = 32 + 50*m", + "checkedRowCount": 74, + "passCount": 74, + "failCount": 0, + "failedInstances": [], + "scope": { + "universalDivisibilityClaim": true, + "universalSquarefreeRepairClaim": false, + "finiteExchangeRowsChecked": 74, + "symbolicVariables": [ + "n: family representative", + "Q: square witness modulus", + "m: lane index in c = 32 + 50*m", + "c: continuation being tested" + ] + }, + "symbolicStatement": "For any representative n and square witness modulus Q, continuation c = 32 + 50*m has Q | c*n + 1 exactly when (50*n)*m ≡ -(32*n + 1) (mod Q). When this congruence is solvable, it defines the bad m-class modulo Q/gcd(50*n,Q).", + "proofSketch": [ + "Substitute c = 32 + 50*m into c*n + 1 ≡ 0 (mod Q).", + "Rearrange to (50*n)*m ≡ -(32*n + 1) (mod Q).", + "Solve the linear congruence; the missed continuation is bad exactly when its lane index lies in the solution class.", + "Avoiding this one witness class is necessary for repair on that row, but not by itself sufficient for global squarefreeness." + ], + "periodCounts": { + "9": 19, + "49": 18, + "169": 2, + "289": 6, + "361": 2, + "529": 9, + "1369": 3, + "1681": 6, + "4489": 6, + "66049": 3 + }, + "strict782Vs1232Instances": [ + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 782, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 782, + "familyIndex": 104, + "representative": 681558029, + "witnessSquareModulus": 1369, + "laneEquation": "500*m ≡ 1048 (mod 1369)", + "laneIndexResidue": 24, + "laneIndexPeriod": 1369, + "missedLaneIndex": 24, + "repairedLaneIndex": 15, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 782, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 782, + "familyIndex": 187, + "representative": 1256825183, + "witnessSquareModulus": 289, + "laneEquation": "83*m ≡ 258 (mod 289)", + "laneIndexResidue": 24, + "laneIndexPeriod": 289, + "missedLaneIndex": 24, + "repairedLaneIndex": 15, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + } + ], + "instanceChecks": [ + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 432, + "contrastContinuation": 332, + "continuation": 332, + "repairedContinuation": 432, + "familyIndex": 100, + "representative": 657348925, + "witnessSquareModulus": 49, + "laneEquation": "9*m ≡ 5 (mod 49)", + "laneIndexResidue": 6, + "laneIndexPeriod": 49, + "missedLaneIndex": 6, + "repairedLaneIndex": 8, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 432, + "contrastContinuation": 332, + "continuation": 332, + "repairedContinuation": 432, + "familyIndex": 107, + "representative": 695323423, + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 6, + "repairedLaneIndex": 8, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 432, + "contrastContinuation": 332, + "continuation": 332, + "repairedContinuation": 432, + "familyIndex": 133, + "representative": 885528547, + "witnessSquareModulus": 1681, + "laneEquation": "172*m ≡ 1032 (mod 1681)", + "laneIndexResidue": 6, + "laneIndexPeriod": 1681, + "missedLaneIndex": 6, + "repairedLaneIndex": 8, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 432, + "contrastContinuation": 332, + "continuation": 332, + "repairedContinuation": 432, + "familyIndex": 161, + "representative": 1079001739, + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 6, + "repairedLaneIndex": 8, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 432, + "contrastContinuation": 332, + "continuation": 332, + "repairedContinuation": 432, + "familyIndex": 194, + "representative": 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"laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 382, + "repairedContinuation": 832, + "familyIndex": 258, + "representative": 1705839349, + "witnessSquareModulus": 289, + "laneEquation": "15*m ≡ 105 (mod 289)", + "laneIndexResidue": 7, + "laneIndexPeriod": 289, + "missedLaneIndex": 7, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 832, + "repairedContinuation": 382, + "familyIndex": 217, + "representative": 1446717451, + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 7, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 832, + "repairedContinuation": 382, + "familyIndex": 270, + "representative": 1797117529, + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 7, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 832, + "repairedContinuation": 382, + "familyIndex": 271, + "representative": 1797117529, + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 7, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 832, + "familyIndex": 104, + "representative": 681558029, + "witnessSquareModulus": 1369, + "laneEquation": "500*m ≡ 1048 (mod 1369)", + "laneIndexResidue": 24, + "laneIndexPeriod": 1369, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 832, + "familyIndex": 107, + "representative": 695323423, + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 832, + "familyIndex": 161, + "representative": 1079001739, + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 832, + "familyIndex": 187, + "representative": 1256825183, + "witnessSquareModulus": 289, + "laneEquation": "83*m ≡ 258 (mod 289)", + "laneIndexResidue": 24, + "laneIndexPeriod": 289, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 832, + "familyIndex": 234, + "representative": 1583883827, + "witnessSquareModulus": 361, + "laneEquation": "99*m ≡ 210 (mod 361)", + "laneIndexResidue": 24, + "laneIndexPeriod": 361, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "repairedContinuation": 832, + "familyIndex": 275, + "representative": 1820631943, + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "repairedContinuation": 1232, + "familyIndex": 217, + "representative": 1446717451, + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "repairedContinuation": 1232, + "familyIndex": 256, + "representative": 1684455347, + "witnessSquareModulus": 9, + "laneEquation": "1*m ≡ 7 (mod 9)", + "laneIndexResidue": 7, + "laneIndexPeriod": 9, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "repairedContinuation": 1232, + "familyIndex": 270, + "representative": 1797117529, + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "repairedContinuation": 1232, + "familyIndex": 271, + "representative": 1797117529, + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "status": "passed", + "checks": { + "laneFormulaAppliesToMissedContinuation": true, + "laneFormulaAppliesToRepairedContinuation": true, + "equationRecomputes": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true, + "congruenceSolvable": true + }, + "failedChecks": [] + } + ], + "conclusion": "The finite mod-50 exchange packet is now backed by a reusable divisibility schema over 74 checked witness instances.", + "nextProofObligations": [ + "Connect the symbolic bad-lane schema to the finite-gap closure target using a theorem-facing handoff family, preferably the strict 782 vs 1232 rows.", + "Prove that the selected handoff family controls all relevant square witnesses, not only the witnessed bad lane in each finite exchange row.", + "If no such control family exists, route the next step to local exact verification beyond 11300 instead of overclaiming the lane schema." + ] + }, + "strict7821232HandoffPacket": { + "checkerId": "p848_782_1232_strict_handoff_checker_v1", + "packetId": "p848_782_1232_strict_handoff_packet_v1", + "source": "mod50_symbolic_schema_to_finite_menu_handoff", + "status": "finite_strict_handoff_certified_not_gap_closure", + "checkedRowCount": 2, + "passCount": 2, + "failCount": 0, + "topContinuation": 782, + "contrastContinuation": 1232, + "topLaneIndex": 15, + "contrastLaneIndex": 24, + "netExtraRepairsForTop": 2, + "topOnlyMissCount": 0, + "contrastOnlyMissCount": 2, + "topRepairedPredictedFamilyCount": 242, + "contrastRepairedPredictedFamilyCount": 240, + "checks": { + "strictDominancePairPresent": true, + "pairwiseDeltaPresent": true, + "topContinuationIs782": true, + "contrastContinuationIs1232": true, + "topRepairsTwoMorePredictedRows": true, + "noTopOnlyMissRows": true, + "contrastOnlyMissRowsAreTwo": true, + "strictRowsCoveredBySymbolicSchema": true, + "rowChecksPass": true + }, + "failedChecks": [], + "rowChecks": [ + { + "familyIndex": 104, + "representative": 681558029, + "tupleKey": "4, 7^2, 41^2, 9, 17^2, 11^2", + "witnessSquareModulus": 1369, + "laneEquation": "500*m ≡ 1048 (mod 1369)", + "laneIndexResidue": 24, + "laneIndexPeriod": 1369, + "missedLaneIndex": 24, + "repairedLaneIndex": 15, + "status": "passed", + "checks": { + "symbolicSchemaInstancePresent": true, + "missedContinuationIs1232": true, + "repairedContinuationIs782": true, + "missedLaneIndexIs24": true, + "repairedLaneIndexIs15": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true + }, + "failedChecks": [] + }, + { + "familyIndex": 187, + "representative": 1256825183, + "tupleKey": "9, 7^2, 4, 13^2, 23^2, 11^2", + "witnessSquareModulus": 289, + "laneEquation": "83*m ≡ 258 (mod 289)", + "laneIndexResidue": 24, + "laneIndexPeriod": 289, + "missedLaneIndex": 24, + "repairedLaneIndex": 15, + "status": "passed", + "checks": { + "symbolicSchemaInstancePresent": true, + "missedContinuationIs1232": true, + "repairedContinuationIs782": true, + "missedLaneIndexIs24": true, + "repairedLaneIndexIs15": true, + "missedLaneHitsBadClass": true, + "repairedLaneAvoidsBadClass": true + }, + "failedChecks": [] + } + ], + "failedRows": [], + "strictRows": [ + { + "familyIndex": 104, + "representative": 681558029, + "tupleKey": "4, 7^2, 41^2, 9, 17^2, 11^2", + "repairValue": 839679491729, + "squareWitnesses": [ + 1369 + ], + "missedLaneIndex": 24, + "repairedLaneIndex": 15 + }, + { + "familyIndex": 187, + "representative": 1256825183, + "tupleKey": "9, 7^2, 4, 13^2, 23^2, 11^2", + "repairValue": 1548408625457, + "squareWitnesses": [ + 289 + ], + "missedLaneIndex": 24, + "repairedLaneIndex": 15 + } + ], + "conclusion": "The strict 782 > 1232 handoff is certified on the current finite menu: 782 repairs exactly two predicted rows that 1232 misses, 1232 repairs no predicted row that 782 misses, and both strict rows are explained by the symbolic mod-50 bad-lane schema.", + "theoremBoundary": { + "finiteMenuHandoffClaim": true, + "allNFiniteGapClosureClaim": false, + "reason": "This packet connects the symbolic bad-lane schema to the finite exchange surface, but it does not prove that all post-11300 candidates are controlled by the strict handoff family." + }, + "nextProofObligations": [ + "Use the strict handoff packet as theorem-side guidance for the next local exact verifier rollout beyond 11300.", + "If exact verification finds a new boundary row, replay it through the bad-lane schema before widening search.", + "Do not claim all-N closure from the 782 > 1232 handoff without a separate coverage theorem over all relevant square witnesses." + ] + }, + "structuralLiftAtomicSurface": { + "surfaceId": "p848_structural_lift_atomic_surface_v1", + "status": "active", + "canonicalSurface": "FORMALIZATION_WORK.currentWork", + "role": "atomic_proof_obligation_surface", + "evidenceArtifact": { + "path": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.json", + "status": "structural_lift_obligation_packet_ready", + "minedExactRowCount": 64, + "primaryExactPrimes": [ + 13, + 17 + ], + "nextTheoremLane": "formalize_cross_side_matching_bound_then_exact_prime_margin_lift" + }, + "matchingPatternArtifact": { + "path": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json", + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 13, + "witnessRowCount": 12, + "minMatchingSlack": 19 + }, + "matchingPatternArtifacts": [ + { + "path": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json", + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 13, + "witnessRowCount": 12, + "minMatchingSlack": 19 + }, + { + "path": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.json", + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 17, + "witnessRowCount": 12, + "minMatchingSlack": 95 + } + ], + "referenceBacklog": { + "path": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json", + "role": "non_canonical_reference_backlog", + "note": "The checklist is a map of possible sub-lemmas. The active theorem lane is the single atomic obligation surfaced here." + }, + "activePacket": { + "packetId": "D_matching_lower_bounds", + "title": "Matching Lower Bounds", + "goal": "Replace Hopcroft-Karp computation with symbolic matching constructions." + }, + "requestedActiveAtom": { + "obligationId": "D2_p13_matching_lower_bound", + "status": "next", + "statement": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality." + }, + "activeAtom": { + "obligationId": "D2_p13_matching_lower_bound", + "status": "in_progress", + "statement": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=13 family row fails the claimed lower bound." + }, + "targetAtom": { + "obligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "status": "blocked_by_D2_D3", + "statement": "If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "dependsOn": [ + "C6_mixed_clique_matching_formula", + "D2_p13_matching_lower_bound", + "D3_p17_matching_lower_bound" + ], + "proofType": "inequality_substitution", + "falsifierBoundary": "The matching lower bound is substituted with the wrong inequality direction." + }, + "dischargedAtoms": [ + { + "obligationId": "C1_same_side_base_clique", + "status": "proved_by_mod25_identity", + "checkerId": "p848_C1_same_side_base_clique_checker_v1", + "conclusion": "The same-side parts of the mixed-base compatibility graph are cliques; only cross-side edges need the missing-cross graph analysis." + }, + { + "obligationId": "C2_two_cliques_plus_cross_edges", + "status": "proved_by_c1_partition_decomposition", + "checkerId": "p848_C2_two_cliques_plus_cross_edges_checker_v1", + "conclusion": "The mixed-base compatible graph is a two-clique/co-bipartite graph; the next theorem atom only needs to name the missing cross-edge bipartite graph." + }, + { + "obligationId": "C3_missing_cross_graph_definition", + "status": "proved_by_definition", + "checkerId": "p848_C3_missing_cross_graph_definition_checker_v1", + "conclusion": "The missing-cross graph H_{x,N} is a well-defined bipartite graph on the B7/B18 compatible partition with edges exactly opposite to cross compatibility." + }, + { + "obligationId": "C4_clique_to_vertex_cover_duality", + "status": "proved_by_clique_vertex_cover_complement", + "checkerId": "p848_C4_clique_to_vertex_cover_duality_checker_v1", + "conclusion": "Mixed-base clique maximization is equivalent to deleting a minimum vertex cover from the missing-cross graph." + }, + { + "obligationId": "C5_konig_matching_reduction", + "status": "proved_by_konig_theorem", + "checkerId": "p848_C5_konig_matching_reduction_checker_v1", + "conclusion": "The minimum vertex cover term in C4 may be replaced by the maximum matching size of H_{x,N}." + }, + { + "obligationId": "C6_mixed_clique_matching_formula", + "status": "proved_by_vertex_cover_konig_composition", + "checkerId": "p848_C6_mixed_clique_matching_formula_checker_v1", + "conclusion": "The verifier Hopcroft-Karp quantity has now been promoted to a theorem-facing graph formula." + }, + { + "obligationId": "D1_residue_block_matching_injection", + "status": "bounded_matching_saturation_extraction_certified", + "checkerId": "p848_D1_matching_saturation_bound_checker_v1", + "conclusion": "All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row." + }, + { + "obligationId": "D2_p13_split_core_witness_extraction", + "status": "bounded_split_core_witness_certified", + "checkerId": "p848_D2_p13_split_core_witness_checker_v1", + "conclusion": "The tight p=13 sample is reduced to 3 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side." + }, + { + "obligationId": "D3_p17_split_core_witness_extraction", + "status": "bounded_split_core_witness_certified", + "checkerId": "p848_D3_p17_split_core_witness_checker_v1", + "conclusion": "The tight p=17 sample is reduced to 2 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side." + } + ], + "proofPackets": { + "C1_same_side_base_clique": { + "checkerId": "p848_C1_same_side_base_clique_checker_v1", + "obligationId": "C1_same_side_base_clique", + "status": "proved_by_mod25_identity", + "checkedRowCount": 2, + "passCount": 2, + "failCount": 0, + "statement": "Inside one principal base side, compatible base vertices form a clique for the fixed outsider graph considered by the verifier.", + "scope": { + "problemId": "848", + "universalSameSideClaim": true, + "dependsOnOutsider": false, + "dependsOnN": false, + "principalBaseResiduesModulo25": [ + 7, + 18 + ] + }, + "hypotheses": [ + "u and v are both in the 7 mod 25 principal base side, or both in the 18 mod 25 principal base side.", + "The verifier graph uses non-squarefree pair compatibility: an edge is present when u*v + 1 is not squarefree." + ], + "proof": [ + "If u and v are both 7 mod 25, then u*v + 1 is congruent to 7^2 + 1 = 50, hence 0 mod 25.", + "If u and v are both 18 mod 25, then u*v + 1 is congruent to 18^2 + 1 = 325, hence 0 mod 25.", + "Because 25 = 5^2 is a square divisor, u*v + 1 is not squarefree in either same-side case.", + "Therefore every pair of same-side principal base vertices has an edge, so each same-side compatible vertex set is a clique." + ], + "residueChecks": [ + { + "sideId": "B7", + "residue": 7, + "productResidueModulo25": 24, + "productPlusOneResidueModulo25": 0 + }, + { + "sideId": "B18", + "residue": 18, + "productResidueModulo25": 24, + "productPlusOneResidueModulo25": 0 + } + ], + "failedRows": [], + "conclusion": "The same-side parts of the mixed-base compatibility graph are cliques; only cross-side edges need the missing-cross graph analysis.", + "falsifierBoundary": "A falsifier would need a pair of same-side principal base residues whose product plus one is not divisible by 25, but both residue checks are 0 mod 25." + }, + "C2_two_cliques_plus_cross_edges": { + "checkerId": "p848_C2_two_cliques_plus_cross_edges_checker_v1", + "obligationId": "C2_two_cliques_plus_cross_edges", + "status": "proved_by_c1_partition_decomposition", + "checkedRowCount": 5, + "passCount": 5, + "failCount": 0, + "statement": "For fixed outsider x, the compatible mixed-base graph is one clique on B7-compatible vertices, one clique on B18-compatible vertices, plus arbitrary cross edges.", + "scope": { + "problemId": "848", + "universalInN": true, + "universalInOutsider": true, + "principalBaseResiduesModulo25": [ + 7, + 18 + ], + "boundedVerifierEvidenceRange": "7307..7600" + }, + "dependencies": [ + "p848_C1_same_side_base_clique_checker_v1", + "definition_of_mixed_base_compatible_vertex_sets" + ], + "hypotheses": [ + "For fixed outsider x and cutoff N, L is the set of x-compatible principal base vertices congruent to 7 mod 25.", + "For fixed outsider x and cutoff N, R is the set of x-compatible principal base vertices congruent to 18 mod 25.", + "The mixed-base graph has vertex set L union R and an edge exactly when the corresponding pair relation is compatible in the verifier graph.", + "C1 has proved that every same-side pair inside L or inside R is an edge." + ], + "proof": [ + "The vertex set is partitioned into the two principal compatible sides L and R by residue modulo 25.", + "By C1, every pair of vertices inside L is adjacent, and every pair of vertices inside R is adjacent.", + "No additional same-side obstruction remains after C1; all non-forced edge information lies between L and R.", + "Therefore the graph is exactly two cliques, L and R, plus whatever cross edges the pair compatibility relation supplies." + ], + "proofChecks": [ + { + "checkId": "C1_dependency_discharged", + "passed": true, + "evidence": "p848_C1_same_side_base_clique_checker_v1" + }, + { + "checkId": "principal_side_partition", + "passed": true, + "evidence": { + "leftSide": "B7-compatible vertices", + "rightSide": "B18-compatible vertices", + "principalResiduesModulo25": [ + 7, + 18 + ] + } + }, + { + "checkId": "same_side_edges_complete_by_C1", + "passed": true, + "evidence": [ + { + "sideId": "B7", + "residue": 7, + "productResidueModulo25": 24, + "productPlusOneResidueModulo25": 0 + }, + { + "sideId": "B18", + "residue": 18, + "productResidueModulo25": 24, + "productPlusOneResidueModulo25": 0 + } + ] + }, + { + "checkId": "cross_edges_are_the_only_unfixed_edges", + "passed": true, + "evidence": "After partitioning into B7 and B18 sides and applying C1 on each side, the only pair relations not forced complete are B7 x B18 cross pairs." + }, + { + "checkId": "verifier_boundary_uses_two_clique_reduction", + "passed": true, + "evidence": "For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges. bounded_outsider_clique_full_mixed_base_structural_verifier formalize_cross_side_matching_bound_then_exact_prime_margin_lift" + } + ], + "failedChecks": [], + "conclusion": "The mixed-base compatible graph is a two-clique/co-bipartite graph; the next theorem atom only needs to name the missing cross-edge bipartite graph.", + "falsifierBoundary": "A falsifier must either break C1 on a same-side pair or exhibit a compatible mixed-base vertex outside the B7/B18 partition." + }, + "C3_missing_cross_graph_definition": { + "checkerId": "p848_C3_missing_cross_graph_definition_checker_v1", + "obligationId": "C3_missing_cross_graph_definition", + "status": "proved_by_definition", + "checkedRowCount": 4, + "passCount": 4, + "failCount": 0, + "statement": "Define H_{x,N} as the bipartite graph whose edges are precisely missing cross edges between compatible B7 and B18 vertices.", + "scope": { + "problemId": "848", + "universalInN": true, + "universalInOutsider": true, + "graphPartitions": [ + "B7-compatible vertices", + "B18-compatible vertices" + ], + "boundedVerifierEvidenceRange": "7307..7600" + }, + "dependencies": [ + "p848_C2_two_cliques_plus_cross_edges_checker_v1" + ], + "hypotheses": [ + "C2 has decomposed the mixed-base compatible graph into two same-side cliques L and R plus cross edges.", + "Cross compatibility is evaluated only for pairs (l,r) with l in L and r in R.", + "A missing cross edge means that the pair (l,r) is not an edge of the compatible graph." + ], + "definition": { + "vertexSet": "V(H_{x,N}) = L union R", + "edgeSet": "E(H_{x,N}) = {{l,r}: l in L, r in R, and {l,r} is not a compatible cross edge}", + "equivalentArithmeticSign": "Because compatible edges are non-squarefree pair relations, H contains (l,r) exactly when l*r+1 is squarefree for the verifier relation." + }, + "proof": [ + "C2 leaves only cross pairs between L and R as possible obstructions to cliquehood.", + "Put exactly those obstructing cross pairs into H_{x,N}.", + "Every edge of H has one endpoint in L and one endpoint in R, so H is bipartite by construction.", + "The sign convention is explicit: H records missing compatible cross edges, not present compatible cross edges." + ], + "proofChecks": [ + { + "checkId": "C2_dependency_discharged", + "passed": true, + "evidence": "p848_C2_two_cliques_plus_cross_edges_checker_v1" + }, + { + "checkId": "missing_cross_graph_is_bipartite_by_definition", + "passed": true, + "evidence": { + "leftPartition": "L = B7-compatible vertices", + "rightPartition": "R = B18-compatible vertices", + "noSameSideMissingEdgesIncluded": true + } + }, + { + "checkId": "edge_sign_is_missing_compatibility", + "passed": true, + "evidence": "An edge (l,r) belongs to H_{x,N} exactly when l in L, r in R, and l*r+1 is squarefree, i.e. the cross pair is missing from the compatible graph." + }, + { + "checkId": "verifier_boundary_names_missing_cross_edges", + "passed": true, + "evidence": "For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges. For each threatening outsider, the missing cross-edge graph between the 7 mod 25 and 18 mod 25 compatible base sides has a matching large enough to force mixedCliqueSize below the strict base threshold." + } + ], + "failedChecks": [], + "conclusion": "The missing-cross graph H_{x,N} is a well-defined bipartite graph on the B7/B18 compatible partition with edges exactly opposite to cross compatibility.", + "falsifierBoundary": "A falsifier must show a same-side H edge or a cross pair whose H membership uses the wrong compatibility sign." + }, + "C4_clique_to_vertex_cover_duality": { + "checkerId": "p848_C4_clique_to_vertex_cover_duality_checker_v1", + "obligationId": "C4_clique_to_vertex_cover_duality", + "status": "proved_by_clique_vertex_cover_complement", + "checkedRowCount": 4, + "passCount": 4, + "failCount": 0, + "statement": "A mixed-base clique equals all compatible vertices minus a vertex cover of H_{x,N}; hence max clique size is |L| + |R| minus minimum vertex cover size.", + "dependencies": [ + "p848_C3_missing_cross_graph_definition_checker_v1" + ], + "hypotheses": [ + "The mixed-base compatible graph is two cliques L and R plus cross edges.", + "H_{x,N} is the bipartite graph of missing cross edges between L and R.", + "A vertex cover of H_{x,N} is a set of vertices meeting every missing cross edge." + ], + "proof": [ + "Let K be a clique in the compatible graph and S be the complement of K in L union R.", + "If an H edge had both endpoints outside S, then both endpoints would lie in K but would be a missing compatible cross edge, contradicting cliquehood.", + "Thus S is a vertex cover of H.", + "Conversely, if S is a vertex cover of H, then K = (L union R) minus S contains no missing cross edge, and same-side pairs are already complete, so K is a clique.", + "The correspondence reverses cardinality, giving maxClique = |L| + |R| - minVertexCover(H)." + ], + "proofChecks": [ + { + "checkId": "C3_dependency_discharged", + "passed": true, + "evidence": "p848_C3_missing_cross_graph_definition_checker_v1" + }, + { + "checkId": "clique_complement_hits_every_missing_cross_edge", + "passed": true, + "evidence": "If a clique kept both endpoints of a missing cross edge, those endpoints would be a non-edge in the compatible graph." + }, + { + "checkId": "vertex_cover_complement_is_clique", + "passed": true, + "evidence": "If removed vertices cover every missing cross edge, then no missing cross edge remains among kept vertices; same-side pairs are already cliques by C2." + }, + { + "checkId": "max_min_cardinality_duality", + "passed": true, + "evidence": "Maximizing kept vertices is equivalent to minimizing removed vertices over vertex covers of H_{x,N}." + } + ], + "failedChecks": [], + "conclusion": "Mixed-base clique maximization is equivalent to deleting a minimum vertex cover from the missing-cross graph.", + "falsifierBoundary": "A falsifier must exhibit a clique whose complement misses an H edge, or a vertex cover whose complement is not a clique." + }, + "C5_konig_matching_reduction": { + "checkerId": "p848_C5_konig_matching_reduction_checker_v1", + "obligationId": "C5_konig_matching_reduction", + "status": "proved_by_konig_theorem", + "checkedRowCount": 3, + "passCount": 3, + "failCount": 0, + "statement": "Because H_{x,N} is bipartite, minimum vertex cover size equals maximum matching size.", + "dependencies": [ + "p848_C3_missing_cross_graph_definition_checker_v1", + "Konig's theorem for finite bipartite graphs" + ], + "hypotheses": [ + "H_{x,N} is finite because it is built from vertices <= N.", + "H_{x,N} is bipartite with parts L and R by C3.", + "Konig's theorem is available as a standard graph-theory lemma for finite bipartite graphs." + ], + "proof": [ + "C3 constructs H with all edges crossing between L and R.", + "Therefore H satisfies the finite bipartite hypotheses of Konig's theorem.", + "Apply Konig's theorem to replace minVertexCover(H) with maxMatching(H)." + ], + "proofChecks": [ + { + "checkId": "C3_dependency_discharged", + "passed": true, + "evidence": "p848_C3_missing_cross_graph_definition_checker_v1" + }, + { + "checkId": "H_is_bipartite", + "passed": true, + "evidence": "Every H edge runs between the B7-compatible side L and the B18-compatible side R." + }, + { + "checkId": "konig_theorem_applies", + "passed": true, + "evidence": "For every finite bipartite graph, minimum vertex cover size equals maximum matching size." + } + ], + "failedChecks": [], + "conclusion": "The minimum vertex cover term in C4 may be replaced by the maximum matching size of H_{x,N}.", + "falsifierBoundary": "A falsifier must show H is not bipartite/finite or that the invoked Konig theorem dependency is unavailable." + }, + "C6_mixed_clique_matching_formula": { + "checkerId": "p848_C6_mixed_clique_matching_formula_checker_v1", + "obligationId": "C6_mixed_clique_matching_formula", + "status": "proved_by_vertex_cover_konig_composition", + "checkedRowCount": 5, + "passCount": 5, + "failCount": 0, + "statement": "sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).", + "dependencies": [ + "p848_C4_clique_to_vertex_cover_duality_checker_v1", + "p848_C5_konig_matching_reduction_checker_v1" + ], + "hypotheses": [ + "C4 proves max mixed clique size equals |L| + |R| minus minVertexCover(H).", + "C5 proves minVertexCover(H) equals maxMatching(H)." + ], + "proof": [ + "Start from the C4 identity maxClique = |L| + |R| - minVertexCover(H).", + "Substitute minVertexCover(H) = maxMatching(H) from C5.", + "The resulting identity is sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N})." + ], + "rowChecks": [ + { + "checkId": "worst_exact_row_matches_formula", + "N": 7343, + "p": 13, + "outsider": 5309, + "leftSize": 108, + "rightSize": 112, + "maxMatchingSize": 108, + "verifierCliqueSize": 112, + "formulaCliqueSize": 112, + "passed": true + } + ], + "proofChecks": [ + { + "checkId": "C4_dependency_discharged", + "passed": true, + "evidence": "p848_C4_clique_to_vertex_cover_duality_checker_v1" + }, + { + "checkId": "C5_dependency_discharged", + "passed": true, + "evidence": "p848_C5_konig_matching_reduction_checker_v1" + }, + { + "checkId": "formula_composes_C4_and_C5", + "passed": true, + "evidence": "maxClique = |L| + |R| - minVertexCover(H) and minVertexCover(H) = maxMatching(H)." + }, + { + "checkId": "verifier_row_formula_replay_available", + "passed": true, + "evidence": [ + { + "checkId": "worst_exact_row_matches_formula", + "N": 7343, + "p": 13, + "outsider": 5309, + "leftSize": 108, + "rightSize": 112, + "maxMatchingSize": 108, + "verifierCliqueSize": 112, + "formulaCliqueSize": 112, + "passed": true + } + ] + } + ], + "failedChecks": [], + "failedRows": [], + "conclusion": "The verifier Hopcroft-Karp quantity has now been promoted to a theorem-facing graph formula.", + "falsifierBoundary": "A falsifier must break C4, break C5, or find a verifier row where |L| + |R| - matching disagrees with sMixed." + }, + "D1_residue_block_matching_injection": { + "checkerId": "p848_D1_matching_saturation_bound_checker_v1", + "obligationId": "D1_residue_block_matching_injection", + "status": "bounded_matching_saturation_extraction_certified", + "checkedRowCount": 1739, + "passCount": 1739, + "failCount": 0, + "statement": "Extract the current D-lane matching target: each bounded exact mixed-base threatening-outsider row has matching at least K(N,x), and the verifier matching saturates the smaller compatible side.", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "boundedVerifierEvidenceRange": "7307..7600", + "boundedRowCount": 1733, + "sourceRowKind": "all_bounded_threatening_outsiders", + "observedPrimes": [ + 13, + 17 + ], + "role": "bounded_extraction_packet_for_symbolic_D2_D3" + }, + "dependencies": [ + "p848_C6_mixed_clique_matching_formula_checker_v1", + "FULL_MIXED_BASE_STRUCTURAL_VERIFIER.liftMiningRows" + ], + "hypotheses": [ + "C6 has promoted the mixed-base clique size to |L| + |R| - maxMatching(H_{x,N}).", + "A strict mixed-base pass needs |L| + |R| - maxMatching(H_{x,N}) <= strictBaseThreshold - 1.", + "Equivalently, it is enough to prove maxMatching(H_{x,N}) >= |L| + |R| - strictBaseThreshold + 1.", + "The current packet is bounded to the exact mixed-base threatening-outsider rows emitted by the repo-owned full mixed-base structural verifier." + ], + "proof": [ + "For each exact mixed-base threatening-outsider row, compute K(N,x) = |L| + |R| - strictBaseThreshold + 1.", + "Replay the C6 formula against the verifier row to ensure |L| + |R| - matching equals the recorded mixed clique size.", + "Check that the recorded maximum matching is at least K(N,x).", + "Check the stronger bounded pattern that the recorded maximum matching saturates the smaller of the two compatible sides.", + "This certifies the bounded extraction target and routes the all-N burden to symbolic lower-bound packets D2 and D3." + ], + "rowCheckSample": [ + { + "N": 7343, + "p": 13, + "outsider": 5309, + "requiredMatchingLowerBound": 89, + "actualMatching": 108, + "matchingSlack": 19, + "smallerSideSize": 108 + }, + { + "N": 7307, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + }, + { + "N": 7318, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + }, + { + "N": 7318, + "p": 13, + "outsider": 5309, + "requiredMatchingLowerBound": 88, + "actualMatching": 108, + "matchingSlack": 20, + "smallerSideSize": 108 + }, + { + "N": 7337, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + } + ], + "rowChecksOmitted": 1728, + "proofChecks": [ + { + "checkId": "C6_dependency_discharged", + "passed": true, + "evidence": "p848_C6_mixed_clique_matching_formula_checker_v1" + }, + { + "checkId": "exact_mixed_lift_rows_available", + "passed": true, + "evidence": { + "rowCount": 1733, + "verifierLiftMiningRowCount": 64, + "verifierThreatLiftMiningRowCount": 1733, + "sourceRowKind": "all_bounded_threatening_outsiders" + } + }, + { + "checkId": "primary_exact_primes_are_current_D_lane", + "passed": true, + "evidence": [ + 13, + 17 + ] + }, + { + "checkId": "matching_lower_bound_formula_extracted", + "passed": true, + "evidence": "K(N,x) = |L| + |R| - strictBaseThreshold + 1 is the matching lower bound needed for strict mixed-clique margin." + }, + { + "checkId": "all_rows_meet_required_matching_bound", + "passed": true, + "evidence": { + "primeSummaries": [ + { + "p": 13, + "rowCount": 1285, + "minRequiredMatchingLowerBound": 26, + "maxRequiredMatchingLowerBound": 90, + "minActualMatching": 79, + "maxActualMatching": 111, + "minMatchingSlack": 19, + "allRowsSaturateSmallerSide": true, + "allRowsMeetRequiredLowerBound": true + }, + { + "p": 17, + "rowCount": 448, + "minRequiredMatchingLowerBound": 1, + "maxRequiredMatchingLowerBound": 14, + "minActualMatching": 103, + "maxActualMatching": 112, + "minMatchingSlack": 95, + "allRowsSaturateSmallerSide": true, + "allRowsMeetRequiredLowerBound": true + } + ], + "tightestRows": [ + { + "N": 7343, + "p": 13, + "outsider": 5309, + "requiredMatchingLowerBound": 89, + "actualMatching": 108, + "matchingSlack": 19, + "smallerSideSize": 108 + }, + { + "N": 7307, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + }, + { + "N": 7318, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + }, + { + "N": 7318, + "p": 13, + "outsider": 5309, + "requiredMatchingLowerBound": 88, + "actualMatching": 108, + "matchingSlack": 20, + "smallerSideSize": 108 + }, + { + "N": 7337, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + } + ] + } + }, + { + "checkId": "all_rows_saturate_smaller_side", + "passed": true, + "evidence": [ + { + "p": 13, + "rowCount": 1285, + "minRequiredMatchingLowerBound": 26, + "maxRequiredMatchingLowerBound": 90, + "minActualMatching": 79, + "maxActualMatching": 111, + "minMatchingSlack": 19, + "allRowsSaturateSmallerSide": true, + "allRowsMeetRequiredLowerBound": true + }, + { + "p": 17, + "rowCount": 448, + "minRequiredMatchingLowerBound": 1, + "maxRequiredMatchingLowerBound": 14, + "minActualMatching": 103, + "maxActualMatching": 112, + "minMatchingSlack": 95, + "allRowsSaturateSmallerSide": true, + "allRowsMeetRequiredLowerBound": true + } + ] + } + ], + "failedChecks": [], + "failedRows": [], + "primeSummaries": [ + { + "p": 13, + "rowCount": 1285, + "minRequiredMatchingLowerBound": 26, + "maxRequiredMatchingLowerBound": 90, + "minActualMatching": 79, + "maxActualMatching": 111, + "minMatchingSlack": 19, + "allRowsSaturateSmallerSide": true, + "allRowsMeetRequiredLowerBound": true + }, + { + "p": 17, + "rowCount": 448, + "minRequiredMatchingLowerBound": 1, + "maxRequiredMatchingLowerBound": 14, + "minActualMatching": 103, + "maxActualMatching": 112, + "minMatchingSlack": 95, + "allRowsSaturateSmallerSide": true, + "allRowsMeetRequiredLowerBound": true + } + ], + "tightestRows": [ + { + "N": 7343, + "p": 13, + "outsider": 5309, + "requiredMatchingLowerBound": 89, + "actualMatching": 108, + "matchingSlack": 19, + "smallerSideSize": 108 + }, + { + "N": 7307, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + }, + { + "N": 7318, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + }, + { + "N": 7318, + "p": 13, + "outsider": 5309, + "requiredMatchingLowerBound": 88, + "actualMatching": 108, + "matchingSlack": 20, + "smallerSideSize": 108 + }, + { + "N": 7337, + "p": 13, + "outsider": 4831, + "requiredMatchingLowerBound": 85, + "actualMatching": 105, + "matchingSlack": 20, + "smallerSideSize": 105 + } + ], + "conclusion": "All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row.", + "falsifierBoundary": "A refreshed verifier row falsifies this bounded extraction if matching < |L| + |R| - strictBaseThreshold + 1, if the C6 formula replay disagrees, or if the smaller-side saturation pattern fails. This is not yet the all-N symbolic matching proof." + }, + "D2_p13_split_core_witness_extraction": { + "checkerId": "p848_D2_p13_split_core_witness_checker_v1", + "obligationId": "D2_p13_split_core_witness_extraction", + "parentObligationId": "D2_p13_matching_lower_bound", + "status": "bounded_split_core_witness_certified", + "checkedRowCount": 12, + "passCount": 12, + "failCount": 0, + "statement": "The tight p=13 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "targetPrime": 13, + "sourceArtifact": "MATCHING_PATTERN_MINER.json", + "sourceAssessedRange": "7307..7600", + "witnessRowCount": 12, + "splitProfileCount": 3, + "role": "bounded_split_core_witness_for_symbolic_D2_lift" + }, + "dependencies": [ + "p848_D1_matching_saturation_bound_checker_v1", + "p848_D2_p13_matching_lower_bound_candidate_v1", + "MATCHING_PATTERN_MINER.patternSummary.splitProfiles" + ], + "hypotheses": [ + "D1 has extracted the p=13 matching lower-bound target K(N,x).", + "The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=13 rows.", + "The sampled tight rows split by outsider residue modulo 13^2, outsider residue modulo 25, and which side is smaller.", + "Within each split profile, the common matching core is a matching present in every sampled row of that profile." + ], + "proof": [ + "Read the p=13 split profiles from MATCHING_PATTERN_MINER.patternSummary.", + "For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.", + "Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.", + "Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.", + "This does not discharge D2 universally; it turns D2 into explicit split symbolic subgoals whose common cores must be proved to persist by residue/block argument." + ], + "proofChecks": [ + { + "checkId": "D1_dependency_discharged", + "passed": true, + "evidence": "p848_D1_matching_saturation_bound_checker_v1" + }, + { + "checkId": "p13_candidate_ready", + "passed": true, + "evidence": "p848_D2_p13_matching_lower_bound_candidate_v1" + }, + { + "checkId": "matching_pattern_artifact_ready", + "passed": true, + "evidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 13, + "witnessRowCount": 12 + } + }, + { + "checkId": "matching_reconstruction_agrees_with_verifier", + "passed": true, + "evidence": true + }, + { + "checkId": "all_witnesses_saturate_smaller_side", + "passed": true, + "evidence": [ + { + "key": "side7", + "count": 7 + }, + { + "key": "side18", + "count": 5 + } + ] + }, + { + "checkId": "split_profiles_available", + "passed": true, + "evidence": { + "splitProfileCount": 3, + "commonAcrossAllProfiles": 0, + "proofHeuristic": "The tight-row witnesses do not share one common matching core; split the symbolic construction by outsider residue and saturated side." + } + }, + { + "checkId": "split_common_cores_meet_required_K", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "commonMatchingPairCount": 108, + "maxRequiredMatchingLowerBound": 89 + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "commonMatchingPairCount": 105, + "maxRequiredMatchingLowerBound": 85 + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "commonMatchingPairCount": 108, + "maxRequiredMatchingLowerBound": 88 + } + ] + }, + { + "checkId": "split_common_core_pairs_exported", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "commonMatchingPairCount": 108, + "exportedPairCount": 108 + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "commonMatchingPairCount": 105, + "exportedPairCount": 105 + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "commonMatchingPairCount": 108, + "exportedPairCount": 108 + } + ] + }, + { + "checkId": "split_common_cores_saturate_smaller_side_on_tight_rows", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "commonMatchingPairCount": 108, + "minSmallerSideSize": 108 + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "commonMatchingPairCount": 105, + "minSmallerSideSize": 105 + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "commonMatchingPairCount": 108, + "minSmallerSideSize": 108 + } + ] + } + ], + "failedChecks": [], + "profileChecks": [ + { + "checkId": "D2_split_core_outP2=70_out25=9_smaller=side7", + "groupKey": "outP2=70|out25=9|smaller=side7", + "witnessCount": 6, + "minN": 7318, + "maxN": 7368, + "minRequiredMatchingLowerBound": 88, + "maxRequiredMatchingLowerBound": 89, + "minReconstructedMatchingSize": 108, + "maxReconstructedMatchingSize": 108, + "minSmallerSideSize": 108, + "maxSmallerSideSize": 108, + "minMatchingSlack": 19, + "commonMatchingPairCount": 108, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 38, + "rightModP2": 74, + "leftModP": 12, + "rightModP": 9, + "productPlusOneModP2": 109 + }, + { + "leftValue": 307, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 138, + "rightModP2": 99, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 143 + }, + { + "leftValue": 407, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 69, + "rightModP2": 5, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 8 + }, + { + "leftValue": 507, + "rightValue": 368, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 0, + "rightModP2": 30, + "leftModP": 0, + "rightModP": 4, + "productPlusOneModP2": 1 + }, + { + "leftValue": 532, + "rightValue": 443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 25, + "rightModP2": 105, + "leftModP": 12, + "rightModP": 1, + "productPlusOneModP2": 91 + }, + { + "leftValue": 607, + "rightValue": 543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 100, + "rightModP2": 36, + "leftModP": 9, + "rightModP": 10, + "productPlusOneModP2": 52 + }, + { + "leftValue": 707, + "rightValue": 568, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 31, + "rightModP2": 61, + "leftModP": 5, + "rightModP": 9, + "productPlusOneModP2": 33 + }, + { + "leftValue": 757, + "rightValue": 718, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 81, + "rightModP2": 42, + "leftModP": 3, + "rightModP": 3, + "productPlusOneModP2": 23 + }, + { + "leftValue": 807, + "rightValue": 643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 131, + "rightModP2": 136, + "leftModP": 1, + "rightModP": 6, + "productPlusOneModP2": 72 + }, + { + "leftValue": 907, + "rightValue": 843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 62, + "rightModP2": 167, + "leftModP": 10, + "rightModP": 11, + "productPlusOneModP2": 46 + }, + { + "leftValue": 957, + "rightValue": 793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 112, + "rightModP2": 117, + "leftModP": 8, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 982, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 137, + "rightModP2": 67, + "leftModP": 7, + "rightModP": 2, + "productPlusOneModP2": 54 + }, + { + "leftValue": 1007, + "rightValue": 943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 162, + "rightModP2": 98, + "leftModP": 6, + "rightModP": 7, + "productPlusOneModP2": 160 + }, + { + "leftValue": 1107, + "rightValue": 1018, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 93, + "rightModP2": 4, + "leftModP": 2, + "rightModP": 4, + "productPlusOneModP2": 35 + }, + { + "leftValue": 1207, + "rightValue": 1068, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 24, + "rightModP2": 54, + "leftModP": 11, + "rightModP": 2, + "productPlusOneModP2": 114 + }, + { + "leftValue": 1307, + "rightValue": 1043, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 124, + "rightModP2": 29, + "leftModP": 7, + "rightModP": 3, + "productPlusOneModP2": 48 + }, + { + "leftValue": 1407, + "rightValue": 1143, + "leftMod25": 7, + "rightMod25": 18, 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"rightModP2": 121, + "leftModP": 9, + "rightModP": 4, + "productPlusOneModP2": 128 + }, + { + "leftValue": 6807, + "rightValue": 6643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 47, + "rightModP2": 52, + "leftModP": 8, + "rightModP": 0, + "productPlusOneModP2": 79 + }, + { + "leftValue": 6907, + "rightValue": 6668, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 147, + "rightModP2": 77, + "leftModP": 4, + "rightModP": 12, + "productPlusOneModP2": 166 + }, + { + "leftValue": 6957, + "rightValue": 6593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 28, + "rightModP2": 2, + "leftModP": 2, + "rightModP": 2, + "productPlusOneModP2": 57 + }, + { + "leftValue": 7007, + "rightValue": 6743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 78, + "rightModP2": 152, + "leftModP": 0, + "rightModP": 9, + "productPlusOneModP2": 27 + }, + { + "leftValue": 7032, + "rightValue": 6818, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 103, + "rightModP2": 58, + "leftModP": 12, + "rightModP": 6, + "productPlusOneModP2": 60 + }, + { + "leftValue": 7107, + "rightValue": 6843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 9, + "rightModP2": 83, + "leftModP": 9, + "rightModP": 5, + "productPlusOneModP2": 72 + }, + { + "leftValue": 7207, + "rightValue": 6943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 109, + "rightModP2": 14, + "leftModP": 5, + "rightModP": 1, + "productPlusOneModP2": 6 + }, + { + "leftValue": 7232, + "rightValue": 7043, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 134, + "rightModP2": 114, + "leftModP": 4, + "rightModP": 10, + "productPlusOneModP2": 67 + }, + { + "leftValue": 7307, + "rightValue": 7143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 40, + "rightModP2": 45, + "leftModP": 1, + "rightModP": 6, + "productPlusOneModP2": 111 + } + ], + "minMatchingSlack": 20 + }, + "falsifierBoundary": "A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size." + } + ], + "conclusion": "The tight p=13 sample is reduced to 3 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side.", + "falsifierBoundary": "A refreshed matching-pattern miner falsifies this bounded witness packet if a split profile has no common core, if the common core falls below max K(N,x), or if the split heuristic changes. D2 remains open until these split cores are proved symbolically." + }, + "D3_p17_split_core_witness_extraction": { + "checkerId": "p848_D3_p17_split_core_witness_checker_v1", + "obligationId": "D3_p17_split_core_witness_extraction", + "parentObligationId": "D3_p17_matching_lower_bound", + "status": "bounded_split_core_witness_certified", + "checkedRowCount": 11, + "passCount": 11, + "failCount": 0, + "statement": "The tight p=17 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "targetPrime": 17, + "sourceArtifact": "MATCHING_PATTERN_MINER_P17.json", + "sourceAssessedRange": "7307..7600", + "witnessRowCount": 12, + "splitProfileCount": 2, + "role": "bounded_split_core_witness_for_symbolic_D3_lift" + }, + "dependencies": [ + "p848_D1_matching_saturation_bound_checker_v1", + "p848_D3_p17_matching_lower_bound_candidate_v1", + "MATCHING_PATTERN_MINER_P17.patternSummary.splitProfiles" + ], + "hypotheses": [ + "D1 has extracted the p=17 matching lower-bound target K(N,x).", + "The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=17 rows.", + "The sampled tight rows split by outsider residue modulo 17^2, outsider residue modulo 25, and which side is smaller.", + "Within each split profile, the common matching core is a matching present in every sampled row of that profile." + ], + "proof": [ + "Read the p=17 split profiles from MATCHING_PATTERN_MINER_P17.patternSummary.", + "For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.", + "Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.", + "Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.", + "This does not discharge D3 universally; it turns D3 into explicit split symbolic subgoals whose common cores must be proved to persist by residue/block argument." + ], + "proofChecks": [ + { + "checkId": "D1_dependency_discharged", + "passed": true, + "evidence": "p848_D1_matching_saturation_bound_checker_v1" + }, + { + "checkId": "p17_candidate_ready", + "passed": true, + "evidence": "p848_D3_p17_matching_lower_bound_candidate_v1" + }, + { + "checkId": "matching_pattern_artifact_ready", + "passed": true, + "evidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 17, + "witnessRowCount": 12 + } + }, + { + "checkId": "matching_reconstruction_agrees_with_verifier", + "passed": true, + "evidence": true + }, + { + "checkId": "all_witnesses_saturate_smaller_side", + "passed": true, + "evidence": [ + { + "key": "side7", + "count": 10 + }, + { + "key": "side18", + "count": 2 + } + ] + }, + { + "checkId": "split_profiles_available", + "passed": true, + "evidence": { + "splitProfileCount": 2, + "commonAcrossAllProfiles": 4, + "proofHeuristic": "The tight-row witnesses share a nonempty stable matching core. Try proving saturation by extending this stable core across residue blocks, then handle boundary insertions separately." + } + }, + { + "checkId": "split_common_cores_meet_required_K", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "commonMatchingPairCount": 109, + "maxRequiredMatchingLowerBound": 14 + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "commonMatchingPairCount": 106, + "maxRequiredMatchingLowerBound": 11 + } + ] + }, + { + "checkId": "split_common_core_pairs_exported", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "commonMatchingPairCount": 109, + "exportedPairCount": 109 + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "commonMatchingPairCount": 106, + "exportedPairCount": 106 + } + ] + }, + { + "checkId": "split_common_cores_saturate_smaller_side_on_tight_rows", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "commonMatchingPairCount": 109, + "minSmallerSideSize": 109 + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "commonMatchingPairCount": 106, + "minSmallerSideSize": 106 + } + ] + } + ], + "failedChecks": [], + "profileChecks": [ + { + "checkId": "D3_split_core_outP2=38_out25=23_smaller=side7", + "groupKey": "outP2=38|out25=23|smaller=side7", + "witnessCount": 10, + "minN": 7307, + "maxN": 7393, + "minRequiredMatchingLowerBound": 12, + "maxRequiredMatchingLowerBound": 14, + "minReconstructedMatchingSize": 109, + "maxReconstructedMatchingSize": 109, + "minSmallerSideSize": 109, + "maxSmallerSideSize": 109, + "minMatchingSlack": 95, + "commonMatchingPairCount": 109, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 13 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + 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"leftModP": 11, + "rightModP": 1, + "productPlusOneModP2": 199 + }, + { + "leftValue": 6257, + "rightValue": 6418, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 188, + "rightModP2": 60, + "leftModP": 1, + "rightModP": 9, + "productPlusOneModP2": 10 + }, + { + "leftValue": 6357, + "rightValue": 6493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 288, + "rightModP2": 135, + "leftModP": 16, + "rightModP": 16, + "productPlusOneModP2": 155 + }, + { + "leftValue": 6382, + "rightValue": 6593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 24, + "rightModP2": 235, + "leftModP": 7, + "rightModP": 14, + "productPlusOneModP2": 150 + }, + { + "leftValue": 6457, + "rightValue": 6693, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 99, + "rightModP2": 46, + "leftModP": 14, + "rightModP": 12, + "productPlusOneModP2": 220 + }, + { + "leftValue": 6507, + "rightValue": 6643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 149, + "rightModP2": 285, + "leftModP": 13, + "rightModP": 13, + "productPlusOneModP2": 272 + }, + { + "leftValue": 6557, + "rightValue": 6868, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 199, + "rightModP2": 221, + "leftModP": 12, + "rightModP": 0, + "productPlusOneModP2": 52 + }, + { + "leftValue": 6657, + "rightValue": 6793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 10, + "rightModP2": 146, + "leftModP": 10, + "rightModP": 10, + "productPlusOneModP2": 16 + }, + { + "leftValue": 6757, + "rightValue": 6893, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 110, + "rightModP2": 246, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 184 + }, + { + "leftValue": 6832, + "rightValue": 6993, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 185, + "rightModP2": 57, + "leftModP": 15, + "rightModP": 6, + "productPlusOneModP2": 142 + }, + { + "leftValue": 6857, + "rightValue": 7193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 210, + "rightModP2": 257, + "leftModP": 6, + "rightModP": 2, + "productPlusOneModP2": 217 + }, + { + "leftValue": 6957, + "rightValue": 7093, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 21, + "rightModP2": 157, + "leftModP": 4, + "rightModP": 4, + "productPlusOneModP2": 119 + }, + { + "leftValue": 7057, + "rightValue": 7293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 121, + "rightModP2": 68, + "leftModP": 2, + "rightModP": 0, + "productPlusOneModP2": 137 + } + ], + "minMatchingSlack": 96 + }, + "falsifierBoundary": "A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size." + } + ], + "conclusion": "The tight p=17 sample is reduced to 2 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side.", + "falsifierBoundary": "A refreshed p=17 matching-pattern miner falsifies this bounded witness packet if a split profile has no common core, if the common core falls below max K(N,x), or if the split heuristic changes. D3 remains open until these split cores are proved symbolically." + } + }, + "candidatePackets": { + "D2_p13_matching_lower_bound": { + "candidateId": "p848_D2_p13_matching_lower_bound_candidate_v1", + "obligationId": "D2_p13_matching_lower_bound", + "status": "bounded_p13_threat_profile_ready_symbolic_proof_needed", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "boundedVerifierEvidenceRange": "7307..7600", + "threatRowCount": 1285, + "structuralRowCount": 32, + "source": "STRUCTURAL_LIFT_MINER.threatMatchingProfiles[p=13]" + }, + "extractedTarget": { + "requiredMatchingLowerBoundRange": [ + 26, + 90 + ], + "actualMatchingRange": [ + 79, + 111 + ], + "minMatchingSlack": 19, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "tightestThreat": { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 5309, + "outsiderMod25": 9, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 220, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 89, + "matchingSlack": 19, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + } + }, + "matchingPatternEvidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 13, + "witnessRowCount": 12, + "allReconstructedMatchesAgree": true, + "allWitnessesSaturateSmallerSide": true, + "minMatchingSlack": 19, + "patternSummary": { + "totalWitnessMatchingPairs": 1281, + "commonMatchingPairCountAcrossWitnesses": 0, + "outsiderResidueGroups": [ + { + "key": "70:9", + "count": 6 + }, + { + "key": "99:6", + "count": 5 + }, + { + "key": "99:14", + "count": 1 + } + ], + "splitProfiles": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "witnessCount": 6, + "minN": 7318, + "maxN": 7368, + "minMatchingSlack": 19, + "commonMatchingPairCount": 108, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 74, + "count": 120 + }, + { + "key": 105, + "count": 102 + }, + { + "key": 149, + "count": 66 + }, + { + "key": 5, + "count": 66 + }, + { + "key": 143, + "count": 48 + }, + { + "key": 30, + "count": 42 + } + ] + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "witnessCount": 5, + "minN": 7307, + "maxN": 7357, + "minMatchingSlack": 20, + "commonMatchingPairCount": 105, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 136, + "count": 135 + }, + { + "key": 36, + "count": 70 + }, + { + "key": 111, + "count": 45 + }, + { + "key": 105, + "count": 40 + }, + { + "key": 67, + "count": 40 + }, + { + "key": 92, + "count": 30 + } + ] + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "witnessCount": 1, + "minN": 7343, + "maxN": 7343, + "minMatchingSlack": 20, + "commonMatchingPairCount": 108, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 136, + "count": 17 + }, + { + "key": 36, + "count": 17 + }, + { + "key": 105, + "count": 14 + }, + { + "key": 5, + "count": 9 + }, + { + "key": 74, + "count": 8 + }, + { + "key": 130, + "count": 6 + } + ] + } + ], + "rightMinusLeftModuloP2Distribution": [ + { + "key": 105, + "count": 156 + }, + { + "key": 136, + "count": 152 + }, + { + "key": 74, + "count": 128 + }, + { + "key": 36, + "count": 123 + }, + { + "key": 5, + "count": 75 + }, + { + "key": 149, + "count": 72 + }, + { + "key": 143, + "count": 49 + }, + { + "key": 111, + "count": 48 + } + ], + "productPlusOneModuloP2Distribution": [ + { + "key": 130, + "count": 25 + }, + { + "key": 131, + "count": 23 + }, + { + "key": 66, + "count": 23 + }, + { + "key": 5, + "count": 22 + }, + { + "key": 97, + "count": 22 + }, + { + "key": 40, + "count": 21 + }, + { + "key": 42, + "count": 21 + }, + { + "key": 54, + "count": 21 + } + ], + "proofHeuristic": "The tight-row witnesses do not share one common matching core; split the symbolic construction by outsider residue and saturated side." + }, + "witnessSample": [ + { + "N": 7343, + "outsider": 5309, + "requiredMatchingLowerBound": 89, + "reconstructedMatchingSize": 108, + "matchingSlack": 19, + "smallerSide": "side7", + "saturatesSmallerSide": true, + "pairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 38, + "rightModP2": 74, + "leftModP": 12, + "rightModP": 9, + "productPlusOneModP2": 109 + }, + { + "leftValue": 307, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 138, + "rightModP2": 99, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 143 + }, + { + "leftValue": 407, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 69, + "rightModP2": 5, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 8 + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "requiredMatchingLowerBound": 88, + "reconstructedMatchingSize": 108, + "matchingSlack": 20, + "smallerSide": "side7", + "saturatesSmallerSide": true, + "pairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 38, + "rightModP2": 74, + "leftModP": 12, + "rightModP": 9, + "productPlusOneModP2": 109 + }, + { + "leftValue": 307, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 138, + "rightModP2": 99, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 143 + }, + { + "leftValue": 407, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 69, + "rightModP2": 5, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 8 + } + ] + } + ] + }, + "suggestedSymbolicShape": [ + "It is enough to prove that H_{x,N} has a matching saturating the smaller compatible side for p=13 threatening outsiders.", + "The bounded p=13 data says this stronger saturation property holds for all 1285 current threatening-outsider rows.", + "The tightest bounded row needs K(N,x)=89 and has matching 108, leaving slack 19.", + "The matching-pattern miner has reconstructed 12 tight p=13 witness rows with actual missing-cross matching pairs for injection mining.", + "A symbolic proof should explain the smaller-side injection by residue blocks, not merely replay Hopcroft-Karp." + ], + "falsifierBoundary": "A refreshed p=13 threatening-outside row breaks this candidate if it does not meet K(N,x), does not saturate the smaller side, or shifts the tightest slack below the symbolic construction target." + }, + "D2_p13_split_core_witness_extraction": { + "checkerId": "p848_D2_p13_split_core_witness_checker_v1", + "obligationId": "D2_p13_split_core_witness_extraction", + "parentObligationId": "D2_p13_matching_lower_bound", + "status": "bounded_split_core_witness_certified", + "checkedRowCount": 12, + "passCount": 12, + "failCount": 0, + "statement": "The tight p=13 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "targetPrime": 13, + "sourceArtifact": "MATCHING_PATTERN_MINER.json", + "sourceAssessedRange": "7307..7600", + "witnessRowCount": 12, + "splitProfileCount": 3, + "role": "bounded_split_core_witness_for_symbolic_D2_lift" + }, + "dependencies": [ + "p848_D1_matching_saturation_bound_checker_v1", + "p848_D2_p13_matching_lower_bound_candidate_v1", + "MATCHING_PATTERN_MINER.patternSummary.splitProfiles" + ], + "hypotheses": [ + "D1 has extracted the p=13 matching lower-bound target K(N,x).", + "The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=13 rows.", + "The sampled tight rows split by outsider residue modulo 13^2, outsider residue modulo 25, and which side is smaller.", + "Within each split profile, the common matching core is a matching present in every sampled row of that profile." + ], + "proof": [ + "Read the p=13 split profiles from MATCHING_PATTERN_MINER.patternSummary.", + "For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.", + "Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.", + "Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.", + "This does not discharge D2 universally; it turns D2 into explicit split symbolic subgoals whose common cores must be proved to persist by residue/block argument." + ], + "proofChecks": [ + { + "checkId": "D1_dependency_discharged", + "passed": true, + "evidence": "p848_D1_matching_saturation_bound_checker_v1" + }, + { + "checkId": "p13_candidate_ready", + "passed": true, + "evidence": "p848_D2_p13_matching_lower_bound_candidate_v1" + }, + { + "checkId": "matching_pattern_artifact_ready", + "passed": true, + "evidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 13, + "witnessRowCount": 12 + } + }, + { + "checkId": "matching_reconstruction_agrees_with_verifier", + "passed": true, + "evidence": true + }, + { + "checkId": "all_witnesses_saturate_smaller_side", + "passed": true, + "evidence": [ + { + "key": "side7", + "count": 7 + }, + { + "key": "side18", + "count": 5 + } + ] + }, + { + "checkId": "split_profiles_available", + "passed": true, + "evidence": { + "splitProfileCount": 3, + "commonAcrossAllProfiles": 0, + "proofHeuristic": "The tight-row witnesses do not share one common matching core; split the symbolic construction by outsider residue and saturated side." + } + }, + { + "checkId": "split_common_cores_meet_required_K", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "commonMatchingPairCount": 108, + "maxRequiredMatchingLowerBound": 89 + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "commonMatchingPairCount": 105, + "maxRequiredMatchingLowerBound": 85 + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "commonMatchingPairCount": 108, + "maxRequiredMatchingLowerBound": 88 + } + ] + }, + { + "checkId": "split_common_core_pairs_exported", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "commonMatchingPairCount": 108, + "exportedPairCount": 108 + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "commonMatchingPairCount": 105, + "exportedPairCount": 105 + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "commonMatchingPairCount": 108, + "exportedPairCount": 108 + } + ] + }, + { + "checkId": "split_common_cores_saturate_smaller_side_on_tight_rows", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "commonMatchingPairCount": 108, + "minSmallerSideSize": 108 + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "commonMatchingPairCount": 105, + "minSmallerSideSize": 105 + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "commonMatchingPairCount": 108, + "minSmallerSideSize": 108 + } + ] + } + ], + "failedChecks": [], + "profileChecks": [ + { + "checkId": "D2_split_core_outP2=70_out25=9_smaller=side7", + "groupKey": "outP2=70|out25=9|smaller=side7", + "witnessCount": 6, + "minN": 7318, + "maxN": 7368, + "minRequiredMatchingLowerBound": 88, + "maxRequiredMatchingLowerBound": 89, + "minReconstructedMatchingSize": 108, + "maxReconstructedMatchingSize": 108, + "minSmallerSideSize": 108, + "maxSmallerSideSize": 108, + "minMatchingSlack": 19, + "commonMatchingPairCount": 108, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 38, + "rightModP2": 74, + "leftModP": 12, + "rightModP": 9, + "productPlusOneModP2": 109 + }, + { + "leftValue": 307, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 138, + "rightModP2": 99, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 143 + }, + { + "leftValue": 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18, + "leftModP2": 85, + "rightModP2": 115, + "leftModP": 7, + "rightModP": 11, + "productPlusOneModP2": 143 + }, + { + "leftValue": 6557, + "rightValue": 6293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 135, + "rightModP2": 40, + "leftModP": 5, + "rightModP": 1, + "productPlusOneModP2": 162 + }, + { + "leftValue": 6607, + "rightValue": 6418, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 16, + "rightModP2": 165, + "leftModP": 3, + "rightModP": 9, + "productPlusOneModP2": 106 + }, + { + "leftValue": 6707, + "rightValue": 6443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 116, + "rightModP2": 21, + "leftModP": 12, + "rightModP": 8, + "productPlusOneModP2": 71 + }, + { + "leftValue": 6782, + "rightValue": 6543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 22, + "rightModP2": 121, + "leftModP": 9, + "rightModP": 4, + "productPlusOneModP2": 128 + }, + { + "leftValue": 6807, + "rightValue": 6643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 47, + "rightModP2": 52, + "leftModP": 8, + "rightModP": 0, + "productPlusOneModP2": 79 + }, + { + "leftValue": 6907, + "rightValue": 6668, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 147, + "rightModP2": 77, + "leftModP": 4, + "rightModP": 12, + "productPlusOneModP2": 166 + }, + { + "leftValue": 6957, + "rightValue": 6593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 28, + "rightModP2": 2, + "leftModP": 2, + "rightModP": 2, + "productPlusOneModP2": 57 + }, + { + "leftValue": 7007, + "rightValue": 6743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 78, + "rightModP2": 152, + "leftModP": 0, + "rightModP": 9, + "productPlusOneModP2": 27 + }, + { + "leftValue": 7032, + "rightValue": 6818, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 103, + "rightModP2": 58, + "leftModP": 12, + "rightModP": 6, + "productPlusOneModP2": 60 + }, + { + "leftValue": 7107, + "rightValue": 6843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 9, + "rightModP2": 83, + "leftModP": 9, + "rightModP": 5, + "productPlusOneModP2": 72 + }, + { + "leftValue": 7207, + "rightValue": 6943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 109, + "rightModP2": 14, + "leftModP": 5, + "rightModP": 1, + "productPlusOneModP2": 6 + }, + { + "leftValue": 7232, + "rightValue": 7043, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 134, + "rightModP2": 114, + "leftModP": 4, + "rightModP": 10, + "productPlusOneModP2": 67 + }, + { + "leftValue": 7307, + "rightValue": 7143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 40, + "rightModP2": 45, + "leftModP": 1, + "rightModP": 6, + "productPlusOneModP2": 111 + } + ], + "minMatchingSlack": 20 + }, + "falsifierBoundary": "A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size." + } + ], + "conclusion": "The tight p=13 sample is reduced to 3 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side.", + "falsifierBoundary": "A refreshed matching-pattern miner falsifies this bounded witness packet if a split profile has no common core, if the common core falls below max K(N,x), or if the split heuristic changes. D2 remains open until these split cores are proved symbolically." + }, + "D3_p17_matching_lower_bound": { + "candidateId": "p848_D3_p17_matching_lower_bound_candidate_v1", + "obligationId": "D3_p17_matching_lower_bound", + "status": "bounded_p17_threat_profile_ready_symbolic_proof_needed", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "boundedVerifierEvidenceRange": "7307..7600", + "threatRowCount": 448, + "structuralRowCount": 32, + "source": "STRUCTURAL_LIFT_MINER.threatMatchingProfiles[p=17]" + }, + "extractedTarget": { + "requiredMatchingLowerBoundRange": [ + 1, + 14 + ], + "actualMatchingRange": [ + 103, + 112 + ], + "minMatchingSlack": 95, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "tightestThreat": { + "N": 7318, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 14, + "matchingSlack": 95, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + } + }, + "matchingPatternEvidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 17, + "witnessRowCount": 12, + "allReconstructedMatchesAgree": true, + "allWitnessesSaturateSmallerSide": true, + "minMatchingSlack": 95, + "patternSummary": { + "totalWitnessMatchingPairs": 1303, + "commonMatchingPairCountAcrossWitnesses": 4, + "outsiderResidueGroups": [ + { + "key": "38:23", + "count": 10 + }, + { + "key": "251:1", + "count": 2 + } + ], + "splitProfiles": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "witnessCount": 10, + "minN": 7307, + "maxN": 7393, + "minMatchingSlack": 95, + "commonMatchingPairCount": 109, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 36, + "count": 270 + }, + { + "key": 225, + "count": 220 + }, + { + "key": 136, + "count": 160 + }, + { + "key": 200, + "count": 70 + }, + { + "key": 250, + "count": 70 + }, + { + "key": 111, + "count": 50 + } + ] + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "witnessCount": 2, + "minN": 7307, + "maxN": 7318, + "minMatchingSlack": 96, + "commonMatchingPairCount": 106, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 136, + "count": 48 + }, + { + "key": 36, + "count": 36 + }, + { + "key": 225, + "count": 26 + }, + { + "key": 161, + "count": 17 + }, + { + "key": 211, + "count": 14 + }, + { + "key": 236, + "count": 14 + } + ] + } + ], + "rightMinusLeftModuloP2Distribution": [ + { + "key": 36, + "count": 306 + }, + { + "key": 225, + "count": 246 + }, + { + "key": 136, + "count": 208 + }, + { + "key": 250, + "count": 82 + }, + { + "key": 200, + "count": 76 + }, + { + "key": 111, + "count": 54 + }, + { + "key": 125, + "count": 42 + }, + { + "key": 50, + "count": 42 + } + ], + "productPlusOneModuloP2Distribution": [ + { + "key": 154, + "count": 32 + }, + { + "key": 172, + "count": 30 + }, + { + "key": 81, + "count": 30 + }, + { + "key": 220, + "count": 22 + }, + { + "key": 139, + "count": 20 + }, + { + "key": 176, + "count": 20 + }, + { + "key": 185, + "count": 20 + }, + { + "key": 256, + "count": 20 + } + ], + "proofHeuristic": "The tight-row witnesses share a nonempty stable matching core. Try proving saturation by extending this stable core across residue blocks, then handle boundary insertions separately." + }, + "witnessSample": [ + { + "N": 7318, + "outsider": 4373, + "requiredMatchingLowerBound": 14, + "reconstructedMatchingSize": 109, + "matchingSlack": 95, + "smallerSide": "side7", + "saturatesSmallerSide": true, + "pairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 13 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 140 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 5, + "rightModP": 7, + "productPlusOneModP2": 274 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 207, + "rightModP2": 243, + "leftModP": 3, + "rightModP": 5, + "productPlusOneModP2": 16 + }, + { + "leftValue": 307, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 18, + "rightModP2": 54, + "leftModP": 1, + "rightModP": 3, + "productPlusOneModP2": 106 + }, + { + "leftValue": 407, + "rightValue": 443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 118, + "rightModP2": 154, + "leftModP": 16, + "rightModP": 1, + "productPlusOneModP2": 255 + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "requiredMatchingLowerBound": 14, + "reconstructedMatchingSize": 109, + "matchingSlack": 95, + "smallerSide": "side7", + "saturatesSmallerSide": true, + "pairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 13 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 140 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 5, + "rightModP": 7, + "productPlusOneModP2": 274 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 207, + "rightModP2": 243, + "leftModP": 3, + "rightModP": 5, + "productPlusOneModP2": 16 + }, + { + "leftValue": 307, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 18, + "rightModP2": 54, + "leftModP": 1, + "rightModP": 3, + "productPlusOneModP2": 106 + }, + { + "leftValue": 407, + "rightValue": 443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 118, + "rightModP2": 154, + "leftModP": 16, + "rightModP": 1, + "productPlusOneModP2": 255 + } + ] + } + ] + }, + "suggestedSymbolicShape": [ + "It is enough to prove that H_{x,N} has a matching saturating the smaller compatible side for p=17 threatening outsiders.", + "The bounded p=17 data says this stronger saturation property holds for all 448 current threatening-outsider rows.", + "The tightest bounded row needs K(N,x)=14 and has matching 109, leaving slack 95.", + "The matching-pattern miner has reconstructed 12 tight p=17 witness rows with actual missing-cross matching pairs for injection mining.", + "A symbolic proof should explain the smaller-side injection by residue blocks, not merely replay Hopcroft-Karp." + ], + "falsifierBoundary": "A refreshed p=17 threatening-outside row breaks this candidate if it does not meet K(N,x), does not saturate the smaller side, or shifts the tightest slack below the symbolic construction target." + }, + "D3_p17_split_core_witness_extraction": { + "checkerId": "p848_D3_p17_split_core_witness_checker_v1", + "obligationId": "D3_p17_split_core_witness_extraction", + "parentObligationId": "D3_p17_matching_lower_bound", + "status": "bounded_split_core_witness_certified", + "checkedRowCount": 11, + "passCount": 11, + "failCount": 0, + "statement": "The tight p=17 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "targetPrime": 17, + "sourceArtifact": "MATCHING_PATTERN_MINER_P17.json", + "sourceAssessedRange": "7307..7600", + "witnessRowCount": 12, + "splitProfileCount": 2, + "role": "bounded_split_core_witness_for_symbolic_D3_lift" + }, + "dependencies": [ + "p848_D1_matching_saturation_bound_checker_v1", + "p848_D3_p17_matching_lower_bound_candidate_v1", + "MATCHING_PATTERN_MINER_P17.patternSummary.splitProfiles" + ], + "hypotheses": [ + "D1 has extracted the p=17 matching lower-bound target K(N,x).", + "The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=17 rows.", + "The sampled tight rows split by outsider residue modulo 17^2, outsider residue modulo 25, and which side is smaller.", + "Within each split profile, the common matching core is a matching present in every sampled row of that profile." + ], + "proof": [ + "Read the p=17 split profiles from MATCHING_PATTERN_MINER_P17.patternSummary.", + "For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.", + "Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.", + "Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.", + "This does not discharge D3 universally; it turns D3 into explicit split symbolic subgoals whose common cores must be proved to persist by residue/block argument." + ], + "proofChecks": [ + { + "checkId": "D1_dependency_discharged", + "passed": true, + "evidence": "p848_D1_matching_saturation_bound_checker_v1" + }, + { + "checkId": "p17_candidate_ready", + "passed": true, + "evidence": "p848_D3_p17_matching_lower_bound_candidate_v1" + }, + { + "checkId": "matching_pattern_artifact_ready", + "passed": true, + "evidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 17, + "witnessRowCount": 12 + } + }, + { + "checkId": "matching_reconstruction_agrees_with_verifier", + "passed": true, + "evidence": true + }, + { + "checkId": "all_witnesses_saturate_smaller_side", + "passed": true, + "evidence": [ + { + "key": "side7", + "count": 10 + }, + { + "key": "side18", + "count": 2 + } + ] + }, + { + "checkId": "split_profiles_available", + "passed": true, + "evidence": { + "splitProfileCount": 2, + "commonAcrossAllProfiles": 4, + "proofHeuristic": "The tight-row witnesses share a nonempty stable matching core. Try proving saturation by extending this stable core across residue blocks, then handle boundary insertions separately." + } + }, + { + "checkId": "split_common_cores_meet_required_K", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "commonMatchingPairCount": 109, + "maxRequiredMatchingLowerBound": 14 + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "commonMatchingPairCount": 106, + "maxRequiredMatchingLowerBound": 11 + } + ] + }, + { + "checkId": "split_common_core_pairs_exported", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "commonMatchingPairCount": 109, + "exportedPairCount": 109 + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "commonMatchingPairCount": 106, + "exportedPairCount": 106 + } + ] + }, + { + "checkId": "split_common_cores_saturate_smaller_side_on_tight_rows", + "passed": true, + "evidence": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "commonMatchingPairCount": 109, + "minSmallerSideSize": 109 + }, + { + "groupKey": "outP2=251|out25=1|smaller=side18", + "commonMatchingPairCount": 106, + "minSmallerSideSize": 106 + } + ] + } + ], + "failedChecks": [], + "profileChecks": [ + { + "checkId": "D3_split_core_outP2=38_out25=23_smaller=side7", + "groupKey": "outP2=38|out25=23|smaller=side7", + "witnessCount": 10, + "minN": 7307, + "maxN": 7393, + "minRequiredMatchingLowerBound": 12, + "maxRequiredMatchingLowerBound": 14, + "minReconstructedMatchingSize": 109, + "maxReconstructedMatchingSize": 109, + "minSmallerSideSize": 109, + "maxSmallerSideSize": 109, + "minMatchingSlack": 95, + "commonMatchingPairCount": 109, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 13 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 140 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 5, + "rightModP": 7, + "productPlusOneModP2": 274 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 207, + "rightModP2": 243, + "leftModP": 3, + "rightModP": 5, + "productPlusOneModP2": 16 + }, + { + "leftValue": 307, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 18, + "rightModP2": 54, + "leftModP": 1, + "rightModP": 3, + "productPlusOneModP2": 106 + }, + { + "leftValue": 407, + "rightValue": 443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 118, + "rightModP2": 154, + "leftModP": 16, + "rightModP": 1, + "productPlusOneModP2": 255 + }, + { + "leftValue": 507, + "rightValue": 543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 218, + "rightModP2": 254, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 174 + }, + { + "leftValue": 532, + "rightValue": 568, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 243, + "rightModP2": 279, + "leftModP": 5, + "rightModP": 7, + "productPlusOneModP2": 172 + }, + { + "leftValue": 607, + "rightValue": 643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 29, + "rightModP2": 65, + "leftModP": 12, + "rightModP": 14, + "productPlusOneModP2": 152 + }, + { + "leftValue": 707, + "rightValue": 668, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 129, + "rightModP2": 90, + "leftModP": 10, + "rightModP": 5, + "productPlusOneModP2": 51 + }, + { + "leftValue": 757, + "rightValue": 793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 179, + "rightModP2": 215, + "leftModP": 9, + "rightModP": 11, + "productPlusOneModP2": 49 + }, + { + "leftValue": 807, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 229, + "rightModP2": 165, + "leftModP": 8, + "rightModP": 12, + 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"productPlusOneModP2": 217 + }, + { + "leftValue": 6957, + "rightValue": 7093, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 21, + "rightModP2": 157, + "leftModP": 4, + "rightModP": 4, + "productPlusOneModP2": 119 + }, + { + "leftValue": 7057, + "rightValue": 7293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 121, + "rightModP2": 68, + "leftModP": 2, + "rightModP": 0, + "productPlusOneModP2": 137 + } + ], + "minMatchingSlack": 96 + }, + "falsifierBoundary": "A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size." + } + ], + "conclusion": "The tight p=17 sample is reduced to 2 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side.", + "falsifierBoundary": "A refreshed p=17 matching-pattern miner falsifies this bounded witness packet if a split profile has no common core, if the common core falls below max K(N,x), or if the split heuristic changes. D3 remains open until these split cores are proved symbolically." + } + }, + "activeAtomEvidence": { + "candidateId": "p848_D2_p13_matching_lower_bound_candidate_v1", + "obligationId": "D2_p13_matching_lower_bound", + "status": "bounded_p13_threat_profile_ready_symbolic_proof_needed", + "scope": { + "problemId": "848", + "universalInN": false, + "promotesAllNClaim": false, + "boundedVerifierEvidenceRange": "7307..7600", + "threatRowCount": 1285, + "structuralRowCount": 32, + "source": "STRUCTURAL_LIFT_MINER.threatMatchingProfiles[p=13]" + }, + "extractedTarget": { + "requiredMatchingLowerBoundRange": [ + 26, + 90 + ], + "actualMatchingRange": [ + 79, + 111 + ], + "minMatchingSlack": 19, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "tightestThreat": { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 5309, + "outsiderMod25": 9, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 220, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 89, + "matchingSlack": 19, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + } + }, + "matchingPatternEvidence": { + "status": "matching_pattern_witness_packet_ready", + "targetPrime": 13, + "witnessRowCount": 12, + "allReconstructedMatchesAgree": true, + "allWitnessesSaturateSmallerSide": true, + "minMatchingSlack": 19, + "patternSummary": { + "totalWitnessMatchingPairs": 1281, + "commonMatchingPairCountAcrossWitnesses": 0, + "outsiderResidueGroups": [ + { + "key": "70:9", + "count": 6 + }, + { + "key": "99:6", + "count": 5 + }, + { + "key": "99:14", + "count": 1 + } + ], + "splitProfiles": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "witnessCount": 6, + "minN": 7318, + "maxN": 7368, + "minMatchingSlack": 19, + "commonMatchingPairCount": 108, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 74, + "count": 120 + }, + { + "key": 105, + "count": 102 + }, + { + "key": 149, + "count": 66 + }, + { + "key": 5, + "count": 66 + }, + { + "key": 143, + "count": 48 + }, + { + "key": 30, + "count": 42 + } + ] + }, + { + "groupKey": "outP2=99|out25=6|smaller=side18", + "witnessCount": 5, + "minN": 7307, + "maxN": 7357, + "minMatchingSlack": 20, + "commonMatchingPairCount": 105, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 136, + "count": 135 + }, + { + "key": 36, + "count": 70 + }, + { + "key": 111, + "count": 45 + }, + { + "key": 105, + "count": 40 + }, + { + "key": 67, + "count": 40 + }, + { + "key": 92, + "count": 30 + } + ] + }, + { + "groupKey": "outP2=99|out25=14|smaller=side7", + "witnessCount": 1, + "minN": 7343, + "maxN": 7343, + "minMatchingSlack": 20, + "commonMatchingPairCount": 108, + "rightMinusLeftModuloP2Distribution": [ + { + "key": 136, + "count": 17 + }, + { + "key": 36, + "count": 17 + }, + { + "key": 105, + "count": 14 + }, + { + "key": 5, + "count": 9 + }, + { + "key": 74, + "count": 8 + }, + { + "key": 130, + "count": 6 + } + ] + } + ], + "rightMinusLeftModuloP2Distribution": [ + { + "key": 105, + "count": 156 + }, + { + "key": 136, + "count": 152 + }, + { + "key": 74, + "count": 128 + }, + { + "key": 36, + "count": 123 + }, + { + "key": 5, + "count": 75 + }, + { + "key": 149, + "count": 72 + }, + { + "key": 143, + "count": 49 + }, + { + "key": 111, + "count": 48 + } + ], + "productPlusOneModuloP2Distribution": [ + { + "key": 130, + "count": 25 + }, + { + "key": 131, + "count": 23 + }, + { + "key": 66, + "count": 23 + }, + { + "key": 5, + "count": 22 + }, + { + "key": 97, + "count": 22 + }, + { + "key": 40, + "count": 21 + }, + { + "key": 42, + "count": 21 + }, + { + "key": 54, + "count": 21 + } + ], + "proofHeuristic": "The tight-row witnesses do not share one common matching core; split the symbolic construction by outsider residue and saturated side." + }, + "witnessSample": [ + { + "N": 7343, + "outsider": 5309, + "requiredMatchingLowerBound": 89, + "reconstructedMatchingSize": 108, + "matchingSlack": 19, + "smallerSide": "side7", + "saturatesSmallerSide": true, + "pairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 38, + "rightModP2": 74, + "leftModP": 12, + "rightModP": 9, + "productPlusOneModP2": 109 + }, + { + "leftValue": 307, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 138, + "rightModP2": 99, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 143 + }, + { + "leftValue": 407, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 69, + "rightModP2": 5, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 8 + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "requiredMatchingLowerBound": 88, + "reconstructedMatchingSize": 108, + "matchingSlack": 20, + "smallerSide": "side7", + "saturatesSmallerSide": true, + "pairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 38, + "rightModP2": 74, + "leftModP": 12, + "rightModP": 9, + "productPlusOneModP2": 109 + }, + { + "leftValue": 307, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 138, + "rightModP2": 99, + "leftModP": 8, + "rightModP": 8, + "productPlusOneModP2": 143 + }, + { + "leftValue": 407, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 69, + "rightModP2": 5, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 8 + } + ] + } + ] + }, + "suggestedSymbolicShape": [ + "It is enough to prove that H_{x,N} has a matching saturating the smaller compatible side for p=13 threatening outsiders.", + "The bounded p=13 data says this stronger saturation property holds for all 1285 current threatening-outsider rows.", + "The tightest bounded row needs K(N,x)=89 and has matching 108, leaving slack 19.", + "The matching-pattern miner has reconstructed 12 tight p=13 witness rows with actual missing-cross matching pairs for injection mining.", + "A symbolic proof should explain the smaller-side injection by residue blocks, not merely replay Hopcroft-Karp." + ], + "falsifierBoundary": "A refreshed p=13 threatening-outside row breaks this candidate if it does not meet K(N,x), does not saturate the smaller side, or shifts the tightest slack below the symbolic construction target.", + "splitCoreWitnessPacket": { + "checkerId": "p848_D2_p13_split_core_witness_checker_v1", + "status": "bounded_split_core_witness_certified", + "splitProfileCount": 3, + "failCount": 0, + "profileSummary": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "witnessCount": 6, + "nRange": "7318..7368", + "requiredMatchingLowerBoundRange": [ + 88, + 89 + ], + "reconstructedMatchingRange": [ + 108, + 108 + ], + "commonMatchingPairCount": 108, + "commonMatchingPairExportComplete": true, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 1, + "productPlusOneModP2": 44 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 3, + "rightModP": 0, + "productPlusOneModP2": 92 + }, + { + "leftValue": 207, + "rightValue": 243, + 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12, + "rightModP": 6, + "productPlusOneModP2": 60 + }, + { + "leftValue": 7107, + "rightValue": 6843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 9, + "rightModP2": 83, + "leftModP": 9, + "rightModP": 5, + "productPlusOneModP2": 72 + }, + { + "leftValue": 7207, + "rightValue": 6943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 109, + "rightModP2": 14, + "leftModP": 5, + "rightModP": 1, + "productPlusOneModP2": 6 + }, + { + "leftValue": 7232, + "rightValue": 7043, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 134, + "rightModP2": 114, + "leftModP": 4, + "rightModP": 10, + "productPlusOneModP2": 67 + }, + { + "leftValue": 7307, + "rightValue": 7143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 40, + "rightModP2": 45, + "leftModP": 1, + "rightModP": 6, + "productPlusOneModP2": 111 + } + ], + "minMatchingSlack": 20 + }, + "falsifierBoundary": "A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size." + } + ], + "conclusion": "The tight p=13 sample is reduced to 3 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side." + } + }, + "proofObligations": [ + { + "obligationId": "D1_residue_block_matching_injection", + "status": "done", + "task": "Extract the current residue-block matching target from all bounded exact mixed-base threatening-outsider rows: K(N,x) = |L| + |R| - strictBaseThreshold + 1, and the recorded matching saturates the smaller compatible side in every current row.", + "statement": "Extract the current residue-block matching target from all bounded exact mixed-base threatening-outsider rows: K(N,x) = |L| + |R| - strictBaseThreshold + 1, and the recorded matching saturates the smaller compatible side in every current row.", + "dependsOn": [ + "C6_mixed_clique_matching_formula" + ], + "proofType": "bounded_matching_saturation_extraction", + "falsifierBoundary": "A refreshed exact mixed-base threatening-outsider row has matching below K(N,x), disagrees with the C6 formula replay, or fails the smaller-side saturation pattern. This bounded extraction is not yet the all-N symbolic matching proof.", + "dischargedBy": "p848_D1_matching_saturation_bound_checker_v1", + "dischargeWith": "All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row." + }, + { + "obligationId": "D2_p13_matching_lower_bound", + "status": "in_progress", + "task": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "statement": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=13 family row fails the claimed lower bound.", + "dischargedBy": null, + "dischargeWith": "Prove the active atom D2_p13_matching_lower_bound at its stated scope, then refresh FORMALIZATION_WORK so the next dependency is selected from the updated evidence." + }, + { + "obligationId": "D3_p17_matching_lower_bound", + "status": "ready", + "task": "For p=17 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "statement": "For p=17 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=17 family row fails the claimed lower bound.", + "dischargedBy": null, + "dischargeWith": null + }, + { + "obligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "status": "blocked_by_D2_D3", + "task": "If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "statement": "If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "dependsOn": [ + "C6_mixed_clique_matching_formula", + "D2_p13_matching_lower_bound", + "D3_p17_matching_lower_bound" + ], + "proofType": "inequality_substitution", + "falsifierBoundary": "The matching lower bound is substituted with the wrong inequality direction.", + "dischargedBy": null, + "dischargeWith": null + } + ], + "atomicDiscipline": [ + "Do not promote the whole checklist as a theorem claim.", + "Work one active atom at a time inside FORMALIZATION_WORK.currentWork.", + "After each atom is discharged or falsified, regenerate this surface from the miner/checklist evidence." + ], + "boundary": { + "claimLevel": "formalization_work_atom_not_proof", + "note": "This surface names the next theorem obligation implied by the structural lift miner; it does not certify any new N by itself." + } + }, + "topRepairClassMechanism": { + "mechanismId": "p848_top_repair_class_mechanism_packet_v1", + "status": "seeded_from_bridge", + "tieClass": [ + 432, + 782, + 832 + ], + "currentFamilyAwareLeader": { + 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"missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 382, + "familyIndex": 258, + "representative": 1705839349, + "tupleKey": "4, 41^2, 11^2, 7^2, 37^2, 9", + "repairValue": 651630631319, + "squareWitnesses": [ + 289 + ], + "missedLaneIndex": 7, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 289, + "laneEquation": "15*m ≡ 105 (mod 289)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 7, + "laneIndexPeriod": 289, + "missedLaneIndex": 7, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 832, + "familyIndex": 217, + "representative": 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"laneEquation": "459*m ≡ 467 (mod 529)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 7, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 382, + "continuation": 832, + "familyIndex": 271, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 9", + "repairValue": 1495201784129, + "squareWitnesses": [ + 529 + ], + "missedLaneIndex": 16, + "repairedContinuation": 382, + "repairedLaneIndex": 7, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 7, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "familyIndex": 104, + "representative": 681558029, + "tupleKey": "4, 7^2, 41^2, 9, 17^2, 11^2", + "repairValue": 839679491729, + "squareWitnesses": [ + 1369 + ], + "missedLaneIndex": 24, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 1369, + "laneEquation": "500*m ≡ 1048 (mod 1369)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 24, + "laneIndexPeriod": 1369, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "familyIndex": 107, + "representative": 695323423, + "tupleKey": "11^2, 13^2, 4, 7^2, 23^2, 19^2", + "repairValue": 856638457137, + "squareWitnesses": [ + 9 + ], + "missedLaneIndex": 24, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "familyIndex": 161, + "representative": 1079001739, + "tupleKey": "31^2, 17^2, 4, 11^2, 61^2, 43^2", + "repairValue": 1329330142449, + "squareWitnesses": [ + 9 + ], + "missedLaneIndex": 24, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "familyIndex": 187, + "representative": 1256825183, + "tupleKey": "9, 7^2, 4, 13^2, 23^2, 11^2", + "repairValue": 1548408625457, + "squareWitnesses": [ + 289 + ], + "missedLaneIndex": 24, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 289, + "laneEquation": "83*m ≡ 258 (mod 289)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 24, + "laneIndexPeriod": 289, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "familyIndex": 234, + "representative": 1583883827, + "tupleKey": "41^2, 59^2, 4, 9, 7^2, 11^2", + "repairValue": 1951344874865, + "squareWitnesses": [ + 361 + ], + "missedLaneIndex": 24, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 361, + "laneEquation": "99*m ≡ 210 (mod 361)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 24, + "laneIndexPeriod": 361, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "contrast_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 1232, + "familyIndex": 275, + "representative": 1820631943, + "tupleKey": "23^2, 19^2, 4, 7^2, 79^2, 11^2", + "repairValue": 2243018553777, + "squareWitnesses": [ + 9 + ], + "missedLaneIndex": 24, + "repairedContinuation": 832, + "repairedLaneIndex": 16, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 9, + "laneEquation": "5*m ≡ 3 (mod 9)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 6, + "laneIndexPeriod": 9, + "missedLaneIndex": 24, + "repairedLaneIndex": 16, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "familyIndex": 217, + "representative": 1446717451, + "tupleKey": "11^2, 29^2, 4, 7^2, 31^2, 9", + "repairValue": 1203668919233, + "squareWitnesses": [ + 529 + ], + "missedLaneIndex": 16, + "repairedContinuation": 1232, + "repairedLaneIndex": 24, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "familyIndex": 256, + "representative": 1684455347, + "tupleKey": "11^2, 47^2, 4, 13^2, 7^2, 31^2", + "repairValue": 1401466848705, + "squareWitnesses": [ + 9 + ], + "missedLaneIndex": 16, + "repairedContinuation": 1232, + "repairedLaneIndex": 24, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 9, + "laneEquation": "1*m ≡ 7 (mod 9)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 7, + "laneIndexPeriod": 9, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "familyIndex": 270, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 11^2", + "repairValue": 1495201784129, + "squareWitnesses": [ + 529 + ], + "missedLaneIndex": 16, + "repairedContinuation": 1232, + "repairedLaneIndex": 24, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + }, + { + "exchangeKind": "top_only_miss", + "topContinuation": 832, + "contrastContinuation": 1232, + "continuation": 832, + "familyIndex": 271, + "representative": 1797117529, + "tupleKey": "4, 53^2, 17^2, 7^2, 61^2, 9", + "repairValue": 1495201784129, + "squareWitnesses": [ + 529 + ], + "missedLaneIndex": 16, + "repairedContinuation": 1232, + "repairedLaneIndex": 24, + "laneWitnessSignatures": [ + { + "witnessSquareModulus": 529, + "laneEquation": "459*m ≡ 467 (mod 529)", + "gcdCoeffWitness": 1, + "laneIndexResidue": 16, + "laneIndexPeriod": 529, + "missedLaneIndex": 16, + "repairedLaneIndex": 24, + "missedLaneIndexMatches": true, + "repairedLaneIndexMatches": false + } + ], + "laneSignatureStatus": "passed" + } + ], + "conclusion": "Every pairwise exchange row is explained by a bad lane-index congruence m modulo the square witness; the missed continuation hits that congruence and the repaired continuation does not.", + "nextProofObligations": [ + "Generalize the finite-menu lane-index congruence schema beyond the currently replayed exchange rows.", + "Choose the strict 782 vs 1232 handoff rows or a broader exchange family as the next theorem-facing symbolic family.", + "Connect the lane-index bad-family schema back to the finite-gap closure target rather than treating it as only a leaderboard feature." + ] + }, + "verifiedAgainstBridge": { + "allScoresMatchLeaderboard": true, + "allScoresMatchTrackedRows": true, + "allTopMiss13": true, + "allPrimaryContrastsMiss15": true, + "allTopRepair242": true, + "allPrimaryContrastsRepair240": true, + "allPairwiseNetPlus2": true + }, + "conclusion": "The current finite menu has 255 predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence." + }, + "commonMissedPredictedRepresentatives": [ + 210290957, + 287180657, + 517124182, + 525631657, + 1229502607 + ], + "tailSpecificMissedPredictedRepresentatives": { + "432": [ + 457148843, + 770426585 + ], + "782": [ + 695323423, + 1079001739 + ], + "832": [ + 1446717451, + 1654841707 + ] + }, + "residueLaneAssessment": { + "tieClassModulo50": [ + 32 + ], + "nearbyModulo50Values": [ + 32 + ], + "verdict": "shared_mod_50_lane_but_not_sufficient", + "note": "The top tie is in the same mod-50 lane as several near contrasts, so the mod-50 lane is useful context but not by itself the repair mechanism." + }, + "mechanismHypotheses": [ + { + "hypothesisId": "shared_repair_count_signature", + "status": "supported_by_bridge", + "note": "All top tails share repaired-known=26, repaired-predicted=242, and clean-through=250075000 on the bridge leaderboard." + }, + { + "hypothesisId": "plus50_lane_context", + "status": "necessary_not_sufficient", + "note": "The top tails share the same mod-50 lane, but nearby contrasts in that lane do not all reach 242 predicted repairs." + }, + { + "hypothesisId": "common_missed_family_boundary", + "status": "supported_by_tracked_tail_matrix", + "note": "The top tails share 5 early missed predicted representatives in the tracked-tail matrix." + }, + { + "hypothesisId": "finite_menu_plus2_separation", + "status": "certified_by_replay", + "note": "The current finite menu has 255 predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence." + } + ], + "falsifierBoundary": [ + "A bridge refresh breaks the 432, 782, 832 tie on repaired-known, repaired-predicted, or clean-through metrics.", + "A near contrast such as 332, 382, or 1232 reaches the same predicted repair count under the same evidence boundary.", + "The apparent common missed-family representatives disappear when the family menu is refreshed.", + "A direct exact extension finds an earlier failure for one member of the top tie inside the claimed clean-through window." + ], + "nextProofObligations": [ + "Generalize the mod-50 lane-index bad-family signature beyond the finite exchange rows.", + "Derive a residue or family signature that separates the top tie from the rest of the mod-50 lane.", + "Choose the strict 782 vs 1232 handoff rows or a broader exchange family as the next theorem-facing symbolic family." + ] + }, + "tupleRowLift132": { + "preAnchorCombinedResidue": 546209, + "preAnchorCombinedModulus": 933156, + "preAnchorResidueModuloWitness": 400, + "anchorResidue": 81, + "anchorSquareModulus": 289, + "liftCoeffModuloAnchor": 264, + "liftRhsModuloAnchor": 82, + "liftedEquation": "546209 + 933156*k ≡ 81 (mod 289)", + "reducedEquation": "264*k ≡ 82 (mod 289)", + "inverseLiftCoeff": 104, + "liftParameter": 147, + "liftedResidue": 137720141, + "liftedResidueModuloWitness": 504 + }, + "tupleRowLift132Proof": { + "checkerId": "p848_132_lift_crt_checker_v1", + "source": "tuple_row_crt_equation_replay", + "status": "proved_from_tuple_row_crt", + "checkedRowCount": 1, + "passCount": 1, + "failCount": 0, + "equation": "546209 + 933156*k ≡ 81 (mod 289)", + "reducedEquation": "264*k ≡ 82 (mod 289)", + "liftParameter": 147, + "liftedResidueByParameter": 137720141, + "liftedResidueModuloWitness": 504, + "targetWitnessResidue": 504, + "checks": { + "liftParameterSolvesReducedEquation": true, + "liftedResidueMatchesCrtStep": true, + "liftedResidueSatisfiesAnchor132": true, + "liftedResiduePreservesPriorCrtPrefix": true, + "liftedResidueHitsWitnessProjection": true, + "liftedResidueHitsBoundaryWitnessResidue": true + }, + "failedChecks": [], + "conclusion": "The 132-row lift from residue 400 to 504 mod 841 is proved by the tuple-row CRT equation." + }, + "tupleRowPreservation182": { + "anchorResidue": 119, + "anchorSquareModulus": 121, + "preserved": true, + "liftedResidueModuloAnchor": 119, + "liftedResidueModuloWitness": 504, + "checkEquation": "137720141 ≡ 119 (mod 121)" + }, + "tupleSquareModuli": [ + 4, + 529, + 49, + 9, + 289, + 121 + ], + "witnessSquareModulus": 841, + "witnessPrime": 29, + "witnessExponent": 2, + "representativeResidueModuloWitness": 504, + "repairResidues": [ + { + "anchor": 157, + "residueModuloWitness": 75, + "squarefree": true + }, + { + "anchor": 232, + "residueModuloWitness": 30, + "squarefree": true + }, + { + "anchor": 282, + "residueModuloWitness": 0, + "squarefree": false + }, + { + "anchor": 332, + "residueModuloWitness": 811, + "squarefree": true + }, + { + "anchor": 382, + "residueModuloWitness": 781, + "squarefree": true + }, + { + "anchor": 432, + "residueModuloWitness": 751, + "squarefree": true + }, + { + "anchor": 782, + "residueModuloWitness": 541, + "squarefree": true + }, + { + "anchor": 832, + "residueModuloWitness": 511, + "squarefree": true + } + ], + "anchorCongruenceTable": [ + { + "anchor": 157, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 766, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": true, + "residueCheck": 75, + "squarefree": true + }, + { + "anchor": 232, + "gcdWithWitness": 29, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": null, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": false, + "residueCheck": 30, + "squarefree": true + }, + { + "anchor": 282, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 504, + "matchesRepresentativeResidue": true, + "solvableModuloWitness": true, + "residueCheck": 0, + "squarefree": false + }, + { + "anchor": 332, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 803, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": true, + "residueCheck": 811, + "squarefree": true + }, + { + "anchor": 382, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 284, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": true, + "residueCheck": 781, + "squarefree": true + }, + { + "anchor": 432, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 329, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": true, + "residueCheck": 751, + "squarefree": true + }, + { + "anchor": 782, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 784, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": true, + "residueCheck": 541, + "squarefree": true + }, + { + "anchor": 832, + "gcdWithWitness": 1, + "representativeResidueModuloWitness": 504, + "requiredNResidueForFailure": 187, + "matchesRepresentativeResidue": false, + "solvableModuloWitness": true, + "residueCheck": 511, + "squarefree": true + } + ], + "rowProgressionAnchorTable": [ + { + "anchor": 157, + "progressionCoeffModuloWitness": 186, + "progressionRhsModuloWitness": 766, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 610, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": true, + "squarefree": true + }, + { + "anchor": 232, + "progressionCoeffModuloWitness": 232, + "progressionRhsModuloWitness": 811, + "gcdCoeffWitness": 29, + "rowIndexForWitness": null, + "rowIndexPeriod": null, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": false, + "squarefree": true + }, + { + "anchor": 282, + "progressionCoeffModuloWitness": 543, + "progressionRhsModuloWitness": 0, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 0, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": true, + "solvableAlongRowProgression": true, + "squarefree": false + }, + { + "anchor": 332, + "progressionCoeffModuloWitness": 13, + "progressionRhsModuloWitness": 30, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 67, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": true, + "squarefree": true + }, + { + "anchor": 382, + "progressionCoeffModuloWitness": 324, + "progressionRhsModuloWitness": 60, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 592, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": true, + "squarefree": true + }, + { + "anchor": 432, + "progressionCoeffModuloWitness": 635, + "progressionRhsModuloWitness": 90, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 318, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": true, + "squarefree": true + }, + { + "anchor": 782, + "progressionCoeffModuloWitness": 289, + "progressionRhsModuloWitness": 300, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 164, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": true, + "squarefree": true + }, + { + "anchor": 832, + "progressionCoeffModuloWitness": 600, + "progressionRhsModuloWitness": 330, + "gcdCoeffWitness": 1, + "rowIndexForWitness": 379, + "rowIndexPeriod": 841, + "witnessOccursAtCurrentRepresentative": false, + "solvableAlongRowProgression": true, + "squarefree": true + } + ], + "rowStartDerivation282": { + "rowFormula": "n_t = 137720141 + 32631532164 * t", + "witnessEquation": "282*n_t + 1 ≡ 0 (mod 841)", + "substitutedEquation": "543*t ≡ 0 (mod 841)", + "gcdCoeffWitness": 1, + "normalizedEquation": "t ≡ 0 (mod 841)", + "representativeResidue": 504, + "requiredFailureResidue": 504, + "representativeAlreadyOnWitnessClass": true + }, + "unsolvableContrast232": { + "witnessEquation": "232*n_t + 1 ≡ 0 (mod 841)", + "substitutedEquation": "232*t ≡ 811 (mod 841)", + "gcdCoeffWitness": 29, + "solvable": false, + "divisibilityFailure": "29 does not divide 811" + }, + "firstFailingRepresentative": 137720141, + "witnessFirstOccurrence": { + "squareModulus": 841, + "firstRepresentative": 137720141, + "firstTupleKey": "4, 23^2, 7^2, 9, 17^2, 11^2", + "earlierRowCount": 25, + "earlierZeroResidueCount": 0 + }, + "familyMenuResidueBoundary": { + "witnessSquareModulus": 841, + "representativeResidueModuloWitness": 504, + "firstRepresentative": 137720141, + "firstTupleKey": "4, 23^2, 7^2, 9, 17^2, 11^2", + "firstFamilyIndex": 25, + "earlierRepresentativeMatchCount": 0, + "sameAsFirstFailingRepresentative": true, + "firstRepresentativeHasWitness": true + }, + "sameTupleCount": 1, + "rowProgressionModuloWitness": { + "gcdModulusWitness": 1, + "modulusModWitness": 494, + "residueModWitness": 504, + "traversesAllWitnessResidues": true + }, + "nextSameRowWitnessFor282": 27443256270065, + "priorRowsModuloWitness": [ + { + "representative": 127484267, + "tupleKey": "9, 17^2, 4, 29^2, 7^2, 11^2", + "residueModuloWitness": 736, + "squarefree": true + }, + { + "representative": 127682743, + "tupleKey": "131^2, 11^2, 4, 29^2, 13^2, 9", + "residueModuloWitness": 736, + "squarefree": true + }, + { + "representative": 136702637, + "tupleKey": "4, 43^2, 11^2, 9, 7^2, 19^2", + "residueModuloWitness": 457, + "squarefree": true + } + ], + "laterWitnessTimeline": [ + { + "representative": 210290957, + "tupleKey": "4, 53^2, 23^2, 9, 13^2, 31^2", + "witnessSquareModulus": 25 + }, + { + "representative": 287180657, + "tupleKey": "19^2, 103^2, 11^2, 9, 7^2, 23^2", + "witnessSquareModulus": 25 + }, + { + "representative": 287180657, + "tupleKey": "4, 103^2, 11^2, 9, 7^2, 23^2", + "witnessSquareModulus": 25 + }, + { + "representative": 517124182, + "tupleKey": "11^2, 17^2, 23^2, 13^2, 7^2, 9", + "witnessSquareModulus": 25 + }, + { + "representative": 525631657, + "tupleKey": "4, 11^2, 13^2, 23^2, 19^2, 9", + "witnessSquareModulus": 25 + } + ], + "mechanismFalsifierBoundary": { + "lowerRepresentativeSameWitnessResidueBreaksMechanism": "A refreshed family menu finds a representative below 137720141 with residue 504 mod 841.", + "differentFirstWitnessBreaksMechanism": "A refreshed family menu finds a 282 failure below 137720141 or with first witness different from 841.", + "bridgeAlignmentBreaksMechanism": "A refreshed bridge no longer matches next unmatched representative 137720141 with tracked tail 282 first failure.", + "commands": [ + "erdos number-theory bridge-refresh 848", + "erdos problem claim-pass 848", + "erdos problem formalization-work-refresh 848" + ] + }, + "familyMenuPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json" + } +} diff --git a/packs/number-theory/problems/848/FORMALIZATION_WORK.md b/packs/number-theory/problems/848/FORMALIZATION_WORK.md new file mode 100644 index 0000000..6c2417d --- /dev/null +++ b/packs/number-theory/problems/848/FORMALIZATION_WORK.md @@ -0,0 +1,235 @@ +# Erdos Problem #848 Formalization Work + +This packet turns the current formalization target into one concrete work unit that can be discharged, falsified, or narrowed without losing the surrounding theorem-search context. + +## Current State + +- Formalization work mode: `bridge_backed`. +- Current claim surface: `bridge_backed_frontier_support`. +- Active route: `finite_check_gap_closure`. +- Route summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. +- Next honest move: Decide whether to extend exact verified coverage beyond `40500` or switch method class. +- Latest verified interval: `1..40500` + +## Current Work + +- Work id: `p848_282_first_failure_mechanism_packet_v1`. +- Focus formalization id: `p848_282_alignment_formalization_v1`. +- Focus id: `lift_132_activation_schema_beyond_finite_menu`. +- Title: Explain the 282 First-Failure Mechanism +- Status: `in_progress`. +- Summary: Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class. +- Why: Once the shared-prefix class is named, the next theorem step is to explain why continuation 282, and not the neighboring tracked tails, is the one that first acquires a square witness there. + +## Working Definition + +- A 282 first-failure mechanism is the first shared-prefix class where the 282 repair row becomes non-squarefree while the neighboring tracked repair rows remain squarefree. +- On the live boundary class, the six defining tuple moduli are 4, 529, 49, 9, 289, 121 and the extra 282 witness is 841. +- The witness 841 is not one of the six tuple-row moduli, so the failure appears as an extra repair witness intersecting the shared-prefix class. +- The representative itself sits in residue class 504 modulo 841. + +## Current Evidence + +- Among the current family-menu rows where continuation 282 is non-squarefree, the earliest representative is 137720141. +- At representative 137720141, 282*n+1 = 38837079763 = 841 * 46179643. +- Modulo 841, the 282 repair row is exactly 0 while the neighboring tracked rows remain nonzero. +- Neighbor residues mod 841: 157->75, 232->30, 332->811, 382->781, 432->751, 782->541, 832->511. +- The first family-menu occurrence of witness 841 on tail 282 is representative 137720141, with 0 earlier rows giving residue 0 mod 841. +- Solving the tuple-row CRT gives n ≡ 137720141 (mod 32631532164), and projecting that class modulo 841 gives 504. +- The tuple-row CRT projection stabilizes at residue 504 mod 841 once anchor 132 is added. +- The last earlier 282 rows before the first failure stay nonzero mod 841: 127484267->736, 127682743->736, 136702637->457. +- Among the tracked repair anchors, the representative residue class modulo 841 matches only anchors 282. +- Some tracked anchors cannot fail via modulus 841 at all because gcd(anchor, 841) > 1: 232. +- The boundary row progression does not itself force witness 841: gcd(modulus, 841) = 1, so the progression visits every residue class mod 841. +- Within that row progression, the representative sits exactly at the witness-start index for tracked anchor(s) 282. +- Substituting the row formula into 282*n+1 ≡ 0 (mod 841) gives 543*t ≡ 0 (mod 841); since gcd(543, 841) = 1, this reduces to t ≡ 0 (mod 841). +- The contrasting 232 equation 232*t ≡ 811 (mod 841) is impossible because 29 does not divide 811. +- The next number in the same shared-prefix progression where tail 282 hits witness 841 is 27443256270065. +- At the family-menu level, the earliest representative in residue class 504 mod 841 is 137720141 at row index 25; the 25 earlier menu rows all miss the 282 witness residue class. +- The packet has an explicit falsifier boundary: it breaks if a refreshed menu finds an earlier representative with residue 504 mod 841, if continuation 282 first fails through a different witness, or if bridge refresh breaks the 137720141 <-> 282 alignment. +- Top repair-class packet seeded from bridge leaderboard: 432, 782, 832 tie at 242 repaired predicted families; nearest contrasts are 332->240, 382->240, 1232->240, 882->236. +- The top tie shares common early missed predicted representatives: 210290957, 287180657, 517124182, 525631657, 1229502607. +- The current finite menu has 255 predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence. +- The replayed top-tie common missed rows now include 9 predicted family rows, so the common-miss boundary is no longer just an eight-row bridge summary. +- The strictest finite-menu contrast certificate is 782 vs 1232. +- The mod-50 lane signature checks 74 exchange rows using continuation = 32 + 50*m and passes all of them. +- The finite mod-50 exchange packet is now backed by a reusable divisibility schema over 74 checked witness instances. +- The strict 782 > 1232 handoff is certified on the current finite menu: 782 repairs exactly two predicted rows that 1232 misses, 1232 repairs no predicted row that 782 misses, and both strict rows are explained by the symbolic mod-50 bad-lane schema. +- The symbolic 132-lift candidate checks 17 finite-menu certificate rows and promotes them into parameterized CRT hypotheses without claiming universal scope. +- Domain-closure assessment rejects a broad 17-row universal lift for now and recommends anchor_832_witness_529 as the next narrow closure lane. +- Every current finite-menu occurrence of anchor_832_witness_529 replays from raw tuple-row CRT data: pre-132 prefixes are clear, anchor 132 uniquely activates tracked tail 832, and anchor 182 preserves residue 316 mod 529. +- The recommended anchor_832_witness_529 lane is not one clean symbolic profile yet: it splits into 2 pre-132 profiles, with successor pre132_7_1_32_224_57_229_82_412. +- In the certified rows, the anchor-132 CRT prefix already satisfies the anchor-182 tuple row, so adding anchor 182 uses lift parameter 0 and cannot move the witness residue modulo 529. +- Rows 270, 271 are a finite duplicate final-anchor variant over the same CRT prefix through anchor 132, not evidence for a separate broad symbolic family. +- Structural atom C1 is discharged by the mod-25 same-side base identity: 7^2+1 and 18^2+1 are both 0 mod 25. +- Structural atom C2 is discharged: after partitioning compatible base vertices into B7 and B18 sides, C1 makes both sides cliques and only cross edges remain unconstrained. +- Structural atom C3 is discharged: H_{x,N} is now explicitly the bipartite graph of missing B7-by-B18 cross edges. +- The C-graph reduction packet is discharged through C6: mixed-base clique size is now the two-side total minus a maximum matching in H_{x,N}. +- The bounded D1 extraction is discharged on current verifier rows: all 1733 exact mixed-base threatening-outsider rows meet the required matching lower bound and saturate the smaller compatible side. +- The active D2 p=13 candidate is now backed by 1285 bounded threatening-outsider rows; K(N,x) ranges 26..90 and the minimum matching slack is 19. +- The D2 split-core witness packet reduces the tight p=13 sample to 3 residue/smaller-side subgoals; each split common core meets the sampled max K(N,x). +- The D3 p=17 split-core witness packet reduces the tight p=17 sample to 2 residue/smaller-side subgoals with minimum sampled slack 95. +- The structural lift miner is now feeding the existing atomic theorem lane: active atom D2_p13_matching_lower_bound targets D4_matching_bound_implies_sMaxMixed_bound from 64 mined exact rows. + +## Discharged Work + +- The family-menu boundary agrees with the tracked-tail boundary: the earliest 282-failing family row is also representative 137720141. +- The extra witness has been isolated: 841 belongs to the 282 repair row, not to the six defining tuple moduli of the shared-prefix class. +- The witness boundary is locally frozen: no earlier family-menu row gives tail 282 residue 0 modulo 841. +- The representative residue is structurally derived: the tuple-row CRT projects the shared-prefix obstruction class to 504 mod 841. +- The congruence boundary is isolated: residue class 504 mod 841 is the failure class for tracked tail 282 and no other tracked coprime tail. +- The row-index boundary is isolated: within the shared-prefix row progression, tracked anchor 282 is the only tracked anchor whose 841 witness class starts at row index 0. +- The row-start derivation is explicit: the boundary representative already lies on the 282 witness class modulo 841, so the row equation reduces to t ≡ 0 (mod 841). +- The menu-level first-occurrence boundary is isolated: 137720141 is the first family-menu representative in the 282 witness class 504 mod 841, so no earlier menu row can fail via witness 841 on that same congruence class. +- The mechanism falsifier boundary is explicit: a lower representative in residue class 504 mod 841, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment would all break this packet. +- The 132-row lift is explicit: adding the 132 row forces the tuple-row CRT class from residue 400 mod 841 to the boundary residue 504 mod 841 via k ≡ 147 (mod 289). +- The activation boundary is explicit: before anchor 132 no tuple-row CRT step lands on any tracked failure residue mod 841, anchor 132 creates the unique tracked 282 match at residue 504, and anchor 182 preserves that same unique match. +- The 132-activation pattern is reusable on the current finite menu: 17 failing witness rows first activate their own failing tracked tail at anchor 132. +- The finite-menu 132-activation pattern has been promoted into lemma schema p848_finite_menu_132_target_activation_schema_v1 with hypotheses, conclusion, falsifier boundary, and 17 row certificates. +- The 17 finite-menu 132-activation row certificates replay successfully in checker p848_132_activation_row_certificate_checker_v1. +- The 132-row lift to residue 504 mod 841 is proved from tuple-row CRT equations by checker p848_132_lift_crt_checker_v1. +- The activation schema lift decision is explicit: finite_menu_certificate_not_universal_yet; next theorem pass is formalize_top_repair_class_mechanism. +- The checked 132 activation schema has been lifted into symbolic CRT hypothesis packet p848_132_activation_symbolic_lift_candidate_v1; the next obligation is domain closure, not merely packet construction. +- The broad domain-closure overclaim is ruled out at the current evidence boundary: The finite symbolic-lift survey splits across 8 failing anchors and 12 witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem. +- The recommended anchor_832_witness_529 closure lane has been executed at finite repeated-group scope: 3 raw rows pass checker p848_832_529_anchor_witness_domain_closure_checker_v1. +- The single-profile symbolic closure over anchor_832_witness_529 is falsified by the finite evidence split into 2 pre-132 residue profiles. +- The anchor_832_witness_529 anchor-182 preservation step is explained: every checked row has lift parameter 0 at anchor 182. +- The repeated pre132_7_1_32_224_57_229_82_412 sublane is closed as a finite duplicate final-anchor variant, not a new symbolic family. +- Structural atom C1_same_side_base_clique is discharged: same-side principal base residues force a 25 divisor of u*v+1, so each same-side component is a clique. +- Structural atom C2_two_cliques_plus_cross_edges is discharged by checker p848_C2_two_cliques_plus_cross_edges_checker_v1: the mixed-base graph is two cliques plus arbitrary cross edges. +- Structural atom C3_missing_cross_graph_definition is discharged by checker p848_C3_missing_cross_graph_definition_checker_v1: H_{x,N} records exactly the missing cross edges between the two clique sides. +- Structural atom C4_clique_to_vertex_cover_duality is discharged by checker p848_C4_clique_to_vertex_cover_duality_checker_v1: clique complements are exactly vertex covers of H_{x,N}. +- Structural atom C5_konig_matching_reduction is discharged by checker p848_C5_konig_matching_reduction_checker_v1: Konig's theorem applies because H_{x,N} is finite bipartite. +- Structural atom C6_mixed_clique_matching_formula is discharged by checker p848_C6_mixed_clique_matching_formula_checker_v1: sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}). +- Structural atom D1_residue_block_matching_injection is discharged at bounded extraction scope by checker p848_D1_matching_saturation_bound_checker_v1: every current exact mixed-base threatening outsider meets K(N,x) and saturates the smaller compatible side. +- D2 split-core witness extraction is discharged at bounded pattern scope by checker p848_D2_p13_split_core_witness_checker_v1: each p=13 split common core reaches the sampled K(N,x) target. +- D3 split-core witness extraction is discharged at bounded pattern scope by checker p848_D3_p17_split_core_witness_checker_v1: each p=17 split common core reaches the sampled K(N,x) target. +- The top repair-class mechanism packet p848_top_repair_class_mechanism_packet_v1 is seeded with shared metrics, nearest contrasts, common missed-family boundary, and falsifier conditions. +- The finite-menu +2 repaired-predicted-family separation is discharged: 432->242, 782->242, 832->242 versus 332->240, 382->240, 1232->240. +- The common missed-family replay is explicit: 9 top-tie shared missed predicted family rows were replayed directly from the family menu. +- The finite-menu +2 separation has been lifted into mod-50 lane-index congruences: 74 exchange rows all pass the bad-m-class certificate. +- The mod-50 bad-lane congruence has been generalized into symbolic schema p848_mod50_bad_lane_symbolic_schema_v1; 74 finite witness instances replay with 0 failures. +- The strict 782 > 1232 handoff is connected to the symbolic mod-50 schema by checker p848_782_1232_strict_handoff_checker_v1; it is certified as finite-menu guidance, not all-N closure. +- The 182 row preserves the boundary residue: the 132-lifted class already satisfies 137720141 ≡ 119 (mod 121), so the final anchor adds no further correction modulo 841. + +## Remaining Gaps + +- Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. +- Advance the same atomic packet toward target D4_matching_bound_implies_sMaxMixed_bound: If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N). +- Decide and run the next post-40500 verification lane using local CPU and opt-in local 4090 compute only. + +## Atomic Proof Obligations + +- `D1_residue_block_matching_injection`: done | Extract the current residue-block matching target from all bounded exact mixed-base threatening-outsider rows: K(N,x) = |L| + |R| - strictBaseThreshold + 1, and the recorded matching saturates the smaller compatible side in every current row. | discharge: All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row. +- `D2_p13_matching_lower_bound`: in_progress | For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. | discharge: Prove the active atom D2_p13_matching_lower_bound at its stated scope, then refresh FORMALIZATION_WORK so the next dependency is selected from the updated evidence. +- `D3_p17_matching_lower_bound`: ready | For p=17 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. +- `D4_matching_bound_implies_sMaxMixed_bound`: blocked_by_D2_D3 | If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N). + +## Mechanism Assessment + +- Verdict: `controlled_congruence_candidate` +- Confidence: `medium` +- Witness 841 first appears for tail 282 at representative 137720141, with 0 earlier zero-residue hits modulo 841. +- Representative residue class 504 mod 841 matches tracked failure equations only for anchor(s) 282. +- At least one tracked anchor cannot fail through modulus 841 at all because gcd(anchor, 841) > 1: 232. +- The boundary tuple key appears exactly once in the current family menu, so this packet is not mixing multiple identical tuple rows. +- Along the shared-prefix row progression itself, the witness 841 occurs at row index 0 only for tracked anchor(s) 282. +- Other tracked anchors hit the same witness only later along the row progression: 332->t=67, 782->t=164, 432->t=318, 832->t=379, 382->t=592, 157->t=610. +- Some tracked anchors never hit witness 841 along this row progression at all: 232. +- At the family-menu level, representative residue 504 mod 841 first appears at representative 137720141 (row index 25), with 0 earlier menu rows on the same residue class. +- The 132 row is the first tuple-row lift that forces residue 504 mod 841: 264*k ≡ 82 (mod 289), so k ≡ 147 and the CRT class lifts to 137720141. +- Before anchor 132, no tuple-row CRT step lands on any tracked failure residue modulo 841; anchor 132 is the first step whose projected residue 504 uniquely matches tracked tail 282. +- The 182 row preserves that residue: 137720141 ≡ 119 (mod 121), so the final CRT class keeps residue 504 mod 841. +- Anchor 182 preserves the same unique tracked match: the projected residue stays on tail 282's failure class and does not activate any neighboring tracked tail. +- This is not a one-row phenomenon in the current menu: 17 failing witness rows have the same first-target-activation-at-132 shape across tracked tails 157, 232, 282, 332, 382, 432, 782, 832. +- The finite-menu 132-activation schema is now explicit with 17 row certificates, six hypotheses, and five falsifier classes. +- The dedicated activation checker replayed 17 row certificates from raw tuple-row CRT projections with 0 failures. +- The 132-row lift is proved directly from the tuple-row CRT equation: 264*k ≡ 82 (mod 289) with k = 147. +- The symbolic-lift decision is explicit: keep the 132 schema finite-menu certified for now and route the next theorem pass to formalize_top_repair_class_mechanism. +- The top repair-class mechanism packet is seeded: 432, 782, 832 share repaired-known=26, repaired-predicted=242, and clean-through=250075000. +- The +2 top repair separation is certified by raw family-menu replay: top tails miss 13 predicted families each, while primary contrasts 332, 382, 1232 miss 15 each. +- The cleanest pairwise handoff is 782>1232: the top tail repairs two predicted rows that the contrast misses and loses no predicted row back. +- The mod-50 symbolic signature is now explicit: each pairwise exchange row solves a bad lane-index congruence for c = 32 + 50*m, and the repaired continuation misses that bad m-class. +- The mod-50 bad-lane rule is now a symbolic divisibility schema checked on 74 witness instances; it is universal for a named witness congruence but not a full squarefree repair theorem. +- The strict 782 > 1232 handoff is finite-menu certified: 782 repairs 2 predicted rows that 1232 misses, with no predicted row lost back. +- The 132 activation lift is now parameterized as symbolic CRT hypotheses S1_pairwise_crt_compatibility, S2_same_witness_projection, S3_pre_132_clear, S4_anchor_132_unique_target, S5_anchor_182_preserves_target, S6_no_scope_promotion_without_domain_closure. +- anchor_832_witness_529 is now replay-certified over 3 raw family-menu rows; the symbolic decision is single_profile_symbolic_domain_falsified_by_profile_split. +- The anchor_832_witness_529 preservation mechanism is a zero-lift at anchor 182: anchor 132 already satisfies the final tuple row, so the witness residue stays fixed. +- pre132_7_1_32_224_57_229_82_412 is resolved as a finite final-anchor duplicate: rows 270, 271 share the CRT prefix through anchor 132 and differ only by zero-lift anchor-182 variants. +- Caveat: The shared-prefix row progression is coprime to 841, so the row itself traverses all residue classes modulo 841; the 841 hit is not forced by the row alone. +- Caveat: The activation-pattern survey is over the current finite family menu, so it supports reusability inside the live search surface but does not by itself prove a universal obstruction-family theorem. +- Caveat: The activation lemma schema is a finite-menu certificate schema until its CRT hypotheses are lifted symbolically. +- Caveat: A universal lift still needs: A symbolic lift needs parameterized tuple-row CRT hypotheses plus a proof that pre-132 prefixes miss tracked failure residues and anchor 132 uniquely activates the target for the whole family. +- Caveat: The anchor_832_witness_529 lane splits into 2 pre-132 profiles, so it should be handled as profile sublanes rather than one broad symbolic family. +- Caveat: The repeated pre132_7_1_32_224_57_229_82_412 rows are a finite duplicate, so this sublane should not be promoted as independent evidence for a broad symbolic domain. +- Caveat: The mod-50 schema proves a bad-lane divisibility equivalence for a named witness Q; it still needs a separate control argument before it can close a squarefree finite-gap theorem lane. +- Caveat: The strict 782 > 1232 handoff is still finite-menu evidence; it guides the next exact verifier rollout but is not an all-N coverage theorem. +- `controlled_congruence_interaction`: favored | The shared-prefix class and the 282 repair row intersect in a distinguished witness residue class modulo 841. +- `one_off_modular_coincidence`: disfavored_by_menu_survey | The current family menu contains 17 rows with the same first-target-activation-at-132 shape, so the one-off explanation is no longer the best finite-menu reading. +- `shared_prefix_row_alone_forces_841`: not_supported | A stronger claim that the family-row progression itself already forces the 841 witness class. + +## Packet Data + +- representative: `137720141` +- tupleKey: `"4, 23^2, 7^2, 9, 17^2, 11^2"` +- tupleRowCrtDerivation: `{"combinedResidue":137720141,"combinedModulus":32631532164,"projectedResidueModuloWitness":504,"firstStableProjectionAnchor":132,"steps":[{"anchor":7,"rowSquareModulus":4,"rowResidue":1,"preCombinedResidue":0,"preCombinedModulus":1,"liftParameter":1,"combinedResidue":1,"combinedModulus":4,"residueModWitness":1},{"anchor":32,"rowSquareModulus":529,"rowResidue":281,"preCombinedResidue":1,"preCombinedModulus":4,"liftParameter":70,"combinedResidue":281,"combinedModulus":2116,"residueModWitness":281},{"anchor":57,"rowSquareModulus":49,"rowResidue":6,"preCombinedResidue":281,"preCombinedModulus":2116,"liftParameter":13,"combinedResidue":27789,"combinedModulus":103684,"residueModWitness":36},{"anchor":82,"rowSquareModulus":9,"rowResidue":8,"preCombinedResidue":27789,"preCombinedModulus":103684,"liftParameter":5,"combinedResidue":546209,"combinedModulus":933156,"residueModWitness":400},{"anchor":132,"rowSquareModulus":289,"rowResidue":81,"preCombinedResidue":546209,"preCombinedModulus":933156,"liftParameter":147,"combinedResidue":137720141,"combinedModulus":269682084,"residueModWitness":504},{"anchor":182,"rowSquareModulus":121,"rowResidue":119,"preCombinedResidue":137720141,"preCombinedModulus":269682084,"liftParameter":0,"combinedResidue":137720141,"combinedModulus":32631532164,"residueModWitness":504}]}` +- tupleRowActivationSequence: `[{"anchor":7,"residueModWitness":1,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":32,"residueModWitness":281,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":57,"residueModWitness":36,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":82,"residueModWitness":400,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":132,"residueModWitness":504,"matchingTrackedAnchors":[282],"uniqueTrackedMatch":282},{"anchor":182,"residueModWitness":504,"matchingTrackedAnchors":[282],"uniqueTrackedMatch":282}]` +- tupleRowActivationBoundary: `{"pre132HasNoTrackedMatch":true,"activationAnchor":132,"activationResidueModuloWitness":504,"activationTrackedAnchors":[282],"activationIsUnique282":true,"preservationAnchor":182,"preservationResidueModuloWitness":504,"preservationTrackedAnchors":[282],"preservationKeepsUnique282":true}` +- menuActivationSurvey: 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11^2","activationSequence":[{"anchor":7,"residueModWitness":5,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":32,"residueModWitness":1004,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":57,"residueModWitness":418,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":82,"residueModWitness":184,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":132,"residueModWitness":4250,"matchingTrackedAnchors":[432],"uniqueTrackedMatch":432},{"anchor":182,"residueModWitness":4250,"matchingTrackedAnchors":[432],"uniqueTrackedMatch":432}]},{"familyIndex":258,"representative":1705839349,"failingAnchor":382,"witnessSquareModulus":289,"firstMatchAnchor":132,"firstMatchTrackedAnchors":[382],"tupleKey":"4, 41^2, 11^2, 7^2, 37^2, 9","activationSequence":[{"anchor":7,"residueModWitness":1,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":32,"residueModWitness":26,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":57,"residueModWitness":252,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":82,"residueModWitness":273,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":132,"residueModWitness":87,"matchingTrackedAnchors":[382],"uniqueTrackedMatch":382},{"anchor":182,"residueModWitness":87,"matchingTrackedAnchors":[382],"uniqueTrackedMatch":382}]},{"familyIndex":270,"representative":1797117529,"failingAnchor":832,"witnessSquareModulus":529,"firstMatchAnchor":132,"firstMatchTrackedAnchors":[832],"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 11^2","activationSequence":[{"anchor":7,"residueModWitness":1,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":32,"residueModWitness":224,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":57,"residueModWitness":229,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":82,"residueModWitness":412,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":132,"residueModWitness":316,"matchingTrackedAnchors":[832],"uniqueTrackedMatch":832},{"anchor":182,"residueModWitness":316,"matchingTrackedAnchors":[832],"uniqueTrackedMatch":832}]},{"familyIndex":271,"representative":1797117529,"failingAnchor":832,"witnessSquareModulus":529,"firstMatchAnchor":132,"firstMatchTrackedAnchors":[832],"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 9","activationSequence":[{"anchor":7,"residueModWitness":1,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":32,"residueModWitness":224,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":57,"residueModWitness":229,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":82,"residueModWitness":412,"matchingTrackedAnchors":[],"uniqueTrackedMatch":null},{"anchor":132,"residueModWitness":316,"matchingTrackedAnchors":[832],"uniqueTrackedMatch":832},{"anchor":182,"residueModWitness":316,"matchingTrackedAnchors":[832],"uniqueTrackedMatch":832}]}],"nextProofObligations":["Replay the 17 row certificates from tuple-row CRT equations in a dedicated checker rather than trusting the summarized packet data.","Decide whether the schema can be lifted from the current finite menu to a symbolic CRT lemma for a reusable obstruction family.","Keep the finite-menu scope explicit until the symbolic lift is proved."]}` +- activationSchemaLiftDecision: `{"decisionId":"p848_activation_schema_symbolic_lift_decision_v1","verdict":"finite_menu_certificate_not_universal_yet","safeUse":"Use the schema as a checked finite-menu lemma/certificate family for the current 848 search surface.","rejectedOverclaim":"Do not state a universal obstruction-family theorem from the 17-row finite-menu certificate alone.","reason":["The current packet has a replayed certificate for all 17 finite-menu 132 target-activation rows.","The current 282 boundary lift is proved from its tuple-row CRT equation.","The packet does not yet contain symbolic hypotheses that characterize every future tuple-row family producing the same 132 activation shape."],"nextTheoremPass":"formalize_top_repair_class_mechanism","nextTheoremPassReason":"The 282-specific mechanism is now narrow, checked, and claim-safe; the live bridge still exposes an independent high-value top cluster 432, 782, 832 with shared repaired-known and repaired-predicted counts.","promotionRequirement":"A symbolic lift needs parameterized tuple-row CRT hypotheses plus a proof that pre-132 prefixes miss tracked failure residues and anchor 132 uniquely activates the target for the whole family.","falsifierBoundary":["A refreshed menu breaks one of the 17 finite row certificates.","A symbolic family instance satisfies the proposed hypotheses but has a pre-132 tracked match.","Anchor 132 activates a non-target or multiple tracked tails under the proposed symbolic hypotheses.","Anchor 182 fails to preserve the target activation under the proposed symbolic hypotheses."]}` +- activationSymbolicLiftCandidate: `{"candidateId":"p848_132_activation_symbolic_lift_candidate_v1","checkerId":"p848_132_activation_symbolic_lift_candidate_checker_v1","source":"finite_menu_certificate_to_symbolic_crt_hypotheses","status":"symbolic_crt_hypothesis_packet_ready","checkedRowCount":17,"passCount":17,"failCount":0,"failedRows":[],"scope":{"problemId":"848","universalClaim":false,"candidateOnly":true,"finiteCertificateRows":17,"boundaryWitnessSquareModulus":841},"parameterization":{"anchorOrder":[7,32,57,82,132,182],"trackedAnchors":[157,232,282,332,382,432,782,832],"variables":["Q: square witness modulus q^2","a: failing tracked repair anchor","M_i: square modulus introduced by tuple anchor i","r_i: tuple-row residue introduced by tuple anchor i","N_i: CRT prefix residue after anchors up to i","R_b(Q): tracked failure residue -b^{-1} mod Q when gcd(b, Q) = 1"],"crtPrefixRecurrence":"N_i is the unique residue modulo lcm(M_7,...,M_i) satisfying all tuple rows through anchor i.","failureResidueFormula":"R_b(Q) = -b^{-1} mod Q for gcd(b,Q)=1; if gcd(b,Q)>1, b cannot supply a residue class modulo Q unless the divisibility condition is satisfied."},"symbolicHypotheses":[{"hypothesisId":"S1_pairwise_crt_compatibility","text":"The tuple-row moduli through anchors 7, 32, 57, 82, 132, 182 are CRT-compatible and define prefixes N_i."},{"hypothesisId":"S2_same_witness_projection","text":"Every prefix N_i is projected modulo the same square witness Q attached to the failing repair row a*n+1."},{"hypothesisId":"S3_pre_132_clear","text":"For i in {7,32,57,82}, N_i is not congruent to R_b(Q) for any tracked anchor b whose failure residue is defined."},{"hypothesisId":"S4_anchor_132_unique_target","text":"N_132 is congruent to R_a(Q), and N_132 is not congruent to R_b(Q) for every tracked b != a whose failure residue is defined."},{"hypothesisId":"S5_anchor_182_preserves_target","text":"N_182 is congruent to N_132 modulo Q, so the target activation survives the final shared-prefix anchor."},{"hypothesisId":"S6_no_scope_promotion_without_domain_closure","text":"A problem-level theorem may use this packet only after a separate domain-closure lemma proves S1-S5 for the intended family, not merely for the current finite menu."}],"symbolicConclusion":{"text":"Any row satisfying S1-S5 has first tracked failure-residue activation at anchor 132, uniquely activates the failing anchor a, and preserves that activation at anchor 182.","proofSketch":["S3 rules out every tracked activation before anchor 132.","S4 makes anchor 132 a unique activation of the target failing anchor.","S5 carries the same witness-residue class through anchor 182 without adding a competing tracked match."]},"finiteEvidence":{"activationCheckerId":"p848_132_activation_row_certificate_checker_v1","activationCheckerStatus":"passed","activationCheckedRows":17,"liftCheckerId":"p848_132_lift_crt_checker_v1","liftCheckerStatus":"proved_from_tuple_row_crt","boundaryLiftEquation":"264*k ≡ 82 (mod 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11^2","failingAnchor":832,"witnessSquareModulus":529,"pre132Residues":[{"anchor":7,"residueModWitness":1,"matchingTrackedAnchors":[]},{"anchor":32,"residueModWitness":224,"matchingTrackedAnchors":[]},{"anchor":57,"residueModWitness":229,"matchingTrackedAnchors":[]},{"anchor":82,"residueModWitness":412,"matchingTrackedAnchors":[]}],"residueAt132":316,"uniqueTrackedMatchAt132":832,"residueAt182":316,"uniqueTrackedMatchAt182":832},{"familyIndex":271,"representative":1797117529,"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 9","failingAnchor":832,"witnessSquareModulus":529,"pre132Residues":[{"anchor":7,"residueModWitness":1,"matchingTrackedAnchors":[]},{"anchor":32,"residueModWitness":224,"matchingTrackedAnchors":[]},{"anchor":57,"residueModWitness":229,"matchingTrackedAnchors":[]},{"anchor":82,"residueModWitness":412,"matchingTrackedAnchors":[]}],"residueAt132":316,"uniqueTrackedMatchAt132":832,"residueAt182":316,"uniqueTrackedMatchAt182":832}],"candidateChecks":[{"familyIndex":25,"failingAnchor":282,"witnessSquareModulus":841,"status":"passed","failedChecks":[]},{"familyIndex":63,"failingAnchor":232,"witnessSquareModulus":121,"status":"passed","failedChecks":[]},{"familyIndex":81,"failingAnchor":382,"witnessSquareModulus":66049,"status":"passed","failedChecks":[]},{"familyIndex":112,"failingAnchor":157,"witnessSquareModulus":4,"status":"passed","failedChecks":[]},{"familyIndex":112,"failingAnchor":232,"witnessSquareModulus":529,"status":"passed","failedChecks":[]},{"familyIndex":133,"failingAnchor":332,"witnessSquareModulus":1681,"status":"passed","failedChecks":[]},{"familyIndex":162,"failingAnchor":232,"witnessSquareModulus":9,"status":"passed","failedChecks":[]},{"familyIndex":188,"failingAnchor":157,"witnessSquareModulus":3481,"status":"passed","failedChecks":[]},{"familyIndex":188,"failingAnchor":232,"witnessSquareModulus":289,"status":"passed","failedChecks":[]},{"familyIndex":206,"failingAnchor":157,"witnessSquareModulus":1849,"status":"passed","failedChecks":[]},{"familyIndex":217,"failingAnchor":832,"witnessSquareModulus":529,"status":"passed","failedChecks":[]},{"familyIndex":234,"failingAnchor":782,"witnessSquareModulus":169,"status":"passed","failedChecks":[]},{"familyIndex":236,"failingAnchor":432,"witnessSquareModulus":4489,"status":"passed","failedChecks":[]},{"familyIndex":237,"failingAnchor":432,"witnessSquareModulus":4489,"status":"passed","failedChecks":[]},{"familyIndex":258,"failingAnchor":382,"witnessSquareModulus":289,"status":"passed","failedChecks":[]},{"familyIndex":270,"failingAnchor":832,"witnessSquareModulus":529,"status":"passed","failedChecks":[]},{"familyIndex":271,"failingAnchor":832,"witnessSquareModulus":529,"status":"passed","failedChecks":[]}]},"nextProofObligations":["Prove a domain-closure lemma that supplies S1-S5 for a reusable class of tuple rows instead of only the 17 current finite-menu rows.","Decide whether the domain-closure class should be the 282 obstruction family, the full 132-activation survey, or the stricter 782-vs-1232 exchange family.","Connect the symbolic activation packet to the finite-gap verifier boundary so it narrows the post-11300 exact work rather than becoming an isolated lemma."]}` +- activationDomainClosureAssessment: `{"assessmentId":"p848_132_activation_domain_closure_assessment_v1","status":"broad_domain_closure_not_supported_yet","checkedRowCount":17,"failCount":0,"broadClosureVerdict":{"verdict":"do_not_promote_broad_17_row_survey_to_universal_domain","reason":"The finite symbolic-lift survey splits across 8 failing anchors and 12 witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem.","failingAnchorCounts":{"157":3,"232":4,"282":1,"332":1,"382":2,"432":2,"782":1,"832":3},"witnessCounts":{"4":1,"9":1,"121":1,"169":1,"289":2,"529":4,"841":1,"1681":1,"1849":1,"3481":1,"4489":2,"66049":1}},"repeatedAnchorWitnessGroups":[{"groupId":"anchor_832_witness_529","failingAnchor":832,"witnessSquareModulus":529,"rowCount":3,"familyIndices":[217,270,271],"representatives":[1446717451,1797117529],"tupleKeys":["11^2, 29^2, 4, 7^2, 31^2, 9","4, 53^2, 17^2, 7^2, 61^2, 11^2","4, 53^2, 17^2, 7^2, 61^2, 9"]},{"groupId":"anchor_432_witness_4489","failingAnchor":432,"witnessSquareModulus":4489,"rowCount":2,"familyIndices":[236,237],"representatives":[1585191353],"tupleKeys":["4, 19^2, 13^2, 7^2, 23^2, 11^2","9, 19^2, 13^2, 7^2, 23^2, 11^2"]}],"narrowedClosureCandidates":[{"candidateId":"p848_282_841_boundary_instance_closure","priority":"high","rowCount":1,"task":"Prove the 282/841 boundary instance from the explicit CRT equations and keep it scoped as the current obstruction packet.","tradeoff":"Best alignment with the 282 north star, but currently only a single finite-menu row."},{"candidateId":"p848_832_529_repeated_activation_family","priority":"high","rowCount":3,"task":"Try to prove a reusable closure lemma for anchor 832 with witness 529.","tradeoff":"Best repeated symbolic-lift family in the current activation survey, but it may be less directly tied to the 282 alignment."},{"candidateId":"p848_782_1232_strict_exchange_closure","priority":"high","rowCount":2,"task":"Use the strict 782 > 1232 exchange rows as a small theorem-facing family for the mod-50 lane closure.","tradeoff":"Best bridge to the top repair-class mechanism, but it is a top-cluster theorem lane rather than the 132 activation lane itself."}],"recommendedClosureLane":{"laneId":"repeat_anchor_witness_activation_family","targetGroupId":"anchor_832_witness_529","why":"This is the largest repeated symbolic-activation class in the 17-row survey: anchor 832 with witness 529 appears 3 times."},"nextProofObligations":["Do not claim a universal 17-row domain theorem until a single structural family supplies S1-S5.","Start with anchor_832_witness_529 and prove or falsify its CRT-domain closure.","After one narrow closure lane is proved, decide whether it genuinely reduces the finite gap or only explains a search-side feature."]}` +- anchorWitnessDomainClosurePacket: 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361)","laneIndexResidue":24,"laneIndexPeriod":361,"missedLaneIndex":24,"repairedLaneIndex":16,"status":"passed","checks":{"laneFormulaAppliesToMissedContinuation":true,"laneFormulaAppliesToRepairedContinuation":true,"equationRecomputes":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true,"congruenceSolvable":true},"failedChecks":[]},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"repairedContinuation":832,"familyIndex":275,"representative":1820631943,"witnessSquareModulus":9,"laneEquation":"5*m ≡ 3 (mod 9)","laneIndexResidue":6,"laneIndexPeriod":9,"missedLaneIndex":24,"repairedLaneIndex":16,"status":"passed","checks":{"laneFormulaAppliesToMissedContinuation":true,"laneFormulaAppliesToRepairedContinuation":true,"equationRecomputes":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true,"congruenceSolvable":true},"failedChecks":[]},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"repairedContinuation":1232,"familyIndex":217,"representative":1446717451,"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":24,"status":"passed","checks":{"laneFormulaAppliesToMissedContinuation":true,"laneFormulaAppliesToRepairedContinuation":true,"equationRecomputes":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true,"congruenceSolvable":true},"failedChecks":[]},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"repairedContinuation":1232,"familyIndex":256,"representative":1684455347,"witnessSquareModulus":9,"laneEquation":"1*m ≡ 7 (mod 9)","laneIndexResidue":7,"laneIndexPeriod":9,"missedLaneIndex":16,"repairedLaneIndex":24,"status":"passed","checks":{"laneFormulaAppliesToMissedContinuation":true,"laneFormulaAppliesToRepairedContinuation":true,"equationRecomputes":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true,"congruenceSolvable":true},"failedChecks":[]},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"repairedContinuation":1232,"familyIndex":270,"representative":1797117529,"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":24,"status":"passed","checks":{"laneFormulaAppliesToMissedContinuation":true,"laneFormulaAppliesToRepairedContinuation":true,"equationRecomputes":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true,"congruenceSolvable":true},"failedChecks":[]},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"repairedContinuation":1232,"familyIndex":271,"representative":1797117529,"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":24,"status":"passed","checks":{"laneFormulaAppliesToMissedContinuation":true,"laneFormulaAppliesToRepairedContinuation":true,"equationRecomputes":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true,"congruenceSolvable":true},"failedChecks":[]}],"conclusion":"The finite mod-50 exchange packet is now backed by a reusable divisibility schema over 74 checked witness instances.","nextProofObligations":["Connect the symbolic bad-lane schema to the finite-gap closure target using a theorem-facing handoff family, preferably the strict 782 vs 1232 rows.","Prove that the selected handoff family controls all relevant square witnesses, not only the witnessed bad lane in each finite exchange row.","If no such control family exists, route the next step to local exact verification beyond 11300 instead of overclaiming the lane schema."]}` +- strict7821232HandoffPacket: `{"checkerId":"p848_782_1232_strict_handoff_checker_v1","packetId":"p848_782_1232_strict_handoff_packet_v1","source":"mod50_symbolic_schema_to_finite_menu_handoff","status":"finite_strict_handoff_certified_not_gap_closure","checkedRowCount":2,"passCount":2,"failCount":0,"topContinuation":782,"contrastContinuation":1232,"topLaneIndex":15,"contrastLaneIndex":24,"netExtraRepairsForTop":2,"topOnlyMissCount":0,"contrastOnlyMissCount":2,"topRepairedPredictedFamilyCount":242,"contrastRepairedPredictedFamilyCount":240,"checks":{"strictDominancePairPresent":true,"pairwiseDeltaPresent":true,"topContinuationIs782":true,"contrastContinuationIs1232":true,"topRepairsTwoMorePredictedRows":true,"noTopOnlyMissRows":true,"contrastOnlyMissRowsAreTwo":true,"strictRowsCoveredBySymbolicSchema":true,"rowChecksPass":true},"failedChecks":[],"rowChecks":[{"familyIndex":104,"representative":681558029,"tupleKey":"4, 7^2, 41^2, 9, 17^2, 11^2","witnessSquareModulus":1369,"laneEquation":"500*m ≡ 1048 (mod 1369)","laneIndexResidue":24,"laneIndexPeriod":1369,"missedLaneIndex":24,"repairedLaneIndex":15,"status":"passed","checks":{"symbolicSchemaInstancePresent":true,"missedContinuationIs1232":true,"repairedContinuationIs782":true,"missedLaneIndexIs24":true,"repairedLaneIndexIs15":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true},"failedChecks":[]},{"familyIndex":187,"representative":1256825183,"tupleKey":"9, 7^2, 4, 13^2, 23^2, 11^2","witnessSquareModulus":289,"laneEquation":"83*m ≡ 258 (mod 289)","laneIndexResidue":24,"laneIndexPeriod":289,"missedLaneIndex":24,"repairedLaneIndex":15,"status":"passed","checks":{"symbolicSchemaInstancePresent":true,"missedContinuationIs1232":true,"repairedContinuationIs782":true,"missedLaneIndexIs24":true,"repairedLaneIndexIs15":true,"missedLaneHitsBadClass":true,"repairedLaneAvoidsBadClass":true},"failedChecks":[]}],"failedRows":[],"strictRows":[{"familyIndex":104,"representative":681558029,"tupleKey":"4, 7^2, 41^2, 9, 17^2, 11^2","repairValue":839679491729,"squareWitnesses":[1369],"missedLaneIndex":24,"repairedLaneIndex":15},{"familyIndex":187,"representative":1256825183,"tupleKey":"9, 7^2, 4, 13^2, 23^2, 11^2","repairValue":1548408625457,"squareWitnesses":[289],"missedLaneIndex":24,"repairedLaneIndex":15}],"conclusion":"The strict 782 > 1232 handoff is certified on the current finite menu: 782 repairs exactly two predicted rows that 1232 misses, 1232 repairs no predicted row that 782 misses, and both strict rows are explained by the symbolic mod-50 bad-lane schema.","theoremBoundary":{"finiteMenuHandoffClaim":true,"allNFiniteGapClosureClaim":false,"reason":"This packet connects the symbolic bad-lane schema to the finite exchange surface, but it does not prove that all post-11300 candidates are controlled by the strict handoff family."},"nextProofObligations":["Use the strict handoff packet as theorem-side guidance for the next local exact verifier rollout beyond 11300.","If exact verification finds a new boundary row, replay it through the bad-lane schema before widening search.","Do not claim all-N closure from the 782 > 1232 handoff without a separate coverage theorem over all relevant square witnesses."]}` +- structuralLiftAtomicSurface: `{"surfaceId":"p848_structural_lift_atomic_surface_v1","status":"active","canonicalSurface":"FORMALIZATION_WORK.currentWork","role":"atomic_proof_obligation_surface","evidenceArtifact":{"path":"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.json","status":"structural_lift_obligation_packet_ready","minedExactRowCount":64,"primaryExactPrimes":[13,17],"nextTheoremLane":"formalize_cross_side_matching_bound_then_exact_prime_margin_lift"},"matchingPatternArtifact":{"path":"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json","status":"matching_pattern_witness_packet_ready","targetPrime":13,"witnessRowCount":12,"minMatchingSlack":19},"matchingPatternArtifacts":[{"path":"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json","status":"matching_pattern_witness_packet_ready","targetPrime":13,"witnessRowCount":12,"minMatchingSlack":19},{"path":"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.json","status":"matching_pattern_witness_packet_ready","targetPrime":17,"witnessRowCount":12,"minMatchingSlack":95}],"referenceBacklog":{"path":"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json","role":"non_canonical_reference_backlog","note":"The checklist is a map of possible sub-lemmas. The active theorem lane is the single atomic obligation surfaced here."},"activePacket":{"packetId":"D_matching_lower_bounds","title":"Matching Lower Bounds","goal":"Replace Hopcroft-Karp computation with symbolic matching constructions."},"requestedActiveAtom":{"obligationId":"D2_p13_matching_lower_bound","status":"next","statement":"For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality."},"activeAtom":{"obligationId":"D2_p13_matching_lower_bound","status":"in_progress","statement":"For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.","dependsOn":["D1_residue_block_matching_injection"],"proofType":"residue_family_matching_bound","falsifierBoundary":"A p=13 family row fails the claimed lower bound."},"targetAtom":{"obligationId":"D4_matching_bound_implies_sMaxMixed_bound","status":"blocked_by_D2_D3","statement":"If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).","dependsOn":["C6_mixed_clique_matching_formula","D2_p13_matching_lower_bound","D3_p17_matching_lower_bound"],"proofType":"inequality_substitution","falsifierBoundary":"The matching lower bound is substituted with the wrong inequality direction."},"dischargedAtoms":[{"obligationId":"C1_same_side_base_clique","status":"proved_by_mod25_identity","checkerId":"p848_C1_same_side_base_clique_checker_v1","conclusion":"The same-side parts of the mixed-base compatibility graph are cliques; only cross-side edges need the missing-cross graph analysis."},{"obligationId":"C2_two_cliques_plus_cross_edges","status":"proved_by_c1_partition_decomposition","checkerId":"p848_C2_two_cliques_plus_cross_edges_checker_v1","conclusion":"The mixed-base compatible graph is a two-clique/co-bipartite graph; the next theorem atom only needs to name the missing cross-edge bipartite graph."},{"obligationId":"C3_missing_cross_graph_definition","status":"proved_by_definition","checkerId":"p848_C3_missing_cross_graph_definition_checker_v1","conclusion":"The missing-cross graph H_{x,N} is a well-defined bipartite graph on the B7/B18 compatible partition with edges exactly opposite to cross compatibility."},{"obligationId":"C4_clique_to_vertex_cover_duality","status":"proved_by_clique_vertex_cover_complement","checkerId":"p848_C4_clique_to_vertex_cover_duality_checker_v1","conclusion":"Mixed-base clique maximization is equivalent to deleting a minimum vertex cover from the missing-cross graph."},{"obligationId":"C5_konig_matching_reduction","status":"proved_by_konig_theorem","checkerId":"p848_C5_konig_matching_reduction_checker_v1","conclusion":"The minimum vertex cover term in C4 may be replaced by the maximum matching size of H_{x,N}."},{"obligationId":"C6_mixed_clique_matching_formula","status":"proved_by_vertex_cover_konig_composition","checkerId":"p848_C6_mixed_clique_matching_formula_checker_v1","conclusion":"The verifier Hopcroft-Karp quantity has now been promoted to a theorem-facing graph formula."},{"obligationId":"D1_residue_block_matching_injection","status":"bounded_matching_saturation_extraction_certified","checkerId":"p848_D1_matching_saturation_bound_checker_v1","conclusion":"All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row."},{"obligationId":"D2_p13_split_core_witness_extraction","status":"bounded_split_core_witness_certified","checkerId":"p848_D2_p13_split_core_witness_checker_v1","conclusion":"The tight p=13 sample is reduced to 3 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side."},{"obligationId":"D3_p17_split_core_witness_extraction","status":"bounded_split_core_witness_certified","checkerId":"p848_D3_p17_split_core_witness_checker_v1","conclusion":"The tight p=17 sample is reduced to 2 split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side."}],"proofPackets":{"C1_same_side_base_clique":{"checkerId":"p848_C1_same_side_base_clique_checker_v1","obligationId":"C1_same_side_base_clique","status":"proved_by_mod25_identity","checkedRowCount":2,"passCount":2,"failCount":0,"statement":"Inside one principal base side, compatible base vertices form a clique for the fixed outsider graph considered by the verifier.","scope":{"problemId":"848","universalSameSideClaim":true,"dependsOnOutsider":false,"dependsOnN":false,"principalBaseResiduesModulo25":[7,18]},"hypotheses":["u and v are both in the 7 mod 25 principal base side, or both in the 18 mod 25 principal base side.","The verifier graph uses non-squarefree pair compatibility: an edge is present when u*v + 1 is not squarefree."],"proof":["If u and v are both 7 mod 25, then u*v + 1 is congruent to 7^2 + 1 = 50, hence 0 mod 25.","If u and v are both 18 mod 25, then u*v + 1 is congruent to 18^2 + 1 = 325, hence 0 mod 25.","Because 25 = 5^2 is a square divisor, u*v + 1 is not squarefree in either same-side case.","Therefore every pair of same-side principal base vertices has an edge, so each same-side compatible vertex set is a clique."],"residueChecks":[{"sideId":"B7","residue":7,"productResidueModulo25":24,"productPlusOneResidueModulo25":0},{"sideId":"B18","residue":18,"productResidueModulo25":24,"productPlusOneResidueModulo25":0}],"failedRows":[],"conclusion":"The same-side parts of the mixed-base compatibility graph are cliques; only cross-side edges need the missing-cross graph analysis.","falsifierBoundary":"A falsifier would need a pair of same-side principal base residues whose product plus one is not divisible by 25, but both residue checks are 0 mod 25."},"C2_two_cliques_plus_cross_edges":{"checkerId":"p848_C2_two_cliques_plus_cross_edges_checker_v1","obligationId":"C2_two_cliques_plus_cross_edges","status":"proved_by_c1_partition_decomposition","checkedRowCount":5,"passCount":5,"failCount":0,"statement":"For fixed outsider x, the compatible mixed-base graph is one clique on B7-compatible vertices, one clique on B18-compatible vertices, plus arbitrary cross edges.","scope":{"problemId":"848","universalInN":true,"universalInOutsider":true,"principalBaseResiduesModulo25":[7,18],"boundedVerifierEvidenceRange":"7307..7600"},"dependencies":["p848_C1_same_side_base_clique_checker_v1","definition_of_mixed_base_compatible_vertex_sets"],"hypotheses":["For fixed outsider x and cutoff N, L is the set of x-compatible principal base vertices congruent to 7 mod 25.","For fixed outsider x and cutoff N, R is the set of x-compatible principal base vertices congruent to 18 mod 25.","The mixed-base graph has vertex set L union R and an edge exactly when the corresponding pair relation is compatible in the verifier graph.","C1 has proved that every same-side pair inside L or inside R is an edge."],"proof":["The vertex set is partitioned into the two principal compatible sides L and R by residue modulo 25.","By C1, every pair of vertices inside L is adjacent, and every pair of vertices inside R is adjacent.","No additional same-side obstruction remains after C1; all non-forced edge information lies between L and R.","Therefore the graph is exactly two cliques, L and R, plus whatever cross edges the pair compatibility relation supplies."],"proofChecks":[{"checkId":"C1_dependency_discharged","passed":true,"evidence":"p848_C1_same_side_base_clique_checker_v1"},{"checkId":"principal_side_partition","passed":true,"evidence":{"leftSide":"B7-compatible vertices","rightSide":"B18-compatible vertices","principalResiduesModulo25":[7,18]}},{"checkId":"same_side_edges_complete_by_C1","passed":true,"evidence":[{"sideId":"B7","residue":7,"productResidueModulo25":24,"productPlusOneResidueModulo25":0},{"sideId":"B18","residue":18,"productResidueModulo25":24,"productPlusOneResidueModulo25":0}]},{"checkId":"cross_edges_are_the_only_unfixed_edges","passed":true,"evidence":"After partitioning into B7 and B18 sides and applying C1 on each side, the only pair relations not forced complete are B7 x B18 cross pairs."},{"checkId":"verifier_boundary_uses_two_clique_reduction","passed":true,"evidence":"For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges. bounded_outsider_clique_full_mixed_base_structural_verifier formalize_cross_side_matching_bound_then_exact_prime_margin_lift"}],"failedChecks":[],"conclusion":"The mixed-base compatible graph is a two-clique/co-bipartite graph; the next theorem atom only needs to name the missing cross-edge bipartite graph.","falsifierBoundary":"A falsifier must either break C1 on a same-side pair or exhibit a compatible mixed-base vertex outside the B7/B18 partition."},"C3_missing_cross_graph_definition":{"checkerId":"p848_C3_missing_cross_graph_definition_checker_v1","obligationId":"C3_missing_cross_graph_definition","status":"proved_by_definition","checkedRowCount":4,"passCount":4,"failCount":0,"statement":"Define H_{x,N} as the bipartite graph whose edges are precisely missing cross edges between compatible B7 and B18 vertices.","scope":{"problemId":"848","universalInN":true,"universalInOutsider":true,"graphPartitions":["B7-compatible vertices","B18-compatible vertices"],"boundedVerifierEvidenceRange":"7307..7600"},"dependencies":["p848_C2_two_cliques_plus_cross_edges_checker_v1"],"hypotheses":["C2 has decomposed the mixed-base compatible graph into two same-side cliques L and R plus cross edges.","Cross compatibility is evaluated only for pairs (l,r) with l in L and r in R.","A missing cross edge means that the pair (l,r) is not an edge of the compatible graph."],"definition":{"vertexSet":"V(H_{x,N}) = L union R","edgeSet":"E(H_{x,N}) = {{l,r}: l in L, r in R, and {l,r} is not a compatible cross edge}","equivalentArithmeticSign":"Because compatible edges are non-squarefree pair relations, H contains (l,r) exactly when l*r+1 is squarefree for the verifier relation."},"proof":["C2 leaves only cross pairs between L and R as possible obstructions to cliquehood.","Put exactly those obstructing cross pairs into H_{x,N}.","Every edge of H has one endpoint in L and one endpoint in R, so H is bipartite by construction.","The sign convention is explicit: H records missing compatible cross edges, not present compatible cross edges."],"proofChecks":[{"checkId":"C2_dependency_discharged","passed":true,"evidence":"p848_C2_two_cliques_plus_cross_edges_checker_v1"},{"checkId":"missing_cross_graph_is_bipartite_by_definition","passed":true,"evidence":{"leftPartition":"L = B7-compatible vertices","rightPartition":"R = B18-compatible vertices","noSameSideMissingEdgesIncluded":true}},{"checkId":"edge_sign_is_missing_compatibility","passed":true,"evidence":"An edge (l,r) belongs to H_{x,N} exactly when l in L, r in R, and l*r+1 is squarefree, i.e. the cross pair is missing from the compatible graph."},{"checkId":"verifier_boundary_names_missing_cross_edges","passed":true,"evidence":"For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges. For each threatening outsider, the missing cross-edge graph between the 7 mod 25 and 18 mod 25 compatible base sides has a matching large enough to force mixedCliqueSize below the strict base threshold."}],"failedChecks":[],"conclusion":"The missing-cross graph H_{x,N} is a well-defined bipartite graph on the B7/B18 compatible partition with edges exactly opposite to cross compatibility.","falsifierBoundary":"A falsifier must show a same-side H edge or a cross pair whose H membership uses the wrong compatibility sign."},"C4_clique_to_vertex_cover_duality":{"checkerId":"p848_C4_clique_to_vertex_cover_duality_checker_v1","obligationId":"C4_clique_to_vertex_cover_duality","status":"proved_by_clique_vertex_cover_complement","checkedRowCount":4,"passCount":4,"failCount":0,"statement":"A mixed-base clique equals all compatible vertices minus a vertex cover of H_{x,N}; hence max clique size is |L| + |R| minus minimum vertex cover size.","dependencies":["p848_C3_missing_cross_graph_definition_checker_v1"],"hypotheses":["The mixed-base compatible graph is two cliques L and R plus cross edges.","H_{x,N} is the bipartite graph of missing cross edges between L and R.","A vertex cover of H_{x,N} is a set of vertices meeting every missing cross edge."],"proof":["Let K be a clique in the compatible graph and S be the complement of K in L union R.","If an H edge had both endpoints outside S, then both endpoints would lie in K but would be a missing compatible cross edge, contradicting cliquehood.","Thus S is a vertex cover of H.","Conversely, if S is a vertex cover of H, then K = (L union R) minus S contains no missing cross edge, and same-side pairs are already complete, so K is a clique.","The correspondence reverses cardinality, giving maxClique = |L| + |R| - minVertexCover(H)."],"proofChecks":[{"checkId":"C3_dependency_discharged","passed":true,"evidence":"p848_C3_missing_cross_graph_definition_checker_v1"},{"checkId":"clique_complement_hits_every_missing_cross_edge","passed":true,"evidence":"If a clique kept both endpoints of a missing cross edge, those endpoints would be a non-edge in the compatible graph."},{"checkId":"vertex_cover_complement_is_clique","passed":true,"evidence":"If removed vertices cover every missing cross edge, then no missing cross edge remains among kept vertices; same-side pairs are already cliques by C2."},{"checkId":"max_min_cardinality_duality","passed":true,"evidence":"Maximizing kept vertices is equivalent to minimizing removed vertices over vertex covers of H_{x,N}."}],"failedChecks":[],"conclusion":"Mixed-base clique maximization is equivalent to deleting a minimum vertex cover from the missing-cross graph.","falsifierBoundary":"A falsifier must exhibit a clique whose complement misses an H edge, or a vertex cover whose complement is not a clique."},"C5_konig_matching_reduction":{"checkerId":"p848_C5_konig_matching_reduction_checker_v1","obligationId":"C5_konig_matching_reduction","status":"proved_by_konig_theorem","checkedRowCount":3,"passCount":3,"failCount":0,"statement":"Because H_{x,N} is bipartite, minimum vertex cover size equals maximum matching size.","dependencies":["p848_C3_missing_cross_graph_definition_checker_v1","Konig's theorem for finite bipartite graphs"],"hypotheses":["H_{x,N} is finite because it is built from vertices <= N.","H_{x,N} is bipartite with parts L and R by C3.","Konig's theorem is available as a standard graph-theory lemma for finite bipartite graphs."],"proof":["C3 constructs H with all edges crossing between L and R.","Therefore H satisfies the finite bipartite hypotheses of Konig's theorem.","Apply Konig's theorem to replace minVertexCover(H) with maxMatching(H)."],"proofChecks":[{"checkId":"C3_dependency_discharged","passed":true,"evidence":"p848_C3_missing_cross_graph_definition_checker_v1"},{"checkId":"H_is_bipartite","passed":true,"evidence":"Every H edge runs between the B7-compatible side L and the B18-compatible side R."},{"checkId":"konig_theorem_applies","passed":true,"evidence":"For every finite bipartite graph, minimum vertex cover size equals maximum matching size."}],"failedChecks":[],"conclusion":"The minimum vertex cover term in C4 may be replaced by the maximum matching size of H_{x,N}.","falsifierBoundary":"A falsifier must show H is not bipartite/finite or that the invoked Konig theorem dependency is unavailable."},"C6_mixed_clique_matching_formula":{"checkerId":"p848_C6_mixed_clique_matching_formula_checker_v1","obligationId":"C6_mixed_clique_matching_formula","status":"proved_by_vertex_cover_konig_composition","checkedRowCount":5,"passCount":5,"failCount":0,"statement":"sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).","dependencies":["p848_C4_clique_to_vertex_cover_duality_checker_v1","p848_C5_konig_matching_reduction_checker_v1"],"hypotheses":["C4 proves max mixed clique size equals |L| + |R| minus minVertexCover(H).","C5 proves minVertexCover(H) equals maxMatching(H)."],"proof":["Start from the C4 identity maxClique = |L| + |R| - minVertexCover(H).","Substitute minVertexCover(H) = maxMatching(H) from C5.","The resulting identity is sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N})."],"rowChecks":[{"checkId":"worst_exact_row_matches_formula","N":7343,"p":13,"outsider":5309,"leftSize":108,"rightSize":112,"maxMatchingSize":108,"verifierCliqueSize":112,"formulaCliqueSize":112,"passed":true}],"proofChecks":[{"checkId":"C4_dependency_discharged","passed":true,"evidence":"p848_C4_clique_to_vertex_cover_duality_checker_v1"},{"checkId":"C5_dependency_discharged","passed":true,"evidence":"p848_C5_konig_matching_reduction_checker_v1"},{"checkId":"formula_composes_C4_and_C5","passed":true,"evidence":"maxClique = |L| + |R| - minVertexCover(H) and minVertexCover(H) = maxMatching(H)."},{"checkId":"verifier_row_formula_replay_available","passed":true,"evidence":[{"checkId":"worst_exact_row_matches_formula","N":7343,"p":13,"outsider":5309,"leftSize":108,"rightSize":112,"maxMatchingSize":108,"verifierCliqueSize":112,"formulaCliqueSize":112,"passed":true}]}],"failedChecks":[],"failedRows":[],"conclusion":"The verifier Hopcroft-Karp quantity has now been promoted to a theorem-facing graph formula.","falsifierBoundary":"A falsifier must break C4, break C5, or find a verifier row where |L| + |R| - matching disagrees with sMixed."},"D1_residue_block_matching_injection":{"checkerId":"p848_D1_matching_saturation_bound_checker_v1","obligationId":"D1_residue_block_matching_injection","status":"bounded_matching_saturation_extraction_certified","checkedRowCount":1739,"passCount":1739,"failCount":0,"statement":"Extract the current D-lane matching target: each bounded exact mixed-base threatening-outsider row has matching at least K(N,x), and the verifier matching saturates the smaller compatible side.","scope":{"problemId":"848","universalInN":false,"promotesAllNClaim":false,"boundedVerifierEvidenceRange":"7307..7600","boundedRowCount":1733,"sourceRowKind":"all_bounded_threatening_outsiders","observedPrimes":[13,17],"role":"bounded_extraction_packet_for_symbolic_D2_D3"},"dependencies":["p848_C6_mixed_clique_matching_formula_checker_v1","FULL_MIXED_BASE_STRUCTURAL_VERIFIER.liftMiningRows"],"hypotheses":["C6 has promoted the mixed-base clique size to |L| + |R| - maxMatching(H_{x,N}).","A strict mixed-base pass needs |L| + |R| - maxMatching(H_{x,N}) <= strictBaseThreshold - 1.","Equivalently, it is enough to prove maxMatching(H_{x,N}) >= |L| + |R| - strictBaseThreshold + 1.","The current packet is bounded to the exact mixed-base threatening-outsider rows emitted by the repo-owned full mixed-base structural verifier."],"proof":["For each exact mixed-base threatening-outsider row, compute K(N,x) = |L| + |R| - strictBaseThreshold + 1.","Replay the C6 formula against the verifier row to ensure |L| + |R| - matching equals the recorded mixed clique size.","Check that the recorded maximum matching is at least K(N,x).","Check the stronger bounded pattern that the recorded maximum matching saturates the smaller of the two compatible sides.","This certifies the bounded extraction target and routes the all-N burden to symbolic lower-bound packets D2 and D3."],"rowCheckSample":[{"N":7343,"p":13,"outsider":5309,"requiredMatchingLowerBound":89,"actualMatching":108,"matchingSlack":19,"smallerSideSize":108},{"N":7307,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105},{"N":7318,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105},{"N":7318,"p":13,"outsider":5309,"requiredMatchingLowerBound":88,"actualMatching":108,"matchingSlack":20,"smallerSideSize":108},{"N":7337,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105}],"rowChecksOmitted":1728,"proofChecks":[{"checkId":"C6_dependency_discharged","passed":true,"evidence":"p848_C6_mixed_clique_matching_formula_checker_v1"},{"checkId":"exact_mixed_lift_rows_available","passed":true,"evidence":{"rowCount":1733,"verifierLiftMiningRowCount":64,"verifierThreatLiftMiningRowCount":1733,"sourceRowKind":"all_bounded_threatening_outsiders"}},{"checkId":"primary_exact_primes_are_current_D_lane","passed":true,"evidence":[13,17]},{"checkId":"matching_lower_bound_formula_extracted","passed":true,"evidence":"K(N,x) = |L| + |R| - strictBaseThreshold + 1 is the matching lower bound needed for strict mixed-clique margin."},{"checkId":"all_rows_meet_required_matching_bound","passed":true,"evidence":{"primeSummaries":[{"p":13,"rowCount":1285,"minRequiredMatchingLowerBound":26,"maxRequiredMatchingLowerBound":90,"minActualMatching":79,"maxActualMatching":111,"minMatchingSlack":19,"allRowsSaturateSmallerSide":true,"allRowsMeetRequiredLowerBound":true},{"p":17,"rowCount":448,"minRequiredMatchingLowerBound":1,"maxRequiredMatchingLowerBound":14,"minActualMatching":103,"maxActualMatching":112,"minMatchingSlack":95,"allRowsSaturateSmallerSide":true,"allRowsMeetRequiredLowerBound":true}],"tightestRows":[{"N":7343,"p":13,"outsider":5309,"requiredMatchingLowerBound":89,"actualMatching":108,"matchingSlack":19,"smallerSideSize":108},{"N":7307,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105},{"N":7318,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105},{"N":7318,"p":13,"outsider":5309,"requiredMatchingLowerBound":88,"actualMatching":108,"matchingSlack":20,"smallerSideSize":108},{"N":7337,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105}]}},{"checkId":"all_rows_saturate_smaller_side","passed":true,"evidence":[{"p":13,"rowCount":1285,"minRequiredMatchingLowerBound":26,"maxRequiredMatchingLowerBound":90,"minActualMatching":79,"maxActualMatching":111,"minMatchingSlack":19,"allRowsSaturateSmallerSide":true,"allRowsMeetRequiredLowerBound":true},{"p":17,"rowCount":448,"minRequiredMatchingLowerBound":1,"maxRequiredMatchingLowerBound":14,"minActualMatching":103,"maxActualMatching":112,"minMatchingSlack":95,"allRowsSaturateSmallerSide":true,"allRowsMeetRequiredLowerBound":true}]}],"failedChecks":[],"failedRows":[],"primeSummaries":[{"p":13,"rowCount":1285,"minRequiredMatchingLowerBound":26,"maxRequiredMatchingLowerBound":90,"minActualMatching":79,"maxActualMatching":111,"minMatchingSlack":19,"allRowsSaturateSmallerSide":true,"allRowsMeetRequiredLowerBound":true},{"p":17,"rowCount":448,"minRequiredMatchingLowerBound":1,"maxRequiredMatchingLowerBound":14,"minActualMatching":103,"maxActualMatching":112,"minMatchingSlack":95,"allRowsSaturateSmallerSide":true,"allRowsMeetRequiredLowerBound":true}],"tightestRows":[{"N":7343,"p":13,"outsider":5309,"requiredMatchingLowerBound":89,"actualMatching":108,"matchingSlack":19,"smallerSideSize":108},{"N":7307,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105},{"N":7318,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105},{"N":7318,"p":13,"outsider":5309,"requiredMatchingLowerBound":88,"actualMatching":108,"matchingSlack":20,"smallerSideSize":108},{"N":7337,"p":13,"outsider":4831,"requiredMatchingLowerBound":85,"actualMatching":105,"matchingSlack":20,"smallerSideSize":105}],"conclusion":"All 1733 current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row.","falsifierBoundary":"A refreshed verifier row falsifies this bounded extraction if matching < |L| + |R| - strictBaseThreshold + 1, if the C6 formula replay disagrees, or if the smaller-side saturation pattern fails. This is not yet the all-N symbolic matching proof."},"D2_p13_split_core_witness_extraction":{"checkerId":"p848_D2_p13_split_core_witness_checker_v1","obligationId":"D2_p13_split_core_witness_extraction","parentObligationId":"D2_p13_matching_lower_bound","status":"bounded_split_core_witness_certified","checkedRowCount":12,"passCount":12,"failCount":0,"statement":"The tight p=13 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.","scope":{"problemId":"848","universalInN":false,"promotesAllNClaim":false,"targetPrime":13,"sourceArtifact":"MATCHING_PATTERN_MINER.json","sourceAssessedRange":"7307..7600","witnessRowCount":12,"splitProfileCount":3,"role":"bounded_split_core_witness_for_symbolic_D2_lift"},"dependencies":["p848_D1_matching_saturation_bound_checker_v1","p848_D2_p13_matching_lower_bound_candidate_v1","MATCHING_PATTERN_MINER.patternSummary.splitProfiles"],"hypotheses":["D1 has extracted the p=13 matching lower-bound target K(N,x).","The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=13 rows.","The sampled tight rows split by outsider residue modulo 13^2, outsider residue modulo 25, and which side is smaller.","Within each split profile, the common matching core is a matching present in every sampled row of that profile."],"proof":["Read the p=13 split profiles from MATCHING_PATTERN_MINER.patternSummary.","For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.","Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.","Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.","This does not discharge D2 universally; it turns D2 into explicit split symbolic subgoals 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66049)","gcdCoeffWitness":1,"laneIndexResidue":7,"laneIndexPeriod":66049,"missedLaneIndex":7,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":382,"continuation":382,"familyIndex":83,"representative":537246638,"tupleKey":"31^2, 37^2, 11^2, 9, 13^2, 17^2","repairValue":205228215717,"squareWitnesses":[49],"missedLaneIndex":7,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":49,"laneEquation":"5*m ≡ 35 (mod 49)","gcdCoeffWitness":1,"laneIndexResidue":7,"laneIndexPeriod":49,"missedLaneIndex":7,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":382,"continuation":382,"familyIndex":130,"representative":850856389,"tupleKey":"4, 9, 17^2, 37^2, 13^2, 11^2","repairValue":325027140599,"squareWitnesses":[49],"missedLaneIndex":7,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":49,"laneEquation":"5*m ≡ 35 (mod 49)","gcdCoeffWitness":1,"laneIndexResidue":7,"laneIndexPeriod":49,"missedLaneIndex":7,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":382,"continuation":382,"familyIndex":258,"representative":1705839349,"tupleKey":"4, 41^2, 11^2, 7^2, 37^2, 9","repairValue":651630631319,"squareWitnesses":[289],"missedLaneIndex":7,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":289,"laneEquation":"15*m ≡ 105 (mod 289)","gcdCoeffWitness":1,"laneIndexResidue":7,"laneIndexPeriod":289,"missedLaneIndex":7,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":382,"continuation":832,"familyIndex":217,"representative":1446717451,"tupleKey":"11^2, 29^2, 4, 7^2, 31^2, 9","repairValue":1203668919233,"squareWitnesses":[529],"missedLaneIndex":16,"repairedContinuation":382,"repairedLaneIndex":7,"laneWitnessSignatures":[{"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","gcdCoeffWitness":1,"laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":7,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":382,"continuation":832,"familyIndex":270,"representative":1797117529,"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 11^2","repairValue":1495201784129,"squareWitnesses":[529],"missedLaneIndex":16,"repairedContinuation":382,"repairedLaneIndex":7,"laneWitnessSignatures":[{"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","gcdCoeffWitness":1,"laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":7,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":382,"continuation":832,"familyIndex":271,"representative":1797117529,"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 9","repairValue":1495201784129,"squareWitnesses":[529],"missedLaneIndex":16,"repairedContinuation":382,"repairedLaneIndex":7,"laneWitnessSignatures":[{"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","gcdCoeffWitness":1,"laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":7,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"familyIndex":104,"representative":681558029,"tupleKey":"4, 7^2, 41^2, 9, 17^2, 11^2","repairValue":839679491729,"squareWitnesses":[1369],"missedLaneIndex":24,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":1369,"laneEquation":"500*m ≡ 1048 (mod 1369)","gcdCoeffWitness":1,"laneIndexResidue":24,"laneIndexPeriod":1369,"missedLaneIndex":24,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"familyIndex":107,"representative":695323423,"tupleKey":"11^2, 13^2, 4, 7^2, 23^2, 19^2","repairValue":856638457137,"squareWitnesses":[9],"missedLaneIndex":24,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":9,"laneEquation":"5*m ≡ 3 (mod 9)","gcdCoeffWitness":1,"laneIndexResidue":6,"laneIndexPeriod":9,"missedLaneIndex":24,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"familyIndex":161,"representative":1079001739,"tupleKey":"31^2, 17^2, 4, 11^2, 61^2, 43^2","repairValue":1329330142449,"squareWitnesses":[9],"missedLaneIndex":24,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":9,"laneEquation":"5*m ≡ 3 (mod 9)","gcdCoeffWitness":1,"laneIndexResidue":6,"laneIndexPeriod":9,"missedLaneIndex":24,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"familyIndex":187,"representative":1256825183,"tupleKey":"9, 7^2, 4, 13^2, 23^2, 11^2","repairValue":1548408625457,"squareWitnesses":[289],"missedLaneIndex":24,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":289,"laneEquation":"83*m ≡ 258 (mod 289)","gcdCoeffWitness":1,"laneIndexResidue":24,"laneIndexPeriod":289,"missedLaneIndex":24,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"familyIndex":234,"representative":1583883827,"tupleKey":"41^2, 59^2, 4, 9, 7^2, 11^2","repairValue":1951344874865,"squareWitnesses":[361],"missedLaneIndex":24,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":361,"laneEquation":"99*m ≡ 210 (mod 361)","gcdCoeffWitness":1,"laneIndexResidue":24,"laneIndexPeriod":361,"missedLaneIndex":24,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"contrast_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":1232,"familyIndex":275,"representative":1820631943,"tupleKey":"23^2, 19^2, 4, 7^2, 79^2, 11^2","repairValue":2243018553777,"squareWitnesses":[9],"missedLaneIndex":24,"repairedContinuation":832,"repairedLaneIndex":16,"laneWitnessSignatures":[{"witnessSquareModulus":9,"laneEquation":"5*m ≡ 3 (mod 9)","gcdCoeffWitness":1,"laneIndexResidue":6,"laneIndexPeriod":9,"missedLaneIndex":24,"repairedLaneIndex":16,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"familyIndex":217,"representative":1446717451,"tupleKey":"11^2, 29^2, 4, 7^2, 31^2, 9","repairValue":1203668919233,"squareWitnesses":[529],"missedLaneIndex":16,"repairedContinuation":1232,"repairedLaneIndex":24,"laneWitnessSignatures":[{"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","gcdCoeffWitness":1,"laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":24,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"familyIndex":256,"representative":1684455347,"tupleKey":"11^2, 47^2, 4, 13^2, 7^2, 31^2","repairValue":1401466848705,"squareWitnesses":[9],"missedLaneIndex":16,"repairedContinuation":1232,"repairedLaneIndex":24,"laneWitnessSignatures":[{"witnessSquareModulus":9,"laneEquation":"1*m ≡ 7 (mod 9)","gcdCoeffWitness":1,"laneIndexResidue":7,"laneIndexPeriod":9,"missedLaneIndex":16,"repairedLaneIndex":24,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"familyIndex":270,"representative":1797117529,"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 11^2","repairValue":1495201784129,"squareWitnesses":[529],"missedLaneIndex":16,"repairedContinuation":1232,"repairedLaneIndex":24,"laneWitnessSignatures":[{"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","gcdCoeffWitness":1,"laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":24,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"},{"exchangeKind":"top_only_miss","topContinuation":832,"contrastContinuation":1232,"continuation":832,"familyIndex":271,"representative":1797117529,"tupleKey":"4, 53^2, 17^2, 7^2, 61^2, 9","repairValue":1495201784129,"squareWitnesses":[529],"missedLaneIndex":16,"repairedContinuation":1232,"repairedLaneIndex":24,"laneWitnessSignatures":[{"witnessSquareModulus":529,"laneEquation":"459*m ≡ 467 (mod 529)","gcdCoeffWitness":1,"laneIndexResidue":16,"laneIndexPeriod":529,"missedLaneIndex":16,"repairedLaneIndex":24,"missedLaneIndexMatches":true,"repairedLaneIndexMatches":false}],"laneSignatureStatus":"passed"}],"conclusion":"Every pairwise exchange row is explained by a bad lane-index congruence m modulo the square witness; the missed continuation hits that congruence and the repaired continuation does not.","nextProofObligations":["Generalize the finite-menu lane-index congruence schema beyond the currently replayed exchange rows.","Choose the strict 782 vs 1232 handoff rows or a broader exchange family as the next theorem-facing symbolic family.","Connect the lane-index bad-family schema back to the finite-gap closure target rather than treating it as only a leaderboard feature."]},"verifiedAgainstBridge":{"allScoresMatchLeaderboard":true,"allScoresMatchTrackedRows":true,"allTopMiss13":true,"allPrimaryContrastsMiss15":true,"allTopRepair242":true,"allPrimaryContrastsRepair240":true,"allPairwiseNetPlus2":true},"conclusion":"The current finite menu has 255 predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence."},"commonMissedPredictedRepresentatives":[210290957,287180657,517124182,525631657,1229502607],"tailSpecificMissedPredictedRepresentatives":{"432":[457148843,770426585],"782":[695323423,1079001739],"832":[1446717451,1654841707]},"residueLaneAssessment":{"tieClassModulo50":[32],"nearbyModulo50Values":[32],"verdict":"shared_mod_50_lane_but_not_sufficient","note":"The top tie is in the same mod-50 lane as several near contrasts, so the mod-50 lane is useful context but not by itself the repair mechanism."},"mechanismHypotheses":[{"hypothesisId":"shared_repair_count_signature","status":"supported_by_bridge","note":"All top tails share repaired-known=26, repaired-predicted=242, and clean-through=250075000 on the bridge leaderboard."},{"hypothesisId":"plus50_lane_context","status":"necessary_not_sufficient","note":"The top tails share the same mod-50 lane, but nearby contrasts in that lane do not all reach 242 predicted repairs."},{"hypothesisId":"common_missed_family_boundary","status":"supported_by_tracked_tail_matrix","note":"The top tails share 5 early missed predicted representatives in the tracked-tail matrix."},{"hypothesisId":"finite_menu_plus2_separation","status":"certified_by_replay","note":"The current finite menu has 255 predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence."}],"falsifierBoundary":["A bridge refresh breaks the 432, 782, 832 tie on repaired-known, repaired-predicted, or clean-through metrics.","A near contrast such as 332, 382, or 1232 reaches the same predicted repair count under the same evidence boundary.","The apparent common missed-family representatives disappear when the family menu is refreshed.","A direct exact extension finds an earlier failure for one member of the top tie inside the claimed clean-through window."],"nextProofObligations":["Generalize the mod-50 lane-index bad-family signature beyond the finite exchange rows.","Derive a residue or family signature that separates the top tie from the rest of the mod-50 lane.","Choose the strict 782 vs 1232 handoff rows or a broader exchange family as the next theorem-facing symbolic family."]}` +- tupleRowLift132: `{"preAnchorCombinedResidue":546209,"preAnchorCombinedModulus":933156,"preAnchorResidueModuloWitness":400,"anchorResidue":81,"anchorSquareModulus":289,"liftCoeffModuloAnchor":264,"liftRhsModuloAnchor":82,"liftedEquation":"546209 + 933156*k ≡ 81 (mod 289)","reducedEquation":"264*k ≡ 82 (mod 289)","inverseLiftCoeff":104,"liftParameter":147,"liftedResidue":137720141,"liftedResidueModuloWitness":504}` +- tupleRowLift132Proof: `{"checkerId":"p848_132_lift_crt_checker_v1","source":"tuple_row_crt_equation_replay","status":"proved_from_tuple_row_crt","checkedRowCount":1,"passCount":1,"failCount":0,"equation":"546209 + 933156*k ≡ 81 (mod 289)","reducedEquation":"264*k ≡ 82 (mod 289)","liftParameter":147,"liftedResidueByParameter":137720141,"liftedResidueModuloWitness":504,"targetWitnessResidue":504,"checks":{"liftParameterSolvesReducedEquation":true,"liftedResidueMatchesCrtStep":true,"liftedResidueSatisfiesAnchor132":true,"liftedResiduePreservesPriorCrtPrefix":true,"liftedResidueHitsWitnessProjection":true,"liftedResidueHitsBoundaryWitnessResidue":true},"failedChecks":[],"conclusion":"The 132-row lift from residue 400 to 504 mod 841 is proved by the tuple-row CRT equation."}` +- tupleRowPreservation182: `{"anchorResidue":119,"anchorSquareModulus":121,"preserved":true,"liftedResidueModuloAnchor":119,"liftedResidueModuloWitness":504,"checkEquation":"137720141 ≡ 119 (mod 121)"}` +- tupleSquareModuli: `[4,529,49,9,289,121]` +- witnessSquareModulus: `841` +- witnessPrime: `29` +- witnessExponent: `2` +- representativeResidueModuloWitness: `504` +- repairResidues: `[{"anchor":157,"residueModuloWitness":75,"squarefree":true},{"anchor":232,"residueModuloWitness":30,"squarefree":true},{"anchor":282,"residueModuloWitness":0,"squarefree":false},{"anchor":332,"residueModuloWitness":811,"squarefree":true},{"anchor":382,"residueModuloWitness":781,"squarefree":true},{"anchor":432,"residueModuloWitness":751,"squarefree":true},{"anchor":782,"residueModuloWitness":541,"squarefree":true},{"anchor":832,"residueModuloWitness":511,"squarefree":true}]` +- anchorCongruenceTable: `[{"anchor":157,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":766,"matchesRepresentativeResidue":false,"solvableModuloWitness":true,"residueCheck":75,"squarefree":true},{"anchor":232,"gcdWithWitness":29,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":null,"matchesRepresentativeResidue":false,"solvableModuloWitness":false,"residueCheck":30,"squarefree":true},{"anchor":282,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":504,"matchesRepresentativeResidue":true,"solvableModuloWitness":true,"residueCheck":0,"squarefree":false},{"anchor":332,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":803,"matchesRepresentativeResidue":false,"solvableModuloWitness":true,"residueCheck":811,"squarefree":true},{"anchor":382,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":284,"matchesRepresentativeResidue":false,"solvableModuloWitness":true,"residueCheck":781,"squarefree":true},{"anchor":432,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":329,"matchesRepresentativeResidue":false,"solvableModuloWitness":true,"residueCheck":751,"squarefree":true},{"anchor":782,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":784,"matchesRepresentativeResidue":false,"solvableModuloWitness":true,"residueCheck":541,"squarefree":true},{"anchor":832,"gcdWithWitness":1,"representativeResidueModuloWitness":504,"requiredNResidueForFailure":187,"matchesRepresentativeResidue":false,"solvableModuloWitness":true,"residueCheck":511,"squarefree":true}]` +- rowProgressionAnchorTable: `[{"anchor":157,"progressionCoeffModuloWitness":186,"progressionRhsModuloWitness":766,"gcdCoeffWitness":1,"rowIndexForWitness":610,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":true,"squarefree":true},{"anchor":232,"progressionCoeffModuloWitness":232,"progressionRhsModuloWitness":811,"gcdCoeffWitness":29,"rowIndexForWitness":null,"rowIndexPeriod":null,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":false,"squarefree":true},{"anchor":282,"progressionCoeffModuloWitness":543,"progressionRhsModuloWitness":0,"gcdCoeffWitness":1,"rowIndexForWitness":0,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":true,"solvableAlongRowProgression":true,"squarefree":false},{"anchor":332,"progressionCoeffModuloWitness":13,"progressionRhsModuloWitness":30,"gcdCoeffWitness":1,"rowIndexForWitness":67,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":true,"squarefree":true},{"anchor":382,"progressionCoeffModuloWitness":324,"progressionRhsModuloWitness":60,"gcdCoeffWitness":1,"rowIndexForWitness":592,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":true,"squarefree":true},{"anchor":432,"progressionCoeffModuloWitness":635,"progressionRhsModuloWitness":90,"gcdCoeffWitness":1,"rowIndexForWitness":318,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":true,"squarefree":true},{"anchor":782,"progressionCoeffModuloWitness":289,"progressionRhsModuloWitness":300,"gcdCoeffWitness":1,"rowIndexForWitness":164,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":true,"squarefree":true},{"anchor":832,"progressionCoeffModuloWitness":600,"progressionRhsModuloWitness":330,"gcdCoeffWitness":1,"rowIndexForWitness":379,"rowIndexPeriod":841,"witnessOccursAtCurrentRepresentative":false,"solvableAlongRowProgression":true,"squarefree":true}]` +- rowStartDerivation282: `{"rowFormula":"n_t = 137720141 + 32631532164 * t","witnessEquation":"282*n_t + 1 ≡ 0 (mod 841)","substitutedEquation":"543*t ≡ 0 (mod 841)","gcdCoeffWitness":1,"normalizedEquation":"t ≡ 0 (mod 841)","representativeResidue":504,"requiredFailureResidue":504,"representativeAlreadyOnWitnessClass":true}` +- unsolvableContrast232: `{"witnessEquation":"232*n_t + 1 ≡ 0 (mod 841)","substitutedEquation":"232*t ≡ 811 (mod 841)","gcdCoeffWitness":29,"solvable":false,"divisibilityFailure":"29 does not divide 811"}` +- firstFailingRepresentative: `137720141` +- witnessFirstOccurrence: `{"squareModulus":841,"firstRepresentative":137720141,"firstTupleKey":"4, 23^2, 7^2, 9, 17^2, 11^2","earlierRowCount":25,"earlierZeroResidueCount":0}` +- familyMenuResidueBoundary: `{"witnessSquareModulus":841,"representativeResidueModuloWitness":504,"firstRepresentative":137720141,"firstTupleKey":"4, 23^2, 7^2, 9, 17^2, 11^2","firstFamilyIndex":25,"earlierRepresentativeMatchCount":0,"sameAsFirstFailingRepresentative":true,"firstRepresentativeHasWitness":true}` +- sameTupleCount: `1` +- rowProgressionModuloWitness: `{"gcdModulusWitness":1,"modulusModWitness":494,"residueModWitness":504,"traversesAllWitnessResidues":true}` +- nextSameRowWitnessFor282: `27443256270065` +- priorRowsModuloWitness: `[{"representative":127484267,"tupleKey":"9, 17^2, 4, 29^2, 7^2, 11^2","residueModuloWitness":736,"squarefree":true},{"representative":127682743,"tupleKey":"131^2, 11^2, 4, 29^2, 13^2, 9","residueModuloWitness":736,"squarefree":true},{"representative":136702637,"tupleKey":"4, 43^2, 11^2, 9, 7^2, 19^2","residueModuloWitness":457,"squarefree":true}]` +- laterWitnessTimeline: `[{"representative":210290957,"tupleKey":"4, 53^2, 23^2, 9, 13^2, 31^2","witnessSquareModulus":25},{"representative":287180657,"tupleKey":"19^2, 103^2, 11^2, 9, 7^2, 23^2","witnessSquareModulus":25},{"representative":287180657,"tupleKey":"4, 103^2, 11^2, 9, 7^2, 23^2","witnessSquareModulus":25},{"representative":517124182,"tupleKey":"11^2, 17^2, 23^2, 13^2, 7^2, 9","witnessSquareModulus":25},{"representative":525631657,"tupleKey":"4, 11^2, 13^2, 23^2, 19^2, 9","witnessSquareModulus":25}]` +- mechanismFalsifierBoundary: `{"lowerRepresentativeSameWitnessResidueBreaksMechanism":"A refreshed family menu finds a representative below 137720141 with residue 504 mod 841.","differentFirstWitnessBreaksMechanism":"A refreshed family menu finds a 282 failure below 137720141 or with first witness different from 841.","bridgeAlignmentBreaksMechanism":"A refreshed bridge no longer matches next unmatched representative 137720141 with tracked tail 282 first failure.","commands":["erdos number-theory bridge-refresh 848","erdos problem claim-pass 848","erdos problem formalization-work-refresh 848"]}` +- familyMenuPath: `"/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/SIX_PREFIX_TWENTY_FOUR_FAMILY_MENU.json"` +- bridgePath: `"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json"` + +## Commands + +- Problem surface: `erdos problem show 848` +- Problem artifacts: `erdos problem artifacts 848` +- Formalization: `erdos problem formalization 848` +- Formalization refresh: `erdos problem formalization-refresh 848` +- Formalization work: `erdos problem formalization-work 848` +- Formalization work refresh: `erdos problem formalization-work-refresh 848` +- Claim pass: `erdos problem claim-pass 848` +- Source refresh: `erdos number-theory bridge-refresh 848` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION_WORK.json` +- formalizationWorkMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION_WORK.md` +- formalizationWorkSvgPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION_WORK.svg` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json` diff --git a/packs/number-theory/problems/848/FORMALIZATION_WORK.svg b/packs/number-theory/problems/848/FORMALIZATION_WORK.svg new file mode 100644 index 0000000..c8beb8f --- /dev/null +++ b/packs/number-theory/problems/848/FORMALIZATION_WORK.svg @@ -0,0 +1 @@ +Erdos Problem #848 formalization work diagramDiagram of the 848 shared-prefix row progression showing when tracked anchors hit witness 841 and why anchor 282 is special at row index 0.Erdos Problem #848: 282 / 841 MechanismRepresentative 137720141 on tuple 4, 23^2, 7^2, 9, 17^2, 11^2Witness 841 is the extra repair witness; the row progression itself still traverses all residues modulo 841.Tuple-row CRT projects to 504 mod 841, stabilizing when anchor 132 is added.Verdictcontrolled_congruence_candidateRepresentative residue504 mod 841282 row startt = 0Next same-row 282 hit27443256270065Verified base1..40500Shared-Prefix Row ProgressionEach point shows the first row index t where a tracked anchor can hit witness 841 along n = residue + modulus * t.never0210420630841157t=610232no solution282t=0332t=67382t=592432t=318782t=164832t=379Residue Match SliceRepresentative residue 504 matches only the 282 failure residue class.157needs 766later/other residueres=75232needs noneunsolvableres=30282needs 504matches repres=0332needs 803later/other residueres=811382needs 284later/other residueres=781432needs 329later/other residueres=751782needs 784later/other residueres=541832needs 187later/other residueres=511Earlier Boundary RowsEarlier rows stay nonzero mod 841 before the first 282 failure lands.127484267res=7369, 17^2, 4, 29^2, 7^2, 11^2127682743res=736131^2, 11^2, 4, 29^2, 13^2, 9136702637res=4574, 43^2, 11^2, 9, 7^2, 19^2Tuple-Row CRT ProjectionAs tuple congruences are added, the projected residue modulo 841 evolves toward the boundary value 504.a=7mod 4res 1a=32mod 2116res 281a=57mod 103684res 36a=82mod 933156res 400a=132mod 269682084res 504a=182mod 32631532164res 504North-star reading: the row does not force 841 by itself, but the boundary representative is the unique tracked start-point of the 282 witness class inside that row progression. \ No newline at end of file diff --git a/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json b/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json new file mode 100644 index 0000000..a1d7751 --- /dev/null +++ b/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json @@ -0,0 +1,75235 @@ +{ + "schema": "erdos.number_theory.p848_full_mixed_base_structural_verifier/1", + "generatedAt": "2026-04-11T20:44:57.829Z", + "problemId": "848", + "method": "bounded_outsider_clique_full_mixed_base_structural_verifier", + "status": "bounded_full_mixed_base_structural_verifier_certified", + "parameters": { + "maxN": 7600, + "minStructuralN": 7307, + "rowSampleLimit": 200, + "assessedRange": "7307..7600" + }, + "summary": { + "assessedRange": "7307..7600", + "witnessBlockCount": 8, + "breakpointCount": 32, + "checkCount": 256, + "globalRootEventCount": 193, + "side7BaseCountAtMax": 304, + "side18BaseCountAtMax": 304, + "unionCertifiedRowCount": 192, + "exactMixedRowCount": 64, + "threateningOutsiderCheckCount": 1733, + "mixedFailureCount": 0, + 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"exact_mixed_base", + "threateningOutsiderCount": 40, + "exactMixedCheckCount": 40, + "sMaxMixed": 112, + "sMaxMixedWitness": 5309, + "mixedBound": 274, + "mixedMargin": 20, + "mixedPass": true, + "maxImprovementOverUnion": 109, + "worstThreat": { + "outsider": 5309, + "unionCount": 220, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "exampleMixedBaseClique": [ + 43, + 118, + 143, + 243, + 268, + 343, + 368, + 443, + 543, + 568, + 643, + 718, + 743, + 793, + 843, + 943, + 1018, + 1043, + 1068, + 1143, + 1243, + 1318, + 1343, + 1443, + 1468, + 1493, + 1543, + 1618, + 1643, + 1693, + 1743, + 1843, + 1918, + 1943, + 2043, + 2143, + 2243, + 2343, + 2368, + 2443, + 2543, + 2593, + 2643, + 2718, + 2743, + 2818, + 2843, + 2943, + 3043, + 3143, + 3243, + 3268, + 3343, + 3443, + 3493, + 3543, + 3643, + 3718, + 3743, + 3843, + 3943, + 4043, + 4143, + 4168, + 4243, + 4343, + 4393, + 4443, + 4543, + 4618, + 4643, + 4743, + 4843, + 4943, + 5043, + 5068, + 5143, + 5168, + 5243, + 5293, + 5343, + 5443, + 5518, + 5543, + 5643, + 5718, + 5743, + 5843, + 5943, + 5968, + 6043, + 6143, + 6193, + 6243, + 6343, + 6393, + 6418, + 6443, + 6543, + 6643, + 6743, + 6768, + 6843, + 6868, + 6943, + 7043, + 7093, + 7143, + 7168, + 7243, + 7318, + 7343 + ] + }, + "threatMatchingSummary": { + "threatCount": 40, + "minRequiredMatchingLowerBound": 29, + "maxRequiredMatchingLowerBound": 89, + "minActualMatching": 79, + "maxActualMatching": 109, + "minMatchingSlack": 19, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "tightestThreats": [ + { + "outsider": 5309, + "outsiderMod25": 9, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 89, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 19, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 1789, + "outsiderMod25": 14, + "compatibleSide7Count": 108, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 88, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 20, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 4831, + "outsiderMod25": 6, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSizeInMissingCrossGraph": 105, + "matchingSlack": 20, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side7" + }, + { + "outsider": 3281, + "outsiderMod25": 6, + "compatibleSide7Count": 108, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 87, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 21, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 6323, + "outsiderMod25": 23, + "compatibleSide7Count": 105, + "compatibleSide18Count": 110, + 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"outsiderMod25": 10, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 217, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 106, + "compatibleSide7Count": 106, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 2, + "matchingSlack": 104, + "smallerSideSize": 106, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7593, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 7187, + "outsiderMod25": 12, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 5, + "matchingSlack": 104, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 251, + "outsiderMod25": 1, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 226, + "mixedBaseCliqueSize": 115, + "matchingSizeInMissingCrossGraph": 111, + "compatibleSide7Count": 115, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 11, + "matchingSlack": 100, + "smallerSideSize": 111, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 115, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 829, + "outsiderMod25": 4, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 224, + "mixedBaseCliqueSize": 113, + "matchingSizeInMissingCrossGraph": 111, + "compatibleSide7Count": 111, + "compatibleSide18Count": 113, + "requiredMatchingLowerBound": 9, + "matchingSlack": 102, + "smallerSideSize": 111, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 113, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 905, + "outsiderMod25": 5, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 223, + "mixedBaseCliqueSize": 113, + "matchingSizeInMissingCrossGraph": 110, + "compatibleSide7Count": 110, + "compatibleSide18Count": 113, + "requiredMatchingLowerBound": 8, + "matchingSlack": 102, + "smallerSideSize": 110, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 113, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 1483, + "outsiderMod25": 8, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 221, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 110, + "compatibleSide7Count": 111, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 6, + "matchingSlack": 104, + "smallerSideSize": 110, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 111, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 1985, + "outsiderMod25": 10, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 222, + "mixedBaseCliqueSize": 114, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 114, + "requiredMatchingLowerBound": 7, + "matchingSlack": 101, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 114, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 2563, + "outsiderMod25": 13, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 111, + "compatibleSide18Count": 109, + "requiredMatchingLowerBound": 5, + "matchingSlack": 104, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 111, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 3217, + "outsiderMod25": 17, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 5, + "matchingSlack": 104, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 3719, + "outsiderMod25": 19, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 226, + "mixedBaseCliqueSize": 114, + "matchingSizeInMissingCrossGraph": 112, + "compatibleSide7Count": 114, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 11, + "matchingSlack": 101, + "smallerSideSize": 112, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 114, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 4297, + "outsiderMod25": 22, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 224, + "mixedBaseCliqueSize": 113, + "matchingSizeInMissingCrossGraph": 111, + "compatibleSide7Count": 113, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 9, + "matchingSlack": 102, + "smallerSideSize": 111, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 113, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 225, + "mixedBaseCliqueSize": 114, + "matchingSizeInMissingCrossGraph": 111, + "compatibleSide7Count": 111, + "compatibleSide18Count": 114, + "requiredMatchingLowerBound": 10, + "matchingSlack": 101, + "smallerSideSize": 111, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 114, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 4951, + "outsiderMod25": 1, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 225, + "mixedBaseCliqueSize": 113, + "matchingSizeInMissingCrossGraph": 112, + "compatibleSide7Count": 112, + "compatibleSide18Count": 113, + "requiredMatchingLowerBound": 10, + "matchingSlack": 102, + "smallerSideSize": 112, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 113, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 6031, + "outsiderMod25": 6, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 223, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 111, + "compatibleSide7Count": 111, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 8, + "matchingSlack": 103, + "smallerSideSize": 111, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 6685, + "outsiderMod25": 10, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 217, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 106, + "compatibleSide7Count": 106, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 2, + "matchingSlack": 104, + "smallerSideSize": 106, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7600, + "certificateMode": "exact_mixed_base", + "nMod25": 0, + "p": 17, + "p2": 289, + "outsider": 7187, + "outsiderMod25": 12, + "activePlus": 24, + "activeMinus": 23, + "activeOutsiderCount": 47, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 251, + "rGreater": 50, + "candidateSize": 304, + "strictBaseThreshold": 216, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 5, + "matchingSlack": 104, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + } + ], + "failureRowsSample": [], + "boundary": { + "claimLevel": "bounded_structural_certificate_not_all_N_proof", + "proofObligation": "Every witness-prime block and structural breakpoint in the assessed range is certified either by the safe union bound or by exact mixed-base clique checks for every threatening active outsider.", + "cliqueReduction": "For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges.", + "promotionRule": "Promote bounded structural coverage only when allMixedChecksPass is true for the full assessed range and all artifact parameters match the intended handoff range.", + "nextUse": "Use this as the repo-owned bounded structural certificate and extend the assessed range or lift the finite-block argument." + } +} diff --git a/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md b/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md new file mode 100644 index 0000000..e714a37 --- /dev/null +++ b/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md @@ -0,0 +1,37 @@ +# Problem 848 Full Mixed-Base Structural Verifier + +- Generated: 2026-04-11T20:44:57.829Z +- Method: `bounded_outsider_clique_full_mixed_base_structural_verifier` +- Status: `bounded_full_mixed_base_structural_verifier_certified` +- Assessed range: `7307..7600` +- Witness blocks: `8` +- Breakpoints: `32` +- Structural rows checked: `256` +- Rows certified by union bound: `192` +- Rows requiring exact mixed-base checks: `64` +- Compact lift-mining rows: `64` +- Compact threatening-outsider rows: `1733` +- Threatening outsider checks: `1733` + +## Pass/Fail Summary + +- All mixed checks pass: `yes` +- Mixed failures: `0` +- Minimum certified margin: `20` +- Minimum exact mixed margin: `20` +- Max threatening outsiders in one row: `41` +- Max improvement over union: `112` + +## Key Rows + +- First mixed failure: `(none)` +- Worst certified row: `{"N":7343,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"activeOutsiderCount":80,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":112,"sMaxSide18Witness":5309,"sMaxUnion":220,"sMaxUnionWitness":5309,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":294,"side7CandidateSize":294,"side18CandidateSize":294,"side7Bound":273,"side18Bound":274,"unionBound":382,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":20,"unionMargin":-88,"side7Pass":true,"side18Pass":true,"unionPass":false,"certificateMode":"exact_mixed_base","threateningOutsiderCount":40,"exactMixedCheckCount":40,"sMaxMixed":112,"sMaxMixedWitness":5309,"mixedBound":274,"mixedMargin":20,"mixedPass":true,"maxImprovementOverUnion":109,"worstThreat":{"outsider":5309,"unionCount":220,"mixedBaseCliqueSize":112,"matchingSizeInMissingCrossGraph":108,"compatibleSide7Count":108,"compatibleSide18Count":112,"mixedCliqueSide7Count":0,"mixedCliqueSide18Count":112,"exampleMixedBaseClique":[43,118,143,243,268,343,368,443,543,568,643,718,743,793,843,943,1018,1043,1068,1143,1243,1318,1343,1443,1468,1493,1543,1618,1643,1693,1743,1843,1918,1943,2043,2143,2243,2343,2368,2443,2543,2593,2643,2718,2743,2818,2843,2943,3043,3143,3243,3268,3343,3443,3493,3543,3643,3718,3743,3843,3943,4043,4143,4168,4243,4343,4393,4443,4543,4618,4643,4743,4843,4943,5043,5068,5143,5168,5243,5293,5343,5443,5518,5543,5643,5718,5743,5843,5943,5968,6043,6143,6193,6243,6343,6393,6418,6443,6543,6643,6743,6768,6843,6868,6943,7043,7093,7143,7168,7243,7318,7343]},"threatMatchingSummary":{"threatCount":40,"minRequiredMatchingLowerBound":29,"maxRequiredMatchingLowerBound":89,"minActualMatching":79,"maxActualMatching":109,"minMatchingSlack":19,"allThreatsMeetRequiredLowerBound":true,"allThreatsSaturateSmallerSide":true,"tightestThreats":[{"outsider":5309,"outsiderMod25":9,"compatibleSide7Count":108,"compatibleSide18Count":112,"requiredMatchingLowerBound":89,"matchingSizeInMissingCrossGraph":108,"matchingSlack":19,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":1789,"outsiderMod25":14,"compatibleSide7Count":108,"compatibleSide18Count":111,"requiredMatchingLowerBound":88,"matchingSizeInMissingCrossGraph":108,"matchingSlack":20,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":4831,"outsiderMod25":6,"compatibleSide7Count":111,"compatibleSide18Count":105,"requiredMatchingLowerBound":85,"matchingSizeInMissingCrossGraph":105,"matchingSlack":20,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side7"},{"outsider":3281,"outsiderMod25":6,"compatibleSide7Count":108,"compatibleSide18Count":110,"requiredMatchingLowerBound":87,"matchingSizeInMissingCrossGraph":108,"matchingSlack":21,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":6323,"outsiderMod25":23,"compatibleSide7Count":105,"compatibleSide18Count":110,"requiredMatchingLowerBound":84,"matchingSizeInMissingCrossGraph":105,"matchingSlack":21,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"}]}}` +- Worst exact mixed row: `{"N":7343,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"activeOutsiderCount":80,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":112,"sMaxSide18Witness":5309,"sMaxUnion":220,"sMaxUnionWitness":5309,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":294,"side7CandidateSize":294,"side18CandidateSize":294,"side7Bound":273,"side18Bound":274,"unionBound":382,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":20,"unionMargin":-88,"side7Pass":true,"side18Pass":true,"unionPass":false,"certificateMode":"exact_mixed_base","threateningOutsiderCount":40,"exactMixedCheckCount":40,"sMaxMixed":112,"sMaxMixedWitness":5309,"mixedBound":274,"mixedMargin":20,"mixedPass":true,"maxImprovementOverUnion":109,"worstThreat":{"outsider":5309,"unionCount":220,"mixedBaseCliqueSize":112,"matchingSizeInMissingCrossGraph":108,"compatibleSide7Count":108,"compatibleSide18Count":112,"mixedCliqueSide7Count":0,"mixedCliqueSide18Count":112,"exampleMixedBaseClique":[43,118,143,243,268,343,368,443,543,568,643,718,743,793,843,943,1018,1043,1068,1143,1243,1318,1343,1443,1468,1493,1543,1618,1643,1693,1743,1843,1918,1943,2043,2143,2243,2343,2368,2443,2543,2593,2643,2718,2743,2818,2843,2943,3043,3143,3243,3268,3343,3443,3493,3543,3643,3718,3743,3843,3943,4043,4143,4168,4243,4343,4393,4443,4543,4618,4643,4743,4843,4943,5043,5068,5143,5168,5243,5293,5343,5443,5518,5543,5643,5718,5743,5843,5943,5968,6043,6143,6193,6243,6343,6393,6418,6443,6543,6643,6743,6768,6843,6868,6943,7043,7093,7143,7168,7243,7318,7343]},"threatMatchingSummary":{"threatCount":40,"minRequiredMatchingLowerBound":29,"maxRequiredMatchingLowerBound":89,"minActualMatching":79,"maxActualMatching":109,"minMatchingSlack":19,"allThreatsMeetRequiredLowerBound":true,"allThreatsSaturateSmallerSide":true,"tightestThreats":[{"outsider":5309,"outsiderMod25":9,"compatibleSide7Count":108,"compatibleSide18Count":112,"requiredMatchingLowerBound":89,"matchingSizeInMissingCrossGraph":108,"matchingSlack":19,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":1789,"outsiderMod25":14,"compatibleSide7Count":108,"compatibleSide18Count":111,"requiredMatchingLowerBound":88,"matchingSizeInMissingCrossGraph":108,"matchingSlack":20,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":4831,"outsiderMod25":6,"compatibleSide7Count":111,"compatibleSide18Count":105,"requiredMatchingLowerBound":85,"matchingSizeInMissingCrossGraph":105,"matchingSlack":20,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side7"},{"outsider":3281,"outsiderMod25":6,"compatibleSide7Count":108,"compatibleSide18Count":110,"requiredMatchingLowerBound":87,"matchingSizeInMissingCrossGraph":108,"matchingSlack":21,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":6323,"outsiderMod25":23,"compatibleSide7Count":105,"compatibleSide18Count":110,"requiredMatchingLowerBound":84,"matchingSizeInMissingCrossGraph":105,"matchingSlack":21,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"}]}}` + +## Boundary + +- Claim level: `bounded_structural_certificate_not_all_N_proof` +- Proof obligation: Every witness-prime block and structural breakpoint in the assessed range is certified either by the safe union bound or by exact mixed-base clique checks for every threatening active outsider. +- Clique reduction: For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges. +- Promotion rule: Promote bounded structural coverage only when allMixedChecksPass is true for the full assessed range and all artifact parameters match the intended handoff range. +- Next use: Use this as the repo-owned bounded structural certificate and extend the assessed range or lift the finite-block argument. diff --git a/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json new file mode 100644 index 0000000..f0bb7b9 --- /dev/null +++ b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.json @@ -0,0 +1,17177 @@ +{ + "schema": "erdos.number_theory.p848_matching_pattern_miner/1", + "generatedAt": "2026-04-11T20:22:52.793Z", + "problemId": "848", + "method": "bounded_missing_cross_matching_pattern_mining", + "status": "matching_pattern_witness_packet_ready", + "parameters": { + "verifierJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json", + "targetPrime": 13, + "topRows": 12, + "pairSampleLimit": 24, + "sourceAssessedRange": "7307..7600" + }, + "sourceVerifier": { + "status": "bounded_full_mixed_base_structural_verifier_certified", + "assessedRange": "7307..7600", + "threatLiftMiningRowCount": 1733 + }, + "summary": { + "witnessRowCount": 12, + "allReconstructedMatchesAgree": true, + "allWitnessesMeetRequiredMatchingLowerBound": true, + "allWitnessesSaturateSmallerSide": true, + "minRequiredMatchingLowerBound": 85, + "maxRequiredMatchingLowerBound": 89, + "minReconstructedMatchingSize": 105, + "maxReconstructedMatchingSize": 108, + "minMatchingSlack": 19, + "saturatedSideDistribution": [ + { + "key": "side7", + "count": 7 + }, + { + "key": "side18", + "count": 5 + } + ], + "outsiderMod25Distribution": [ + { + "key": 9, + "count": 6 + }, + { + "key": 6, + "count": 5 + }, + { + "key": 14, + "count": 1 + } + ], + "outsiderModP2Distribution": [ + { + "key": 70, + "count": 6 + }, + { + "key": 99, + "count": 6 + } + ] + }, + "patternSummary": { + "totalWitnessMatchingPairs": 1281, + "commonMatchingPairCountAcrossWitnesses": 0, + "commonMatchingPairsAcrossWitnesses": [], + "commonMatchingPairExportCompleteAcrossWitnesses": true, + "commonMatchingPairSample": [], + "outsiderResidueGroups": [ + { + "key": "70:9", + "count": 6 + }, + { + "key": "99:6", + "count": 5 + }, + { + "key": "99:14", + "count": 1 + } + ], + "splitProfiles": [ + { + "groupKey": "outP2=70|out25=9|smaller=side7", + "witnessCount": 6, + "minN": 7318, + "maxN": 7368, + "minRequiredMatchingLowerBound": 88, + "maxRequiredMatchingLowerBound": 89, + "minReconstructedMatchingSize": 108, + "maxReconstructedMatchingSize": 108, + "minSmallerSideSize": 108, + "maxSmallerSideSize": 108, + "minMatchingSlack": 19, + "commonMatchingPairCount": 108, + "commonCoreMeetsMaxRequiredBound": true, + 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"saturatesSmallerSide": true, + "matchedSmallerSideCount": 105, + "unmatchedSmallerSideCount": 0, + "unmatchedLargerSideCount": 7, + "missingCrossEdgeCount": 8951, + "compatibleCrossEdgeCount": 2809, + "matchingPairResidueProfiles": { + "modulo25": [ + { + "key": "7:18", + "count": 105 + } + ], + "moduloP": [ + { + "key": "0:6", + "count": 3 + }, + { + "key": "12:5", + "count": 3 + }, + { + "key": "2:8", + "count": 3 + }, + { + "key": "5:11", + "count": 3 + }, + { + "key": "6:12", + "count": 3 + }, + { + "key": "9:2", + "count": 3 + }, + { + "key": "1:11", + "count": 2 + }, + { + "key": "1:8", + "count": 2 + }, + { + "key": "10:3", + "count": 2 + }, + { + "key": "10:4", + "count": 2 + }, + { + "key": "10:7", + "count": 2 + }, + { + "key": "11:12", + "count": 2 + }, + { + "key": "2:3", + "count": 2 + }, + { + "key": "3:10", + "count": 2 + }, + { + "key": "3:4", + "count": 2 + }, + { + "key": "4:10", + "count": 2 + }, + { + "key": "4:7", + "count": 2 + }, + { + "key": "5:2", + "count": 2 + }, + { + "key": "6:1", + "count": 2 + }, + { + "key": "6:3", + "count": 2 + }, + { + "key": "7:0", + "count": 2 + }, + { + "key": "7:8", + "count": 2 + }, + { + "key": "8:10", + "count": 2 + }, + { + "key": "8:2", + "count": 2 + }, + { + "key": "0:1", + "count": 1 + }, + { + "key": "0:11", + "count": 1 + }, + { + "key": "0:12", + "count": 1 + }, + { + "key": "0:9", + "count": 1 + }, + { + "key": "1:0", + "count": 1 + }, + { + "key": "1:3", + "count": 1 + }, + { + "key": "1:6", + "count": 1 + }, + { + "key": "1:7", + "count": 1 + }, + { + "key": "1:9", + "count": 1 + }, + { + "key": "10:0", + "count": 1 + }, + { + "key": "10:11", + "count": 1 + }, + { + "key": "10:12", + "count": 1 + }, + { + "key": "11:0", + "count": 1 + }, + { + "key": "11:10", + "count": 1 + }, + { + "key": "11:11", + "count": 1 + }, + { + "key": "11:4", + "count": 1 + }, + { + "key": "11:5", + "count": 1 + }, + { + "key": "11:8", + "count": 1 + }, + { + "key": "12:0", + "count": 1 + }, + { + "key": "12:4", + "count": 1 + }, + { + "key": "12:9", + "count": 1 + }, + { + "key": "2:0", + "count": 1 + }, + { + "key": "2:7", + "count": 1 + }, + { + "key": "2:9", + "count": 1 + }, + { + "key": "3:0", + "count": 1 + }, + { + "key": "3:1", + "count": 1 + }, + { + "key": "3:5", + "count": 1 + }, + { + "key": "4:1", + "count": 1 + }, + { + "key": "4:2", + "count": 1 + }, + { + "key": "4:5", + "count": 1 + }, + { + "key": "5:1", + "count": 1 + }, + { + "key": "5:12", + "count": 1 + }, + { + "key": "5:6", + "count": 1 + }, + { + "key": "5:7", + "count": 1 + }, + { + "key": "6:6", + "count": 1 + }, + { + "key": "6:8", + "count": 1 + }, + { + "key": "6:9", + "count": 1 + }, + { + "key": "7:4", + "count": 1 + }, + { + "key": "7:7", + "count": 1 + }, + { + "key": "7:9", + "count": 1 + }, + { + "key": "8:1", + "count": 1 + }, + { + "key": "8:11", + "count": 1 + }, + { + "key": "8:3", + "count": 1 + }, + { + "key": "8:4", + "count": 1 + }, + { + "key": "8:5", + "count": 1 + }, + { + "key": "8:6", + "count": 1 + }, + { + "key": "9:1", + "count": 1 + }, + { + "key": "9:10", + "count": 1 + }, + { + "key": "9:6", + "count": 1 + }, + { + "key": "9:7", + "count": 1 + }, + { + "key": "9:9", + "count": 1 + } + ], + "moduloP2": [ + { + "key": "1:137", + "count": 1 + }, + { + "key": "101:68", + "count": 1 + }, + { + "key": "104:102", + "count": 1 + }, + { + "key": "105:9", + "count": 1 + }, + { + "key": "108:75", + "count": 1 + }, + { + "key": "11:47", + "count": 1 + }, + { + "key": "110:133", + "count": 1 + }, + { + "key": "111:78", + "count": 1 + }, + { + "key": "112:123", + "count": 1 + }, + { + "key": "115:82", + "count": 1 + }, + { + "key": "118:60", + "count": 1 + }, + { + "key": "119:55", + "count": 1 + }, + { + "key": "119:61", + "count": 1 + }, + { + "key": "12:117", + "count": 1 + }, + { + "key": "122:89", + "count": 1 + }, + { + "key": "125:11", + "count": 1 + }, + { + "key": "125:92", + "count": 1 + }, + { + "key": "129:96", + "count": 1 + }, + { + "key": "132:99", + "count": 1 + }, + { + "key": "135:58", + "count": 1 + }, + { + "key": "136:103", + "count": 1 + }, + { + "key": "136:9", + "count": 1 + }, + { + "key": "137:4", + "count": 1 + }, + { + "key": "138:30", + "count": 1 + } + ], + "productPlusOneModuloP2": [ + { + "key": 101, + "count": 3 + }, + { + "key": 131, + "count": 3 + }, + { + "key": 40, + "count": 3 + }, + { + "key": 42, + "count": 3 + }, + { + "key": 5, + "count": 3 + }, + { + "key": 54, + "count": 3 + }, + { + "key": 66, + "count": 3 + }, + { + "key": 9, + "count": 3 + }, + { + "key": 97, + "count": 3 + }, + { + "key": 108, + "count": 2 + }, + { + "key": 109, + "count": 2 + }, + { + "key": 111, + "count": 2 + }, + { + "key": 136, + "count": 2 + }, + { + "key": 138, + "count": 2 + }, + { + "key": 30, + "count": 2 + }, + { + "key": 53, + "count": 2 + }, + { + "key": 56, + "count": 2 + }, + { + "key": 57, + "count": 2 + }, + { + "key": 63, + "count": 2 + }, + { + "key": 98, + "count": 2 + }, + { + "key": 100, + "count": 1 + }, + { + "key": 106, + "count": 1 + }, + { + "key": 11, + "count": 1 + }, + { + "key": 110, + "count": 1 + } + ] + }, + "matchedSmallerSideResidues": { + "modulo25": [ + { + "key": 18, + "count": 105 + } + ], + "moduloP": [ + { + "key": 11, + "count": 9 + }, + { + "key": 7, + "count": 9 + }, + { + "key": 8, + "count": 9 + }, + { + "key": 0, + "count": 8 + }, + { + "key": 1, + "count": 8 + }, + { + "key": 10, + "count": 8 + }, + { + "key": 12, + "count": 8 + }, + { + "key": 2, + "count": 8 + }, + { + "key": 3, + "count": 8 + }, + { + "key": 4, + "count": 8 + }, + { + "key": 6, + "count": 8 + }, + { + "key": 5, + "count": 7 + }, + { + "key": 9, + "count": 7 + } + ], + "moduloP2": [ + { + "key": 117, + "count": 2 + }, + { + "key": 123, + "count": 2 + }, + { + "key": 130, + "count": 2 + }, + { + "key": 3, + "count": 2 + }, + { + "key": 33, + "count": 2 + }, + { + "key": 58, + "count": 2 + }, + { + "key": 64, + "count": 2 + }, + { + "key": 68, + "count": 2 + }, + { + "key": 9, + "count": 2 + }, + { + "key": 99, + "count": 2 + }, + { + "key": 1, + "count": 1 + }, + { + "key": 10, + "count": 1 + }, + { + "key": 102, + "count": 1 + }, + { + "key": 103, + "count": 1 + }, + { + "key": 106, + "count": 1 + }, + { + "key": 109, + "count": 1 + }, + { + "key": 11, + "count": 1 + }, + { + "key": 110, + "count": 1 + }, + { + "key": 113, + "count": 1 + }, + { + "key": 114, + "count": 1 + }, + { + "key": 115, + "count": 1 + }, + { + "key": 116, + "count": 1 + }, + { + "key": 118, + "count": 1 + }, + { + "key": 119, + "count": 1 + } + ] + }, + "unmatchedLargerSideResidues": { + "modulo25": [ + { + "key": 7, + "count": 7 + } + ], + "moduloP": [ + { + "key": 0, + "count": 1 + }, + { + "key": 11, + "count": 1 + }, + { + "key": 12, + "count": 1 + }, + { + "key": 3, + "count": 1 + }, + { + "key": 4, + "count": 1 + }, + { + "key": 7, + "count": 1 + }, + { + "key": 8, + "count": 1 + } + ], + "moduloP2": [ + { + "key": 128, + "count": 1 + }, + { + "key": 134, + "count": 1 + }, + { + "key": 159, + "count": 1 + }, + { + "key": 34, + "count": 1 + }, + { + "key": 59, + "count": 1 + }, + { + "key": 78, + "count": 1 + }, + { + "key": 90, + "count": 1 + } + ] + }, + "matchingPairSample": [ + { + "leftValue": 32, + "rightValue": 68, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 32, + "rightModP2": 68, + "leftModP": 6, + "rightModP": 3, + "productPlusOneModP2": 149 + }, + { + "leftValue": 57, + "rightValue": 93, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 57, + "rightModP2": 93, + "leftModP": 5, + "rightModP": 2, + "productPlusOneModP2": 63 + }, + { + "leftValue": 157, + "rightValue": 193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 157, + "rightModP2": 24, + "leftModP": 1, + "rightModP": 11, + "productPlusOneModP2": 51 + }, + { + "leftValue": 257, + "rightValue": 293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 88, + "rightModP2": 124, + "leftModP": 10, + "rightModP": 7, + "productPlusOneModP2": 97 + }, + { + "leftValue": 357, + "rightValue": 268, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 19, + "rightModP2": 99, + "leftModP": 6, + "rightModP": 8, + "productPlusOneModP2": 23 + }, + { + "leftValue": 457, + "rightValue": 393, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 119, + "rightModP2": 55, + "leftModP": 2, + "rightModP": 3, + "productPlusOneModP2": 124 + }, + { + "leftValue": 482, + "rightValue": 468, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 144, + "rightModP2": 130, + "leftModP": 1, + "rightModP": 0, + "productPlusOneModP2": 131 + }, + { + "leftValue": 557, + "rightValue": 493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 50, + "rightModP2": 155, + "leftModP": 11, + "rightModP": 12, + "productPlusOneModP2": 146 + }, + { + "leftValue": 632, + "rightValue": 518, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 125, + "rightModP2": 11, + "leftModP": 8, + "rightModP": 11, + "productPlusOneModP2": 24 + }, + { + "leftValue": 657, + "rightValue": 593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 150, + "rightModP2": 86, + "leftModP": 7, + "rightModP": 8, + "productPlusOneModP2": 57 + }, + { + "leftValue": 707, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 31, + "rightModP2": 67, + "leftModP": 5, + "rightModP": 2, + "productPlusOneModP2": 50 + }, + { + "leftValue": 757, + "rightValue": 693, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 81, + "rightModP2": 17, + "leftModP": 3, + "rightModP": 4, + "productPlusOneModP2": 26 + }, + { + "leftValue": 857, + "rightValue": 793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 12, + "rightModP2": 117, + "leftModP": 12, + "rightModP": 0, + "productPlusOneModP2": 53 + }, + { + "leftValue": 932, + "rightValue": 893, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 87, + "rightModP2": 48, + "leftModP": 9, + "rightModP": 9, + "productPlusOneModP2": 121 + }, + { + "leftValue": 957, + "rightValue": 968, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 112, + "rightModP2": 123, + "leftModP": 8, + "rightModP": 6, + "productPlusOneModP2": 88 + }, + { + "leftValue": 1007, + "rightValue": 1418, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 162, + "rightModP2": 66, + "leftModP": 6, + "rightModP": 1, + "productPlusOneModP2": 46 + }, + { + "leftValue": 1057, + "rightValue": 993, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 43, + "rightModP2": 148, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 112 + }, + { + "leftValue": 1082, + "rightValue": 1193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 68, + "rightModP2": 10, + "leftModP": 3, + "rightModP": 10, + "productPlusOneModP2": 5 + }, + { + "leftValue": 1157, + "rightValue": 1093, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 143, + "rightModP2": 79, + "leftModP": 0, + "rightModP": 1, + "productPlusOneModP2": 144 + }, + { + "leftValue": 1257, + "rightValue": 1293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 74, + "rightModP2": 110, + "leftModP": 9, + "rightModP": 6, + "productPlusOneModP2": 29 + }, + { + "leftValue": 1282, + "rightValue": 1393, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 99, + "rightModP2": 41, + "leftModP": 8, + "rightModP": 2, + "productPlusOneModP2": 4 + }, + { + "leftValue": 1357, + "rightValue": 1493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 5, + "rightModP2": 141, + "leftModP": 5, + "rightModP": 11, + "productPlusOneModP2": 30 + }, + { + "leftValue": 1382, + "rightValue": 1593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 30, + "rightModP2": 72, + "leftModP": 4, + "rightModP": 7, + "productPlusOneModP2": 133 + }, + { + "leftValue": 1457, + "rightValue": 1868, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 105, + "rightModP2": 9, + "leftModP": 1, + "rightModP": 9, + "productPlusOneModP2": 101 + } + ] + } + ], + "symbolicUse": { + "activeAtom": "D2_p13_matching_lower_bound", + "constructionTarget": "Replace Hopcroft-Karp replay with a residue/block injection that saturates the smaller compatible side of H_{x,N}.", + "proofHint": "Each witness records actual missing-cross matching pairs. A human/prover lane should look for a residue-parametric injection from the smaller compatible side into squarefree cross pairs.", + "nextExtractor": "Generalize from these tight-row pair residues into a symbolic side-saturation lemma, then rerun this miner for any newly tight prime family." + }, + "boundary": { + "claimLevel": "bounded_pattern_witness_not_symbolic_proof", + "note": "This artifact reconstructs matching witnesses for selected bounded threat rows. It does not certify rows outside the source verifier range and does not prove the all-N matching lemma.", + "promotionRule": "Promote D2/D3 only after the observed matching pattern is replaced by a symbolic construction and checked against the structural-lift atom." + } +} diff --git a/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.md b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.md new file mode 100644 index 0000000..5e3e5d9 --- /dev/null +++ b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER.md @@ -0,0 +1,61 @@ +# Problem 848 Matching Pattern Miner + +- Generated: 2026-04-11T20:22:52.793Z +- Method: `bounded_missing_cross_matching_pattern_mining` +- Status: `matching_pattern_witness_packet_ready` +- Target prime: `13` +- Source range: `7307..7600` +- Witness rows: `12` +- Reconstructed matches agree: `yes` +- Saturates smaller side: `yes` +- K range: `85..89` +- Matching range: `105..108` +- Minimum slack: `19` +- Common matching core across witnesses: `0` + +## Pattern Summary + +- Total witness matching pairs: `1281` +- Outsider residue groups: `[{"key":"70:9","count":6},{"key":"99:6","count":5},{"key":"99:14","count":1}]` +- Top right-left deltas: `[{"key":-64,"count":156},{"key":136,"count":152},{"key":-264,"count":128},{"key":36,"count":123},{"key":-164,"count":75},{"key":-189,"count":72},{"key":-364,"count":49},{"key":111,"count":48}]` +- Top product+1 residues mod p^2: `[{"key":130,"count":25},{"key":131,"count":23},{"key":66,"count":23},{"key":5,"count":22},{"key":97,"count":22},{"key":40,"count":21},{"key":42,"count":21},{"key":54,"count":21}]` +- Proof heuristic: The tight-row witnesses do not share one common matching core; split the symbolic construction by outsider residue and saturated side. + +## Split Profiles + +- `outP2=70|out25=9|smaller=side7`: witnesses 6, N 7318..7368, K 88..89, min slack 19, common pairs 108, full core exported yes, core >= max K yes +- `outP2=99|out25=6|smaller=side18`: witnesses 5, N 7307..7357, K 85..85, min slack 20, common pairs 105, full core exported yes, core >= max K yes +- `outP2=99|out25=14|smaller=side7`: witnesses 1, N 7343..7343, K 88..88, min slack 20, common pairs 108, full core exported yes, core >= max K yes + +## Witness Rows + +- N=7343, outsider=5309, K=89, matching=108, slack=19, smaller=side7, unmatched larger=4 +- N=7318, outsider=5309, K=88, matching=108, slack=20, smaller=side7, unmatched larger=3 +- N=7337, outsider=5309, K=88, matching=108, slack=20, smaller=side7, unmatched larger=3 +- N=7343, outsider=1789, K=88, matching=108, slack=20, smaller=side7, unmatched larger=3 +- N=7357, outsider=5309, K=88, matching=108, slack=20, smaller=side7, unmatched larger=4 +- N=7366, outsider=5309, K=88, matching=108, slack=20, smaller=side7, unmatched larger=4 +- N=7368, outsider=5309, K=88, matching=108, slack=20, smaller=side7, unmatched larger=4 +- N=7307, outsider=4831, K=85, matching=105, slack=20, smaller=side18, unmatched larger=6 +- N=7318, outsider=4831, K=85, matching=105, slack=20, smaller=side18, unmatched larger=6 +- N=7337, outsider=4831, K=85, matching=105, slack=20, smaller=side18, unmatched larger=6 +- N=7343, outsider=4831, K=85, matching=105, slack=20, smaller=side18, unmatched larger=6 +- N=7357, outsider=4831, K=85, matching=105, slack=20, smaller=side18, unmatched larger=7 + +## Tightest Pair Samples + +- N=7343, outsider=5309: [{"leftValue":7,"rightValue":43,"leftMod25":7,"rightMod25":18,"leftModP2":7,"rightModP2":43,"leftModP":7,"rightModP":4,"productPlusOneModP2":133},{"leftValue":82,"rightValue":118,"leftMod25":7,"rightMod25":18,"leftModP2":82,"rightModP2":118,"leftModP":4,"rightModP":1,"productPlusOneModP2":44},{"leftValue":107,"rightValue":143,"leftMod25":7,"rightMod25":18,"leftModP2":107,"rightModP2":143,"leftModP":3,"rightModP":0,"productPlusOneModP2":92},{"leftValue":207,"rightValue":243,"leftMod25":7,"rightMod25":18,"leftModP2":38,"rightModP2":74,"leftModP":12,"rightModP":9,"productPlusOneModP2":109},{"leftValue":307,"rightValue":268,"leftMod25":7,"rightMod25":18,"leftModP2":138,"rightModP2":99,"leftModP":8,"rightModP":8,"productPlusOneModP2":143},{"leftValue":407,"rightValue":343,"leftMod25":7,"rightMod25":18,"leftModP2":69,"rightModP2":5,"leftModP":4,"rightModP":5,"productPlusOneModP2":8},{"leftValue":507,"rightValue":368,"leftMod25":7,"rightMod25":18,"leftModP2":0,"rightModP2":30,"leftModP":0,"rightModP":4,"productPlusOneModP2":1},{"leftValue":532,"rightValue":443,"leftMod25":7,"rightMod25":18,"leftModP2":25,"rightModP2":105,"leftModP":12,"rightModP":1,"productPlusOneModP2":91}] +- N=7318, outsider=5309: [{"leftValue":7,"rightValue":43,"leftMod25":7,"rightMod25":18,"leftModP2":7,"rightModP2":43,"leftModP":7,"rightModP":4,"productPlusOneModP2":133},{"leftValue":82,"rightValue":118,"leftMod25":7,"rightMod25":18,"leftModP2":82,"rightModP2":118,"leftModP":4,"rightModP":1,"productPlusOneModP2":44},{"leftValue":107,"rightValue":143,"leftMod25":7,"rightMod25":18,"leftModP2":107,"rightModP2":143,"leftModP":3,"rightModP":0,"productPlusOneModP2":92},{"leftValue":207,"rightValue":243,"leftMod25":7,"rightMod25":18,"leftModP2":38,"rightModP2":74,"leftModP":12,"rightModP":9,"productPlusOneModP2":109},{"leftValue":307,"rightValue":268,"leftMod25":7,"rightMod25":18,"leftModP2":138,"rightModP2":99,"leftModP":8,"rightModP":8,"productPlusOneModP2":143},{"leftValue":407,"rightValue":343,"leftMod25":7,"rightMod25":18,"leftModP2":69,"rightModP2":5,"leftModP":4,"rightModP":5,"productPlusOneModP2":8},{"leftValue":507,"rightValue":368,"leftMod25":7,"rightMod25":18,"leftModP2":0,"rightModP2":30,"leftModP":0,"rightModP":4,"productPlusOneModP2":1},{"leftValue":532,"rightValue":443,"leftMod25":7,"rightMod25":18,"leftModP2":25,"rightModP2":105,"leftModP":12,"rightModP":1,"productPlusOneModP2":91}] +- N=7337, outsider=5309: [{"leftValue":7,"rightValue":43,"leftMod25":7,"rightMod25":18,"leftModP2":7,"rightModP2":43,"leftModP":7,"rightModP":4,"productPlusOneModP2":133},{"leftValue":82,"rightValue":118,"leftMod25":7,"rightMod25":18,"leftModP2":82,"rightModP2":118,"leftModP":4,"rightModP":1,"productPlusOneModP2":44},{"leftValue":107,"rightValue":143,"leftMod25":7,"rightMod25":18,"leftModP2":107,"rightModP2":143,"leftModP":3,"rightModP":0,"productPlusOneModP2":92},{"leftValue":207,"rightValue":243,"leftMod25":7,"rightMod25":18,"leftModP2":38,"rightModP2":74,"leftModP":12,"rightModP":9,"productPlusOneModP2":109},{"leftValue":307,"rightValue":268,"leftMod25":7,"rightMod25":18,"leftModP2":138,"rightModP2":99,"leftModP":8,"rightModP":8,"productPlusOneModP2":143},{"leftValue":407,"rightValue":343,"leftMod25":7,"rightMod25":18,"leftModP2":69,"rightModP2":5,"leftModP":4,"rightModP":5,"productPlusOneModP2":8},{"leftValue":507,"rightValue":368,"leftMod25":7,"rightMod25":18,"leftModP2":0,"rightModP2":30,"leftModP":0,"rightModP":4,"productPlusOneModP2":1},{"leftValue":532,"rightValue":443,"leftMod25":7,"rightMod25":18,"leftModP2":25,"rightModP2":105,"leftModP":12,"rightModP":1,"productPlusOneModP2":91}] + +## Symbolic Use + +- Active atom: `D2_p13_matching_lower_bound` +- Construction target: Replace Hopcroft-Karp replay with a residue/block injection that saturates the smaller compatible side of H_{x,N}. +- Proof hint: Each witness records actual missing-cross matching pairs. A human/prover lane should look for a residue-parametric injection from the smaller compatible side into squarefree cross pairs. + +## Boundary + +- Claim level: `bounded_pattern_witness_not_symbolic_proof` +- Note: This artifact reconstructs matching witnesses for selected bounded threat rows. It does not certify rows outside the source verifier range and does not prove the all-N matching lemma. +- Promotion rule: Promote D2/D3 only after the observed matching pattern is replaced by a symbolic construction and checked against the structural-lift atom. diff --git a/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.json b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.json new file mode 100644 index 0000000..d2bb372 --- /dev/null +++ b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.json @@ -0,0 +1,15938 @@ +{ + "schema": "erdos.number_theory.p848_matching_pattern_miner/1", + "generatedAt": "2026-04-11T20:22:52.793Z", + "problemId": "848", + "method": "bounded_missing_cross_matching_pattern_mining", + "status": "matching_pattern_witness_packet_ready", + "parameters": { + "verifierJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json", + "targetPrime": 17, + "topRows": 12, + "pairSampleLimit": 24, + "sourceAssessedRange": "7307..7600" + }, + "sourceVerifier": { + "status": "bounded_full_mixed_base_structural_verifier_certified", + "assessedRange": "7307..7600", + "threatLiftMiningRowCount": 1733 + }, + "summary": { + "witnessRowCount": 12, + "allReconstructedMatchesAgree": true, + "allWitnessesMeetRequiredMatchingLowerBound": true, + "allWitnessesSaturateSmallerSide": true, + "minRequiredMatchingLowerBound": 10, + "maxRequiredMatchingLowerBound": 14, + "minReconstructedMatchingSize": 106, + "maxReconstructedMatchingSize": 109, + "minMatchingSlack": 95, + "saturatedSideDistribution": [ + { + "key": "side7", + "count": 10 + }, + { + "key": "side18", + "count": 2 + } + ], + "outsiderMod25Distribution": [ + { + "key": 23, + "count": 10 + }, + { + "key": 1, + "count": 2 + } + ], + "outsiderModP2Distribution": [ + { + "key": 38, + "count": 10 + }, + { + "key": 251, + "count": 2 + } + ] + }, + "patternSummary": { + "totalWitnessMatchingPairs": 1303, + 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343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 18, + "rightModP2": 54, + "leftModP": 1, + "rightModP": 3, + "productPlusOneModP2": 106 + }, + { + "leftValue": 1407, + "rightValue": 1468, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 251, + "rightModP2": 23, + "leftModP": 13, + "rightModP": 6, + "productPlusOneModP2": 283 + }, + { + "leftValue": 1657, + "rightValue": 1693, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 212, + "rightModP2": 248, + "leftModP": 8, + "rightModP": 10, + "productPlusOneModP2": 268 + }, + { + "leftValue": 4807, + "rightValue": 4843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 183, + "rightModP2": 219, + "leftModP": 13, + "rightModP": 15, + "productPlusOneModP2": 196 + } + ], + "outsiderResidueGroups": [ + { + "key": "38:23", + "count": 10 + }, + { + "key": "251:1", + "count": 2 + } + ], + "splitProfiles": [ + { + "groupKey": "outP2=38|out25=23|smaller=side7", + "witnessCount": 10, + "minN": 7307, + "maxN": 7393, + 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"key": 107, + "count": 1 + }, + { + "key": 11, + "count": 1 + }, + { + "key": 115, + "count": 1 + }, + { + "key": 116, + "count": 1 + }, + { + "key": 117, + "count": 1 + }, + { + "key": 118, + "count": 1 + }, + { + "key": 119, + "count": 1 + }, + { + "key": 121, + "count": 1 + }, + { + "key": 127, + "count": 1 + }, + { + "key": 128, + "count": 1 + }, + { + "key": 129, + "count": 1 + }, + { + "key": 133, + "count": 1 + }, + { + "key": 138, + "count": 1 + }, + { + "key": 139, + "count": 1 + }, + { + "key": 140, + "count": 1 + }, + { + "key": 146, + "count": 1 + }, + { + "key": 148, + "count": 1 + }, + { + "key": 149, + "count": 1 + }, + { + "key": 150, + "count": 1 + }, + { + "key": 151, + "count": 1 + }, + { + "key": 152, + "count": 1 + } + ] + }, + "unmatchedLargerSideResidues": { + "modulo25": [ + { + "key": 18, + "count": 3 + } + ], + "moduloP": [ + { + "key": 16, + "count": 1 + }, + { + "key": 4, + "count": 1 + }, + { + "key": 8, + "count": 1 + } + ], + "moduloP2": [ + { + "key": 118, + "count": 1 + }, + { + "key": 157, + "count": 1 + }, + { + "key": 93, + "count": 1 + } + ] + }, + "matchingPairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 13 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 140 + }, + { + "leftValue": 107, + "rightValue": 143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 107, + "rightModP2": 143, + "leftModP": 5, + "rightModP": 7, + "productPlusOneModP2": 274 + }, + { + "leftValue": 207, + "rightValue": 243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 207, + "rightModP2": 243, + "leftModP": 3, + "rightModP": 5, + "productPlusOneModP2": 16 + }, + { + "leftValue": 307, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 18, + "rightModP2": 54, + "leftModP": 1, + "rightModP": 3, + "productPlusOneModP2": 106 + }, + { + "leftValue": 407, + "rightValue": 443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 118, + "rightModP2": 154, + "leftModP": 16, + "rightModP": 1, + "productPlusOneModP2": 255 + }, + { + "leftValue": 507, + "rightValue": 543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 218, + "rightModP2": 254, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 174 + }, + { + "leftValue": 532, + "rightValue": 568, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 243, + "rightModP2": 279, + "leftModP": 5, + "rightModP": 7, + "productPlusOneModP2": 172 + }, + { + "leftValue": 607, + "rightValue": 643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 29, + "rightModP2": 65, + "leftModP": 12, + "rightModP": 14, + "productPlusOneModP2": 152 + }, + { + "leftValue": 707, + "rightValue": 668, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 129, + "rightModP2": 90, + "leftModP": 10, + "rightModP": 5, + "productPlusOneModP2": 51 + }, + { + "leftValue": 757, + "rightValue": 793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 179, + "rightModP2": 215, + "leftModP": 9, + "rightModP": 11, + "productPlusOneModP2": 49 + }, + { + "leftValue": 807, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 229, + "rightModP2": 165, + "leftModP": 8, + "rightModP": 12, + "productPlusOneModP2": 216 + }, + { + "leftValue": 907, + "rightValue": 843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 40, + "rightModP2": 265, + "leftModP": 6, + "rightModP": 10, + "productPlusOneModP2": 197 + }, + { + "leftValue": 982, + "rightValue": 943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 115, + "rightModP2": 76, + "leftModP": 13, + "rightModP": 8, + "productPlusOneModP2": 71 + }, + { + "leftValue": 1007, + "rightValue": 1043, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 140, + "rightModP2": 176, + "leftModP": 4, + "rightModP": 6, + "productPlusOneModP2": 76 + }, + { + "leftValue": 1032, + "rightValue": 1018, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 165, + "rightModP2": 151, + "leftModP": 12, + "rightModP": 15, + "productPlusOneModP2": 62 + }, + { + "leftValue": 1082, + "rightValue": 1143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 215, + "rightModP2": 276, + "leftModP": 11, + "rightModP": 4, + "productPlusOneModP2": 96 + }, + { + "leftValue": 1107, + "rightValue": 1243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 240, + "rightModP2": 87, + "leftModP": 2, + "rightModP": 2, + "productPlusOneModP2": 73 + }, + { + "leftValue": 1207, + "rightValue": 1343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 51, + "rightModP2": 187, + "leftModP": 0, + "rightModP": 0, + "productPlusOneModP2": 1 + }, + { + "leftValue": 1307, + "rightValue": 1443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 151, + "rightModP2": 287, + "leftModP": 15, + "rightModP": 15, + "productPlusOneModP2": 277 + }, + { + "leftValue": 1407, + "rightValue": 1468, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 251, + "rightModP2": 23, + "leftModP": 13, + "rightModP": 6, + "productPlusOneModP2": 283 + }, + { + "leftValue": 1432, + "rightValue": 1543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 276, + "rightModP2": 98, + "leftModP": 4, + "rightModP": 13, + "productPlusOneModP2": 172 + }, + { + "leftValue": 1507, + "rightValue": 1643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 62, + "rightModP2": 198, + "leftModP": 11, + "rightModP": 11, + "productPlusOneModP2": 139 + }, + { + "leftValue": 1607, + "rightValue": 1743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 162, + "rightModP2": 9, + "leftModP": 9, + "rightModP": 9, + "productPlusOneModP2": 14 + } + ] + } + ], + "symbolicUse": { + "activeAtom": "D3_p17_matching_lower_bound", + "constructionTarget": "Replace Hopcroft-Karp replay with a residue/block injection that saturates the smaller compatible side of H_{x,N}.", + "proofHint": "Each witness records actual missing-cross matching pairs. A human/prover lane should look for a residue-parametric injection from the smaller compatible side into squarefree cross pairs.", + "nextExtractor": "Generalize from these tight-row pair residues into a symbolic side-saturation lemma, then rerun this miner for any newly tight prime family." + }, + "boundary": { + "claimLevel": "bounded_pattern_witness_not_symbolic_proof", + "note": "This artifact reconstructs matching witnesses for selected bounded threat rows. It does not certify rows outside the source verifier range and does not prove the all-N matching lemma.", + "promotionRule": "Promote D2/D3 only after the observed matching pattern is replaced by a symbolic construction and checked against the structural-lift atom." + } +} diff --git a/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.md b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.md new file mode 100644 index 0000000..22d3554 --- /dev/null +++ b/packs/number-theory/problems/848/MATCHING_PATTERN_MINER_P17.md @@ -0,0 +1,60 @@ +# Problem 848 Matching Pattern Miner + +- Generated: 2026-04-11T20:22:52.793Z +- Method: `bounded_missing_cross_matching_pattern_mining` +- Status: `matching_pattern_witness_packet_ready` +- Target prime: `17` +- Source range: `7307..7600` +- Witness rows: `12` +- Reconstructed matches agree: `yes` +- Saturates smaller side: `yes` +- K range: `10..14` +- Matching range: `106..109` +- Minimum slack: `95` +- Common matching core across witnesses: `4` + +## Pattern Summary + +- Total witness matching pairs: `1303` +- Outsider residue groups: `[{"key":"38:23","count":10},{"key":"251:1","count":2}]` +- Top right-left deltas: `[{"key":36,"count":306},{"key":-64,"count":246},{"key":136,"count":208},{"key":-39,"count":82},{"key":-89,"count":76},{"key":111,"count":54},{"key":-164,"count":42},{"key":-239,"count":42}]` +- Top product+1 residues mod p^2: `[{"key":154,"count":32},{"key":172,"count":30},{"key":81,"count":30},{"key":220,"count":22},{"key":139,"count":20},{"key":176,"count":20},{"key":185,"count":20},{"key":256,"count":20}]` +- Proof heuristic: The tight-row witnesses share a nonempty stable matching core. Try proving saturation by extending this stable core across residue blocks, then handle boundary insertions separately. + +## Split Profiles + +- `outP2=38|out25=23|smaller=side7`: witnesses 10, N 7307..7393, K 12..14, min slack 95, common pairs 109, full core exported yes, core >= max K yes +- `outP2=251|out25=1|smaller=side18`: witnesses 2, N 7307..7318, K 10..11, min slack 96, common pairs 106, full core exported yes, core >= max K yes + +## Witness Rows + +- N=7318, outsider=4373, K=14, matching=109, slack=95, smaller=side7, unmatched larger=2 +- N=7343, outsider=4373, K=14, matching=109, slack=95, smaller=side7, unmatched larger=3 +- N=7307, outsider=4373, K=13, matching=109, slack=96, smaller=side7, unmatched larger=1 +- N=7332, outsider=4373, K=13, matching=109, slack=96, smaller=side7, unmatched larger=2 +- N=7337, outsider=4373, K=13, matching=109, slack=96, smaller=side7, unmatched larger=2 +- N=7357, outsider=4373, K=13, matching=109, slack=96, smaller=side7, unmatched larger=3 +- N=7366, outsider=4373, K=13, matching=109, slack=96, smaller=side7, unmatched larger=3 +- N=7368, outsider=4373, K=13, matching=109, slack=96, smaller=side7, unmatched larger=3 +- N=7318, outsider=251, K=11, matching=107, slack=96, smaller=side18, unmatched larger=3 +- N=7307, outsider=251, K=10, matching=106, slack=96, smaller=side18, unmatched larger=4 +- N=7382, outsider=4373, K=12, matching=109, slack=97, smaller=side7, unmatched larger=3 +- N=7393, outsider=4373, K=12, matching=109, slack=97, smaller=side7, unmatched larger=3 + +## Tightest Pair Samples + +- N=7318, outsider=4373: [{"leftValue":7,"rightValue":43,"leftMod25":7,"rightMod25":18,"leftModP2":7,"rightModP2":43,"leftModP":7,"rightModP":9,"productPlusOneModP2":13},{"leftValue":82,"rightValue":118,"leftMod25":7,"rightMod25":18,"leftModP2":82,"rightModP2":118,"leftModP":14,"rightModP":16,"productPlusOneModP2":140},{"leftValue":107,"rightValue":143,"leftMod25":7,"rightMod25":18,"leftModP2":107,"rightModP2":143,"leftModP":5,"rightModP":7,"productPlusOneModP2":274},{"leftValue":207,"rightValue":243,"leftMod25":7,"rightMod25":18,"leftModP2":207,"rightModP2":243,"leftModP":3,"rightModP":5,"productPlusOneModP2":16},{"leftValue":307,"rightValue":343,"leftMod25":7,"rightMod25":18,"leftModP2":18,"rightModP2":54,"leftModP":1,"rightModP":3,"productPlusOneModP2":106},{"leftValue":407,"rightValue":443,"leftMod25":7,"rightMod25":18,"leftModP2":118,"rightModP2":154,"leftModP":16,"rightModP":1,"productPlusOneModP2":255},{"leftValue":507,"rightValue":543,"leftMod25":7,"rightMod25":18,"leftModP2":218,"rightModP2":254,"leftModP":14,"rightModP":16,"productPlusOneModP2":174},{"leftValue":532,"rightValue":568,"leftMod25":7,"rightMod25":18,"leftModP2":243,"rightModP2":279,"leftModP":5,"rightModP":7,"productPlusOneModP2":172}] +- N=7343, outsider=4373: [{"leftValue":7,"rightValue":43,"leftMod25":7,"rightMod25":18,"leftModP2":7,"rightModP2":43,"leftModP":7,"rightModP":9,"productPlusOneModP2":13},{"leftValue":82,"rightValue":118,"leftMod25":7,"rightMod25":18,"leftModP2":82,"rightModP2":118,"leftModP":14,"rightModP":16,"productPlusOneModP2":140},{"leftValue":107,"rightValue":143,"leftMod25":7,"rightMod25":18,"leftModP2":107,"rightModP2":143,"leftModP":5,"rightModP":7,"productPlusOneModP2":274},{"leftValue":207,"rightValue":243,"leftMod25":7,"rightMod25":18,"leftModP2":207,"rightModP2":243,"leftModP":3,"rightModP":5,"productPlusOneModP2":16},{"leftValue":307,"rightValue":343,"leftMod25":7,"rightMod25":18,"leftModP2":18,"rightModP2":54,"leftModP":1,"rightModP":3,"productPlusOneModP2":106},{"leftValue":407,"rightValue":443,"leftMod25":7,"rightMod25":18,"leftModP2":118,"rightModP2":154,"leftModP":16,"rightModP":1,"productPlusOneModP2":255},{"leftValue":507,"rightValue":543,"leftMod25":7,"rightMod25":18,"leftModP2":218,"rightModP2":254,"leftModP":14,"rightModP":16,"productPlusOneModP2":174},{"leftValue":532,"rightValue":568,"leftMod25":7,"rightMod25":18,"leftModP2":243,"rightModP2":279,"leftModP":5,"rightModP":7,"productPlusOneModP2":172}] +- N=7307, outsider=4373: [{"leftValue":7,"rightValue":43,"leftMod25":7,"rightMod25":18,"leftModP2":7,"rightModP2":43,"leftModP":7,"rightModP":9,"productPlusOneModP2":13},{"leftValue":82,"rightValue":118,"leftMod25":7,"rightMod25":18,"leftModP2":82,"rightModP2":118,"leftModP":14,"rightModP":16,"productPlusOneModP2":140},{"leftValue":107,"rightValue":143,"leftMod25":7,"rightMod25":18,"leftModP2":107,"rightModP2":143,"leftModP":5,"rightModP":7,"productPlusOneModP2":274},{"leftValue":207,"rightValue":243,"leftMod25":7,"rightMod25":18,"leftModP2":207,"rightModP2":243,"leftModP":3,"rightModP":5,"productPlusOneModP2":16},{"leftValue":307,"rightValue":343,"leftMod25":7,"rightMod25":18,"leftModP2":18,"rightModP2":54,"leftModP":1,"rightModP":3,"productPlusOneModP2":106},{"leftValue":407,"rightValue":443,"leftMod25":7,"rightMod25":18,"leftModP2":118,"rightModP2":154,"leftModP":16,"rightModP":1,"productPlusOneModP2":255},{"leftValue":507,"rightValue":543,"leftMod25":7,"rightMod25":18,"leftModP2":218,"rightModP2":254,"leftModP":14,"rightModP":16,"productPlusOneModP2":174},{"leftValue":532,"rightValue":568,"leftMod25":7,"rightMod25":18,"leftModP2":243,"rightModP2":279,"leftModP":5,"rightModP":7,"productPlusOneModP2":172}] + +## Symbolic Use + +- Active atom: `D3_p17_matching_lower_bound` +- Construction target: Replace Hopcroft-Karp replay with a residue/block injection that saturates the smaller compatible side of H_{x,N}. +- Proof hint: Each witness records actual missing-cross matching pairs. A human/prover lane should look for a residue-parametric injection from the smaller compatible side into squarefree cross pairs. + +## Boundary + +- Claim level: `bounded_pattern_witness_not_symbolic_proof` +- Note: This artifact reconstructs matching witnesses for selected bounded threat rows. It does not certify rows outside the source verifier range and does not prove the all-N matching lemma. +- Promotion rule: Promote D2/D3 only after the observed matching pattern is replaced by a symbolic construction and checked against the structural-lift atom. diff --git a/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.json b/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.json new file mode 100644 index 0000000..c2787aa --- /dev/null +++ b/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.json @@ -0,0 +1,1241 @@ +{ + "schema": "erdos.number_theory.p848_mixed_base_failure_scout/1", + "generatedAt": "2026-04-11T20:37:02.856Z", + "problemId": "848", + "method": "exact_mixed_base_clique_on_structural_union_failures", + "status": "sampled_union_failures_repaired_by_mixed_base_clique", + "sourceStructuralJson": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json", + "parameters": { + "maxRows": 8, + "structuralAssessedRange": "7307..7600", + "structuralStatus": "side_specific_bounds_pass_but_union_bound_fails" + }, + "summary": { + "analyzedRowCount": 8, + "mixedPassCount": 8, + "mixedFailureCount": 0, + "allAnalyzedRowsMixedPass": true, + "minMixedMargin": 22, + "maxImprovementOverUnion": 111 + }, + "firstMixedFailure": null, + "worstMixedRow": { + "source": "first_union_failure", + "N": 7307, + "p": 13, + "outsider": 1789, + "candidateSize": 293, + "sMaxSide7": 111, + "sMaxSide18": 110, + "sMaxUnion": 218, + "mixedBaseCliqueSize": 110, + "mixedBaseSide7Count": 0, + "mixedBaseSide18Count": 110, + "mixedBaseCliqueMatchesSingleSide": true, + "mixedBound": 271, + "mixedMargin": 22, + "mixedPass": true, + "originalUnionMargin": -86, + "improvementOverUnion": 108, + "vMax": 43, + "dMax": 18, + "rGreater": 100, + "exampleMixedBaseClique": [ + 43, + 68, + 143, + 243, + 268, + 293, + 343, + 443, + 518, + 543, + 643, + 743, + 843, + 943, + 968, + 1043, + 1143, + 1193, + 1243, + 1343, + 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"mixedBaseCliqueMatchesSingleSide": true, + "mixedBound": 271, + "mixedMargin": 22, + "mixedPass": true, + "originalUnionMargin": -86, + "improvementOverUnion": 108, + "vMax": 43, + "dMax": 18, + "rGreater": 100, + "exampleMixedBaseClique": [ + 43, + 68, + 143, + 243, + 268, + 293, + 343, + 443, + 518, + 543, + 643, + 743, + 843, + 943, + 968, + 1043, + 1143, + 1193, + 1243, + 1343, + 1418, + 1443, + 1468, + 1543, + 1643, + 1743, + 1843, + 1868, + 1943, + 2043, + 2093, + 2143, + 2243, + 2318, + 2343, + 2443, + 2543, + 2643, + 2693, + 2743, + 2768, + 2843, + 2918, + 2943, + 2993, + 3043, + 3143, + 3218, + 3243, + 3343, + 3443, + 3543, + 3643, + 3668, + 3743, + 3768, + 3843, + 3893, + 3918, + 3943, + 4043, + 4068, + 4118, + 4143, + 4243, + 4343, + 4443, + 4493, + 4543, + 4568, + 4618, + 4643, + 4743, + 4793, + 4843, + 4943, + 5018, + 5043, + 5143, + 5243, + 5343, + 5443, + 5468, + 5543, + 5643, + 5693, + 5743, + 5843, + 5918, + 5943, + 6043, + 6143, + 6243, + 6293, + 6343, + 6368, + 6418, + 6443, + 6543, + 6593, + 6643, + 6668, + 6743, + 6818, + 6843, + 6943, + 7043, + 7143, + 7243, + 7268 + ] + }, + { + "source": "worst_union_row", + "N": 7552, + "p": 13, + "outsider": 1789, + "candidateSize": 302, + "sMaxSide7": 113, + "sMaxSide18": 114, + "sMaxUnion": 225, + "mixedBaseCliqueSize": 114, + "mixedBaseSide7Count": 0, + "mixedBaseSide18Count": 114, + "mixedBaseCliqueMatchesSingleSide": true, + "mixedBound": 280, + "mixedMargin": 22, + "mixedPass": true, + "originalUnionMargin": -89, + "improvementOverUnion": 111, + "vMax": 45, + "dMax": 18, + "rGreater": 103, + "exampleMixedBaseClique": [ + 43, + 68, + 143, + 243, + 268, + 293, + 343, + 443, + 518, + 543, + 643, + 743, + 843, + 943, + 968, + 1043, + 1143, + 1193, + 1243, + 1343, + 1418, + 1443, + 1468, + 1543, + 1643, + 1743, + 1843, + 1868, + 1943, + 2043, + 2093, + 2143, + 2243, + 2318, + 2343, + 2443, + 2543, + 2643, + 2693, + 2743, + 2768, + 2843, + 2918, + 2943, + 2993, + 3043, + 3143, + 3218, + 3243, + 3343, + 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"exampleMixedBaseClique": [ + 43, + 118, + 143, + 243, + 343, + 443, + 543, + 568, + 643, + 668, + 743, + 793, + 843, + 943, + 1018, + 1043, + 1143, + 1243, + 1343, + 1443, + 1468, + 1543, + 1643, + 1693, + 1743, + 1768, + 1843, + 1918, + 1943, + 2043, + 2143, + 2243, + 2343, + 2368, + 2443, + 2543, + 2593, + 2643, + 2743, + 2818, + 2843, + 2943, + 2968, + 2993, + 3043, + 3093, + 3143, + 3243, + 3268, + 3293, + 3343, + 3443, + 3493, + 3543, + 3643, + 3718, + 3743, + 3843, + 3943, + 4043, + 4143, + 4168, + 4218, + 4243, + 4343, + 4393, + 4443, + 4543, + 4618, + 4643, + 4743, + 4843, + 4893, + 4943, + 5043, + 5068, + 5143, + 5243, + 5293, + 5343, + 5443, + 5518, + 5543, + 5643, + 5693, + 5743, + 5818, + 5843, + 5943, + 5968, + 5993, + 6043, + 6143, + 6193, + 6243, + 6343, + 6418, + 6443, + 6543, + 6618, + 6643, + 6668, + 6743, + 6843, + 6868, + 6943, + 7043, + 7093, + 7143, + 7243 + ] + }, + { + "source": "block_17_worst_union_row", + "N": 7318, + "p": 17, + "outsider": 4373, + "candidateSize": 293, + "sMaxSide7": 110, + "sMaxSide18": 111, + "sMaxUnion": 220, + "mixedBaseCliqueSize": 111, + "mixedBaseSide7Count": 0, + "mixedBaseSide18Count": 111, + "mixedBaseCliqueMatchesSingleSide": true, + "mixedBound": 197, + "mixedMargin": 96, + "mixedPass": true, + "originalUnionMargin": -13, + "improvementOverUnion": 109, + "vMax": 26, + "dMax": 11, + "rGreater": 49, + "exampleMixedBaseClique": [ + 43, + 118, + 143, + 243, + 343, + 443, + 543, + 568, + 643, + 668, + 743, + 793, + 843, + 943, + 1018, + 1043, + 1143, + 1243, + 1343, + 1443, + 1468, + 1543, + 1643, + 1693, + 1743, + 1768, + 1843, + 1918, + 1943, + 2043, + 2143, + 2243, + 2343, + 2368, + 2443, + 2543, + 2593, + 2643, + 2743, + 2818, + 2843, + 2943, + 2968, + 2993, + 3043, + 3093, + 3143, + 3243, + 3268, + 3293, + 3343, + 3443, + 3493, + 3543, + 3643, + 3718, + 3743, + 3843, + 3943, + 4043, + 4143, + 4168, + 4218, + 4243, + 4343, + 4393, + 4443, + 4543, + 4618, + 4643, + 4743, + 4843, + 4893, + 4943, + 5043, 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"mixedMargin": 155, + "mixedPass": true, + "originalUnionMargin": 48, + "improvementOverUnion": 107, + "vMax": 6, + "dMax": 4, + "rGreater": 21, + "exampleMixedBaseClique": [ + 57, + 157, + 182, + 257, + 357, + 407, + 457, + 557, + 607, + 632, + 657, + 757, + 857, + 957, + 1057, + 1082, + 1107, + 1157, + 1257, + 1307, + 1357, + 1457, + 1532, + 1557, + 1657, + 1732, + 1757, + 1832, + 1857, + 1957, + 1982, + 2057, + 2157, + 2207, + 2257, + 2357, + 2432, + 2457, + 2557, + 2657, + 2757, + 2857, + 2882, + 2957, + 3057, + 3107, + 3157, + 3257, + 3332, + 3357, + 3457, + 3557, + 3657, + 3757, + 3782, + 3857, + 3957, + 4007, + 4057, + 4157, + 4232, + 4257, + 4282, + 4357, + 4457, + 4557, + 4632, + 4657, + 4682, + 4757, + 4832, + 4857, + 4907, + 4957, + 5057, + 5132, + 5157, + 5257, + 5357, + 5457, + 5507, + 5557, + 5582, + 5657, + 5682, + 5757, + 5807, + 5857, + 5957, + 6032, + 6057, + 6157, + 6257, + 6357, + 6457, + 6482, + 6557, + 6657, + 6707, + 6732, + 6757, + 6857, + 6932, + 6957, + 7057, + 7157, + 7257 + ] + }, + { + "source": "block_41_worst_union_row", + "N": 7307, + "p": 41, + "outsider": 1303, + "candidateSize": 293, + "sMaxSide7": 110, + "sMaxSide18": 111, + "sMaxUnion": 221, + "mixedBaseCliqueSize": 111, + "mixedBaseSide7Count": 0, + "mixedBaseSide18Count": 111, + "mixedBaseCliqueMatchesSingleSide": true, + "mixedBound": 130, + "mixedMargin": 163, + "mixedPass": true, + "originalUnionMargin": 53, + "improvementOverUnion": 110, + "vMax": 5, + "dMax": 2, + "rGreater": 12, + "exampleMixedBaseClique": [ + 68, + 93, + 193, + 293, + 393, + 468, + 493, + 518, + 593, + 618, + 693, + 743, + 793, + 893, + 968, + 993, + 1093, + 1193, + 1293, + 1393, + 1418, + 1493, + 1593, + 1618, + 1643, + 1693, + 1793, + 1868, + 1893, + 1993, + 2093, + 2193, + 2293, + 2318, + 2393, + 2493, + 2543, + 2593, + 2693, + 2768, + 2793, + 2893, + 2918, + 2993, + 3093, + 3193, + 3218, + 3293, + 3393, + 3443, + 3493, + 3593, + 3618, + 3643, + 3668, + 3693, + 3793, + 3893, + 3993, + 4093, + 4118, + 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743, + 843, + 943, + 1043, + 1143, + 1168, + 1243, + 1343, + 1393, + 1443, + 1543, + 1618, + 1643, + 1743, + 1843, + 1943, + 1968, + 2043, + 2068, + 2143, + 2243, + 2293, + 2343, + 2443, + 2518, + 2543, + 2643, + 2743, + 2843, + 2943, + 2968, + 3043, + 3143, + 3193, + 3243, + 3343, + 3418, + 3443, + 3493, + 3543, + 3593, + 3643, + 3743, + 3843, + 3868, + 3943, + 4043, + 4093, + 4143, + 4243, + 4318, + 4343, + 4368, + 4418, + 4443, + 4543, + 4643, + 4743, + 4768, + 4818, + 4843, + 4943, + 4993, + 5043, + 5118, + 5143, + 5218, + 5243, + 5343, + 5443, + 5543, + 5643, + 5668, + 5693, + 5743, + 5843, + 5893, + 5943, + 6043, + 6118, + 6143, + 6243, + 6343, + 6443, + 6543, + 6568, + 6643, + 6743, + 6793, + 6843, + 6868, + 6943, + 7018, + 7043, + 7143, + 7243, + 7318, + 7343, + 7393, + 7418, + 7443 + ] + } + ], + "boundary": { + "claimLevel": "sampled_failure_scout_not_full_structural_certificate", + "note": "This scout exactly solves the mixed-base clique on selected union-failure rows from the two-sided structural scout. It does not yet certify every structural breakpoint.", + "nextUse": "Promote this into the full two-sided structural verifier by replacing the union-base overcount with the exact mixed-base clique bound at every breakpoint." + } +} diff --git a/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.md b/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.md new file mode 100644 index 0000000..388fff8 --- /dev/null +++ b/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.md @@ -0,0 +1,20 @@ +# Problem 848 Mixed-Base Failure Scout + +- Generated: 2026-04-11T20:37:02.856Z +- Method: `exact_mixed_base_clique_on_structural_union_failures` +- Status: `sampled_union_failures_repaired_by_mixed_base_clique` +- Source structural scout: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json` +- Analyzed rows: `8` +- Mixed failures: `0` +- Minimum mixed margin: `22` +- Max improvement over union: `111` + +## Worst Mixed Row + +- `{"source":"first_union_failure","N":7307,"p":13,"outsider":1789,"candidateSize":293,"sMaxSide7":111,"sMaxSide18":110,"sMaxUnion":218,"mixedBaseCliqueSize":110,"mixedBaseSide7Count":0,"mixedBaseSide18Count":110,"mixedBaseCliqueMatchesSingleSide":true,"mixedBound":271,"mixedMargin":22,"mixedPass":true,"originalUnionMargin":-86,"improvementOverUnion":108,"vMax":43,"dMax":18,"rGreater":100,"exampleMixedBaseClique":[43,68,143,243,268,293,343,443,518,543,643,743,843,943,968,1043,1143,1193,1243,1343,1418,1443,1468,1543,1643,1743,1843,1868,1943,2043,2093,2143,2243,2318,2343,2443,2543,2643,2693,2743,2768,2843,2918,2943,2993,3043,3143,3218,3243,3343,3443,3543,3643,3668,3743,3768,3843,3893,3918,3943,4043,4068,4118,4143,4243,4343,4443,4493,4543,4568,4618,4643,4743,4793,4843,4943,5018,5043,5143,5243,5343,5443,5468,5543,5643,5693,5743,5843,5918,5943,6043,6143,6243,6293,6343,6368,6418,6443,6543,6593,6643,6668,6743,6818,6843,6943,7043,7143,7243,7268]}` + +## Boundary + +- Claim level: `sampled_failure_scout_not_full_structural_certificate` +- This scout exactly solves the mixed-base clique on selected union-failure rows from the two-sided structural scout. It does not yet certify every structural breakpoint. +- Next use: Promote this into the full two-sided structural verifier by replacing the union-base overcount with the exact mixed-base clique bound at every breakpoint. diff --git a/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json b/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json new file mode 100644 index 0000000..b9a09d9 --- /dev/null +++ b/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json @@ -0,0 +1,530 @@ +{ + "schema": "frontier_engine.p848_search_theorem_bridge/1", + "generated_at_utc": "2026-04-12T10:07:04Z", + "problem_id": "848", + "shared_prefix": [ + 7, + 32, + 57, + 82, + 132, + 182 + ], + "sources": { + "live_frontier_root": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05", + "family_menu_source_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/SIX_PREFIX_TWENTY_FOUR_FAMILY_MENU.json", + "gpu_manifest_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/artifacts/p848-anchor-ladder/p848_anchor_ladder-seeds-20260408T165349Z/manifest.json" + }, + "current_bridge_state": { + "shared_prefix_failure_count": 24, + "latest_shared_prefix_failure": 136702637, + "family_menu_count": 280, + "known_family_matches": 25, + "next_unmatched_representative": 137720141, + "next_unmatched_matches_282_failure": true, + "strongest_completed_structured_tail": { + "continuation": 332, + "clean_through": 250000000 + }, + "current_family_aware_leader": { + "continuation": 432, + "repaired_known_packets": 26, + "repaired_predicted_families": 242, + "effective_clean_through": 250075000 + }, + "top_gpu_tie_class": [ + 432, + 782, + 832 + ], + "recent_pool_expansion_moduli": [ + 1369, + 841, + 17161, + 1849 + ] + }, + "shared_prefix_packet_ledger": [ + { + "n": 90512581, + "tuple_key": "4, 7^2, 11^2, 13^2, 19^2, 9", + "square_moduli": [ + 4, + 49, + 121, + 169, + 361, + 9 + ], + "new_square_moduli": [ + 4, + 49, + 121, + 169, + 361, + 9 + ], + "packet_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/chunks/six_anchor_frontier_after_eighteenth_failure/ANCHOR_FIRST_FAILURE_7_32_57_82_132_182_90036164_to_90512581.json", + "singleton_crt_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/ANCHOR_SINGLETON_CRT_90512581.json", + "singleton_crt_modulus": null, + "singleton_crt_residue": null + }, + { + "n": 102428617, + "tuple_key": "2^7, 19^2, 13^2, 7^2, 17^2, 9", + "square_moduli": [ + 4, + 361, + 169, + 49, + 289, + 9 + ], + "new_square_moduli": [ + 289 + ], + "packet_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/chunks/six_anchor_frontier_after_nineteenth_failure/ANCHOR_FIRST_FAILURE_7_32_57_82_132_182_101512582_to_102428617.json", + "singleton_crt_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/ANCHOR_SINGLETON_CRT_102428617.json", + "singleton_crt_modulus": null, + "singleton_crt_residue": null + }, + { + "n": 106393589, + "tuple_key": "4, 37^2, 11^2, 9, 7^2, 17^2", + "square_moduli": [ + 4, + 1369, + 121, + 9, + 49, + 289 + ], + "new_square_moduli": [ + 1369 + ], + "packet_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/chunks/six_anchor_frontier_after_twentieth_failure/ANCHOR_FIRST_FAILURE_7_32_57_82_132_182_105428618_to_106393589.json", + "singleton_crt_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/ANCHOR_SINGLETON_CRT_106393589.json", + "singleton_crt_modulus": null, + "singleton_crt_residue": null + }, + { + "n": 127484267, + "tuple_key": "9, 17^2, 4, 29^2, 7^2, 11^2", + "square_moduli": [ + 9, + 289, + 4, + 841, + 49, + 121 + ], + "new_square_moduli": [ + 841 + ], + "packet_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/chunks/six_anchor_frontier_after_twenty_first_failure/ANCHOR_FIRST_FAILURE_7_32_57_82_132_182_127393590_to_127484267.json", + "singleton_crt_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/ANCHOR_SINGLETON_CRT_127484267.json", + "singleton_crt_modulus": null, + "singleton_crt_residue": null + }, + { + "n": 127682743, + "tuple_key": "131^2, 11^2, 2^6, 29^2, 13^2, 9", + "square_moduli": [ + 17161, + 121, + 4, + 841, + 169, + 9 + ], + "new_square_moduli": [ + 17161 + ], + "packet_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/chunks/six_anchor_frontier_after_twenty_second_failure/ANCHOR_FIRST_FAILURE_7_32_57_82_132_182_127484268_to_128484267.json", + "singleton_crt_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/ANCHOR_SINGLETON_CRT_127682743.json", + "singleton_crt_modulus": null, + "singleton_crt_residue": null + }, + { + "n": 136702637, + "tuple_key": "4, 43^2, 11^2, 9, 7^3, 19^2", + "square_moduli": [ + 4, + 1849, + 121, + 9, + 49, + 361 + ], + "new_square_moduli": [ + 1849 + ], + "packet_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/chunks/six_anchor_frontier_after_twenty_third_failure/ANCHOR_FIRST_FAILURE_7_32_57_82_132_182_136682744_to_137682743.json", + "singleton_crt_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/ANCHOR_SINGLETON_CRT_136702637.json", + "singleton_crt_modulus": null, + "singleton_crt_residue": null + } + ], + "tracked_tail_matrix": [ + { + "continuation": 157, + "observed_status": "fails", + "observed_clean_through": null, + "observed_first_failure": 19094395, + "repaired_known_packets": 16, + "missed_known_packets": 10, + "repaired_known_family_count": 14, + "repaired_predicted_family_count": 110, + "first_missed_predicted_representatives": [ + 144139279, + 152156551, + 160007135, + 170465989, + 187536119, + 210290957, + 230927471, + 241546751 + ], + "effective_clean_through": 19094394, + "effective_first_failure": 19094395, + "extension_mode": "historical_failure_locked", + "direct_scan_performed": false, + "direct_scan_skipped": true, + "plus50_alignment": false + }, + { + "continuation": 232, + "observed_status": "fails", + "observed_clean_through": null, + "observed_first_failure": 27949928, + "repaired_known_packets": 20, + "missed_known_packets": 6, + "repaired_known_family_count": 20, + "repaired_predicted_family_count": 201, + "first_missed_predicted_representatives": [ + 160007135, + 187536119, + 193809001, + 210290957, + 248711747, + 248711747, + 277343771, + 287180657 + ], + "effective_clean_through": 27949927, + "effective_first_failure": 27949928, + "extension_mode": "historical_failure_locked", + "direct_scan_performed": false, + "direct_scan_skipped": true, + "plus50_alignment": true + }, + { + "continuation": 282, + "observed_status": "fails", + "observed_clean_through": null, + "observed_first_failure": 137720141, + "repaired_known_packets": 25, + "missed_known_packets": 1, + "repaired_known_family_count": 25, + "repaired_predicted_family_count": 244, + "first_missed_predicted_representatives": [ + 137720141, + 210290957, + 287180657, + 287180657, + 517124182, + 525631657, + 1229502607, + 1654841707 + ], + "effective_clean_through": 137720140, + "effective_first_failure": 137720141, + "extension_mode": "historical_failure_locked", + "direct_scan_performed": false, + "direct_scan_skipped": true, + "plus50_alignment": true + }, + { + "continuation": 332, + "observed_status": "clean_through", + "observed_clean_through": 250000000, + "observed_first_failure": null, + "repaired_known_packets": 26, + "missed_known_packets": 0, + "repaired_known_family_count": 25, + "repaired_predicted_family_count": 240, + "first_missed_predicted_representatives": [ + 210290957, + 287180657, + 287180657, + 517124182, + 525631657, + 657348925, + 695323423, + 885528547 + ], + "effective_clean_through": 250050000, + "effective_first_failure": null, + "extension_mode": "contiguous_clean_extension", + "direct_scan_performed": true, + "direct_scan_skipped": false, + "plus50_alignment": true + }, + { + "continuation": 382, + "observed_status": "unseen", + "observed_clean_through": null, + "observed_first_failure": null, + "repaired_known_packets": 26, + "missed_known_packets": 0, + "repaired_known_family_count": 25, + "repaired_predicted_family_count": 240, + "first_missed_predicted_representatives": [ + 210290957, + 287180657, + 287180657, + 342292837, + 517124182, + 520923103, + 525631657, + 537246638 + ], + "effective_clean_through": 250050000, + "effective_first_failure": null, + "extension_mode": "direct_window_only", + "direct_scan_performed": true, + "direct_scan_skipped": false, + "plus50_alignment": true + }, + { + "continuation": 432, + "observed_status": "unseen", + "observed_clean_through": null, + "observed_first_failure": null, + "repaired_known_packets": 26, + "missed_known_packets": 0, + "repaired_known_family_count": 25, + "repaired_predicted_family_count": 242, + "first_missed_predicted_representatives": [ + 210290957, + 287180657, + 287180657, + 457148843, + 517124182, + 525631657, + 770426585, + 1229502607 + ], + "effective_clean_through": 250050000, + "effective_first_failure": null, + "extension_mode": "direct_window_only", + "direct_scan_performed": true, + "direct_scan_skipped": false, + "plus50_alignment": true + }, + { + "continuation": 782, + "observed_status": "unseen", + "observed_clean_through": null, + "observed_first_failure": null, + "repaired_known_packets": 26, + "missed_known_packets": 0, + "repaired_known_family_count": 25, + "repaired_predicted_family_count": 242, + "first_missed_predicted_representatives": [ + 210290957, + 287180657, + 287180657, + 517124182, + 525631657, + 695323423, + 1079001739, + 1229502607 + ], + "effective_clean_through": 250050000, + "effective_first_failure": null, + "extension_mode": "direct_window_only", + "direct_scan_performed": true, + "direct_scan_skipped": false, + "plus50_alignment": true + }, + { + "continuation": 832, + "observed_status": "unseen", + "observed_clean_through": null, + "observed_first_failure": null, + "repaired_known_packets": 26, + "missed_known_packets": 0, + "repaired_known_family_count": 25, + "repaired_predicted_family_count": 242, + "first_missed_predicted_representatives": [ + 210290957, + 287180657, + 287180657, + 517124182, + 525631657, + 1229502607, + 1446717451, + 1654841707 + ], + "effective_clean_through": 250050000, + "effective_first_failure": null, + "extension_mode": "direct_window_only", + "direct_scan_performed": true, + "direct_scan_skipped": false, + "plus50_alignment": true + } + ], + "gpu_leaderboard": [ + { + "rank": 1, + "continuation": 432, + "repaired_known_packets": 26, + "repaired_predicted_families": 242, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 2, + "continuation": 782, + "repaired_known_packets": 26, + "repaired_predicted_families": 242, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 3, + "continuation": 832, + "repaired_known_packets": 26, + "repaired_predicted_families": 242, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 4, + "continuation": 332, + "repaired_known_packets": 26, + "repaired_predicted_families": 240, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 5, + "continuation": 382, + "repaired_known_packets": 26, + "repaired_predicted_families": 240, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 6, + "continuation": 1232, + "repaired_known_packets": 26, + "repaired_predicted_families": 240, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 7, + "continuation": 882, + "repaired_known_packets": 26, + "repaired_predicted_families": 236, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 8, + "continuation": 1182, + "repaired_known_packets": 25, + "repaired_predicted_families": 242, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 9, + "continuation": 582, + "repaired_known_packets": 25, + "repaired_predicted_families": 238, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 10, + "continuation": 492, + "repaired_known_packets": 25, + "repaired_predicted_families": 233, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 11, + "continuation": 942, + "repaired_known_packets": 25, + "repaired_predicted_families": 232, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 12, + "continuation": 742, + "repaired_known_packets": 25, + "repaired_predicted_families": 231, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 13, + "continuation": 642, + "repaired_known_packets": 25, + "repaired_predicted_families": 230, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 14, + "continuation": 342, + "repaired_known_packets": 25, + "repaired_predicted_families": 229, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 15, + "continuation": 672, + "repaired_known_packets": 24, + "repaired_predicted_families": 247, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + }, + { + "rank": 16, + "continuation": 372, + "repaired_known_packets": 24, + "repaired_predicted_families": 245, + "direct_clean_through": 250075000, + "effective_clean_through": 250075000 + } + ], + "candidate_theorem_hooks": [ + { + "hook_id": "next_unmatched_equals_282_failure", + "status": "supported", + "detail": "The next unmatched shared-prefix representative currently coincides with the known first failure of the 282 continuation." + }, + { + "hook_id": "completed_tail_vs_search_leader_split", + "status": "supported", + "detail": "The strongest completed structured tail remains 332, while the current family-aware search leader can move on the finite tested window." + }, + { + "hook_id": "repair_pool_not_closed", + "status": "supported", + "detail": "Recent shared-prefix packets introduced new square moduli into the live family menu, so the repaired local square pool is not yet closed." + }, + { + "hook_id": "top_repair_class_cluster", + "status": "supported", + "detail": "The current top continuation class shares the same repaired-known, repaired-predicted, and tested-clean-through profile on the live finite window." + } + ] +} diff --git a/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md b/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md new file mode 100644 index 0000000..9b9bd2e --- /dev/null +++ b/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md @@ -0,0 +1,60 @@ +# Problem 848 Search-Theorem Bridge + +This note is the canonical bridge between the live `frontier-engine` search lane and the theorem-facing `erdos-problems` pack. + +## Current state + +- Shared-prefix failures frozen: `24` through `136702637`. +- Current family menu: `research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/2026-04-05/SIX_PREFIX_TWENTY_FOUR_FAMILY_MENU.json` with `280` rows and `25` matched known-family rows. +- Strongest completed structured tail: `332` clean through `250000000`. +- Current family-aware leader on the tested window: `432` with `26` repaired known packets and `242` repaired predicted-family rows. +- Next unmatched representative: `137720141`. +- `282` tail alignment: `matches` the next unmatched representative. +- Current top GPU tie class: `432, 782, 832`. + +## Recent Packet Ledger + +| n | Tuple | New Square Moduli | CRT Modulus | +| --- | --- | --- | --- | +| `90512581` | `4, 7^2, 11^2, 13^2, 19^2, 9` | `4, 49, 121, 169, 361, 9` | `-` | +| `102428617` | `2^7, 19^2, 13^2, 7^2, 17^2, 9` | `289` | `-` | +| `106393589` | `4, 37^2, 11^2, 9, 7^2, 17^2` | `1369` | `-` | +| `127484267` | `9, 17^2, 4, 29^2, 7^2, 11^2` | `841` | `-` | +| `127682743` | `131^2, 11^2, 2^6, 29^2, 13^2, 9` | `17161` | `-` | +| `136702637` | `4, 43^2, 11^2, 9, 7^3, 19^2` | `1849` | `-` | + +## Tracked Tail Matrix + +| Tail | Known Packets | Predicted Families | Effective Clean Through | Observed Status | +| --- | --- | --- | --- | --- | +| `157` | `16` | `110` | `19094394` | `fails` | +| `232` | `20` | `201` | `27949927` | `fails` | +| `282` | `25` | `244` | `137720140` | `fails` | +| `332` | `26` | `240` | `250050000` | `clean_through` | +| `382` | `26` | `240` | `250050000` | `unseen` | +| `432` | `26` | `242` | `250050000` | `unseen` | +| `782` | `26` | `242` | `250050000` | `unseen` | +| `832` | `26` | `242` | `250050000` | `unseen` | + +## GPU Leaderboard + +| Rank | Tail | Known Packets | Predicted Families | Effective Clean Through | +| --- | --- | --- | --- | --- | +| `1` | `432` | `26` | `242` | `250075000` | +| `2` | `782` | `26` | `242` | `250075000` | +| `3` | `832` | `26` | `242` | `250075000` | +| `4` | `332` | `26` | `240` | `250075000` | +| `5` | `382` | `26` | `240` | `250075000` | + +## Theorem Hooks + +- `next_unmatched_equals_282_failure`: supported | The next unmatched shared-prefix representative currently coincides with the known first failure of the 282 continuation. +- `completed_tail_vs_search_leader_split`: supported | The strongest completed structured tail remains 332, while the current family-aware search leader can move on the finite tested window. +- `repair_pool_not_closed`: supported | Recent shared-prefix packets introduced new square moduli into the live family menu, so the repaired local square pool is not yet closed. +- `top_repair_class_cluster`: supported | The current top continuation class shares the same repaired-known, repaired-predicted, and tested-clean-through profile on the live finite window. + +## Refresh + +```bash +python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-theorem-bridge +``` diff --git a/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json b/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json new file mode 100644 index 0000000..5719f2b --- /dev/null +++ b/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json @@ -0,0 +1,379 @@ +{ + "schema": "erdos.number_theory.p848_structural_lift_checklist/1", + "generatedAt": "2026-04-11T05:30:00.000Z", + "problemId": "848", + "title": "Problem 848 Structural Lift Checklist", + "status": "active", + "sourceArtifacts": { + "fullMixedBaseStructuralVerifier": "FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json", + "structuralLiftMiner": "STRUCTURAL_LIFT_MINER.json", + "exactBaseCertificate": "EXACT_SMALL_N_1_40500_RESULTS.json" + }, + "northStar": "Turn the bounded mixed-base structural verifier into an all-N proof lane by proving the cross-side matching reduction, then the p=13 and p=17 margin lifts, while keeping exact finite coverage separate.", + "currentFocus": { + "packetId": "D_matching_lower_bounds", + "targetStepId": "D4_matching_bound_implies_sMaxMixed_bound", + "firstActionableStepId": "D2_p13_matching_lower_bound", + "why": "The C graph-reduction packet is theorem-facing through C6, and D1 now extracts the bounded matching target from every current exact mixed-base threatening-outsider row. The next decisive lift is the symbolic p=13 matching lower bound, which is the tightest current D-lane family." + }, + "completionRule": "Each step is complete only when it has a statement, hypotheses, proof sketch or proof artifact, falsifier boundary, dependencies, and the next downstream step updated.", + "phases": [ + { + "phaseId": "A_counting_language", + "title": "Counting Language", + "goal": "Turn verifier counts into exact residue-count and floor-function terms.", + "steps": [ + { + "stepId": "A1_residue_count_formula", + "status": "todo", + "statement": "# {m <= N : m == r mod q} = floor((N - r) / q) + 1 when N >= r, else 0.", + "dependsOn": [], + "proofType": "floor_count_identity", + "falsifierBoundary": "A boundary case with r <= 0, r > q, or N < r is mishandled." + }, + { + "stepId": "A2_base_side_count_formula", + "status": "todo", + "statement": "|B7(N)| and |B18(N)| are residue counts modulo 25, and candidateSize(N) is their maximum.", + "dependsOn": [ + "A1_residue_count_formula" + ], + "proofType": "floor_count_identity", + "falsifierBoundary": "The formula disagrees with the verifier's base-side candidate counts." + }, + { + "stepId": "A3_root_progression_count_formula", + "status": "todo", + "statement": "For each witness prime p == 1 mod 4, n^2 + 1 == 0 mod p^2 has two Hensel-lifted root progressions, counted by residue-count formulas.", + "dependsOn": [ + "A1_residue_count_formula" + ], + "proofType": "hensel_plus_floor_count", + "falsifierBoundary": "A root progression fails the n^2 + 1 == 0 mod p^2 check or the count disagrees with the verifier." + }, + { + "stepId": "A4_vmax_formula", + "status": "todo", + "statement": "vMax(N,p) = max(rawPlus(N,p), rawMinus(N,p)).", + "dependsOn": [ + "A3_root_progression_count_formula" + ], + "proofType": "definition_alignment", + "falsifierBoundary": "The verifier uses a different witness-count maximum." + }, + { + "stepId": "A5_higher_root_event_count_formula", + "status": "todo", + "statement": "rGreater(N,p) is the sum of active root-event counts from witness-prime blocks q > p.", + "dependsOn": [ + "A3_root_progression_count_formula" + ], + "proofType": "finite_sum_floor_count", + "falsifierBoundary": "A higher-prime event is double-counted, omitted, or ordered differently from the verifier." + } + ] + }, + { + "phaseId": "B_compatibility_language", + "title": "Compatibility Language", + "goal": "Convert outsider/base compatibility into congruence conditions.", + "steps": [ + { + "stepId": "B1_square_witness_compatibility", + "status": "todo", + "statement": "For fixed outsider x and base b, compatibility is witnessed by some prime square q^2 dividing x*b + 1.", + "dependsOn": [], + "proofType": "definition_alignment", + "falsifierBoundary": "The compatibility definition diverges from squarefree/non-squarefree semantics." + }, + { + "stepId": "B2_residue_compatibility_condition", + "status": "todo", + "statement": "If gcd(x,q)=1, then q^2 | x*b + 1 iff b == -x^{-1} mod q^2.", + "dependsOn": [ + "B1_square_witness_compatibility" + ], + "proofType": "modular_inverse_identity", + "falsifierBoundary": "A non-invertible x modulo q^2 is treated as invertible." + }, + { + "stepId": "B3_noncoprime_exception_boundary", + "status": "todo", + "statement": "If gcd(x,q) != 1, compatibility is either impossible or recorded as a finite exception boundary before using inverse formulas.", + "dependsOn": [ + "B2_residue_compatibility_condition" + ], + "proofType": "case_split", + "falsifierBoundary": "A noncoprime case creates a compatibility family not covered by the stated exception boundary." + }, + { + "stepId": "B4_compatible_base_union_of_residue_hits", + "status": "todo", + "statement": "For fixed x and N, the compatible base set is the union of all base-side residue hits produced by active square witnesses.", + "dependsOn": [ + "B1_square_witness_compatibility", + "B2_residue_compatibility_condition", + "B3_noncoprime_exception_boundary" + ], + "proofType": "finite_union_of_residue_classes", + "falsifierBoundary": "A compatible base vertex is missing from the union or an incompatible vertex is included." + } + ] + }, + { + "phaseId": "C_graph_reduction_packet", + "title": "Mixed-Base Graph Reduction", + "goal": "Prove the graph identity used by the exact mixed-base verifier.", + "steps": [ + { + "stepId": "C1_same_side_base_clique", + "status": "done", + "statement": "Inside one principal base side, compatible base vertices form a clique for the fixed outsider graph considered by the verifier.", + "dependsOn": [ + "B4_compatible_base_union_of_residue_hits" + ], + "proofType": "mod25_same_side_clique_identity", + "proofArtifact": "p848_C1_same_side_base_clique_checker_v1", + "falsifierBoundary": "Two same-side compatible vertices fail the pair compatibility relation used by the verifier." + }, + { + "stepId": "C2_two_cliques_plus_cross_edges", + "status": "done", + "statement": "For fixed outsider x, the compatible mixed-base graph is one clique on B7-compatible vertices, one clique on B18-compatible vertices, plus arbitrary cross edges.", + "dependsOn": [ + "C1_same_side_base_clique" + ], + "proofType": "graph_decomposition", + "proofArtifact": "p848_C2_two_cliques_plus_cross_edges_checker_v1", + "falsifierBoundary": "The graph has a same-side missing edge or an extra vertex outside the two compatible sides." + }, + { + "stepId": "C3_missing_cross_graph_definition", + "status": "done", + "statement": "Define H_{x,N} as the bipartite graph whose edges are precisely missing cross edges between compatible B7 and B18 vertices.", + "dependsOn": [ + "C2_two_cliques_plus_cross_edges" + ], + "proofType": "definition", + "proofArtifact": "p848_C3_missing_cross_graph_definition_checker_v1", + "falsifierBoundary": "A cross edge is assigned the wrong sign between compatibility and missing-cross membership." + }, + { + "stepId": "C4_clique_to_vertex_cover_duality", + "status": "done", + "statement": "A mixed-base clique equals all compatible vertices minus a vertex cover of H_{x,N}; hence max clique size is |L| + |R| minus minimum vertex cover size.", + "dependsOn": [ + "C3_missing_cross_graph_definition" + ], + "proofType": "graph_duality", + "proofArtifact": "p848_C4_clique_to_vertex_cover_duality_checker_v1", + "falsifierBoundary": "A selected clique contains a missing cross edge or a vertex cover removes more vertices than necessary." + }, + { + "stepId": "C5_konig_matching_reduction", + "status": "done", + "statement": "Because H_{x,N} is bipartite, minimum vertex cover size equals maximum matching size.", + "dependsOn": [ + "C3_missing_cross_graph_definition" + ], + "proofType": "konig_theorem", + "proofArtifact": "p848_C5_konig_matching_reduction_checker_v1", + "falsifierBoundary": "H_{x,N} is not bipartite or Konig's theorem is used outside its hypotheses." + }, + { + "stepId": "C6_mixed_clique_matching_formula", + "status": "done", + "statement": "sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).", + "dependsOn": [ + "C4_clique_to_vertex_cover_duality", + "C5_konig_matching_reduction" + ], + "proofType": "graph_formula", + "proofArtifact": "p848_C6_mixed_clique_matching_formula_checker_v1", + "falsifierBoundary": "The formula disagrees with the verifier's Hopcroft-Karp mixed-clique computation on a certified row." + } + ] + }, + { + "phaseId": "D_matching_lower_bounds", + "title": "Matching Lower Bounds", + "goal": "Replace Hopcroft-Karp computation with symbolic matching constructions.", + "steps": [ + { + "stepId": "D1_residue_block_matching_injection", + "status": "done", + "statement": "Extract the current residue-block matching target from all bounded exact mixed-base threatening-outsider rows: K(N,x) = |L| + |R| - strictBaseThreshold + 1, and the recorded matching saturates the smaller compatible side in every current row.", + "dependsOn": [ + "C6_mixed_clique_matching_formula" + ], + "proofType": "bounded_matching_saturation_extraction", + "proofArtifact": "p848_D1_matching_saturation_bound_checker_v1", + "falsifierBoundary": "A refreshed exact mixed-base threatening-outsider row has matching below K(N,x), disagrees with the C6 formula replay, or fails the smaller-side saturation pattern. This bounded extraction is not yet the all-N symbolic matching proof." + }, + { + "stepId": "D2_p13_matching_lower_bound", + "status": "next", + "statement": "For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=13 family row fails the claimed lower bound." + }, + { + "stepId": "D3_p17_matching_lower_bound", + "status": "ready", + "statement": "For p=17 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "dependsOn": [ + "D1_residue_block_matching_injection" + ], + "proofType": "residue_family_matching_bound", + "falsifierBoundary": "A p=17 family row fails the claimed lower bound." + }, + { + "stepId": "D4_matching_bound_implies_sMaxMixed_bound", + "status": "blocked_by_D2_D3", + "statement": "If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "dependsOn": [ + "C6_mixed_clique_matching_formula", + "D2_p13_matching_lower_bound", + "D3_p17_matching_lower_bound" + ], + "proofType": "inequality_substitution", + "falsifierBoundary": "The matching lower bound is substituted with the wrong inequality direction." + } + ] + }, + { + "phaseId": "E_margin_lifts", + "title": "Margin Lifts", + "goal": "Prove eventual positivity of the structural margins.", + "steps": [ + { + "stepId": "E1_p13_term_bound", + "status": "blocked_by_D4", + "statement": "Bound sMaxMixed, vMax, dMax, and rGreater for p=13 by explicit floor-function expressions.", + "dependsOn": [ + "A_counting_language", + "D4_matching_bound_implies_sMaxMixed_bound" + ], + "proofType": "floor_function_bound", + "falsifierBoundary": "The symbolic bound is lower than a verifier row term." + }, + { + "stepId": "E2_p13_margin_floor_inequality", + "status": "blocked_by_E1", + "statement": "candidateSize(N) - (sMixedBound13(N) + vMax13(N) + dMax13(N) + rGreater13(N)) > 0 for all N >= T13.", + "dependsOn": [ + "E1_p13_term_bound" + ], + "proofType": "eventual_floor_inequality", + "falsifierBoundary": "A residue class modulo the proof period gives nonpositive margin beyond T13." + }, + { + "stepId": "E3_p17_term_bound", + "status": "blocked_by_D4", + "statement": "Bound sMaxMixed, vMax, dMax, and rGreater for p=17 by explicit floor-function expressions.", + "dependsOn": [ + "A_counting_language", + "D4_matching_bound_implies_sMaxMixed_bound" + ], + "proofType": "floor_function_bound", + "falsifierBoundary": "The symbolic bound is lower than a verifier row term." + }, + { + "stepId": "E4_p17_margin_floor_inequality", + "status": "blocked_by_E3", + "statement": "candidateSize(N) - (sMixedBound17(N) + vMax17(N) + dMax17(N) + rGreater17(N)) > 0 for all N >= T17.", + "dependsOn": [ + "E3_p17_term_bound" + ], + "proofType": "eventual_floor_inequality", + "falsifierBoundary": "A residue class modulo the proof period gives nonpositive margin beyond T17." + }, + { + "stepId": "E5_easy_prime_union_tail", + "status": "blocked_by_A_counting", + "statement": "For witness primes outside {13,17}, the safe union-bound structural margin is eventually positive.", + "dependsOn": [ + "A_counting_language" + ], + "proofType": "union_bound_tail_inequality", + "falsifierBoundary": "A non-{13,17} witness-prime block needs exact mixed-base repair beyond the finite verifier range." + } + ] + }, + { + "phaseId": "F_finite_closure", + "title": "Finite Closure", + "goal": "Attach symbolic lemmas to existing finite certificates without overclaiming.", + "steps": [ + { + "stepId": "F1_exact_base_certificate", + "status": "available", + "statement": "The exact verifier certifies N <= 40500.", + "dependsOn": [], + "proofType": "repo_artifact_certificate", + "falsifierBoundary": "The exact certificate is stale, missing, or fails rerun." + }, + { + "stepId": "F2_bounded_structural_certificate", + "status": "available", + "statement": "The full mixed-base structural verifier certifies 7307..7600 with zero mixed failures.", + "dependsOn": [], + "proofType": "repo_artifact_certificate", + "falsifierBoundary": "The full verifier artifact loses allMixedChecksPass or its parameters drift." + }, + { + "stepId": "F3_threshold_overlap", + "status": "blocked_by_E2_E4_E5", + "statement": "The symbolic thresholds T13, T17, and Ttail overlap the finite exact or structural certificates.", + "dependsOn": [ + "E2_p13_margin_floor_inequality", + "E4_p17_margin_floor_inequality", + "E5_easy_prime_union_tail" + ], + "proofType": "interval_cover_check", + "falsifierBoundary": "A gap remains between the finite certificate end and a symbolic threshold." + }, + { + "stepId": "F4_all_ranges_cover_positive_integers", + "status": "blocked_by_F3", + "statement": "Exact base plus symbolic structural lift cover all positive integers in the problem claim.", + "dependsOn": [ + "F1_exact_base_certificate", + "F2_bounded_structural_certificate", + "F3_threshold_overlap" + ], + "proofType": "range_cover_argument", + "falsifierBoundary": "A positive integer N is covered by neither exact verification nor symbolic structural lift." + } + ] + } + ], + "recommendedNextSteps": [ + { + "stepId": "prove_p13_matching_lower_bound", + "priority": "critical", + "task": "Prove the symbolic p=13 lower bound that explains why maxMatching(H_{x,N}) always reaches the D1-extracted K(N,x) target in the tightest current exact-mixed family.", + "command": "erdos problem formalization-work-refresh 848" + }, + { + "stepId": "regression_check_C6_against_verifier", + "priority": "high", + "task": "Keep the discharged C6 mixed-clique matching formula regression-checked against representative full-verifier rows.", + "command": "erdos number-theory dispatch 848 --apply --action structural_lift_miner" + }, + { + "stepId": "extract_p13_residue_matching_pattern", + "priority": "high", + "task": "For the top p=13 families, extract the residue-block pattern behind the smaller-side-saturating matchings so D2 can become a symbolic construction rather than bounded evidence.", + "command": "erdos number-theory dispatch 848 --apply --action structural_lift_miner" + } + ], + "boundary": { + "claimLevel": "task_checklist_not_proof", + "note": "This checklist records a proof plan and dependencies. It does not certify any new N by itself.", + "promotionRule": "Only mark a step done after the statement, hypotheses, proof/falsifier boundary, and downstream dependency updates are committed." + } +} diff --git a/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.md b/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.md new file mode 100644 index 0000000..e994f29 --- /dev/null +++ b/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.md @@ -0,0 +1,83 @@ +# Problem 848 Structural Lift Checklist + +This checklist breaks the structural lift into proof tasks small enough to reference, +prove, falsify, or hand to a theorem-proving lane. It is a task surface, not a proof. + +## Current Focus + +- Packet: `D_matching_lower_bounds` +- Target step: `D4_matching_bound_implies_sMaxMixed_bound` +- First actionable step: `D2_p13_matching_lower_bound` +- Why: the C graph-reduction packet is theorem-facing through C6, and D1 now extracts + the bounded matching target from every current exact mixed-base threatening-outsider row. The next + decisive lift is the symbolic `p=13` matching lower bound, which is the tightest + current D-lane family. + +## Completion Rule + +Each step is complete only when it has: + +- a precise statement +- explicit hypotheses +- a proof sketch or proof artifact +- a falsifier boundary +- dependencies recorded +- the next downstream step updated + +## A. Counting Language + +- `A1_residue_count_formula` [todo]: Prove `# {m <= N : m == r mod q} = floor((N - r) / q) + 1` when `N >= r`, else `0`. +- `A2_base_side_count_formula` [todo]: Express `|B7(N)|`, `|B18(N)|`, and `candidateSize(N)` as modulo-25 floor counts. +- `A3_root_progression_count_formula` [todo]: Count the two Hensel-lifted root progressions for `n^2 + 1 == 0 mod p^2`. +- `A4_vmax_formula` [todo]: Define `vMax(N,p) = max(rawPlus(N,p), rawMinus(N,p))`. +- `A5_higher_root_event_count_formula` [todo]: Express `rGreater(N,p)` as the sum of active higher-prime root-event counts. + +## B. Compatibility Language + +- `B1_square_witness_compatibility` [todo]: Define outsider/base compatibility by square witnesses `q^2 | x*b + 1`. +- `B2_residue_compatibility_condition` [todo]: Prove `q^2 | x*b + 1` iff `b == -x^{-1} mod q^2` when `gcd(x,q)=1`. +- `B3_noncoprime_exception_boundary` [todo]: Isolate noninvertible `gcd(x,q) != 1` cases before inverse formulas are used. +- `B4_compatible_base_union_of_residue_hits` [todo]: Prove compatible base sets are finite unions of residue hits from active square witnesses. + +## C. Mixed-Base Graph Reduction + +- `C1_same_side_base_clique` [done]: Same-side principal base residues force a `25` divisor of `u*v+1`, so each same-side component is a clique. +- `C2_two_cliques_plus_cross_edges` [done]: Decompose the mixed-base graph into a `B7` clique, a `B18` clique, and cross edges. +- `C3_missing_cross_graph_definition` [done]: Define `H_{x,N}` as the bipartite graph of missing cross edges. +- `C4_clique_to_vertex_cover_duality` [done]: Prove a mixed clique is all compatible vertices minus a vertex cover of `H_{x,N}`. +- `C5_konig_matching_reduction` [done]: Apply Konig's theorem because `H_{x,N}` is bipartite. +- `C6_mixed_clique_matching_formula` [done]: Prove `sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N})`. + +## D. Matching Lower Bounds + +- `D1_residue_block_matching_injection` [done]: Extract `K(N,x) = |L| + |R| - strictBaseThreshold + 1` and certify that every current exact mixed-base threatening-outsider row meets the target and saturates the smaller compatible side. +- `D2_p13_matching_lower_bound` [next]: Prove the required matching lower bound for `p=13` threatening rows. +- `D3_p17_matching_lower_bound` [ready]: Prove the required matching lower bound for `p=17` threatening rows. +- `D4_matching_bound_implies_sMaxMixed_bound` [blocked_by_D2_D3]: Substitute the matching lower bound into the mixed-clique formula. + +## E. Margin Lifts + +- `E1_p13_term_bound` [blocked_by_D4]: Bound `sMaxMixed`, `vMax`, `dMax`, and `rGreater` for `p=13` by floor-function expressions. +- `E2_p13_margin_floor_inequality` [blocked_by_E1]: Prove the `p=13` margin is positive for all `N >= T13`. +- `E3_p17_term_bound` [blocked_by_D4]: Bound `sMaxMixed`, `vMax`, `dMax`, and `rGreater` for `p=17` by floor-function expressions. +- `E4_p17_margin_floor_inequality` [blocked_by_E3]: Prove the `p=17` margin is positive for all `N >= T17`. +- `E5_easy_prime_union_tail` [blocked_by_A_counting]: Prove non-`{13,17}` witness-prime blocks are eventually handled by the safe union bound. + +## F. Finite Closure + +- `F1_exact_base_certificate` [available]: Use the exact verifier certificate for `N <= 40500`. +- `F2_bounded_structural_certificate` [available]: Use the full mixed-base structural verifier for `7307..7600`. +- `F3_threshold_overlap` [blocked_by_E2_E4_E5]: Verify symbolic thresholds overlap the finite exact or structural certificates. +- `F4_all_ranges_cover_positive_integers` [blocked_by_F3]: Combine exact base plus symbolic structural lift into an all-range cover. + +## Recommended Next Steps + +- `prove_p13_matching_lower_bound` [critical]: Prove the symbolic `p=13` lower bound that explains why `maxMatching(H_{x,N})` always reaches the D1-extracted `K(N,x)` target in the tightest current exact-mixed family. Command: `erdos problem formalization-work-refresh 848` +- `regression_check_C6_against_verifier` [high]: Keep the discharged C6 mixed-clique matching formula regression-checked against representative full-verifier rows. Command: `erdos number-theory dispatch 848 --apply --action structural_lift_miner` +- `extract_p13_residue_matching_pattern` [high]: For the top `p=13` families, extract the residue-block pattern behind the smaller-side-saturating matchings so D2 can become a symbolic construction rather than bounded evidence. Command: `erdos number-theory dispatch 848 --apply --action structural_lift_miner` + +## Boundary + +- Claim level: `task_checklist_not_proof` +- Note: this checklist records a proof plan and dependencies. It does not certify any new `N`. +- Promotion rule: only mark a step done after the statement, hypotheses, proof/falsifier boundary, and downstream dependency updates are committed. diff --git a/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.json b/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.json new file mode 100644 index 0000000..2825aba --- /dev/null +++ b/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.json @@ -0,0 +1,5095 @@ +{ + "schema": "erdos.number_theory.p848_structural_lift_miner/1", + "generatedAt": "2026-04-11T14:10:06.048Z", + "problemId": "848", + "method": "mixed_base_structural_lift_pattern_mining", + "status": "structural_lift_obligation_packet_ready", + "parameters": { + "verifierJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json", + "topRows": 12, + "familyLimit": 20 + }, + "sourceVerifier": { + "status": "bounded_full_mixed_base_structural_verifier_certified", + "method": "bounded_outsider_clique_full_mixed_base_structural_verifier", + "assessedRange": "7307..7600", + "exactMixedRowCount": 64, + "compactLiftMiningRowCount": 64, + "compactThreatMiningRowCount": 1733, + "minedExactRowCount": 64, + "coverageComplete": true + }, + "summary": { + "assessedRange": "7307..7600", + "exactMixedRowCount": 64, + "minedExactRowCount": 64, + "threatMiningRowCount": 1733, + "coverageComplete": true, + "exactPrimeCount": 2, + "primaryExactPrimes": [ + 13, + 17 + ], + "topFamilyCount": 20, + "minMixedMargin": 20, + "minUnionMargin": -89, + "minThreatMatchingSlack": 19, + "maxThreateningOutsidersInRow": 41, + "maxImprovementOverUnion": 112, + "nextTheoremLane": "formalize_cross_side_matching_bound_then_exact_prime_margin_lift" + }, + "periodicityHints": { + "nMod25Distribution": [ + { + "key": 18, + "count": 24 + }, + { + "key": 7, + "count": 24 + }, + { + "key": 0, + "count": 2 + }, + { + "key": 1, + "count": 2 + }, + { + "key": 10, + "count": 2 + }, + { + "key": 12, + "count": 2 + }, + { + "key": 16, + "count": 2 + }, + { + "key": 2, + "count": 2 + }, + { + "key": 3, + "count": 2 + }, + { + "key": 6, + "count": 2 + } + ], + "dMaxWitnessSideDistribution": [ + { + "key": "minus", + "count": 32 + }, + { + "key": "plus", + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side7", + "count": 38 + }, + { + "key": "side18", + "count": 26 + } + ], + "worstOutsiderMod25Distribution": [ + { + "key": 1, + "count": 22 + }, + { + "key": 6, + "count": 16 + }, + { + "key": 14, + "count": 14 + }, + { + "key": 23, + "count": 10 + }, + { + "key": 9, + "count": 2 + } + ] + }, + "primeProfiles": [ + { + "p": 13, + "p2": 169, + "count": 32, + "firstN": 7307, + "lastN": 7600, + "minMixedMargin": 20, + "maxMixedMargin": 24, + "averageMixedMargin": 22.71875, + "minUnionMargin": -89, + "maxThreateningOutsiders": 41, + "maxImprovementOverUnion": 111, + "marginDeltaAcrossMinedRows": 2, + "approximateMarginSlopePerN": 0.006825938566552901, + "nMod25Distribution": [ + { + "key": 18, + "count": 12 + }, + { + "key": 7, + "count": 12 + }, + { + "key": 0, + "count": 1 + }, + { + "key": 1, + "count": 1 + }, + { + "key": 10, + "count": 1 + }, + { + "key": 12, + "count": 1 + }, + { + "key": 16, + "count": 1 + }, + { + "key": 2, + "count": 1 + }, + { + "key": 3, + "count": 1 + }, + { + "key": 6, + "count": 1 + } + ], + "dMaxWitnessSideDistribution": [ + { + "key": "plus", + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side18", + "count": 16 + }, + { + "key": "side7", + "count": 16 + } + ], + "worstOutsiderMod25Distribution": [ + { + "key": 6, + "count": 16 + }, + { + "key": 14, + "count": 14 + }, + { + "key": 9, + "count": 2 + } + ] + }, + { + "p": 17, + "p2": 289, + "count": 32, + "firstN": 7307, + "lastN": 7600, + "minMixedMargin": 96, + "maxMixedMargin": 101, + "averageMixedMargin": 99.3125, + "minUnionMargin": -13, + "maxThreateningOutsiders": 14, + 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"matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 14, + "matchingSlack": 95, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 294, + "strictBaseThreshold": 208, + "unionCount": 221, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 14, + "matchingSlack": 95, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 251, + "outsiderMod25": 1, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 216, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 106, + "compatibleSide7Count": 110, + "compatibleSide18Count": 106, + "requiredMatchingLowerBound": 10, + "matchingSlack": 96, + "smallerSideSize": 106, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 110, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 219, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 110, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7318, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 251, + "outsiderMod25": 1, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 217, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 107, + "compatibleSide7Count": 110, + "compatibleSide18Count": 107, + "requiredMatchingLowerBound": 11, + "matchingSlack": 96, + "smallerSideSize": 107, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 110, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7332, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 294, + "strictBaseThreshold": 208, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7337, + "certificateMode": "exact_mixed_base", + "nMod25": 12, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 294, + "strictBaseThreshold": 208, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7357, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 295, + "strictBaseThreshold": 209, + "unionCount": 221, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + } + ] + } + ] + }, + "proofUse": "This is the exact step that turns the computational co-bipartite clique repair into a reusable lemma." + }, + { + "obligationId": "p848_exact_prime_margin_lift", + "priority": "critical", + "status": "bounded_evidence_ready", + "statementTemplate": "For the exact-mixed witness-prime families 13, 17, prove candidateSize > sMaxMixed + vMax + dMax + rGreater either eventually or by a finite periodic residue split.", + "currentEvidence": { + "exactPrimeProfiles": [ + { + "p": 13, + "p2": 169, + "count": 32, + "firstN": 7307, + "lastN": 7600, + "minMixedMargin": 20, + "maxMixedMargin": 24, + "averageMixedMargin": 22.71875, + "minUnionMargin": -89, + "maxThreateningOutsiders": 41, + "maxImprovementOverUnion": 111, + "marginDeltaAcrossMinedRows": 2, + "approximateMarginSlopePerN": 0.006825938566552901, + "nMod25Distribution": [ + { + "key": 18, + "count": 12 + }, + { + "key": 7, + "count": 12 + }, + { + "key": 0, + "count": 1 + }, + { + "key": 1, + "count": 1 + }, + { + "key": 10, + "count": 1 + }, + { + "key": 12, + "count": 1 + }, + { + "key": 16, + "count": 1 + }, + { + "key": 2, + "count": 1 + }, + { + "key": 3, + "count": 1 + }, + { + "key": 6, + "count": 1 + } + ], + "dMaxWitnessSideDistribution": [ + { + "key": "plus", + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side18", + "count": 16 + }, + { + "key": "side7", + "count": 16 + } + ], + "worstOutsiderMod25Distribution": [ + { + "key": 6, + "count": 16 + }, + { + "key": 14, + "count": 14 + }, + { + "key": 9, + "count": 2 + } + ] + }, + { + "p": 17, + "p2": 289, + "count": 32, + "firstN": 7307, + "lastN": 7600, + "minMixedMargin": 96, + "maxMixedMargin": 101, + "averageMixedMargin": 99.3125, + "minUnionMargin": -13, + "maxThreateningOutsiders": 14, + "maxImprovementOverUnion": 112, + "marginDeltaAcrossMinedRows": 4, + "approximateMarginSlopePerN": 0.013651877133105802, + "nMod25Distribution": [ + { + "key": 18, + "count": 12 + }, + { + "key": 7, + "count": 12 + }, + { + "key": 0, + "count": 1 + }, + { + "key": 1, + "count": 1 + }, + { + "key": 10, + "count": 1 + }, + { + "key": 12, + "count": 1 + }, + { + "key": 16, + "count": 1 + }, + { + "key": 2, + "count": 1 + }, + { + "key": 3, + "count": 1 + }, + { + "key": 6, + "count": 1 + } + ], + "dMaxWitnessSideDistribution": [ + { + "key": "minus", + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side7", + "count": 22 + }, + { + "key": "side18", + "count": 10 + } + ], + "worstOutsiderMod25Distribution": [ + { + "key": 1, + "count": 22 + }, + { + "key": 23, + "count": 10 + } + ] + } + ] + }, + "proofUse": "This is the likely all-N lift of the hardest bounded structural rows." + }, + { + "obligationId": "p848_union_bound_tail_lift", + "priority": "high", + "status": "bounded_evidence_ready", + "statementTemplate": "Prove that every non-exact witness-prime block is certified by the safe union bound past the base interval, with only finitely many exceptional rows delegated to exact verification.", + "currentEvidence": { + "unionCertifiedRowCount": 192, + "exactMixedRowCount": 64, + "minCertifiedMargin": 20 + }, + "proofUse": "This separates the easy tail from the p-specific exact mixed-base obligations." + }, + { + "obligationId": "p848_top_repeating_family_lift", + "priority": "high", + "status": "bounded_evidence_ready", + "statementTemplate": "Use family p=17|Nmod25=7|d=minus|clique=side7|outMod25=1 as the first symbolic family to formalize.", + "currentEvidence": { + "familyKey": "p=17|Nmod25=7|d=minus|clique=side7|outMod25=1", + "count": 9, + "firstN": 7307, + "lastN": 7582, + "minMixedMargin": 97, + "maxMixedMargin": 101, + "averageMixedMargin": 100, + "minUnionMargin": -12, + "maxThreateningOutsiders": 14, + "maxImprovementOverUnion": 112, + "representativeRows": [ + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "rawPlus": 26, + "rawMinus": 25, + "vMax": 26, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "side7Margin": 97, + "side18Margin": 97, + "unionMargin": -12, + "mixedMargin": 97, + "sMaxMixed": 110, + "sMaxMixedWitness": 251, + "sMaxMixedWitnessMod25": 1, + "threateningOutsiderCount": 14, + "maxImprovementOverUnion": 109, + "worstOutsider": 251, + "worstOutsiderMod25": 1, + "worstUnionCount": 216, + "worstMixedCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 106, + "compatibleSide7Count": 110, + "compatibleSide18Count": 106, + "mixedCliqueSide7Count": 110, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7407, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "rawPlus": 26, + "rawMinus": 25, + "vMax": 26, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 297, + "strictBaseThreshold": 211, + "side7Margin": 99, + "side18Margin": 99, + "unionMargin": -11, + "mixedMargin": 99, + "sMaxMixed": 112, + "sMaxMixedWitness": 251, + "sMaxMixedWitnessMod25": 1, + "threateningOutsiderCount": 14, + "maxImprovementOverUnion": 110, + "worstOutsider": 251, + "worstOutsiderMod25": 1, + "worstUnionCount": 220, + "worstMixedCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 112, + "compatibleSide18Count": 108, + "mixedCliqueSide7Count": 112, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7432, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "rawPlus": 26, + "rawMinus": 25, + "vMax": 26, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 298, + "strictBaseThreshold": 212, + "side7Margin": 100, + "side18Margin": 100, + "unionMargin": -10, + "mixedMargin": 100, + "sMaxMixed": 112, + "sMaxMixedWitness": 251, + "sMaxMixedWitnessMod25": 1, + "threateningOutsiderCount": 14, + "maxImprovementOverUnion": 110, + "worstOutsider": 251, + "worstOutsiderMod25": 1, + "worstUnionCount": 220, + "worstMixedCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 112, + "compatibleSide18Count": 108, + "mixedCliqueSide7Count": 112, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + } + ] + }, + "proofUse": "A repeated row family is the best handhold for converting the verifier into a theorem packet." + } + ], + "recommendedNextSteps": [ + { + "stepId": "mine_matching_pattern_witnesses", + "priority": "critical", + "command": "erdos number-theory dispatch 848 --apply --action matching_pattern_miner --matching-pattern-prime 13", + "why": "The active D2 atom needs a symbolic matching construction, and the matching-pattern miner extracts actual tight-row missing-cross pairs without bloating the verifier artifact." + }, + { + "stepId": "formalize_cross_side_matching_bound", + "priority": "critical", + "command": "erdos problem formalization-work-refresh 848", + "why": "The full verifier succeeds exactly because mixed-base cliques are much smaller than the safe union overcount; this is the theorem-shaped repair mechanism." + }, + { + "stepId": "formalize_exact_prime_margin_lift", + "priority": "critical", + "command": "erdos problem formalization 848", + "why": "The mined rows identify which witness-prime blocks still need symbolic margin control after the union-bound rows are separated." + }, + { + "stepId": "extend_structural_range_after_lift_target", + "priority": "high", + "command": "erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min 7307 --structural-max 15200", + "why": "Once the first symbolic family is named, extend the bounded verifier beyond 7307..7600 to falsify or strengthen the family before claiming a lift." + } + ], + "boundary": { + "claimLevel": "theorem_obligation_packet_not_all_N_proof", + "note": "This miner extracts proof obligations from a bounded structural verifier. It does not certify any N outside the source verifier range.", + "promotionRule": "Use this packet to choose and formalize symbolic lemmas. Promote all-N closure only after those lemmas are independently proved and linked to the finite exact base." + } +} diff --git a/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.md b/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.md new file mode 100644 index 0000000..ea99355 --- /dev/null +++ b/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.md @@ -0,0 +1,68 @@ +# Problem 848 Structural Lift Miner + +- Generated: 2026-04-11T14:10:06.048Z +- Method: `mixed_base_structural_lift_pattern_mining` +- Status: `structural_lift_obligation_packet_ready` +- Source verifier status: `bounded_full_mixed_base_structural_verifier_certified` +- Assessed range: `7307..7600` +- Exact mixed rows reported: `64` +- Exact mixed rows mined: `64` +- Threatening-outsider rows mined: `1733` +- Coverage complete: `yes` +- Primary exact primes: `13, 17` +- Minimum mixed margin: `20` +- Minimum threat matching slack: `19` + +## Prime Profiles + +- p=13: rows 32, N 7307..7600, min margin 20, margin delta 2 +- p=17: rows 32, N 7307..7600, min margin 96, margin delta 4 + +## Threat Matching Profiles + +- p=13: threats 1285, rows 32, K 26..90, matching 79..111, min slack 19, saturates smaller side yes +- p=17: threats 448, rows 32, K 1..14, matching 103..112, min slack 95, saturates smaller side yes + +## Top Families + +- `p=17|Nmod25=7|d=minus|clique=side7|outMod25=1`: rows 9, N 7307..7582, min margin 97, max union repair 112 +- `p=13|Nmod25=7|d=plus|clique=side7|outMod25=6`: rows 8, N 7307..7482, min margin 21, max union repair 110 +- `p=17|Nmod25=18|d=minus|clique=side7|outMod25=1`: rows 7, N 7418..7593, min margin 99, max union repair 112 +- `p=13|Nmod25=18|d=plus|clique=side7|outMod25=6`: rows 5, N 7318..7468, min margin 21, max union repair 110 +- `p=13|Nmod25=18|d=plus|clique=side18|outMod25=14`: rows 5, N 7493..7593, min margin 23, max union repair 111 +- `p=17|Nmod25=18|d=minus|clique=side18|outMod25=23`: rows 5, N 7318..7443, min margin 96, max union repair 110 +- `p=13|Nmod25=7|d=plus|clique=side18|outMod25=14`: rows 4, N 7507..7582, min margin 23, max union repair 111 +- `p=17|Nmod25=7|d=minus|clique=side18|outMod25=23`: rows 3, N 7332..7382, min margin 97, max union repair 109 +- `p=13|Nmod25=18|d=plus|clique=side18|outMod25=9`: rows 2, N 7343..7443, min margin 20, max union repair 110 +- `p=13|Nmod25=12|d=plus|clique=side7|outMod25=6`: rows 1, N 7337..7337, min margin 21, max union repair 108 + +## Worst Rows + +- {"N":7343,"certificateMode":"exact_mixed_base","nMod25":18,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"activeOutsiderCount":80,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":294,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":20,"unionMargin":-88,"mixedMargin":20,"sMaxMixed":112,"sMaxMixedWitness":5309,"sMaxMixedWitnessMod25":9,"threateningOutsiderCount":40,"maxImprovementOverUnion":109,"worstOutsider":5309,"worstOutsiderMod25":9,"worstUnionCount":220,"worstMixedCliqueSize":112,"matchingSizeInMissingCrossGraph":108,"compatibleSide7Count":108,"compatibleSide18Count":112,"mixedCliqueSide7Count":0,"mixedCliqueSide18Count":112,"dominantMixedCliqueSide":"side18"} +- {"N":7307,"certificateMode":"exact_mixed_base","nMod25":7,"p":13,"p2":169,"rawPlus":43,"rawMinus":43,"vMax":43,"activePlus":40,"activeMinus":39,"activeOutsiderCount":79,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":293,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":22,"unionMargin":-86,"mixedMargin":21,"sMaxMixed":111,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":39,"maxImprovementOverUnion":108,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":216,"worstMixedCliqueSize":111,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":111,"compatibleSide18Count":105,"mixedCliqueSide7Count":111,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} +- {"N":7318,"certificateMode":"exact_mixed_base","nMod25":18,"p":13,"p2":169,"rawPlus":43,"rawMinus":43,"vMax":43,"activePlus":40,"activeMinus":39,"activeOutsiderCount":79,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":293,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":21,"unionMargin":-87,"mixedMargin":21,"sMaxMixed":111,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":39,"maxImprovementOverUnion":108,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":216,"worstMixedCliqueSize":111,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":111,"compatibleSide18Count":105,"mixedCliqueSide7Count":111,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} +- {"N":7337,"certificateMode":"exact_mixed_base","nMod25":12,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"activeOutsiderCount":80,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":294,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":21,"unionMargin":-87,"mixedMargin":21,"sMaxMixed":111,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":40,"maxImprovementOverUnion":108,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":216,"worstMixedCliqueSize":111,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":111,"compatibleSide18Count":105,"mixedCliqueSide7Count":111,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} +- {"N":7357,"certificateMode":"exact_mixed_base","nMod25":7,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"activeOutsiderCount":80,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":295,"strictBaseThreshold":133,"side7Margin":21,"side18Margin":21,"unionMargin":-87,"mixedMargin":21,"sMaxMixed":112,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":40,"maxImprovementOverUnion":109,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":217,"worstMixedCliqueSize":112,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":112,"compatibleSide18Count":105,"mixedCliqueSide7Count":112,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} +- {"N":7366,"certificateMode":"exact_mixed_base","nMod25":16,"p":13,"p2":169,"rawPlus":44,"rawMinus":44,"vMax":44,"activePlus":41,"activeMinus":40,"activeOutsiderCount":81,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":295,"strictBaseThreshold":133,"side7Margin":21,"side18Margin":21,"unionMargin":-87,"mixedMargin":21,"sMaxMixed":112,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":40,"maxImprovementOverUnion":109,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":217,"worstMixedCliqueSize":112,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":112,"compatibleSide18Count":105,"mixedCliqueSide7Count":112,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} +- {"N":7368,"certificateMode":"exact_mixed_base","nMod25":18,"p":13,"p2":169,"rawPlus":44,"rawMinus":44,"vMax":44,"activePlus":41,"activeMinus":40,"activeOutsiderCount":81,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":295,"strictBaseThreshold":133,"side7Margin":21,"side18Margin":21,"unionMargin":-87,"mixedMargin":21,"sMaxMixed":112,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":40,"maxImprovementOverUnion":109,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":217,"worstMixedCliqueSize":112,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":112,"compatibleSide18Count":105,"mixedCliqueSide7Count":112,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} +- {"N":7332,"certificateMode":"exact_mixed_base","nMod25":7,"p":13,"p2":169,"rawPlus":43,"rawMinus":43,"vMax":43,"activePlus":40,"activeMinus":39,"activeOutsiderCount":79,"dMax":18,"dMaxWitnessSide":"plus","dMaxWitnessValue":1591,"rGreater":100,"candidateSize":294,"strictBaseThreshold":133,"side7Margin":22,"side18Margin":22,"unionMargin":-86,"mixedMargin":22,"sMaxMixed":111,"sMaxMixedWitness":4831,"sMaxMixedWitnessMod25":6,"threateningOutsiderCount":39,"maxImprovementOverUnion":108,"worstOutsider":4831,"worstOutsiderMod25":6,"worstUnionCount":216,"worstMixedCliqueSize":111,"matchingSizeInMissingCrossGraph":105,"compatibleSide7Count":111,"compatibleSide18Count":105,"mixedCliqueSide7Count":111,"mixedCliqueSide18Count":0,"dominantMixedCliqueSide":"side7"} + +## Lift Obligations + +- `p848_cross_side_matching_bound` [critical, bounded_evidence_ready]: For each threatening outsider, the missing cross-edge graph between the 7 mod 25 and 18 mod 25 compatible base sides has a matching large enough to force mixedCliqueSize below the strict base threshold. +- `p848_exact_prime_margin_lift` [critical, bounded_evidence_ready]: For the exact-mixed witness-prime families 13, 17, prove candidateSize > sMaxMixed + vMax + dMax + rGreater either eventually or by a finite periodic residue split. +- `p848_union_bound_tail_lift` [high, bounded_evidence_ready]: Prove that every non-exact witness-prime block is certified by the safe union bound past the base interval, with only finitely many exceptional rows delegated to exact verification. +- `p848_top_repeating_family_lift` [high, bounded_evidence_ready]: Use family p=17|Nmod25=7|d=minus|clique=side7|outMod25=1 as the first symbolic family to formalize. + +## Recommended Next Steps + +- `mine_matching_pattern_witnesses` [critical]: The active D2 atom needs a symbolic matching construction, and the matching-pattern miner extracts actual tight-row missing-cross pairs without bloating the verifier artifact. | command: `erdos number-theory dispatch 848 --apply --action matching_pattern_miner --matching-pattern-prime 13` +- `formalize_cross_side_matching_bound` [critical]: The full verifier succeeds exactly because mixed-base cliques are much smaller than the safe union overcount; this is the theorem-shaped repair mechanism. | command: `erdos problem formalization-work-refresh 848` +- `formalize_exact_prime_margin_lift` [critical]: The mined rows identify which witness-prime blocks still need symbolic margin control after the union-bound rows are separated. | command: `erdos problem formalization 848` +- `extend_structural_range_after_lift_target` [high]: Once the first symbolic family is named, extend the bounded verifier beyond 7307..7600 to falsify or strengthen the family before claiming a lift. | command: `erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min 7307 --structural-max 15200` + +## Boundary + +- Claim level: `theorem_obligation_packet_not_all_N_proof` +- Note: This miner extracts proof obligations from a bounded structural verifier. It does not certify any N outside the source verifier range. +- Promotion rule: Use this packet to choose and formalize symbolic lemmas. Promote all-N closure only after those lemmas are independently proved and linked to the finite exact base. diff --git a/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json b/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json new file mode 100644 index 0000000..e1c90c8 --- /dev/null +++ b/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json @@ -0,0 +1,2780 @@ +{ + "schema": "erdos.number_theory.p848_structural_two_side_scout/1", + "generatedAt": "2026-04-11T20:36:56.648Z", + "problemId": "848", + "method": "bounded_outsider_clique_two_side_structural_scout", + "status": "side_specific_bounds_pass_but_union_bound_fails", + "parameters": { + "maxN": 7600, + "minStructuralN": 7307, + "assessedRange": "7307..7600" + }, + "summary": { + "assessedRange": "7307..7600", + "witnessBlockCount": 8, + "breakpointCount": 32, + "checkCount": 256, + "globalRootEventCount": 193, + "side7BaseCountAtMax": 304, + "side18BaseCountAtMax": 304, + "allSide7ChecksPass": true, + "allSide18ChecksPass": true, + "allUnionChecksPass": false, + "side7FailureCount": 0, + "side18FailureCount": 0, + "unionFailureCount": 64 + }, + "firstFailures": { + "side7": null, + "side18": null, + "union": { + "N": 7307, + "p": 13, + "p2": 169, + "rawPlus": 43, + "rawMinus": 43, + "vMax": 43, + "activePlus": 40, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 110, + "sMaxSide18Witness": 1789, + "sMaxUnion": 218, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 293, + "side7CandidateSize": 293, + "side18CandidateSize": 292, + "side7Bound": 272, + "side18Bound": 271, + "unionBound": 379, + "side7Margin": 21, + "side18Margin": 22, + "unionMargin": -86, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + } + }, + "worstRows": { + "side7": { + "N": 7307, + "p": 13, + "p2": 169, + "rawPlus": 43, + "rawMinus": 43, + "vMax": 43, + "activePlus": 40, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 110, + "sMaxSide18Witness": 1789, + "sMaxUnion": 218, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 293, + "side7CandidateSize": 293, + "side18CandidateSize": 292, + "side7Bound": 272, + "side18Bound": 271, + "unionBound": 379, + "side7Margin": 21, + "side18Margin": 22, + "unionMargin": -86, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + "side18": { + "N": 7343, + "p": 13, + "p2": 169, + "rawPlus": 44, + "rawMinus": 43, + "vMax": 44, + "activePlus": 41, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 112, + "sMaxSide18Witness": 5309, + "sMaxUnion": 220, + "sMaxUnionWitness": 5309, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 294, + "side7CandidateSize": 294, + "side18CandidateSize": 294, + "side7Bound": 273, + "side18Bound": 274, + "unionBound": 382, + "side7Margin": 21, + "side18Margin": 20, + "unionMargin": -88, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + "union": { + "N": 7552, + "p": 13, + "p2": 169, + "rawPlus": 45, + "rawMinus": 45, + "vMax": 45, + "activePlus": 42, + "activeMinus": 41, + "sMaxSide7": 113, + "sMaxSide7Witness": 4831, + "sMaxSide18": 114, + "sMaxSide18Witness": 1789, + "sMaxUnion": 225, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 103, + "candidateSize": 302, + "side7CandidateSize": 302, + "side18CandidateSize": 302, + "side7Bound": 279, + "side18Bound": 280, + "unionBound": 391, + "side7Margin": 23, + "side18Margin": 22, + "unionMargin": -89, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + } + }, + "blockSummaries": [ + { + "p": 13, + "p2": 169, + "rPlus": 70, + "rMinus": 99, + "rawPlusCountAtMax": 45, + "rawMinusCountAtMax": 45, + "leastWitnessPlusCountAtMax": 42, + "leastWitnessMinusCountAtMax": 41, + "unionFailureCount": 32, + "firstUnionFailure": { + "N": 7307, + "p": 13, + "p2": 169, + "rawPlus": 43, + "rawMinus": 43, + "vMax": 43, + "activePlus": 40, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 110, + "sMaxSide18Witness": 1789, + "sMaxUnion": 218, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 293, + "side7CandidateSize": 293, + "side18CandidateSize": 292, + "side7Bound": 272, + "side18Bound": 271, + "unionBound": 379, + "side7Margin": 21, + "side18Margin": 22, + "unionMargin": -86, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + "worstUnionRow": { + "N": 7552, + "p": 13, + "p2": 169, + "rawPlus": 45, + "rawMinus": 45, + "vMax": 45, + "activePlus": 42, + "activeMinus": 41, + "sMaxSide7": 113, + "sMaxSide7Witness": 4831, + 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"unionPass": false + } + }, + { + "p": 29, + "p2": 841, + "rPlus": 41, + "rMinus": 800, + "rawPlusCountAtMax": 9, + "rawMinusCountAtMax": 9, + "leastWitnessPlusCountAtMax": 8, + "leastWitnessMinusCountAtMax": 8, + "unionFailureCount": 0, + "firstUnionFailure": null, + "worstUnionRow": { + "N": 7307, + "p": 29, + "p2": 841, + "rawPlus": 9, + "rawMinus": 8, + "vMax": 9, + "activePlus": 8, + "activeMinus": 7, + "sMaxSide7": 109, + "sMaxSide7Witness": 41, + "sMaxSide18": 109, + "sMaxSide18Witness": 1723, + "sMaxUnion": 217, + "sMaxUnionWitness": 1723, + "dMax": 4, + "dMaxWitness": { + "side": "plus", + "value": 6769 + }, + "rGreater": 32, + "candidateSize": 293, + "side7CandidateSize": 293, + "side18CandidateSize": 292, + "side7Bound": 154, + "side18Bound": 154, + "unionBound": 262, + "side7Margin": 139, + "side18Margin": 139, + "unionMargin": 31, + "side7Pass": true, + "side18Pass": true, + "unionPass": true + } + }, + { + "p": 37, + "p2": 1369, + "rPlus": 117, + "rMinus": 1252, + 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"unionBound": 313, + "side7Margin": 100, + "side18Margin": 101, + "unionMargin": -10, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + { + "N": 7582, + "p": 17, + "p2": 289, + "rawPlus": 27, + "rawMinus": 26, + "vMax": 27, + "activePlus": 24, + "activeMinus": 23, + "sMaxSide7": 115, + "sMaxSide7Witness": 251, + "sMaxSide18": 114, + "sMaxSide18Witness": 4373, + "sMaxUnion": 225, + "sMaxUnionWitness": 251, + "dMax": 11, + "dMaxWitness": { + "side": "minus", + "value": 251 + }, + "rGreater": 50, + "candidateSize": 304, + "side7CandidateSize": 304, + "side18CandidateSize": 303, + "side7Bound": 203, + "side18Bound": 202, + "unionBound": 313, + "side7Margin": 101, + "side18Margin": 102, + "unionMargin": -9, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + { + "N": 7593, + "p": 17, + "p2": 289, + "rawPlus": 27, + "rawMinus": 26, + "vMax": 27, + "activePlus": 24, + "activeMinus": 23, + "sMaxSide7": 115, + "sMaxSide7Witness": 251, + "sMaxSide18": 114, + "sMaxSide18Witness": 1985, + "sMaxUnion": 226, + "sMaxUnionWitness": 251, + "dMax": 11, + "dMaxWitness": { + "side": "minus", + "value": 251 + }, + "rGreater": 50, + "candidateSize": 304, + "side7CandidateSize": 304, + "side18CandidateSize": 304, + "side7Bound": 203, + "side18Bound": 202, + "unionBound": 314, + "side7Margin": 101, + "side18Margin": 102, + "unionMargin": -10, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + { + "N": 7600, + "p": 17, + "p2": 289, + "rawPlus": 27, + "rawMinus": 26, + "vMax": 27, + "activePlus": 24, + "activeMinus": 23, + "sMaxSide7": 115, + "sMaxSide7Witness": 251, + "sMaxSide18": 114, + "sMaxSide18Witness": 1985, + "sMaxUnion": 226, + "sMaxUnionWitness": 251, + "dMax": 11, + "dMaxWitness": { + "side": "minus", + "value": 251 + }, + "rGreater": 50, + "candidateSize": 304, + "side7CandidateSize": 304, + "side18CandidateSize": 304, + "side7Bound": 203, + "side18Bound": 202, + "unionBound": 314, + "side7Margin": 101, + "side18Margin": 102, + "unionMargin": -10, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + } + ], + "boundary": { + "claimLevel": "bounded_scout_not_all_n_proof", + "safety": "The union-base bound is safe but intentionally loose: it allows every compatible element from both principal sides even though a real clique may not be able to mix them.", + "promotionRule": "Promote only bounded structural coverage when unionPass is true for every checked witness-prime block and structural breakpoint in the assessed range.", + "nextUse": "Use the first/worst union failures to decide whether we need a sharper mixed-base lemma rather than a raw union overcount." + } +} diff --git a/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.md b/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.md new file mode 100644 index 0000000..2aec259 --- /dev/null +++ b/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.md @@ -0,0 +1,34 @@ +# Problem 848 Two-Sided Structural Scout + +- Generated: 2026-04-11T20:36:56.648Z +- Method: `bounded_outsider_clique_two_side_structural_scout` +- Status: `side_specific_bounds_pass_but_union_bound_fails` +- Assessed range: `7307..7600` +- Witness blocks: `8` +- Breakpoints: `32` +- Checks: `256` + +## Pass/Fail Summary + +- Side 7 checks pass: `yes` (0 failures) +- Side 18 checks pass: `yes` (0 failures) +- Union-base checks pass: `no` (64 failures) + +## First Failures + +- Side 7: `(none)` +- Side 18: `(none)` +- Union: `{"N":7307,"p":13,"p2":169,"rawPlus":43,"rawMinus":43,"vMax":43,"activePlus":40,"activeMinus":39,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":110,"sMaxSide18Witness":1789,"sMaxUnion":218,"sMaxUnionWitness":1789,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":293,"side7CandidateSize":293,"side18CandidateSize":292,"side7Bound":272,"side18Bound":271,"unionBound":379,"side7Margin":21,"side18Margin":22,"unionMargin":-86,"side7Pass":true,"side18Pass":true,"unionPass":false}` + +## Worst Rows + +- Side 7: `{"N":7307,"p":13,"p2":169,"rawPlus":43,"rawMinus":43,"vMax":43,"activePlus":40,"activeMinus":39,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":110,"sMaxSide18Witness":1789,"sMaxUnion":218,"sMaxUnionWitness":1789,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":293,"side7CandidateSize":293,"side18CandidateSize":292,"side7Bound":272,"side18Bound":271,"unionBound":379,"side7Margin":21,"side18Margin":22,"unionMargin":-86,"side7Pass":true,"side18Pass":true,"unionPass":false}` +- Side 18: `{"N":7343,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":112,"sMaxSide18Witness":5309,"sMaxUnion":220,"sMaxUnionWitness":5309,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":294,"side7CandidateSize":294,"side18CandidateSize":294,"side7Bound":273,"side18Bound":274,"unionBound":382,"side7Margin":21,"side18Margin":20,"unionMargin":-88,"side7Pass":true,"side18Pass":true,"unionPass":false}` +- Union: `{"N":7552,"p":13,"p2":169,"rawPlus":45,"rawMinus":45,"vMax":45,"activePlus":42,"activeMinus":41,"sMaxSide7":113,"sMaxSide7Witness":4831,"sMaxSide18":114,"sMaxSide18Witness":1789,"sMaxUnion":225,"sMaxUnionWitness":1789,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":103,"candidateSize":302,"side7CandidateSize":302,"side18CandidateSize":302,"side7Bound":279,"side18Bound":280,"unionBound":391,"side7Margin":23,"side18Margin":22,"unionMargin":-89,"side7Pass":true,"side18Pass":true,"unionPass":false}` + +## Boundary + +- Claim level: `bounded_scout_not_all_n_proof` +- Safety: The union-base bound is safe but intentionally loose: it allows every compatible element from both principal sides even though a real clique may not be able to mix them. +- Promotion rule: Promote only bounded structural coverage when unionPass is true for every checked witness-prime block and structural breakpoint in the assessed range. +- Next use: Use the first/worst union failures to decide whether we need a sharper mixed-base lemma rather than a raw union overcount. diff --git a/packs/number-theory/problems/848/TASK_LIST.json b/packs/number-theory/problems/848/TASK_LIST.json new file mode 100644 index 0000000..fcb8e4b --- /dev/null +++ b/packs/number-theory/problems/848/TASK_LIST.json @@ -0,0 +1,22248 @@ +{ + "schema": "erdos.problem_task_list/1", + "generatedAt": "2026-04-14T11:46:16.229Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "cluster": "number-theory", + "sourceKind": "claim_pass_plus_bridge", + "taskListMode": "bridge_backed", + "currentState": { + "activeRoute": "finite_check_gap_closure", + "currentClaimSurface": "bridge_backed_frontier_support", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `40500` or switch method class.", + "latestVerifiedInterval": "1..40500" + }, + "finiteGapStrategy": { + "status": "ready", + "verdict": "exact_endpoint_rollout_is_not_a_sole_all_N_closure_strategy", + "latestVerifiedInterval": "1..40500", + "exactMax": 40500, + "operationalThreshold": { + "raw": "2.64 x 10^17", + "integer": "264000000000000000", + "trustStatus": "external_public_claim", + "source": "forum_thread_2026_03_23" + }, + "remainingRowsToOperationalThreshold": "263999999999959500", + "remainingRowsToOperationalThresholdLabel": "263,999,999,999,959,500", + "endpointCertificate": { + "interval": "1..40500", + "rowCount": 40500, + "endpointCheckCount": 1621, + "compressionRatio": 24.98457742134485, + "approximateRowsPerEndpointCheck": 24.98457742134485 + }, + "projectedEndpointChecksToOperationalThreshold": "10566518518516898", + "projectedEndpointChecksToOperationalThresholdLabel": "10,566,518,518,516,898", + "recommendedMode": "hybrid_threshold_audit_plus_structural_verifier", + "guidance": [ + "Continue endpoint rollouts only as bounded base expansion and regression evidence.", + "Do not wait for direct endpoint checks to close the imported finite gap.", + "Prioritize auditing the imported threshold handoff or proving a stronger structural verifier lane.", + "Use GPU/frontier sweeps to generate structural candidates and counterexamples, not as a substitute for the all-N handoff proof." + ] + }, + "granularBreakdownMode": { + "status": "core_loop_enabled", + "modeId": "granular-breakdown", + "label": "ORP Granular Breakdown", + "topic": "problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound", + "activationPhrase": "Break it down until it can move.", + "invocationRule": "Use the full breakdown before executing a complex theorem/search packet; use the nudge card whenever the agent or user is confused, the target feels too broad, or the next action is not deterministic.", + "commands": { + "fullBreakdown": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json", + "nudge": "orp mode nudge granular-breakdown --json", + "unscopedBreakdown": "orp mode breakdown granular-breakdown --json" + }, + "outputContract": [ + "Broad Frame", + "Boundary", + "Major Lanes", + "Subclaims", + "Atomic Obligations", + "Dependency Ladder", + "Active Target", + "Durable Checklist", + "Next Verification" + ], + "loopIntegration": [ + "Run the full breakdown after the theorem/search surfaces are audited and before executing the current work packet.", + "Write operationally important decompositions into TASK_LIST, FORMALIZATION_WORK, or a dedicated checklist artifact rather than leaving them in chat.", + "Use the nudge card for quick reorientation when a step becomes blurry during implementation.", + "Compress the breakdown back into one active target and one verification command before continuing." + ], + "durableArtifactRule": "If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state." + }, + "orpModeOverlays": { + "status": "core_loop_palette_enabled", + "sourceCommand": "orp mode list --json", + "defaultModeId": "granular-breakdown", + "selectionRule": "Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default.", + "alwaysDurableWhenOperational": true, + "overlays": [ + { + "modeId": "granular-breakdown", + "label": "Granular Breakdown", + "role": "core_decomposition_loop", + "useWhen": "The work is broad, confusing, theorem-heavy, or needs a durable dependency ladder before execution.", + "command": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json", + "nudgeCommand": "orp mode nudge granular-breakdown --json", + "loopPlacement": "Before execute_current_work_packet and whenever the active target becomes fuzzy.", + "outputExpectation": "Boundary, lanes, subclaims, atomic obligations, dependency ladder, active target, durable checklist, and next verification." + }, + { + "modeId": "ruthless-simplification", + "label": "Ruthless Simplification", + "role": "compression_and_signal_filter", + "useWhen": "A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision.", + "command": "orp mode nudge ruthless-simplification --json", + "nudgeCommand": "orp mode nudge ruthless-simplification --json", + "loopPlacement": "After granular decomposition, before committing a plan to TASK_LIST, and before final summaries.", + "outputExpectation": "One core sentence, one surviving move, and a list of noise to delete or defer." + }, + { + "modeId": "systems-constellation", + "label": "Systems Constellation", + "role": "dependency_and_downstream_effects", + "useWhen": "A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow.", + "command": "orp mode nudge systems-constellation --json", + "nudgeCommand": "orp mode nudge systems-constellation --json", + "loopPlacement": "Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow.", + "outputExpectation": "Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision." + }, + { + "modeId": "bold-concept-generation", + "label": "Bold Concept Generation", + "role": "candidate_generation_when_stuck", + "useWhen": "The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions.", + "command": "orp mode nudge bold-concept-generation --json", + "nudgeCommand": "orp mode nudge bold-concept-generation --json", + "loopPlacement": "After a falsifier, before launching broad compute, or when inventing the next symbolic construction.", + "outputExpectation": "Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment." + }, + { + "modeId": "sleek-minimal-progressive", + "label": "Sleek Minimal Progressive", + "role": "fresh_lens_and_low_friction_motion", + "useWhen": "The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up.", + "command": "orp mode nudge sleek-minimal-progressive --json", + "nudgeCommand": "orp mode nudge sleek-minimal-progressive --json", + "loopPlacement": "When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation.", + "outputExpectation": "One subtraction, one tasteful surprise, and one concrete next move that keeps momentum." + } + ] + }, + "agentFlow": { + "schema": "erdos.problem_agent_flow/1", + "status": "ready", + "audience": "agent", + "problemId": "848", + "purpose": "Give agents one compact execution contract without forcing humans or agents through every task-list section.", + "operatingRule": "Read this object first; execute the primary next action unless a guardrail blocks it or the task list is stale.", + "primaryNextAction": { + "source": "split_core_atomization_plan", + "stepId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift", + "status": "highest", + "task": "Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row.", + "command": null, + "completionRule": "A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.", + "packetAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + "modePolicy": { + "defaultAction": "execute_primary_next_action", + "doNotRunEveryMode": true, + "selectionRule": "Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default.", + "granularBreakdown": { + "modeId": "granular-breakdown", + "useWhen": "Use when the primary action is broad, fuzzy, theorem-heavy, or has unclear dependencies.", + "fullBreakdownCommand": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json", + "nudgeCommand": "orp mode nudge granular-breakdown --json", + "compressionRule": "After any breakdown, compress back to one active target and one verification command." + }, + "situationalOverlays": [ + { + "modeId": "ruthless-simplification", + "role": "compression_and_signal_filter", + "useWhen": "A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision.", + "command": "orp mode nudge ruthless-simplification --json", + "loopPlacement": "After granular decomposition, before committing a plan to TASK_LIST, and before final summaries.", + "outputExpectation": "One core sentence, one surviving move, and a list of noise to delete or defer." + }, + { + "modeId": "systems-constellation", + "role": "dependency_and_downstream_effects", + "useWhen": "A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow.", + "command": "orp mode nudge systems-constellation --json", + "loopPlacement": "Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow.", + "outputExpectation": "Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision." + }, + { + "modeId": "bold-concept-generation", + "role": "candidate_generation_when_stuck", + "useWhen": "The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions.", + "command": "orp mode nudge bold-concept-generation --json", + "loopPlacement": "After a falsifier, before launching broad compute, or when inventing the next symbolic construction.", + "outputExpectation": "Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment." + }, + { + "modeId": "sleek-minimal-progressive", + "role": "fresh_lens_and_low_friction_motion", + "useWhen": "The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up.", + "command": "orp mode nudge sleek-minimal-progressive --json", + "loopPlacement": "When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation.", + "outputExpectation": "One subtraction, one tasteful surprise, and one concrete next move that keeps momentum." + } + ] + }, + "executionLoop": [ + "Load agentFlow.primaryNextAction.", + "If the action is clear, execute its command or implement the named task directly.", + "If the action is fuzzy, run the granular nudge or full breakdown, then compress to one target and one command.", + "Use at most one additional ORP overlay when it clearly reduces friction for the current decision.", + "Refresh the canonical task list after material progress and continue from the regenerated agentFlow." + ], + "guardrails": [ + "Do not run paid or remote compute unless the frontier configuration explicitly enables that paid rung.", + "Prefer local/free compute before opt-in paid compute.", + "Do not treat bounded search evidence as an all-N proof without a theorem-facing handoff.", + "Do not run every ORP mode by default.", + "Persist operationally important changes into canonical artifacts rather than chat-only state." + ], + "writeback": { + "refreshCommand": "erdos problem task-list-refresh 848", + "taskListCommand": "erdos problem task-list 848", + "durableArtifactRule": "If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state." + } + }, + "splitCoreAtomizationPlan": { + "planId": "p848_split_core_atomization_master_plan_v1", + "status": "active", + "scope": { + "problemId": "848", + "activeParentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "splitAtomCount": 5, + "totalCommonCoreEdges": 536, + "d2SplitCount": 3, + "d3SplitCount": 2 + }, + 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"firstPacketEdgeCongruencePersistenceVerified": true, + "verifiedEdgeCongruencePacketCount": 5, + "allManifestPacketsEdgeCongruenceVerified": true, + "firstPacketMatchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "firstPacketMatchingKEnvelopeVerified": true, + "verifiedMatchingKEnvelopePacketCount": 5, + "allManifestPacketsMatchingKEnvelopeVerified": true, + "firstPacketSplitDischargeReadinessStatus": "split_discharge_readiness_candidate", + "firstPacketSplitDischargeReady": true, + "splitDischargeReadyPacketCount": 3, + "p13SplitDischargeReadyPacketCount": 3, + "allP13SplitDischargeReady": true, + "p13PrimeLaneHandoffStatus": "prime_lane_handoff_candidate_with_open_all_n_gaps", + "p13PrimeLaneHandoffOpenGapCount": 3, + "p13PrimeLaneHandoffFirstOpenGap": "row_universe_split_coverage", + "p13RowUniverseCoverageStatus": "bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder", + "p13RowUniverseCoverageScope": "bounded_p13_threat_rows_tight_splits_plus_slack_dominated_remainder", + "p13RowUniverseFirstMissingAtom": "D2_p13_slack_dominance_symbolic_lift", + "p13SlackDominanceLiftStatus": "bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed", + "p13SlackDominanceFirstOpenLemma": "D2_p13_non_tight_side_count_slack_floor_lift", + "firstSideCountFloorPacketToAttack": "D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "firstSideCountFloorStructuralMarginLemma": "D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18", + "firstSideCountFloorMovingTermSubatom": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "nextUndischargedP13PacketToAttack": null, + "firstPacketToAttack": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "firstSuccessorPacketToAttack": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1", + "firstUnverifiedSuccessorPacketToAttack": null, + "refreshCommand": "erdos problem task-list-refresh 848" + }, + "northStar": "Make the D2/D3 matching lower-bound proof deterministic by turning every split-core persistence claim into replayable vertex, edge, congruence, matching, and K-envelope atoms.", + "deterministicRule": "No split may be promoted from bounded witness support to theorem support until every layer below has a pass/fail checker and every failure emits a smaller successor atom.", + "mostConfusingPart": { + "question": "Are the common matching pairs literal fixed vertices, or formulaic residue-family vertices that move with N?", + "whyItMatters": "This determines whether the proof obligation is fixed vertex presence across a split, or extraction of a parameterized vertex formula before edge persistence can be proved.", + "firstPlaceToAttack": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "reason": "Start with D2.3_persist_outP2=99_out25=14_smaller=side7 because it is the sharpest active split atom: highest_singleton_profile." + }, + "rowUniverseCoverage": { + "schema": "erdos.p848_row_universe_split_coverage_candidate/1", + "coverageId": "D2_p13_row_universe_split_coverage", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetPrime": 13, + "status": "bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder", + "promotesAllNClaim": false, + "currentCoverage": { + "coverageScope": "bounded_p13_threat_rows_tight_splits_plus_slack_dominated_remainder", + "threatRowCount": 1285, + "tightWitnessRowCount": 12, + "boundedThreatRowsOutsideTightWitnessPacket": 1273, + "boundedThreatRowsCoveredByEmittedTightSplitStrata": 96, + "boundedThreatRowsOutsideEmittedTightSplitStrata": 1189, + "boundedThreatRowsSlackDominatedOutsideTightSplitStrata": 1189, + "boundedThreatRowsNeedingAdditionalSplitPacket": 0, + "splitProfileCount": 3, + "emittedP13SplitPacketCount": 3, + "matchingPatternSplitKeys": [ + "outP2=70|out25=9|smaller=side7", + "outP2=99|out25=6|smaller=side18", + "outP2=99|out25=14|smaller=side7" + ], + "emittedSplitKeys": [ + "outP2=70|out25=9|smaller=side7", + "outP2=99|out25=6|smaller=side18", + "outP2=99|out25=14|smaller=side7" + ], + "missingMatchingPatternSplitKeys": [], + "extraEmittedSplitKeys": [], + "allTightSampleSplitKeysEmitted": true, + "allP13SplitPacketsReady": true, + "allBoundedP13ThreatRowsStratified": true + }, + "boundedStratificationAudit": { + "sourceArtifact": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json", + "auditScope": "FULL_MIXED_BASE_STRUCTURAL_VERIFIER.threatLiftMiningRows[p=13]", + "boundedThreatRowCount": 1285, + "splitStratumCount": 52, + "emittedTightSplitStratumCount": 3, + "emittedTightSplitCoveredRowCount": 96, + "outsideTightSplitStratumCount": 49, + "outsideTightSplitRowCount": 1189, + "slackDominanceRule": "A bounded p13 row outside the emitted tight split packets is slack-dominated when its minimum matching slack is strictly larger than the emitted tight-packet slack floor.", + "minEmittedTightSplitSlack": 19, + "minOutsideSlack": 21, + "slackDominanceMarginAboveTightFloor": 2, + "slackDominatedOutsideStratumCount": 49, + "slackDominatedOutsideRowCount": 1189, + "outsideRowsNeedingAdditionalSplitPacket": 0, + "allOutsideRowsSlackDominated": true, + "emittedTightSplitStrata": [ + { + "splitKey": "outP2=70|out25=9|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 86, + "maxRequiredMatchingLowerBound": 89, + "minActualMatching": 108, + "maxActualMatching": 110, + "minMatchingSlack": 19, + "maxMatchingSlack": 23, + "inEmittedTightSplitPacket": true + }, + { + "splitKey": "outP2=99|out25=14|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 85, + "maxRequiredMatchingLowerBound": 90, + "minActualMatching": 108, + "maxActualMatching": 111, + "minMatchingSlack": 20, + "maxMatchingSlack": 24, + "inEmittedTightSplitPacket": true + }, + { + "splitKey": "outP2=99|out25=6|smaller=side18", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 83, + "maxRequiredMatchingLowerBound": 85, + "minActualMatching": 105, + "maxActualMatching": 108, + "minMatchingSlack": 20, + "maxMatchingSlack": 23, + "inEmittedTightSplitPacket": true + } + ], + "weakestOutsideStrata": [ + { + "splitKey": "outP2=70|out25=23|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 83, + "maxRequiredMatchingLowerBound": 86, + "minActualMatching": 105, + "maxActualMatching": 109, + "minMatchingSlack": 21, + "maxMatchingSlack": 25, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=70|out25=6|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 85, + "maxRequiredMatchingLowerBound": 89, + "minActualMatching": 108, + "maxActualMatching": 111, + "minMatchingSlack": 21, + "maxMatchingSlack": 25, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=70|out25=22|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 82, + "maxRequiredMatchingLowerBound": 85, + "minActualMatching": 105, + "maxActualMatching": 109, + "minMatchingSlack": 22, + "maxMatchingSlack": 25, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=99|out25=9|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 81, + "maxRequiredMatchingLowerBound": 85, + "minActualMatching": 105, + "maxActualMatching": 109, + "minMatchingSlack": 22, + "maxMatchingSlack": 26, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=99|out25=15|smaller=side7", + "rowCount": 20, + "firstN": 7343, + "lastN": 7600, + "minRequiredMatchingLowerBound": 84, + "maxRequiredMatchingLowerBound": 87, + "minActualMatching": 109, + "maxActualMatching": 111, + "minMatchingSlack": 22, + "maxMatchingSlack": 26, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=99|out25=15|smaller=side18", + "rowCount": 12, + "firstN": 7307, + "lastN": 7535, + "minRequiredMatchingLowerBound": 84, + "maxRequiredMatchingLowerBound": 86, + "minActualMatching": 107, + "maxActualMatching": 110, + "minMatchingSlack": 22, + "maxMatchingSlack": 25, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=70|out25=16|smaller=side18", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 82, + "maxRequiredMatchingLowerBound": 84, + "minActualMatching": 106, + "maxActualMatching": 110, + "minMatchingSlack": 23, + "maxMatchingSlack": 26, + "inEmittedTightSplitPacket": false + }, + { + "splitKey": "outP2=70|out25=8|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 81, + "maxRequiredMatchingLowerBound": 87, + "minActualMatching": 107, + "maxActualMatching": 110, + "minMatchingSlack": 23, + "maxMatchingSlack": 27, + "inEmittedTightSplitPacket": false + } + ] + }, + "slackDominanceSymbolicLiftCandidate": { + "candidateId": "D2_p13_slack_dominance_symbolic_lift", + "status": "bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed", + "promotesAllNClaim": false, + "targetPrime": 13, + "boundedRowCount": 1189, + "boundedStratumCount": 49, + "targetTightSlackFloor": 19, + "targetNonTightSlackLowerBound": 20, + "observedMinNonTightSlack": 21, + "failedFormulaReplayRowCount": 0, + "firstFailedFormulaReplayRows": [], + "proofReduction": { + "statement": "For non-tight p13 rows, reduce slack dominance to a side-count inequality after matching saturation.", + "matchingSaturationHypothesis": "matchingSizeInMissingCrossGraph = min(compatibleSide7Count, compatibleSide18Count)", + "requiredMatchingFormula": "K = compatibleSide7Count + compatibleSide18Count - strictBaseThreshold + 1", + "derivedSlackFormula": "matchingSlack = strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count)", + "sufficientSideCountInequality": "max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 1 - 20" + }, + "boundedFormulaChecks": [ + { + "checkId": "non_tight_row_formula_replay", + "status": "verified_bounded", + "evidence": "1189/1189 bounded non-tight p13 rows replay the slack formula and target floor" + }, + { + "checkId": "future_symbolic_side_count_floor", + "status": "open_symbolic_lift", + "evidence": "The bounded formula replay names the exact side-count inequality still needed for all future p13 non-tight rows." + } + ], + "formulaStrata": [ + { + "splitKey": "outP2=70|out25=23|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 21, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 110, + "maxLargerSideSize": 114, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 1, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=6|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 21, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 109, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 1, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=22|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 109, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 2, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=9|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 26, + "minLargerSideSize": 108, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 2, + "maxStructuralMargin": 6, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=15|smaller=side7", + "rowCount": 20, + "firstN": 7343, + "lastN": 7600, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 26, + "minLargerSideSize": 109, + "maxLargerSideSize": 111, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side7", + "minCandidateSize": 294, + "maxCandidateSize": 304, + "minReconstructedVMax": 44, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 2, + "maxStructuralMargin": 6, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + 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"maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 3, + "maxStructuralMargin": 6, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=8|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 23, + "maxSideCountSlackFormula": 27, + "minLargerSideSize": 107, + "maxLargerSideSize": 112, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side7", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 3, + "maxStructuralMargin": 7, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=0|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 23, + "maxSideCountSlackFormula": 27, + "minLargerSideSize": 107, + "maxLargerSideSize": 112, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 3, + "maxStructuralMargin": 7, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=17|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 23, + "maxSideCountSlackFormula": 27, + "minLargerSideSize": 107, + "maxLargerSideSize": 111, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + 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"meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=8|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 23, + "maxSideCountSlackFormula": 27, + "minLargerSideSize": 107, + "maxLargerSideSize": 112, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side7", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 3, + "maxStructuralMargin": 7, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + } + ], + "firstOpenSymbolicLemma": { + "lemmaId": "D2_p13_non_tight_side_count_slack_floor_lift", + "status": "needed", + "statement": "For every future p=13 threat row outside the three tight split keys, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) stays above the tight slack floor." + }, + "proofBoundary": "This candidate verifies the bounded algebraic slack reduction and side-count floor; it does not prove the all-N side-count inequality." + }, + "lowerLayerChecks": [ + { + "checkId": "tight_matching_pattern_split_keys_emitted", + "status": "verified", + "evidence": "3/3 tight split keys have emitted packets" + }, + { + "checkId": "tight_matching_pattern_split_packets_ready", + "status": "verified", + "evidence": "prime_lane_handoff_candidate_with_open_all_n_gaps" + }, + { + "checkId": "full_bounded_threat_universe_stratified", + "status": "verified_bounded", + "evidence": "96/1285 bounded p13 rows are in emitted tight split strata; 1189/1189 outside rows are slack-dominated above tight floor 19" + }, + { + "checkId": "bounded_slack_dominated_remainder", + "status": "verified_bounded", + "evidence": "1189/1189 bounded outside-tight p13 rows have min slack > 19" + }, + { + "checkId": "future_all_n_row_universe_covered", + "status": "open_symbolic_lift", + "evidence": "The bounded p13 row universe is stratified, but the slack-dominance split still needs a symbolic all-N lift." + } + ], + "emittedMissingAtom": { + "atomId": "D2_p13_slack_dominance_symbolic_lift", + "status": "needed", + "statement": "Lift the bounded p=13 row stratification into a symbolic theorem: the 49 non-tight residue/side strata remain slack-dominated above the tight split floor for all future rows, or the first failing stratum emits a new deterministic split packet." + }, + "proofBoundary": "This is a bounded row-universe stratification audit. It verifies that the current bounded p13 threat rows outside the tight packets are slack-dominated; it does not prove the all-N slack theorem.", + "nextTheoremAction": "Prove D2_p13_slack_dominance_symbolic_lift: turn the bounded slack-dominated remainder into a symbolic all-N row-family theorem." + }, + "slackDominanceSymbolicLift": { + "candidateId": "D2_p13_slack_dominance_symbolic_lift", + "status": "bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed", + "promotesAllNClaim": false, + "targetPrime": 13, + "boundedRowCount": 1189, + "boundedStratumCount": 49, + "targetTightSlackFloor": 19, + "targetNonTightSlackLowerBound": 20, + "observedMinNonTightSlack": 21, + "failedFormulaReplayRowCount": 0, + "firstFailedFormulaReplayRows": [], + "proofReduction": { + "statement": "For non-tight p13 rows, reduce slack dominance to a side-count inequality after matching saturation.", + "matchingSaturationHypothesis": "matchingSizeInMissingCrossGraph = min(compatibleSide7Count, 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"maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 1, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=6|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 21, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 109, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 1, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=22|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 109, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 2, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=9|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 26, + "minLargerSideSize": 108, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side18", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 2, + "maxStructuralMargin": 6, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=15|smaller=side7", + "rowCount": 20, + "firstN": 7343, + "lastN": 7600, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 26, + "minLargerSideSize": 109, + "maxLargerSideSize": 111, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side7", + "minCandidateSize": 294, + "maxCandidateSize": 304, + "minReconstructedVMax": 44, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 2, + "maxStructuralMargin": 6, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=99|out25=15|smaller=side18", + "rowCount": 12, + "firstN": 7307, + "lastN": 7535, + "minSideCountSlackFormula": 22, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 109, + "maxLargerSideSize": 111, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 137, + "largerSideLabel": "side7", + "minCandidateSize": 293, + "maxCandidateSize": 302, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 102, + "minStructuralMargin": 2, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=16|smaller=side18", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 23, + "maxSideCountSlackFormula": 26, + "minLargerSideSize": 108, + "maxLargerSideSize": 111, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side7", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 3, + "maxStructuralMargin": 6, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + { + "splitKey": "outP2=70|out25=8|smaller=side7", + "rowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minSideCountSlackFormula": 23, + "maxSideCountSlackFormula": 27, + "minLargerSideSize": 107, + "maxLargerSideSize": 112, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "largerSideLabel": "side7", + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 3, + "maxStructuralMargin": 7, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + } + ], + "firstOpenSymbolicLemma": { + "lemmaId": "D2_p13_non_tight_side_count_slack_floor_lift", + "status": "needed", + "statement": "For every future p=13 threat row outside the three tight split keys, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) stays above the tight slack floor." + }, + "proofBoundary": "This candidate verifies the bounded algebraic slack reduction and side-count floor; it does not prove the all-N side-count inequality." + }, + "masterLayers": [ + { + "layerId": "A0_input_universe_freeze", + "status": "done_bounded", + "objective": "Freeze the exact threatening-outsider row universe, prime lanes, and K(N,x) formula used by D1.", + "deterministicOutput": "A row-universe manifest keyed by prime, N, outsider, side counts, K(N,x), actual matching, and smaller-side size.", + "currentEvidence": "p848_D1_matching_saturation_bound_checker_v1" + }, + { + "layerId": "A1_split_profile_inventory", + "status": "done_bounded", + "objective": "Freeze the p13 and p17 split keys and attach each bounded split-core witness packet to a parent D-lane obligation.", + "deterministicOutput": "One split atom per residue/smaller-side profile.", + "currentEvidence": [ + "D2.1_persist_outP2=70_out25=9_smaller=side7", + "D2.2_persist_outP2=99_out25=6_smaller=side18", + "D2.3_persist_outP2=99_out25=14_smaller=side7", + "D3.1_persist_outP2=38_out25=23_smaller=side7", + "D3.2_persist_outP2=251_out25=1_smaller=side18" + ] + }, + { + "layerId": "A2_full_common_core_pair_export", + "status": "done", + "objective": "Export the full common matching core for each split, not only a pair sample.", + "deterministicOutput": "For every split atom, a complete ordered list of common matching pairs with left/right values and residues modulo 25, p, and p^2.", + "falsifierBoundary": "A split packet reports commonMatchingPairCount but cannot provide exactly that many explicit pair records." + }, + { + "layerId": "A3_vertex_presence_atoms", + "status": "next", + "objective": "Prove every left/right vertex used by the split core is present on the correct compatible side for every row in the split.", + "deterministicOutput": "One pass/fail vertex-presence certificate per split-core vertex family.", + "falsifierBoundary": "A core vertex leaves the compatible side, changes side, or requires an unstated N-dependent formula." + }, + { + "layerId": "A4_edge_obstruction_atoms", + "status": "next", + "objective": "For every selected pair, identify the exact reason the cross edge is missing.", + "deterministicOutput": "One obstruction certificate per pair, preferably a square-divisor witness or explicit modular contradiction.", + "falsifierBoundary": "A selected pair is compatible in any row of the split or lacks a stable obstruction witness." + }, + { + "layerId": "A5_congruence_persistence_atoms", + "status": "done_literal", + "objective": "Prove each edge obstruction is implied by the split congruence assumptions, not by accidental sampled N values.", + "deterministicOutput": "A symbolic congruence proof per obstruction family.", + "falsifierBoundary": "The obstruction depends on a sampled representative rather than the split key and row-universe hypotheses." + }, + { + "layerId": "A6_matching_disjointness_atoms", + "status": "done_literal", + "objective": "Prove the exported pairs form a matching by checking left and right uniqueness.", + "deterministicOutput": "A deterministic disjointness certificate per split core.", + "falsifierBoundary": "Two core pairs reuse a left or right vertex after parameterization." + }, + { + "layerId": "A7_K_envelope_atoms", + "status": "done_sampled_envelope", + "objective": "Prove the symbolic core size is always at least the required K(N,x) throughout the split.", + "deterministicOutput": "One K-envelope inequality certificate per split.", + "currentEvidence": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "commonMatchingPairCount": 108, + "requiredMatchingLowerBoundRange": [ + 88, + 89 + ] + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "commonMatchingPairCount": 105, + "requiredMatchingLowerBoundRange": [ + 85, + 85 + ] + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "commonMatchingPairCount": 108, + "requiredMatchingLowerBoundRange": [ + 88, + 88 + ] + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7", + "commonMatchingPairCount": 109, + "requiredMatchingLowerBoundRange": [ + 12, + 14 + ] + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18", + "commonMatchingPairCount": 106, + "requiredMatchingLowerBoundRange": [ + 10, + 11 + ] + } + ] + }, + { + "layerId": "A8_split_discharge_atoms", + "status": "p13_readiness_complete_p17_pending", + "objective": "Promote each split from bounded support to a symbolic split lemma only after all lower atoms pass.", + "deterministicOutput": "One theorem-facing split lemma per split key.", + "falsifierBoundary": "Any lower atom fails or emits a new sub-split that is not yet discharged." + }, + { + "layerId": "A9_prime_lane_promotion", + "status": "p13_ready_for_D2_promotion", + "objective": "Promote D2 once all p13 split lemmas pass, and promote D3 once all p17 split lemmas pass.", + "deterministicOutput": "D2_p13_matching_lower_bound and D3_p17_matching_lower_bound can feed D4 without bounded-only caveats.", + "falsifierBoundary": "A prime lane has an uncovered split, an unproved split, or an unbounded K envelope." + } + ], + "splitAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "prime": 13, + "parentObligationId": "D2_p13_matching_lower_bound", + "splitKey": "outP2=70|out25=9|smaller=side7", + "status": "needs_symbolic_persistence_proof", + "priority": "high_p13_active_lane", + "witnessCount": 6, + "nRange": "7318..7368", + "commonMatchingPairCount": 108, + "commonMatchingPairExportComplete": true, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 4, + "productPlusOneModP2": 133 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 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+ "status": "needed", + "reason": "The split-core proof should not silently assume every future threatening row belongs to the current split keys.", + "focusPlan": "Create a checker that partitions every bounded threatening row by the split key and emits new split obligations whenever a refreshed verifier discovers a new key." + }, + { + "layerId": "B2_vertex_formula_extraction", + "status": "needed_if_vertices_move", + "reason": "If core vertices are not literal constants across N, we need formulas for the moving vertex families before edge persistence is meaningful.", + "focusPlan": "Mine affine/residue formulas for common-core left/right vertices and verify them against every sampled witness row." + }, + { + "layerId": "B3_obstruction_witness_normal_form", + "status": "needed", + "reason": "Edge persistence becomes deterministic only when every missing edge has a normalized obstruction witness.", + "focusPlan": "Normalize each missing edge into product-plus-one divisibility, square-witness, or explicit incompatibility schema." + }, + { + "layerId": "B4_all_N_handoff_guard", + "status": "needed_later", + "reason": "Even after split cores are symbolic, the final 848 decision still needs a clean handoff from D2/D3/D4 into the all-N threshold route.", + "focusPlan": "Keep this separate from split-core work; do not let final threshold or endpoint-regime logic pollute the matching-core proof." + } + ], + "recommendedImmediateTasks": [ + { + "taskId": "implement_full_common_core_pair_export", + "status": "done", + "task": "Extend the matching-pattern miner so every split profile exports the full common matching core, not only commonMatchingPairSample.", + "completionRule": "Each split profile has commonMatchingPairs.length === commonMatchingPairCount for p13 and p17." + }, + { + "taskId": "emit_split_atom_packets", + "status": "done", + "task": "Generate one atom packet per split with inputs, common pairs, K envelope, required lower-bound range, and falsifier boundary.", + "completionRule": "The task list points at concrete split atom IDs instead of one broad D2/D3 persistence phrase.", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "materialize_square_residue_successor_packets", + "status": "done", + "task": "Materialize square-residue successor packets for every p13 split profile so D2 can be discharged profile-by-profile.", + "completionRule": "The packet manifest lists verified successor packet files for every p13 refinement condition.", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "attack_top_square_residue_successor", + "status": "done_symbolic_family_verified", + "task": "Attack successor D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1: prove the 145 affected vertex-presence atoms as a symbolic square-residue subfamily.", + "completionRule": "The successor packet is promoted to a symbolic vertex-family lemma or emits a still smaller deterministic obstruction.", + "command": null, + "packetAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md" + }, + { + "taskId": "materialize_remaining_square_residue_successor_packets", + "status": "blocked_by_successor_family_proofs", + "task": "Materialize the remaining square-residue successor packets; 29 of 10 refinement conditions currently have packet files.", + "completionRule": "Every refinement condition from the singleton p13 packet has a successor packet file and symbolic family check.", + "command": null, + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null + }, + { + "taskId": "emit_singleton_edge_obstruction_certificate", + "status": "done_literal_edge_certificate_verified", + "task": "Emit the literal edge-obstruction certificate for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7, proving every exported cross-edge obstruction has a checked squarefree product-plus-one certificate.", + "completionRule": "The first packet manifest reports literal_edge_obstruction_certificate_verified for the singleton p13 packet.", + "command": "erdos problem task-list-refresh 848", + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "promote_singleton_edge_congruence_persistence", + "status": "done_literal_edge_persistence_verified", + "task": "Promote the singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from literal edge-obstruction certificates into A5 congruence-persistence families.", + "completionRule": "Each edge-obstruction family is either proved from the split hypotheses or emits a sharper deterministic successor atom.", + "command": null, + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "promote_singleton_matching_disjointness_and_k_envelope", + "status": "done_literal_matching_sampled_k_verified", + "task": "Promote singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 through A6 matching disjointness and A7 K-envelope checks.", + "completionRule": "The literal matching pairs are pairwise disjoint and the common-core count dominates the required K-envelope without bounded-only overclaim.", + "command": null, + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "assemble_singleton_split_discharge_readiness", + "status": "done_split_discharge_readiness_candidate", + "task": "Assemble split-discharge readiness for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from verified vertex successors, edge persistence, matching disjointness, and sampled K-envelope certificates.", + "completionRule": "The packet either becomes a theorem-facing split lemma candidate with explicit all-N handoff gaps, or emits the first missing lower atom.", + "command": null, + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "attack_next_p13_split_profile", + "status": "done_p13_split_readiness_candidates", + "task": "All p13 split profiles have split-discharge readiness candidates; promote the D2 p13 lane through the explicit all-N handoff gaps next.", + "completionRule": "D2 promotion either discharges the row-universe and symbolic-K handoff gaps or emits the first missing all-N atom.", + "command": null, + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "promote_d2_p13_all_n_handoff", + "status": "done_bounded_row_universe_stratified", + "task": "Bounded p13 row-universe stratification is audited; D2_p13_slack_dominance_symbolic_lift is now the symbolic all-N lift before D2 can be promoted.", + "completionRule": "The D2 p13 lane either closes row-universe coverage and symbolic K(N,x), or emits the first missing all-N atom.", + "command": null, + "packetAtomId": "D2_p13_slack_dominance_symbolic_lift", + "packetId": "D2_p13_matching_lower_bound", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "attack_d2_p13_row_universe_stratification_lift", + "status": "done_bounded_slack_stratification_audited", + "task": "Lift the bounded p=13 row stratification into a symbolic theorem: the 49 non-tight residue/side strata remain slack-dominated above the tight split floor for all future rows, or the first failing stratum emits a new deterministic split packet.", + "completionRule": "Every bounded p13 threat row is either assigned to a split profile, proved slack-dominated outside the tight split packet, or emitted as a new deterministic split atom.", + "command": null, + "packetAtomId": "D2_p13_slack_dominance_symbolic_lift", + "packetId": "D2_p13_row_universe_split_coverage", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_d2_p13_slack_dominance_symbolic_lift", + "status": "done_bounded_formula_reduction_emitted", + "task": "Slack dominance reduced to D2_p13_non_tight_side_count_slack_floor_lift; prove the side-count floor next.", + "completionRule": "The 49 non-tight p13 residue/side strata either get a symbolic slack-dominance proof, or the first failing stratum emits a deterministic successor split atom.", + "command": null, + "packetAtomId": "D2_p13_slack_dominance_symbolic_lift", + "packetId": "D2_p13_row_universe_split_coverage", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_d2_p13_non_tight_side_count_slack_floor_lift", + "status": "done_weakest_side_count_atoms_emitted", + "task": "Weakest side-count floor atom packets are emitted; attack D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7 next.", + "completionRule": "Either prove max(side7, side18) <= strictBaseThreshold - 1 - targetSlack for all non-tight p13 rows, or emit the weakest failing residue/side stratum as a deterministic atom.", + "command": null, + "packetAtomId": "D2_p13_non_tight_side_count_slack_floor_lift", + "packetId": "D2_p13_row_universe_split_coverage", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "attack_weakest_p13_side_count_floor_atom", + "status": "done_structural_margin_decomposition_emitted", + "task": "Attack weakest p13 side-count floor atom D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7: prove its side-count inequality or split the first failing term.", + "completionRule": "The weakest side-count floor packet either becomes a symbolic side-count lemma or emits a sharper deterministic sub-atom.", + "command": null, + "packetAtomId": "D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_structural_margin_atom", + "status": "done_moving_term_subatoms_emitted", + "task": "Prove structural margin lemma D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18 for outP2=70|out25=23|smaller=side7, or emit the first moving-term sub-atom.", + "completionRule": "The structural margin inequality either gets a symbolic bound for candidateSize, vMax, dMax, rGreater, and the larger side count, or emits the first moving term as a sharper atom.", + "command": null, + "packetAtomId": "D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_bound_atom", + "status": "done_constant_bound_falsified_successor_atom_emitted", + "task": "The original dMax constant-bound atom is closed by a bounded falsifier and successor growth profile; continue with the current downstream moving-term atom.", + "completionRule": "The dMax subatom either proves the uniform same-prime degree bound used by the structural margin, or emits the sharper term family that controls dMax.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "attack_weakest_p13_dmax_growth_atom", + "status": "done_dmax_growth_tail_profile_closed", + "task": "The dMax growth tail profile is closed through q>=587 for outP2=70|out25=23|smaller=side7; attack the residual dynamic margin next.", + "completionRule": "The dMax growth atom either proves a symbolic envelope for the same-prime degree term or emits the first residue/floor-function sub-split controlling the degree growth.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": 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+ "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_q3_progression_atom", + "status": "blocked_by_q2_progression_certificate", + "task": "Wait for the q=2 progression proof to emit the q=3 square-divisor progression 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minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q41_progression_atom", + "status": "done_q41_tail_progression_upper_bound_verified", + "task": "The q=41 residual tail-prime component is certified; attack q=43 next, starting with the plus-side witness-divisibility exclusion.", + "completionRule": "The q=41 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q47_progression_atom", + "status": "done_q47_tail_progression_upper_bound_verified", + "task": "The q=47 residual tail-prime component is certified; attack q=53 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=47 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q53_progression_atom", + "status": "done_q53_tail_progression_upper_bound_verified", + "task": "The q=53 residual tail-prime component is certified; attack q=59 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=53 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q67_progression_atom", + "status": "done_q67_tail_progression_upper_bound_verified", + "task": "The q=67 residual tail-prime component is certified; attack q=71 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=67 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q71_progression_atom", + "status": "done_q71_tail_progression_upper_bound_verified", + "task": "The q=71 residual tail-prime component is certified; attack q=73 next, starting with the minus-side witness-divisibility exclusion.", + "completionRule": "The q=71 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q79_progression_atom", + "status": "done_q79_tail_progression_upper_bound_verified", + "task": "The q=79 residual tail-prime component is certified; attack q=83 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=79 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q83_progression_atom", + "status": "done_q83_tail_progression_upper_bound_verified", + "task": "The q=83 residual tail-prime component is certified; attack q=89 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=83 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q101_progression_atom", + "status": "done_q101_tail_progression_upper_bound_verified", + "task": "The q=101 residual tail-prime component is certified; attack q=103 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=101 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q103_progression_atom", + "status": "done_q103_tail_progression_upper_bound_verified", + "task": "The q=103 residual tail-prime component is certified; attack q=107 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=103 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q107_progression_atom", + "status": "done_q107_tail_progression_upper_bound_verified", + "task": "The q=107 residual tail-prime component is certified; attack q=109 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=107 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q109_progression_atom", + "status": "done_q109_tail_progression_upper_bound_verified", + "task": "The q=109 residual tail-prime component is certified; attack q=113 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=109 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q113_progression_atom", + "status": "done_q113_tail_progression_upper_bound_verified", + "task": "The q=113 residual tail-prime component is certified; attack q=127 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=113 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q127_progression_atom", + "status": "done_q127_tail_progression_upper_bound_verified", + "task": "The q=127 residual tail-prime component is certified; attack q=131 next, combining the minus-side witness-divisibility exclusion with the plus-side CRT floor bound.", + "completionRule": "The q=127 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q131_progression_atom", + "status": "done_q131_tail_progression_upper_bound_verified", + "task": "The q=131 residual tail-prime component is certified; attack q=137 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=131 tail contribution is bounded by the minus-side exclusion and plus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q137_progression_atom", + "status": "done_q137_tail_progression_upper_bound_verified", + "task": "The q=137 residual tail-prime component is certified; attack q=139 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=137 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q139_progression_atom", + "status": "done_q139_tail_progression_upper_bound_verified", + "task": "The q=139 residual tail-prime component is certified; attack q=149 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=139 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q149_progression_atom", + "status": "done_q149_tail_progression_upper_bound_verified", + "task": "The q=149 residual tail-prime component is certified; attack q=151 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=149 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q151_progression_atom", + "status": "done_q151_tail_progression_upper_bound_verified", + "task": "The q=151 residual tail-prime component is certified; attack q=157 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=151 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q157_progression_atom", + "status": "done_q157_tail_progression_upper_bound_verified", + "task": "The q=157 residual tail-prime component is certified; attack q=163 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=157 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q163_progression_atom", + "status": "done_q163_tail_progression_upper_bound_verified", + "task": "The q=163 residual tail-prime component is certified; attack q=167 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=163 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q167_progression_atom", + "status": "done_q167_tail_progression_upper_bound_verified", + "task": "The q=167 residual tail-prime component is certified; attack q=173 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=167 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q173_progression_atom", + "status": "done_q173_tail_progression_upper_bound_verified", + "task": "The q=173 residual tail-prime component is certified; attack q=179 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=173 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q179_progression_atom", + "status": "done_q179_tail_progression_upper_bound_verified", + "task": "The q=179 residual tail-prime component is certified; attack q=181 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=179 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q191_progression_atom", + "status": "done_q191_tail_progression_upper_bound_verified", + "task": "The q=191 residual tail-prime component is certified; attack q=193 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=191 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q193_progression_atom", + "status": "done_q193_tail_progression_upper_bound_verified", + "task": "The q=193 residual tail-prime component is certified; attack q=197 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=193 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q211_progression_atom", + "status": "done_q211_tail_progression_upper_bound_verified", + "task": "The q=211 residual tail-prime component is certified; attack q=223 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=211 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q223_progression_atom", + "status": "done_q223_tail_progression_upper_bound_verified", + "task": "The q=223 residual tail-prime component is certified; attack q=227 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=223 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q229_progression_atom", + "status": "done_q229_tail_progression_upper_bound_verified", + "task": "The q=229 residual tail-prime component is certified; attack q=233 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=229 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q233_progression_atom", + "status": "done_q233_tail_progression_upper_bound_verified", + "task": "The q=233 residual tail-prime component is certified; attack q=239 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=233 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q257_progression_atom", + "status": "done_q257_tail_progression_upper_bound_verified", + "task": "The q=257 residual tail-prime component is certified; attack q=263 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=257 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q263_progression_atom", + "status": "done_q263_tail_progression_upper_bound_verified", + "task": "The q=263 residual tail-prime component is certified; attack q=269 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=263 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q277_progression_atom", + "status": "done_q277_tail_progression_upper_bound_verified", + "task": "The q=277 residual tail-prime component is certified; attack q=281 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=277 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q281_progression_atom", + "status": "done_q281_tail_progression_upper_bound_verified", + "task": "The q=281 residual tail-prime component is certified; attack q=283 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=281 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q293_progression_atom", + "status": "done_q293_tail_progression_upper_bound_verified", + "task": "The q=293 residual tail-prime component is certified; attack q=307 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=293 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q307_progression_atom", + "status": "done_q307_tail_progression_upper_bound_verified", + "task": "The q=307 residual tail-prime component is certified; attack q=311 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=307 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q313_progression_atom", + "status": "done_q313_tail_progression_upper_bound_verified", + "task": "The q=313 residual tail-prime component is certified; attack q=317 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=313 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q317_progression_atom", + "status": "done_q317_tail_progression_upper_bound_verified", + "task": "The q=317 residual tail-prime component is certified; attack q=331 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=317 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q331_progression_atom", + "status": "done_q331_tail_progression_upper_bound_verified", + "task": "The q=331 residual tail-prime component is certified; attack q=337 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=331 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q347_progression_atom", + "status": "done_q347_tail_progression_upper_bound_verified", + "task": "The q=347 residual tail-prime component is certified; attack q=349 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=347 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q349_progression_atom", + "status": "done_q349_tail_progression_upper_bound_verified", + "task": "The q=349 residual tail-prime component is certified; attack q=353 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=349 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q359_progression_atom", + "status": "done_q359_tail_progression_upper_bound_verified", + "task": "The q=359 residual tail-prime component is certified; attack q=367 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=359 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q367_progression_atom", + "status": "done_q367_tail_progression_upper_bound_verified", + "task": "The q=367 residual tail-prime component is certified; attack q=373 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=367 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q383_progression_atom", + "status": "done_q383_tail_progression_upper_bound_verified", + "task": "The q=383 residual tail-prime component is certified; attack q=389 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=383 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q389_progression_atom", + "status": "done_q389_tail_progression_upper_bound_verified", + "task": "The q=389 residual tail-prime component is certified; attack q=397 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=389 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q401_progression_atom", + "status": "done_q401_tail_progression_upper_bound_verified", + "task": "The q=401 residual tail-prime component is certified; attack q=409 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=401 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q409_progression_atom", + "status": "done_q409_tail_progression_upper_bound_verified", + "task": "The q=409 residual tail-prime component is certified; attack q=419 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=409 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q431_progression_atom", + "status": "done_q431_tail_progression_upper_bound_verified", + "task": "The q=431 residual tail-prime component is certified; attack q=433 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=431 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q433_progression_atom", + "status": "done_q433_tail_progression_upper_bound_verified", + "task": "The q=433 residual tail-prime component is certified; attack q=439 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=433 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q443_progression_atom", + "status": "done_q443_tail_progression_upper_bound_verified", + "task": "The q=443 residual tail-prime component is certified; attack q=449 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=443 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q449_progression_atom", + "status": "done_q449_tail_progression_upper_bound_verified", + "task": "The q=449 residual tail-prime component is certified; attack q=457 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=449 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q463_progression_atom", + "status": "done_q463_tail_progression_upper_bound_verified", + "task": "The q=463 residual tail-prime component is certified; attack q=467 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=463 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q467_progression_atom", + "status": "done_q467_tail_progression_upper_bound_verified", + "task": "The q=467 residual tail-prime component is certified; attack q=479 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=467 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q479_progression_atom", + "status": "done_q479_tail_progression_upper_bound_verified", + "task": "The q=479 residual tail-prime component is certified; attack q=487 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=479 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q487_progression_atom", + "status": "done_q487_tail_progression_upper_bound_verified", + "task": "The q=487 residual tail-prime component is certified; attack q=491 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=487 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q491_progression_atom", + "status": "done_q491_tail_progression_upper_bound_verified", + "task": "The q=491 residual tail-prime component is certified; attack q=499 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=491 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q499_progression_atom", + "status": "done_q499_tail_progression_upper_bound_verified", + "task": "The q=499 residual tail-prime component is certified; attack q=503 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=499 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q503_progression_atom", + "status": "done_q503_tail_progression_upper_bound_verified", + "task": "The q=503 residual tail-prime component is certified; attack q=509 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=503 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q509_progression_atom", + "status": "done_q509_tail_progression_upper_bound_verified", + "task": "The q=509 residual tail-prime component is certified; attack q=521 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=509 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q521_progression_atom", + "status": "done_q521_tail_progression_upper_bound_verified", + "task": "The q=521 residual tail-prime component is certified; attack q=523 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=521 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q523_progression_atom", + "status": "done_q523_tail_progression_upper_bound_verified", + "task": "The q=523 residual tail-prime component is certified; attack q=541 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=523 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q541_progression_atom", + "status": "done_q541_tail_progression_upper_bound_verified", + "task": "The q=541 residual tail-prime component is certified; attack q=547 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=541 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q547_progression_atom", + "status": "done_q547_tail_progression_upper_bound_verified", + "task": "The q=547 residual tail-prime component is certified; attack q=557 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=547 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q557_progression_atom", + "status": "done_q557_tail_progression_upper_bound_verified", + "task": "The q=557 residual tail-prime component is certified; attack q=563 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=557 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q563_progression_atom", + "status": "done_q563_tail_progression_upper_bound_verified", + "task": "The q=563 residual tail-prime component is certified; attack q=569 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=563 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q569_progression_atom", + "status": "done_q569_tail_progression_upper_bound_verified", + "task": "The q=569 residual tail-prime component is certified; attack q=571 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=569 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_weakest_p13_dmax_tail_q571_progression_atom", + "status": "done_q571_tail_progression_upper_bound_verified", + "task": "The q=571 residual tail-prime component is certified; attack q=577 next as a two-sided residual tail-prime CRT floor-bound.", + "completionRule": "The q=571 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift", + "status": "blocked_by_bounded_matching_profile", + "task": "Wait for the bounded matching-injection profile to identify the parametric insertion target.", + "completionRule": "A symbolic small-prime CRT selector handles the right-compatibility escape rows, or the first finite-window miss outside that selector becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift", + "status": "blocked_by_bounded_matching_profile", + "task": "Wait for the bounded matching-injection profile to identify the parametric insertion target.", + "completionRule": "A symbolic cross-squarefree fallback selector handles the p=7 endpoint cross-bad rows, or the first finite-window miss outside that fallback rule becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift", + "status": "blocked_by_bounded_matching_profile", + "task": "Wait for the bounded matching-injection profile to identify the parametric insertion target.", + "completionRule": "A symbolic finite endpoint-menu lift covers all p=7 endpoint cross-bad rows without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift", + "status": "done_q17_residual_window_relaxed_fallback_menu_lift_emitted", + "task": "The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed selector target.", + "completionRule": "A symbolic sieve/hitting lemma proves cross-squarefree endpoint existence for the menu, or the first fully cross-blocked row becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift", + "status": "done_q17_residual_window_relaxed_fallback_menu_emitted", + "task": "The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed fallback selector.", + "completionRule": "A symbolic p7-shift plus q17 residual lemma proves cross-squarefree endpoint existence for the menu, or the first q17 residual cross-bad row becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift", + "status": "done_window_relaxed_fallback_menu_emitted", + "task": "The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu.", + "completionRule": "A symbolic fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully fallback-blocked row becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "status": "done_window_relaxed_fallback_menu_emitted", + "task": "The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu.", + "completionRule": "A symbolic expanded fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully expanded-menu-blocked row becomes the next deterministic packet.", + "command": null, + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift", + "status": "highest", + "task": "Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row.", + "completionRule": "A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.", + "command": null, + "packetAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "taskId": "start_singleton_p13_profile", + "status": "done_successor_packets_emitted", + "task": "Attack the singleton p13 split outP2=99|out25=14|smaller=side7 first to determine whether it is a real symbolic class or an under-split boundary artifact.", + "completionRule": "The singleton split either gets a persistence atom or emits a sharper split key.", + "command": null, + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md" + } + ] + }, + "structuralVerifierAudit": { + "status": "blocked", + "conclusion": "The external verifier is useful as an idea source, but it is blocked from canonical promotion.", + "summary": { + "sourceFileCount": 3, + "markdownFileCount": 2, + "cppFileCount": 1, + "certificateLikeFileCount": 0, + "blockerCount": 2, + "warningCount": 1, + "supportCount": 3, + "baseSevenMaskPresent": true, + "baseEighteenMaskPresent": false, + "baseResidueBothPresent": true, + "claimsTenMillionSawhneyHandoff": true + }, + "blockerIds": [ + "sawhney_handoff_not_claimed_at_1e7", + "base_exchange_mask_covers_both_principal_sides" + ], + "nextActions": [ + "Keep the external computation in EXTERNAL_VERIFICATION_LEDGER as blocked, not promoted.", + "Patch or independently reimplement the structural verifier with both base sides covered.", + "Replace the false 10^7 Sawhney handoff with a repo-audited explicit threshold before any all-N claim.", + "Port only the outsider-clique inequality shape into a repo-owned structural verifier lane." + ] + }, + "baseSideScout": { + "status": "counterexample_to_global_7_side_domination_found", + "summary": { + "interval": "1..200", + "outsiderCount": 5, + "side7CountAtMax": 8, + "side18CountAtMax": 8, + "globalMaxSide18Minus7": 1, + "globalMaxPerOutsider18Minus7": 1, + "maxSide18ExceedsSide7": true, + "perOutsiderSide18ExceedsSide7": true + }, + "firstNWithSide18MaxExceedingSide7": { + "N": 143, + "maxSide7": 2, + "maxSide18": 3, + "maxSide7Outsider": 41, + "maxSide18Outsider": 117, + "maxSide18Minus7": 1, + "maxPerOutsider18Minus7": 1, + "maxPerOutsider7Minus18": 1, + "perOutsider18Winner": { + "outsider": 117, + "side7": 2, + "side18": 3, + "delta18Minus7": 1 + }, + "perOutsider7Winner": { + "outsider": 38, + "side7": 1, + "side18": 0, + "delta7Minus18": 1 + } + }, + "boundary": { + "claimLevel": "bounded_scout_not_proof", + "note": "This scout compares principal-base compatibility counts on a finite interval only. It does not prove all-N base-side domination.", + "nextUse": "A one-sided 7 mod 25 base mask is not safe on this bounded scout; a two-sided structural verifier is needed." + } + }, + "structuralTwoSideScout": { + "status": "side_specific_bounds_pass_but_union_bound_fails", + "summary": { + "assessedRange": "7307..7600", + "witnessBlockCount": 8, + "breakpointCount": 32, + "checkCount": 256, + "globalRootEventCount": 193, + "side7BaseCountAtMax": 304, + "side18BaseCountAtMax": 304, + "allSide7ChecksPass": true, + "allSide18ChecksPass": true, + "allUnionChecksPass": false, + "side7FailureCount": 0, + "side18FailureCount": 0, + "unionFailureCount": 64 + }, + "firstFailures": { + "side7": null, + "side18": null, + "union": { + "N": 7307, + "p": 13, + "p2": 169, + "rawPlus": 43, + "rawMinus": 43, + "vMax": 43, + "activePlus": 40, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 110, + "sMaxSide18Witness": 1789, + "sMaxUnion": 218, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 293, + "side7CandidateSize": 293, + "side18CandidateSize": 292, + "side7Bound": 272, + "side18Bound": 271, + "unionBound": 379, + "side7Margin": 21, + "side18Margin": 22, + "unionMargin": -86, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + } + }, + "worstRows": { + "side7": { + "N": 7307, + "p": 13, + "p2": 169, + "rawPlus": 43, + "rawMinus": 43, + "vMax": 43, + "activePlus": 40, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 110, + "sMaxSide18Witness": 1789, + "sMaxUnion": 218, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 293, + "side7CandidateSize": 293, + "side18CandidateSize": 292, + "side7Bound": 272, + "side18Bound": 271, + "unionBound": 379, + "side7Margin": 21, + "side18Margin": 22, + "unionMargin": -86, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + "side18": { + "N": 7343, + "p": 13, + "p2": 169, + "rawPlus": 44, + "rawMinus": 43, + "vMax": 44, + "activePlus": 41, + "activeMinus": 39, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 112, + "sMaxSide18Witness": 5309, + "sMaxUnion": 220, + "sMaxUnionWitness": 5309, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 294, + "side7CandidateSize": 294, + "side18CandidateSize": 294, + "side7Bound": 273, + "side18Bound": 274, + "unionBound": 382, + "side7Margin": 21, + "side18Margin": 20, + "unionMargin": -88, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + }, + "union": { + "N": 7552, + "p": 13, + "p2": 169, + "rawPlus": 45, + "rawMinus": 45, + "vMax": 45, + "activePlus": 42, + "activeMinus": 41, + "sMaxSide7": 113, + "sMaxSide7Witness": 4831, + "sMaxSide18": 114, + "sMaxSide18Witness": 1789, + "sMaxUnion": 225, + "sMaxUnionWitness": 1789, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 103, + "candidateSize": 302, + "side7CandidateSize": 302, + "side18CandidateSize": 302, + "side7Bound": 279, + "side18Bound": 280, + "unionBound": 391, + "side7Margin": 23, + "side18Margin": 22, + "unionMargin": -89, + "side7Pass": true, + "side18Pass": true, + "unionPass": false + } + }, + "boundary": { + "claimLevel": "bounded_scout_not_all_n_proof", + "safety": "The union-base bound is safe but intentionally loose: it allows every compatible element from both principal sides even though a real clique may not be able to mix them.", + "promotionRule": "Promote only bounded structural coverage when unionPass is true for every checked witness-prime block and structural breakpoint in the assessed range.", + "nextUse": "Use the first/worst union failures to decide whether we need a sharper mixed-base lemma rather than a raw union overcount." + } + }, + "mixedBaseFailureScout": { + "status": "sampled_union_failures_repaired_by_mixed_base_clique", + "summary": { + "analyzedRowCount": 8, + "mixedPassCount": 8, + "mixedFailureCount": 0, + "allAnalyzedRowsMixedPass": true, + "minMixedMargin": 22, + "maxImprovementOverUnion": 111 + }, + "firstMixedFailure": null, + "worstMixedRow": { + "source": "first_union_failure", + "N": 7307, + "p": 13, + "outsider": 1789, + "candidateSize": 293, + "sMaxSide7": 111, + "sMaxSide18": 110, + "sMaxUnion": 218, + "mixedBaseCliqueSize": 110, + "mixedBaseSide7Count": 0, + "mixedBaseSide18Count": 110, + "mixedBaseCliqueMatchesSingleSide": true, + "mixedBound": 271, + "mixedMargin": 22, + "mixedPass": true, + "originalUnionMargin": -86, + "improvementOverUnion": 108, + "vMax": 43, + "dMax": 18, + "rGreater": 100, + "exampleMixedBaseClique": [ + 43, + 68, + 143, + 243, + 268, + 293, + 343, + 443, + 518, + 543, + 643, + 743, + 843, + 943, + 968, + 1043, + 1143, + 1193, + 1243, + 1343, + 1418, + 1443, + 1468, + 1543, + 1643, + 1743, + 1843, + 1868, + 1943, + 2043, + 2093, + 2143, + 2243, + 2318, + 2343, + 2443, + 2543, + 2643, + 2693, + 2743, + 2768, + 2843, + 2918, + 2943, + 2993, + 3043, + 3143, + 3218, + 3243, + 3343, + 3443, + 3543, + 3643, + 3668, + 3743, + 3768, + 3843, + 3893, + 3918, + 3943, + 4043, + 4068, + 4118, + 4143, + 4243, + 4343, + 4443, + 4493, + 4543, + 4568, + 4618, + 4643, + 4743, + 4793, + 4843, + 4943, + 5018, + 5043, + 5143, + 5243, + 5343, + 5443, + 5468, + 5543, + 5643, + 5693, + 5743, + 5843, + 5918, + 5943, + 6043, + 6143, + 6243, + 6293, + 6343, + 6368, + 6418, + 6443, + 6543, + 6593, + 6643, + 6668, + 6743, + 6818, + 6843, + 6943, + 7043, + 7143, + 7243, + 7268 + ] + }, + "boundary": { + "claimLevel": "sampled_failure_scout_not_full_structural_certificate", + "note": "This scout exactly solves the mixed-base clique on selected union-failure rows from the two-sided structural scout. It does not yet certify every structural breakpoint.", + "nextUse": "Promote this into the full two-sided structural verifier by replacing the union-base overcount with the exact mixed-base clique bound at every breakpoint." + } + }, + "fullMixedBaseStructuralVerifier": { + "status": "bounded_full_mixed_base_structural_verifier_certified", + "summary": { + "assessedRange": "7307..7600", + "witnessBlockCount": 8, + "breakpointCount": 32, + "checkCount": 256, + "globalRootEventCount": 193, + "side7BaseCountAtMax": 304, + "side18BaseCountAtMax": 304, + "unionCertifiedRowCount": 192, + "exactMixedRowCount": 64, + "threateningOutsiderCheckCount": 1733, + "mixedFailureCount": 0, + "allMixedChecksPass": true, + "minCertifiedMargin": 20, + "minExactMixedMargin": 20, + "maxThreateningOutsidersInRow": 41, + "maxImprovementOverUnion": 112, + "liftMiningRowCount": 64, + "threatLiftMiningRowCount": 1733 + }, + "firstMixedFailure": null, + "worstCertifiedRow": { + "N": 7343, + "p": 13, + "p2": 169, + "rawPlus": 44, + "rawMinus": 43, + "vMax": 44, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 112, + "sMaxSide18Witness": 5309, + "sMaxUnion": 220, + "sMaxUnionWitness": 5309, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 294, + "side7CandidateSize": 294, + "side18CandidateSize": 294, + "side7Bound": 273, + "side18Bound": 274, + "unionBound": 382, + "strictBaseThreshold": 132, + "side7Margin": 21, + "side18Margin": 20, + "unionMargin": -88, + "side7Pass": true, + "side18Pass": true, + "unionPass": false, + "certificateMode": "exact_mixed_base", + "threateningOutsiderCount": 40, + "exactMixedCheckCount": 40, + "sMaxMixed": 112, + "sMaxMixedWitness": 5309, + "mixedBound": 274, + "mixedMargin": 20, + "mixedPass": true, + "maxImprovementOverUnion": 109, + "worstThreat": { + "outsider": 5309, + "unionCount": 220, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "exampleMixedBaseClique": [ + 43, + 118, + 143, + 243, + 268, + 343, + 368, + 443, + 543, + 568, + 643, + 718, + 743, + 793, + 843, + 943, + 1018, + 1043, + 1068, + 1143, + 1243, + 1318, + 1343, + 1443, + 1468, + 1493, + 1543, + 1618, + 1643, + 1693, + 1743, + 1843, + 1918, + 1943, + 2043, + 2143, + 2243, + 2343, + 2368, + 2443, + 2543, + 2593, + 2643, + 2718, + 2743, + 2818, + 2843, + 2943, + 3043, + 3143, + 3243, + 3268, + 3343, + 3443, + 3493, + 3543, + 3643, + 3718, + 3743, + 3843, + 3943, + 4043, + 4143, + 4168, + 4243, + 4343, + 4393, + 4443, + 4543, + 4618, + 4643, + 4743, + 4843, + 4943, + 5043, + 5068, + 5143, + 5168, + 5243, + 5293, + 5343, + 5443, + 5518, + 5543, + 5643, + 5718, + 5743, + 5843, + 5943, + 5968, + 6043, + 6143, + 6193, + 6243, + 6343, + 6393, + 6418, + 6443, + 6543, + 6643, + 6743, + 6768, + 6843, + 6868, + 6943, + 7043, + 7093, + 7143, + 7168, + 7243, + 7318, + 7343 + ] + }, + "threatMatchingSummary": { + "threatCount": 40, + "minRequiredMatchingLowerBound": 29, + "maxRequiredMatchingLowerBound": 89, + "minActualMatching": 79, + "maxActualMatching": 109, + "minMatchingSlack": 19, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "tightestThreats": [ + { + "outsider": 5309, + "outsiderMod25": 9, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 89, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 19, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 1789, + "outsiderMod25": 14, + "compatibleSide7Count": 108, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 88, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 20, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 4831, + "outsiderMod25": 6, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSizeInMissingCrossGraph": 105, + "matchingSlack": 20, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side7" + }, + { + "outsider": 3281, + "outsiderMod25": 6, + "compatibleSide7Count": 108, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 87, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 21, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 6323, + "outsiderMod25": 23, + "compatibleSide7Count": 105, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 84, + "matchingSizeInMissingCrossGraph": 105, + "matchingSlack": 21, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + } + ] + } + }, + "worstExactMixedRow": { + "N": 7343, + "p": 13, + "p2": 169, + "rawPlus": 44, + "rawMinus": 43, + "vMax": 44, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "sMaxSide7": 111, + "sMaxSide7Witness": 4831, + "sMaxSide18": 112, + "sMaxSide18Witness": 5309, + "sMaxUnion": 220, + "sMaxUnionWitness": 5309, + "dMax": 18, + "dMaxWitness": { + "side": "plus", + "value": 1591 + }, + "rGreater": 100, + "candidateSize": 294, + "side7CandidateSize": 294, + "side18CandidateSize": 294, + "side7Bound": 273, + "side18Bound": 274, + "unionBound": 382, + "strictBaseThreshold": 132, + "side7Margin": 21, + "side18Margin": 20, + "unionMargin": -88, + "side7Pass": true, + "side18Pass": true, + "unionPass": false, + "certificateMode": "exact_mixed_base", + "threateningOutsiderCount": 40, + "exactMixedCheckCount": 40, + "sMaxMixed": 112, + "sMaxMixedWitness": 5309, + "mixedBound": 274, + "mixedMargin": 20, + "mixedPass": true, + "maxImprovementOverUnion": 109, + "worstThreat": { + "outsider": 5309, + "unionCount": 220, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "exampleMixedBaseClique": [ + 43, + 118, + 143, + 243, + 268, + 343, + 368, + 443, + 543, + 568, + 643, + 718, + 743, + 793, + 843, + 943, + 1018, + 1043, + 1068, + 1143, + 1243, + 1318, + 1343, + 1443, + 1468, + 1493, + 1543, + 1618, + 1643, + 1693, + 1743, + 1843, + 1918, + 1943, + 2043, + 2143, + 2243, + 2343, + 2368, + 2443, + 2543, + 2593, + 2643, + 2718, + 2743, + 2818, + 2843, + 2943, + 3043, + 3143, + 3243, + 3268, + 3343, + 3443, + 3493, + 3543, + 3643, + 3718, + 3743, + 3843, + 3943, + 4043, + 4143, + 4168, + 4243, + 4343, + 4393, + 4443, + 4543, + 4618, + 4643, + 4743, + 4843, + 4943, + 5043, + 5068, + 5143, + 5168, + 5243, + 5293, + 5343, + 5443, + 5518, + 5543, + 5643, + 5718, + 5743, + 5843, + 5943, + 5968, + 6043, + 6143, + 6193, + 6243, + 6343, + 6393, + 6418, + 6443, + 6543, + 6643, + 6743, + 6768, + 6843, + 6868, + 6943, + 7043, + 7093, + 7143, + 7168, + 7243, + 7318, + 7343 + ] + }, + "threatMatchingSummary": { + "threatCount": 40, + "minRequiredMatchingLowerBound": 29, + "maxRequiredMatchingLowerBound": 89, + "minActualMatching": 79, + "maxActualMatching": 109, + "minMatchingSlack": 19, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "tightestThreats": [ + { + "outsider": 5309, + "outsiderMod25": 9, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 89, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 19, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 1789, + "outsiderMod25": 14, + "compatibleSide7Count": 108, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 88, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 20, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 4831, + "outsiderMod25": 6, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSizeInMissingCrossGraph": 105, + "matchingSlack": 20, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side7" + }, + { + "outsider": 3281, + "outsiderMod25": 6, + "compatibleSide7Count": 108, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 87, + "matchingSizeInMissingCrossGraph": 108, + "matchingSlack": 21, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + }, + { + "outsider": 6323, + "outsiderMod25": 23, + "compatibleSide7Count": 105, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 84, + "matchingSizeInMissingCrossGraph": 105, + "matchingSlack": 21, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18" + } + ] + } + }, + "boundary": { + "claimLevel": "bounded_structural_certificate_not_all_N_proof", + "proofObligation": "Every witness-prime block and structural breakpoint in the assessed range is certified either by the safe union bound or by exact mixed-base clique checks for every threatening active outsider.", + "cliqueReduction": "For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges.", + "promotionRule": "Promote bounded structural coverage only when allMixedChecksPass is true for the full assessed range and all artifact parameters match the intended handoff range.", + "nextUse": "Use this as the repo-owned bounded structural certificate and extend the assessed range or lift the finite-block argument." + } + }, + "structuralLiftMiner": { + "status": "structural_lift_obligation_packet_ready", + "summary": { + "assessedRange": "7307..7600", + "exactMixedRowCount": 64, + "minedExactRowCount": 64, + "threatMiningRowCount": 1733, + "coverageComplete": true, + "exactPrimeCount": 2, + "primaryExactPrimes": [ + 13, + 17 + ], + "topFamilyCount": 20, + "minMixedMargin": 20, + "minUnionMargin": -89, + "minThreatMatchingSlack": 19, + "maxThreateningOutsidersInRow": 41, + "maxImprovementOverUnion": 112, + "nextTheoremLane": "formalize_cross_side_matching_bound_then_exact_prime_margin_lift" + }, + "sourceVerifier": { + "status": "bounded_full_mixed_base_structural_verifier_certified", + "method": "bounded_outsider_clique_full_mixed_base_structural_verifier", + "assessedRange": "7307..7600", + "exactMixedRowCount": 64, + "compactLiftMiningRowCount": 64, + "compactThreatMiningRowCount": 1733, + "minedExactRowCount": 64, + "coverageComplete": true + }, + "liftObligations": [ + { + "obligationId": "p848_cross_side_matching_bound", + "priority": "critical", + "status": "bounded_evidence_ready", + "statementTemplate": "For each threatening outsider, the missing cross-edge graph between the 7 mod 25 and 18 mod 25 compatible base sides has a matching large enough to force mixedCliqueSize below the strict base threshold.", + "currentEvidence": { + "assessedRange": "7307..7600", + "threateningOutsiderCheckCount": 1733, + "compactThreatMiningRowCount": 1733, + "maxImprovementOverUnion": 112, + "minMixedMargin": 20, + "minThreatMatchingSlack": 19, + "threatMatchingProfiles": [ + { + "p": 13, + "threatRowCount": 1285, + "structuralRowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 26, + "maxRequiredMatchingLowerBound": 90, + "minActualMatching": 79, + "maxActualMatching": 111, + "minMatchingSlack": 19, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "outsiderMod25Distribution": [ + { + "key": 14, + "count": 64 + }, + { + "key": 15, + "count": 64 + }, + { + "key": 16, + "count": 64 + }, + { + "key": 17, + "count": 64 + }, + { + "key": 19, + "count": 64 + }, + { + "key": 2, + "count": 64 + }, + { + "key": 20, + "count": 64 + }, + { + "key": 21, + "count": 64 + }, + { + "key": 22, + "count": 64 + }, + { + "key": 24, + "count": 64 + }, + { + "key": 3, + "count": 64 + }, + { + "key": 4, + "count": 64 + }, + { + "key": 5, + "count": 64 + }, + { + "key": 6, + "count": 64 + }, + { + "key": 8, + "count": 64 + }, + { + "key": 9, + "count": 64 + }, + { + "key": 12, + "count": 61 + }, + { + "key": 10, + "count": 40 + }, + { + "key": 0, + "count": 32 + }, + { + "key": 1, + "count": 32 + }, + { + "key": 11, + "count": 32 + }, + { + "key": 13, + "count": 32 + }, + { + "key": 23, + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side18", + "count": 770 + }, + { + "key": "side7", + "count": 515 + } + ], + "tightestThreats": [ + { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 5309, + "outsiderMod25": 9, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 220, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 89, + "matchingSlack": 19, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 13, + "p2": 169, + "outsider": 4831, + "outsiderMod25": 6, + "activePlus": 40, + "activeMinus": 39, + "activeOutsiderCount": 79, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 293, + "strictBaseThreshold": 132, + "unionCount": 216, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 105, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSlack": 20, + "smallerSideSize": 105, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 111, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7318, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 4831, + "outsiderMod25": 6, + "activePlus": 40, + "activeMinus": 39, + "activeOutsiderCount": 79, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 293, + "strictBaseThreshold": 132, + "unionCount": 216, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 105, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSlack": 20, + "smallerSideSize": 105, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 111, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7318, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 5309, + "outsiderMod25": 9, + "activePlus": 40, + "activeMinus": 39, + "activeOutsiderCount": 79, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 293, + "strictBaseThreshold": 132, + "unionCount": 219, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 88, + "matchingSlack": 20, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7337, + "certificateMode": "exact_mixed_base", + "nMod25": 12, + "p": 13, + "p2": 169, + "outsider": 4831, + "outsiderMod25": 6, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 216, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 105, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSlack": 20, + "smallerSideSize": 105, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 111, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7337, + "certificateMode": "exact_mixed_base", + "nMod25": 12, + "p": 13, + "p2": 169, + "outsider": 5309, + "outsiderMod25": 9, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 219, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 88, + "matchingSlack": 20, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 1789, + "outsiderMod25": 14, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 219, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 108, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 88, + "matchingSlack": 20, + "smallerSideSize": 108, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 13, + "p2": 169, + "outsider": 4831, + "outsiderMod25": 6, + "activePlus": 41, + "activeMinus": 39, + "activeOutsiderCount": 80, + "dMax": 18, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "rGreater": 100, + "candidateSize": 294, + "strictBaseThreshold": 132, + "unionCount": 216, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 105, + "compatibleSide7Count": 111, + "compatibleSide18Count": 105, + "requiredMatchingLowerBound": 85, + "matchingSlack": 20, + "smallerSideSize": 105, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 111, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + } + ] + }, + { + "p": 17, + "threatRowCount": 448, + "structuralRowCount": 32, + "firstN": 7307, + "lastN": 7600, + "minRequiredMatchingLowerBound": 1, + "maxRequiredMatchingLowerBound": 14, + "minActualMatching": 103, + "maxActualMatching": 112, + "minMatchingSlack": 95, + "allThreatsMeetRequiredLowerBound": true, + "allThreatsSaturateSmallerSide": true, + "outsiderMod25Distribution": [ + { + "key": 1, + "count": 64 + }, + { + "key": 10, + "count": 64 + }, + { + "key": 12, + "count": 32 + }, + { + "key": 13, + "count": 32 + }, + { + "key": 17, + "count": 32 + }, + { + "key": 19, + "count": 32 + }, + { + "key": 22, + "count": 32 + }, + { + "key": 23, + "count": 32 + }, + { + "key": 4, + "count": 32 + }, + { + "key": 5, + "count": 32 + }, + { + "key": 6, + "count": 32 + }, + { + "key": 8, + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side18", + "count": 297 + }, + { + "key": "side7", + "count": 151 + } + ], + "tightestThreats": [ + { + "N": 7318, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 14, + "matchingSlack": 95, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7343, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 294, + "strictBaseThreshold": 208, + "unionCount": 221, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 14, + "matchingSlack": 95, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 251, + "outsiderMod25": 1, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 216, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 106, + "compatibleSide7Count": 110, + "compatibleSide18Count": 106, + "requiredMatchingLowerBound": 10, + "matchingSlack": 96, + "smallerSideSize": 106, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 110, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 219, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 110, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 110, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7318, + "certificateMode": "exact_mixed_base", + "nMod25": 18, + "p": 17, + "p2": 289, + "outsider": 251, + "outsiderMod25": 1, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "unionCount": 217, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 107, + "compatibleSide7Count": 110, + "compatibleSide18Count": 107, + "requiredMatchingLowerBound": 11, + "matchingSlack": 96, + "smallerSideSize": 107, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 110, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7332, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 294, + "strictBaseThreshold": 208, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7337, + "certificateMode": "exact_mixed_base", + "nMod25": 12, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 294, + "strictBaseThreshold": 208, + "unionCount": 220, + "mixedBaseCliqueSize": 111, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 111, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 111, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7357, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "outsider": 4373, + "outsiderMod25": 23, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 295, + "strictBaseThreshold": 209, + "unionCount": 221, + "mixedBaseCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 109, + "compatibleSide7Count": 109, + "compatibleSide18Count": 112, + "requiredMatchingLowerBound": 13, + "matchingSlack": 96, + "smallerSideSize": 109, + "saturatesSmallerSide": true, + "mixedCliqueSide7Count": 0, + "mixedCliqueSide18Count": 112, + "dominantMixedCliqueSide": "side18" + } + ] + } + ] + }, + "proofUse": "This is the exact step that turns the computational co-bipartite clique repair into a reusable lemma." + }, + { + "obligationId": "p848_exact_prime_margin_lift", + "priority": "critical", + "status": "bounded_evidence_ready", + "statementTemplate": "For the exact-mixed witness-prime families 13, 17, prove candidateSize > sMaxMixed + vMax + dMax + rGreater either eventually or by a finite periodic residue split.", + "currentEvidence": { + "exactPrimeProfiles": [ + { + "p": 13, + "p2": 169, + "count": 32, + "firstN": 7307, + "lastN": 7600, + "minMixedMargin": 20, + "maxMixedMargin": 24, + "averageMixedMargin": 22.71875, + "minUnionMargin": -89, + "maxThreateningOutsiders": 41, + "maxImprovementOverUnion": 111, + "marginDeltaAcrossMinedRows": 2, + "approximateMarginSlopePerN": 0.006825938566552901, + "nMod25Distribution": [ + { + "key": 18, + "count": 12 + }, + { + "key": 7, + "count": 12 + }, + { + "key": 0, + "count": 1 + }, + { + "key": 1, + "count": 1 + }, + { + "key": 10, + "count": 1 + }, + { + "key": 12, + "count": 1 + }, + { + "key": 16, + "count": 1 + }, + { + "key": 2, + "count": 1 + }, + { + "key": 3, + "count": 1 + }, + { + "key": 6, + "count": 1 + } + ], + "dMaxWitnessSideDistribution": [ + { + "key": "plus", + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side18", + "count": 16 + }, + { + "key": "side7", + "count": 16 + } + ], + "worstOutsiderMod25Distribution": [ + { + "key": 6, + "count": 16 + }, + { + "key": 14, + "count": 14 + }, + { + "key": 9, + "count": 2 + } + ] + }, + { + "p": 17, + "p2": 289, + "count": 32, + "firstN": 7307, + "lastN": 7600, + "minMixedMargin": 96, + "maxMixedMargin": 101, + "averageMixedMargin": 99.3125, + "minUnionMargin": -13, + "maxThreateningOutsiders": 14, + "maxImprovementOverUnion": 112, + "marginDeltaAcrossMinedRows": 4, + "approximateMarginSlopePerN": 0.013651877133105802, + "nMod25Distribution": [ + { + "key": 18, + "count": 12 + }, + { + "key": 7, + "count": 12 + }, + { + "key": 0, + "count": 1 + }, + { + "key": 1, + "count": 1 + }, + { + "key": 10, + "count": 1 + }, + { + "key": 12, + "count": 1 + }, + { + "key": 16, + "count": 1 + }, + { + "key": 2, + "count": 1 + }, + { + "key": 3, + "count": 1 + }, + { + "key": 6, + "count": 1 + } + ], + "dMaxWitnessSideDistribution": [ + { + "key": "minus", + "count": 32 + } + ], + "dominantMixedCliqueSideDistribution": [ + { + "key": "side7", + "count": 22 + }, + { + "key": "side18", + "count": 10 + } + ], + "worstOutsiderMod25Distribution": [ + { + "key": 1, + "count": 22 + }, + { + "key": 23, + "count": 10 + } + ] + } + ] + }, + "proofUse": "This is the likely all-N lift of the hardest bounded structural rows." + }, + { + "obligationId": "p848_union_bound_tail_lift", + "priority": "high", + "status": "bounded_evidence_ready", + "statementTemplate": "Prove that every non-exact witness-prime block is certified by the safe union bound past the base interval, with only finitely many exceptional rows delegated to exact verification.", + "currentEvidence": { + "unionCertifiedRowCount": 192, + "exactMixedRowCount": 64, + "minCertifiedMargin": 20 + }, + "proofUse": "This separates the easy tail from the p-specific exact mixed-base obligations." + }, + { + "obligationId": "p848_top_repeating_family_lift", + "priority": "high", + "status": "bounded_evidence_ready", + "statementTemplate": "Use family p=17|Nmod25=7|d=minus|clique=side7|outMod25=1 as the first symbolic family to formalize.", + "currentEvidence": { + "familyKey": "p=17|Nmod25=7|d=minus|clique=side7|outMod25=1", + "count": 9, + "firstN": 7307, + "lastN": 7582, + "minMixedMargin": 97, + "maxMixedMargin": 101, + "averageMixedMargin": 100, + "minUnionMargin": -12, + "maxThreateningOutsiders": 14, + "maxImprovementOverUnion": 112, + "representativeRows": [ + { + "N": 7307, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "rawPlus": 26, + "rawMinus": 25, + "vMax": 26, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 293, + "strictBaseThreshold": 207, + "side7Margin": 97, + "side18Margin": 97, + "unionMargin": -12, + "mixedMargin": 97, + "sMaxMixed": 110, + "sMaxMixedWitness": 251, + "sMaxMixedWitnessMod25": 1, + "threateningOutsiderCount": 14, + "maxImprovementOverUnion": 109, + "worstOutsider": 251, + "worstOutsiderMod25": 1, + "worstUnionCount": 216, + "worstMixedCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 106, + "compatibleSide7Count": 110, + "compatibleSide18Count": 106, + "mixedCliqueSide7Count": 110, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7407, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "rawPlus": 26, + "rawMinus": 25, + "vMax": 26, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 297, + "strictBaseThreshold": 211, + "side7Margin": 99, + "side18Margin": 99, + "unionMargin": -11, + "mixedMargin": 99, + "sMaxMixed": 112, + "sMaxMixedWitness": 251, + "sMaxMixedWitnessMod25": 1, + "threateningOutsiderCount": 14, + "maxImprovementOverUnion": 110, + "worstOutsider": 251, + "worstOutsiderMod25": 1, + "worstUnionCount": 220, + "worstMixedCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 112, + "compatibleSide18Count": 108, + "mixedCliqueSide7Count": 112, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + }, + { + "N": 7432, + "certificateMode": "exact_mixed_base", + "nMod25": 7, + "p": 17, + "p2": 289, + "rawPlus": 26, + "rawMinus": 25, + "vMax": 26, + "activePlus": 23, + "activeMinus": 22, + "activeOutsiderCount": 45, + "dMax": 11, + "dMaxWitnessSide": "minus", + "dMaxWitnessValue": 829, + "rGreater": 49, + "candidateSize": 298, + "strictBaseThreshold": 212, + "side7Margin": 100, + "side18Margin": 100, + "unionMargin": -10, + "mixedMargin": 100, + "sMaxMixed": 112, + "sMaxMixedWitness": 251, + "sMaxMixedWitnessMod25": 1, + "threateningOutsiderCount": 14, + "maxImprovementOverUnion": 110, + "worstOutsider": 251, + "worstOutsiderMod25": 1, + "worstUnionCount": 220, + "worstMixedCliqueSize": 112, + "matchingSizeInMissingCrossGraph": 108, + "compatibleSide7Count": 112, + "compatibleSide18Count": 108, + "mixedCliqueSide7Count": 112, + "mixedCliqueSide18Count": 0, + "dominantMixedCliqueSide": "side7" + } + ] + }, + "proofUse": "A repeated row family is the best handhold for converting the verifier into a theorem packet." + } + ], + "recommendedNextSteps": [ + { + "stepId": "mine_matching_pattern_witnesses", + "priority": "critical", + "command": "erdos number-theory dispatch 848 --apply --action matching_pattern_miner --matching-pattern-prime 13", + "why": "The active D2 atom needs a symbolic matching construction, and the matching-pattern miner extracts actual tight-row missing-cross pairs without bloating the verifier artifact." + }, + { + "stepId": "formalize_cross_side_matching_bound", + "priority": "critical", + "command": "erdos problem formalization-work-refresh 848", + "why": "The full verifier succeeds exactly because mixed-base cliques are much smaller than the safe union overcount; this is the theorem-shaped repair mechanism." + }, + { + "stepId": "formalize_exact_prime_margin_lift", + "priority": "critical", + "command": "erdos problem formalization 848", + "why": "The mined rows identify which witness-prime blocks still need symbolic margin control after the union-bound rows are separated." + }, + { + "stepId": "extend_structural_range_after_lift_target", + "priority": "high", + "command": "erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min 7307 --structural-max 15200", + "why": "Once the first symbolic family is named, extend the bounded verifier beyond 7307..7600 to falsify or strengthen the family before claiming a lift." + } + ], + "boundary": { + "claimLevel": "theorem_obligation_packet_not_all_N_proof", + "note": "This miner extracts proof obligations from a bounded structural verifier. It does not certify any N outside the source verifier range.", + "promotionRule": "Use this packet to choose and formalize symbolic lemmas. Promote all-N closure only after those lemmas are independently proved and linked to the finite exact base." + } + }, + "structuralLiftChecklist": { + "status": "active", + "northStar": "Turn the bounded mixed-base structural verifier into an all-N proof lane by proving the cross-side matching reduction, then the p=13 and p=17 margin lifts, while keeping exact finite coverage separate.", + "currentFocus": { + "packetId": "D_matching_lower_bounds", + "targetStepId": "D4_matching_bound_implies_sMaxMixed_bound", + "firstActionableStepId": "D2_p13_matching_lower_bound", + "why": "The C graph-reduction packet is theorem-facing through C6, and D1 now extracts the bounded matching target from every current exact mixed-base threatening-outsider row. The next decisive lift is the symbolic p=13 matching lower bound, which is the tightest current D-lane family." + }, + "completionRule": "Each step is complete only when it has a statement, hypotheses, proof sketch or proof artifact, falsifier boundary, dependencies, and the next downstream step updated.", + "recommendedNextSteps": [ + { + "stepId": "prove_p13_matching_lower_bound", + "priority": "critical", + "task": "Prove the symbolic p=13 lower bound that explains why maxMatching(H_{x,N}) always reaches the D1-extracted K(N,x) target in the tightest current exact-mixed family.", + "command": "erdos problem formalization-work-refresh 848" + }, + { + "stepId": "regression_check_C6_against_verifier", + "priority": "high", + "task": "Keep the discharged C6 mixed-clique matching formula regression-checked against representative full-verifier rows.", + "command": "erdos number-theory dispatch 848 --apply --action structural_lift_miner" + }, + { + "stepId": "extract_p13_residue_matching_pattern", + "priority": "high", + "task": "For the top p=13 families, extract the residue-block pattern behind the smaller-side-saturating matchings so D2 can become a symbolic construction rather than bounded evidence.", + "command": "erdos number-theory dispatch 848 --apply --action structural_lift_miner" + } + ], + "boundary": { + "claimLevel": "task_checklist_not_proof", + "note": "This checklist records a proof plan and dependencies. It does not certify any new N by itself.", + "promotionRule": "Only mark a step done after the statement, hypotheses, proof/falsifier boundary, and downstream dependency updates are committed." + } + }, + "executionRule": { + "stance": "concrete_execution", + "summary": "Treat the task list as a concrete research loop for problem 848: execute the highest-value task itself, not wrapper prose about the task.", + "afterEachCompletion": [ + "Cross off the completed task.", + "Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary.", + "Use ORP granular breakdown when the next step is broad or confusing: orp mode nudge granular-breakdown --json", + "Use the smallest relevant ORP mode overlay when it simplifies the work: simplification for bloat, systems for cross-surface consequences, bold generation for new candidates, and sleek-progressive for clearer handoff shape.", + "Invent the next highest-value step from the updated evidence rather than following a stale fixed script.", + "Append that next step to the task list and refresh the canonical task-list artifacts." + ], + "granularBreakdownMode": { + "modeId": "granular-breakdown", + "status": "core_loop_enabled", + "fullBreakdownCommand": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json", + "nudgeCommand": "orp mode nudge granular-breakdown --json" + }, + "repetitionProtocol": "To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass.", + "lowStressLongHorizonNote": "This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan." + }, + "loopTemplate": [ + { + "stepId": "freeze_current_state", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search.", + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 848" + }, + { + "stepId": "audit_theorem_surfaces", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 848" + }, + { + "stepId": "verify_canonical_inputs", + "title": "Verify canonical bridge inputs against the latest harvested compute artifacts", + "task": "Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.", + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos number-theory bridge-refresh 848" + }, + { + "stepId": "verify_primary_structural_hook", + "title": "Verify the primary structural hook remains canonical", + "task": "Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.", + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 848" + }, + { + "stepId": "verify_verifier_boundary", + "title": "Verify the current exact/verifier boundary and next target", + "task": "Verify that the certified interval 1..40500 and the next verifier target remain current across the pack surfaces.", + "completionRule": "The interval work queue or verifier boundary packet still matches the theorem-facing status.", + "command": "erdos number-theory dispatch 848" + }, + { + "stepId": "apply_granular_breakdown", + "title": "Apply ORP granular breakdown before execution", + "task": "Run ORP granular breakdown on the active topic `problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound` and compress it into one active target plus one verification command.", + "completionRule": "The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification.", + "command": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json" + }, + { + "stepId": "execute_current_work_packet", + "title": "Explain the 282 First-Failure Mechanism", + "task": "Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "command": "erdos problem formalization-work 848" + }, + { + "stepId": "refresh_and_rerank", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 848" + } + ], + "currentObjective": { + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "title": "Formalize the 282 Obstruction Alignment", + "activeWorkId": "p848_282_first_failure_mechanism_packet_v1", + "activeWorkTitle": "Explain the 282 First-Failure Mechanism", + "activeWorkStatus": "in_progress" + }, + "currentTasks": [ + { + "taskId": "freeze_current_state", + "status": "ready", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search.", + "why": null, + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 848" + }, + { + "taskId": "audit_theorem_surfaces", + "status": "ready", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "why": null, + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 848" + }, + { + "taskId": "verify_canonical_inputs", + "status": "ready", + "title": "Verify canonical bridge inputs against the latest harvested compute artifacts", + "task": "Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.", + "why": null, + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos number-theory bridge-refresh 848" + }, + { + "taskId": "verify_primary_structural_hook", + "status": "ready", + "title": "Verify the primary structural hook remains canonical", + "task": "Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.", + "why": null, + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 848" + }, + { + "taskId": "verify_verifier_boundary", + "status": "ready", + "title": "Verify the current exact/verifier boundary and next target", + "task": "Verify that the certified interval 1..40500 and the next verifier target remain current across the pack surfaces.", + "why": null, + "completionRule": "The interval work queue or verifier boundary packet still matches the theorem-facing status.", + "command": "erdos number-theory dispatch 848" + }, + { + "taskId": "apply_granular_breakdown", + "status": "ready", + "title": "Apply ORP granular breakdown before execution", + "task": "Run ORP granular breakdown on the active topic `problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound` and compress it into one active target plus one verification command.", + "why": null, + "completionRule": "The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification.", + "command": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json" + }, + { + "taskId": "execute_current_work_packet", + "status": "in_progress", + "title": "Explain the 282 First-Failure Mechanism", + "task": "Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.", + "why": "The live 137720141 / 282 obstruction packet is checked at finite-menu scope; the remaining theorem work is the narrower symbolic-lift boundary.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "command": "erdos problem formalization-work 848" + }, + { + "taskId": "discharge_first_remaining_gap", + "status": "ready", + "title": "Discharge the first remaining gap in the active theorem packet", + "task": "Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "why": "This is the sharpest unresolved statement already named by the active theorem-work packet.", + "completionRule": "The first remaining gap is either resolved or replaced by a more precise successor gap.", + "command": "erdos problem formalization-work-refresh 848" + }, + { + "taskId": "refresh_and_rerank", + "status": "ready", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "why": null, + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 848" + } + ], + "completedAnchors": [ + { + "itemId": "completed_anchor_1", + "status": "done", + "note": "The family-menu boundary agrees with the tracked-tail boundary: the earliest 282-failing family row is also representative 137720141." + }, + { + "itemId": "completed_anchor_2", + "status": "done", + "note": "The extra witness has been isolated: 841 belongs to the 282 repair row, not to the six defining tuple moduli of the shared-prefix class." + }, + { + "itemId": "completed_anchor_3", + "status": "done", + "note": "The witness boundary is locally frozen: no earlier family-menu row gives tail 282 residue 0 modulo 841." + }, + { + "itemId": "completed_anchor_4", + "status": "done", + "note": "The representative residue is structurally derived: the tuple-row CRT projects the shared-prefix obstruction class to 504 mod 841." + }, + { + "itemId": "completed_anchor_5", + "status": "done", + "note": "The congruence boundary is isolated: residue class 504 mod 841 is the failure class for tracked tail 282 and no other tracked coprime tail." + }, + { + "itemId": "completed_anchor_6", + "status": "done", + "note": "The row-index boundary is isolated: within the shared-prefix row progression, tracked anchor 282 is the only tracked anchor whose 841 witness class starts at row index 0." + }, + { + "itemId": "completed_anchor_7", + "status": "done", + "note": "The row-start derivation is explicit: the boundary representative already lies on the 282 witness class modulo 841, so the row equation reduces to t ≡ 0 (mod 841)." + }, + { + "itemId": "completed_anchor_8", + "status": "done", + "note": "The menu-level first-occurrence boundary is isolated: 137720141 is the first family-menu representative in the 282 witness class 504 mod 841, so no earlier menu row can fail via witness 841 on that same congruence class." + }, + { + "itemId": "completed_anchor_9", + "status": "done", + "note": "The mechanism falsifier boundary is explicit: a lower representative in residue class 504 mod 841, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment would all break this packet." + }, + { + "itemId": "completed_anchor_10", + "status": "done", + "note": "The 132-row lift is explicit: adding the 132 row forces the tuple-row CRT class from residue 400 mod 841 to the boundary residue 504 mod 841 via k ≡ 147 (mod 289)." + }, + { + "itemId": "completed_anchor_11", + "status": "done", + "note": "The activation boundary is explicit: before anchor 132 no tuple-row CRT step lands on any tracked failure residue mod 841, anchor 132 creates the unique tracked 282 match at residue 504, and anchor 182 preserves that same unique match." + }, + { + "itemId": "completed_anchor_12", + "status": "done", + "note": "The 132-activation pattern is reusable on the current finite menu: 17 failing witness rows first activate their own failing tracked tail at anchor 132." + }, + { + "itemId": "completed_anchor_13", + "status": "done", + "note": "The finite-menu 132-activation pattern has been promoted into lemma schema p848_finite_menu_132_target_activation_schema_v1 with hypotheses, conclusion, falsifier boundary, and 17 row certificates." + }, + { + "itemId": "completed_anchor_14", + "status": "done", + "note": "The 17 finite-menu 132-activation row certificates replay successfully in checker p848_132_activation_row_certificate_checker_v1." + }, + { + "itemId": "completed_anchor_15", + "status": "done", + "note": "The 132-row lift to residue 504 mod 841 is proved from tuple-row CRT equations by checker p848_132_lift_crt_checker_v1." + }, + { + "itemId": "completed_anchor_16", + "status": "done", + "note": "The activation schema lift decision is explicit: finite_menu_certificate_not_universal_yet; next theorem pass is formalize_top_repair_class_mechanism." + }, + { + "itemId": "completed_anchor_17", + "status": "done", + "note": "The checked 132 activation schema has been lifted into symbolic CRT hypothesis packet p848_132_activation_symbolic_lift_candidate_v1; the next obligation is domain closure, not merely packet construction." + }, + { + "itemId": "completed_anchor_18", + "status": "done", + "note": "The broad domain-closure overclaim is ruled out at the current evidence boundary: The finite symbolic-lift survey splits across 8 failing anchors and 12 witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem." + }, + { + "itemId": "completed_anchor_19", + "status": "done", + "note": "The recommended anchor_832_witness_529 closure lane has been executed at finite repeated-group scope: 3 raw rows pass checker p848_832_529_anchor_witness_domain_closure_checker_v1." + }, + { + "itemId": "completed_anchor_20", + "status": "done", + "note": "The single-profile symbolic closure over anchor_832_witness_529 is falsified by the finite evidence split into 2 pre-132 residue profiles." + }, + { + "itemId": "completed_anchor_21", + "status": "done", + "note": "The anchor_832_witness_529 anchor-182 preservation step is explained: every checked row has lift parameter 0 at anchor 182." + }, + { + "itemId": "completed_anchor_22", + "status": "done", + "note": "The repeated pre132_7_1_32_224_57_229_82_412 sublane is closed as a finite duplicate final-anchor variant, not a new symbolic family." + }, + { + "itemId": "completed_anchor_23", + "status": "done", + "note": "Structural atom C1_same_side_base_clique is discharged: same-side principal base residues force a 25 divisor of u*v+1, so each same-side component is a clique." + }, + { + "itemId": "completed_anchor_24", + "status": "done", + "note": "Structural atom C2_two_cliques_plus_cross_edges is discharged by checker p848_C2_two_cliques_plus_cross_edges_checker_v1: the mixed-base graph is two cliques plus arbitrary cross edges." + }, + { + "itemId": "completed_anchor_25", + "status": "done", + "note": "Structural atom C3_missing_cross_graph_definition is discharged by checker p848_C3_missing_cross_graph_definition_checker_v1: H_{x,N} records exactly the missing cross edges between the two clique sides." + }, + { + "itemId": "completed_anchor_26", + "status": "done", + "note": "Structural atom C4_clique_to_vertex_cover_duality is discharged by checker p848_C4_clique_to_vertex_cover_duality_checker_v1: clique complements are exactly vertex covers of H_{x,N}." + }, + { + "itemId": "completed_anchor_27", + "status": "done", + "note": "Structural atom C5_konig_matching_reduction is discharged by checker p848_C5_konig_matching_reduction_checker_v1: Konig's theorem applies because H_{x,N} is finite bipartite." + }, + { + "itemId": "completed_anchor_28", + "status": "done", + "note": "Structural atom C6_mixed_clique_matching_formula is discharged by checker p848_C6_mixed_clique_matching_formula_checker_v1: sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N})." + }, + { + "itemId": "completed_anchor_29", + "status": "done", + "note": "Structural atom D1_residue_block_matching_injection is discharged at bounded extraction scope by checker p848_D1_matching_saturation_bound_checker_v1: every current exact mixed-base threatening outsider meets K(N,x) and saturates the smaller compatible side." + }, + { + "itemId": "completed_anchor_30", + "status": "done", + "note": "D2 split-core witness extraction is discharged at bounded pattern scope by checker p848_D2_p13_split_core_witness_checker_v1: each p=13 split common core reaches the sampled K(N,x) target." + }, + { + "itemId": "completed_anchor_31", + "status": "done", + "note": "D3 split-core witness extraction is discharged at bounded pattern scope by checker p848_D3_p17_split_core_witness_checker_v1: each p=17 split common core reaches the sampled K(N,x) target." + }, + { + "itemId": "completed_anchor_32", + "status": "done", + "note": "The top repair-class mechanism packet p848_top_repair_class_mechanism_packet_v1 is seeded with shared metrics, nearest contrasts, common missed-family boundary, and falsifier conditions." + }, + { + "itemId": "completed_anchor_33", + "status": "done", + "note": "The finite-menu +2 repaired-predicted-family separation is discharged: 432->242, 782->242, 832->242 versus 332->240, 382->240, 1232->240." + }, + { + "itemId": "completed_anchor_34", + "status": "done", + "note": "The common missed-family replay is explicit: 9 top-tie shared missed predicted family rows were replayed directly from the family menu." + }, + { + "itemId": "completed_anchor_35", + "status": "done", + "note": "The finite-menu +2 separation has been lifted into mod-50 lane-index congruences: 74 exchange rows all pass the bad-m-class certificate." + }, + { + "itemId": "completed_anchor_36", + "status": "done", + "note": "The mod-50 bad-lane congruence has been generalized into symbolic schema p848_mod50_bad_lane_symbolic_schema_v1; 74 finite witness instances replay with 0 failures." + }, + { + "itemId": "completed_anchor_37", + "status": "done", + "note": "The strict 782 > 1232 handoff is connected to the symbolic mod-50 schema by checker p848_782_1232_strict_handoff_checker_v1; it is certified as finite-menu guidance, not all-N closure." + }, + { + "itemId": "completed_anchor_38", + "status": "done", + "note": "The 182 row preserves the boundary residue: the 132-lifted class already satisfies 137720141 ≡ 119 (mod 121), so the final anchor adds no further correction modulo 841." + } + ], + "nextNeededSteps": [ + { + "stepId": "gap_1", + "status": "next", + "task": "Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 848" + }, + { + "stepId": "gap_2", + "status": "next", + "task": "Advance the same atomic packet toward target D4_matching_bound_implies_sMaxMixed_bound: If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N).", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 848" + }, + { + "stepId": "gap_3", + "status": "next", + "task": "Decide and run the next post-40500 verification lane using local CPU and opt-in local 4090 compute only.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 848" + }, + { + "stepId": "formalize_282_alignment", + "status": "high", + "task": "The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.", + "source": "theorem_formalization", + "command": "erdos problem formalization 848" + }, + { + "stepId": "formalize_top_repair_cluster", + "status": "high", + "task": "Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.", + "source": "theorem_formalization", + "command": "erdos problem formalization 848" + }, + { + "stepId": "decide_post_40500_verification_lane", + "status": "high", + "task": "The canonical exact base currently ends at 1..40500. The next verification move is still open.", + "source": "exact_verifier", + "command": "erdos number-theory dispatch 848" + }, + { + "stepId": "model_repair_pool_growth", + "status": "medium", + "task": "Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.", + "source": "theorem_formalization", + "command": "erdos problem formalization 848" + }, + { + "stepId": "finite_gap_strategy_handoff", + "status": "high", + "task": "Use the finite-gap strategy readout: endpoint rollout is useful, but exact-only closure would still require about 10,566,518,518,516,898 endpoint checks to reach the imported 2.64 x 10^17 handoff.", + "source": "finite_gap_strategy", + "command": "erdos problem task-list-refresh 848" + }, + { + "stepId": "implement_full_common_core_pair_export", + "status": "done", + "task": "Extend the matching-pattern miner so every split profile exports the full common matching core, not only commonMatchingPairSample.", + "source": "split_core_atomization_plan", + "command": "erdos problem task-list-refresh 848", + "completionRule": "Each split profile has commonMatchingPairs.length === commonMatchingPairCount for p13 and p17.", + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": null, + "manifestMarkdownPath": null + }, + { + "stepId": "emit_split_atom_packets", + "status": "done", + "task": "Generate one atom packet per split with inputs, common pairs, K envelope, required lower-bound range, and falsifier boundary.", + "source": "split_core_atomization_plan", + "command": "erdos problem task-list-refresh 848", + "completionRule": "The task list points at concrete split atom IDs instead of one broad D2/D3 persistence phrase.", + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "materialize_square_residue_successor_packets", + "status": "done", + "task": "Materialize square-residue successor packets for every p13 split profile so D2 can be discharged profile-by-profile.", + "source": "split_core_atomization_plan", + "command": "erdos problem task-list-refresh 848", + "completionRule": "The packet manifest lists verified successor packet files for every p13 refinement condition.", + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "attack_top_square_residue_successor", + "status": "done_symbolic_family_verified", + "task": "Attack successor D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1: prove the 145 affected vertex-presence atoms as a symbolic square-residue subfamily.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The successor packet is promoted to a symbolic vertex-family lemma or emits a still smaller deterministic obstruction.", + "packetAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md", + "manifestJsonPath": null, + "manifestMarkdownPath": null + }, + { + "stepId": "materialize_remaining_square_residue_successor_packets", + "status": "blocked_by_successor_family_proofs", + "task": "Materialize the remaining square-residue successor packets; 29 of 10 refinement conditions currently have packet files.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "Every refinement condition from the singleton p13 packet has a successor packet file and symbolic family check.", + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": null, + "manifestMarkdownPath": null + }, + { + "stepId": "emit_singleton_edge_obstruction_certificate", + "status": "done_literal_edge_certificate_verified", + "task": "Emit the literal edge-obstruction certificate for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7, proving every exported cross-edge obstruction has a checked squarefree product-plus-one certificate.", + "source": "split_core_atomization_plan", + "command": "erdos problem task-list-refresh 848", + "completionRule": "The first packet manifest reports literal_edge_obstruction_certificate_verified for the singleton p13 packet.", + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "promote_singleton_edge_congruence_persistence", + "status": "done_literal_edge_persistence_verified", + "task": "Promote the singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from literal edge-obstruction certificates into A5 congruence-persistence families.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "Each edge-obstruction family is either proved from the split hypotheses or emits a sharper deterministic successor atom.", + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "promote_singleton_matching_disjointness_and_k_envelope", + "status": "done_literal_matching_sampled_k_verified", + "task": "Promote singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 through A6 matching disjointness and A7 K-envelope checks.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The literal matching pairs are pairwise disjoint and the common-core count dominates the required K-envelope without bounded-only overclaim.", + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "assemble_singleton_split_discharge_readiness", + "status": "done_split_discharge_readiness_candidate", + "task": "Assemble split-discharge readiness for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from verified vertex successors, edge persistence, matching disjointness, and sampled K-envelope certificates.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The packet either becomes a theorem-facing split lemma candidate with explicit all-N handoff gaps, or emits the first missing lower atom.", + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "attack_next_p13_split_profile", + "status": "done_p13_split_readiness_candidates", + "task": "All p13 split profiles have split-discharge readiness candidates; promote the D2 p13 lane through the explicit all-N handoff gaps next.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "D2 promotion either discharges the row-universe and symbolic-K handoff gaps or emits the first missing all-N atom.", + "packetAtomId": null, + "packetId": null, + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "promote_d2_p13_all_n_handoff", + "status": "done_bounded_row_universe_stratified", + "task": "Bounded p13 row-universe stratification is audited; D2_p13_slack_dominance_symbolic_lift is now the symbolic all-N lift before D2 can be promoted.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The D2 p13 lane either closes row-universe coverage and symbolic K(N,x), or emits the first missing all-N atom.", + "packetAtomId": "D2_p13_slack_dominance_symbolic_lift", + "packetId": "D2_p13_matching_lower_bound", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "attack_d2_p13_row_universe_stratification_lift", + "status": "done_bounded_slack_stratification_audited", + "task": "Lift the bounded p=13 row stratification into a symbolic theorem: the 49 non-tight residue/side strata remain slack-dominated above the tight split floor for all future rows, or the first failing stratum emits a new deterministic split packet.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "Every bounded p13 threat row is either assigned to a split profile, proved slack-dominated outside the tight split packet, or emitted as a new deterministic split atom.", + "packetAtomId": "D2_p13_slack_dominance_symbolic_lift", + "packetId": "D2_p13_row_universe_split_coverage", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_d2_p13_slack_dominance_symbolic_lift", + "status": "done_bounded_formula_reduction_emitted", + "task": "Slack dominance reduced to D2_p13_non_tight_side_count_slack_floor_lift; prove the side-count floor next.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The 49 non-tight p13 residue/side strata either get a symbolic slack-dominance proof, or the first failing stratum emits a deterministic successor split atom.", + "packetAtomId": "D2_p13_slack_dominance_symbolic_lift", + "packetId": "D2_p13_row_universe_split_coverage", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_d2_p13_non_tight_side_count_slack_floor_lift", + "status": "done_weakest_side_count_atoms_emitted", + "task": "Weakest side-count floor atom packets are emitted; attack D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7 next.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "Either prove max(side7, side18) <= strictBaseThreshold - 1 - targetSlack for all non-tight p13 rows, or emit the weakest failing residue/side stratum as a deterministic atom.", + "packetAtomId": "D2_p13_non_tight_side_count_slack_floor_lift", + "packetId": "D2_p13_row_universe_split_coverage", + "packetJsonPath": null, + "packetMarkdownPath": null, + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "attack_weakest_p13_side_count_floor_atom", + "status": "done_structural_margin_decomposition_emitted", + "task": "Attack weakest p13 side-count floor atom D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7: prove its side-count inequality or split the first failing term.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The weakest side-count floor packet either becomes a symbolic side-count lemma or emits a sharper deterministic sub-atom.", + "packetAtomId": "D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_structural_margin_atom", + "status": "done_moving_term_subatoms_emitted", + "task": "Prove structural margin lemma D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18 for outP2=70|out25=23|smaller=side7, or emit the first moving-term sub-atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The structural margin inequality either gets a symbolic bound for candidateSize, vMax, dMax, rGreater, and the larger side count, or emits the first moving term as a sharper atom.", + "packetAtomId": "D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_bound_atom", + "status": "done_constant_bound_falsified_successor_atom_emitted", + "task": "The original dMax constant-bound atom is closed by a bounded falsifier and successor growth profile; continue with the current downstream moving-term atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The dMax subatom either proves the uniform same-prime degree bound used by the structural margin, or emits the sharper term family that controls dMax.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "attack_weakest_p13_dmax_growth_atom", + "status": "done_dmax_growth_tail_profile_closed", + "task": "The dMax growth tail profile is closed through q>=587 for outP2=70|out25=23|smaller=side7; attack the residual dynamic margin next.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The dMax growth atom either proves a symbolic envelope for the same-prime degree term or emits the first residue/floor-function sub-split controlling the degree growth.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q2_progression_atom", + "status": "blocked_by_dmax_growth_profile", + "task": "Wait for the dMax growth profile to emit its first square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=2 progression contribution is bounded by a floor-function with exclusions, or the first unresolved exclusion class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q3_progression_atom", + "status": "blocked_by_q2_progression_certificate", + "task": "Wait for the q=2 progression proof to emit the q=3 square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=3 progression contribution is bounded by CRT floor-functions, or the first unresolved q=3 exclusion/overlap class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q5_progression_atom", + "status": "blocked_by_q3_progression_certificate", + "task": "Wait for the q=3 progression proof to emit the q=5 square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=5 progression contribution is bounded by CRT floor-functions, or the first unresolved q=5 exclusion/overlap class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q7_progression_atom", + "status": "blocked_by_q5_progression_certificate", + "task": "Wait for the q=5 progression proof to emit the q=7 square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=7 progression contribution is bounded by CRT floor-functions, or the first unresolved q=7 exclusion/overlap class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q11_progression_atom", + "status": "blocked_by_q7_progression_certificate", + "task": "Wait for the q=7 progression proof to emit the q=11 square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=11 progression contribution is bounded by CRT floor-functions, or the first unresolved q=11 exclusion/overlap class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q19_progression_atom", + "status": "blocked_by_q11_progression_certificate", + "task": "Wait for the q=11 progression proof to emit the q=19 square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=19 progression contribution is bounded by CRT floor-functions, or the first unresolved q=19 exclusion/overlap class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_q23_progression_atom", + "status": "blocked_by_q19_progression_certificate", + "task": "Wait for the q=19 progression proof to emit the q=23 square-divisor progression atom.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=23 progression contribution is bounded by CRT floor-functions, or the first unresolved q=23 exclusion/overlap class becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_recombination_atom", + "status": "done_tail_scaffold_q13_residue_exclusion_verified", + "task": "The tail/recombination scaffold excludes q=13 by split residue; attack the first unresolved tail prime q=17 next.", + 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q11_minus_progression_atom", + "status": "done_q11_minus_tail_progression_upper_bound_verified", + "task": "The minus-side q=11 tail complement is certified; attack the plus-side q=23 complement next.", + "source": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q251_minus_progression_atom", + "status": "done_q251_minus_tail_progression_upper_bound_verified", + "task": "The minus-side q=251 tail complement is certified; attack the first remaining non-observed q=29 tail prime next.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The minus-side q=251 tail contribution is bounded by its CRT floor function, or the next unresolved tail range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q29_progression_atom", + "status": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q41_progression_atom", + "status": "done_q41_tail_progression_upper_bound_verified", + "task": "The q=41 residual tail-prime component is certified; attack q=43 next, starting with the plus-side witness-divisibility exclusion.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=41 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q43_progression_atom", + "status": "done_q43_tail_progression_upper_bound_verified", + "task": "The q=43 residual tail-prime component is certified; attack q=47 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=43 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q59_progression_atom", + "status": "done_q59_tail_progression_upper_bound_verified", + "task": "The q=59 residual tail-prime component is certified; attack q=61 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=59 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q67_progression_atom", + "status": "done_q67_tail_progression_upper_bound_verified", + "task": "The q=67 residual tail-prime component is certified; attack q=71 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=67 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q71_progression_atom", + "status": "done_q71_tail_progression_upper_bound_verified", + "task": "The q=71 residual tail-prime component is certified; attack q=73 next, starting with the minus-side witness-divisibility exclusion.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=71 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q79_progression_atom", + "status": "done_q79_tail_progression_upper_bound_verified", + "task": "The q=79 residual tail-prime component is certified; attack q=83 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=79 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q83_progression_atom", + "status": "done_q83_tail_progression_upper_bound_verified", + "task": "The q=83 residual tail-prime component is certified; attack q=89 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=83 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q97_progression_atom", + "status": "done_q97_tail_progression_upper_bound_verified", + "task": "The q=97 residual tail-prime component is certified; attack q=101 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=97 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q101_progression_atom", + "status": "done_q101_tail_progression_upper_bound_verified", + "task": "The q=101 residual tail-prime component is certified; attack q=103 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=101 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q107_progression_atom", + "status": "done_q107_tail_progression_upper_bound_verified", + "task": "The q=107 residual tail-prime component is certified; attack q=109 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=107 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q109_progression_atom", + "status": "done_q109_tail_progression_upper_bound_verified", + "task": "The q=109 residual tail-prime component is certified; attack q=113 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=109 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q127_progression_atom", + "status": "done_q127_tail_progression_upper_bound_verified", + "task": "The q=127 residual tail-prime component is certified; attack q=131 next, combining the minus-side witness-divisibility exclusion with the plus-side CRT floor bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=127 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q131_progression_atom", + "status": "done_q131_tail_progression_upper_bound_verified", + "task": "The q=131 residual tail-prime component is certified; attack q=137 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=131 tail contribution is bounded by the minus-side exclusion and plus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q139_progression_atom", + "status": "done_q139_tail_progression_upper_bound_verified", + "task": "The q=139 residual tail-prime component is certified; attack q=149 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=139 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q157_progression_atom", + "status": "done_q157_tail_progression_upper_bound_verified", + "task": "The q=157 residual tail-prime component is certified; attack q=163 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=157 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q167_progression_atom", + "status": "done_q167_tail_progression_upper_bound_verified", + "task": "The q=167 residual tail-prime component is certified; attack q=173 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=167 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q173_progression_atom", + "status": "done_q173_tail_progression_upper_bound_verified", + "task": "The q=173 residual tail-prime component is certified; attack q=179 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=173 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q191_progression_atom", + "status": "done_q191_tail_progression_upper_bound_verified", + "task": "The q=191 residual tail-prime component is certified; attack q=193 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=191 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q199_progression_atom", + "status": "done_q199_tail_progression_upper_bound_verified", + "task": "The q=199 residual tail-prime component is certified; attack q=211 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=199 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q223_progression_atom", + "status": "done_q223_tail_progression_upper_bound_verified", + "task": "The q=223 residual tail-prime component is certified; attack q=227 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=223 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q227_progression_atom", + "status": "done_q227_tail_progression_upper_bound_verified", + "task": "The q=227 residual tail-prime component is certified; attack q=229 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=227 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q233_progression_atom", + "status": "done_q233_tail_progression_upper_bound_verified", + "task": "The q=233 residual tail-prime component is certified; attack q=239 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=233 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q239_progression_atom", + "status": "done_q239_tail_progression_upper_bound_verified", + "task": "The q=239 residual tail-prime component is certified; attack q=241 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=239 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q257_progression_atom", + "status": "done_q257_tail_progression_upper_bound_verified", + "task": "The q=257 residual tail-prime component is certified; attack q=263 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=257 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q263_progression_atom", + "status": "done_q263_tail_progression_upper_bound_verified", + "task": "The q=263 residual tail-prime component is certified; attack q=269 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=263 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q271_progression_atom", + "status": "done_q271_tail_progression_upper_bound_verified", + "task": "The q=271 residual tail-prime component is certified; attack q=277 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=271 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q277_progression_atom", + "status": "done_q277_tail_progression_upper_bound_verified", + "task": "The q=277 residual tail-prime component is certified; attack q=281 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=277 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q293_progression_atom", + "status": "done_q293_tail_progression_upper_bound_verified", + "task": "The q=293 residual tail-prime component is certified; attack q=307 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=293 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q313_progression_atom", + "status": "done_q313_tail_progression_upper_bound_verified", + "task": "The q=313 residual tail-prime component is certified; attack q=317 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=313 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q337_progression_atom", + "status": "done_q337_tail_progression_upper_bound_verified", + "task": "The q=337 residual tail-prime component is certified; attack q=347 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=337 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q353_progression_atom", + "status": "done_q353_tail_progression_upper_bound_verified", + "task": "The q=353 residual tail-prime component is certified; attack q=359 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=353 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q373_progression_atom", + "status": "done_q373_tail_progression_upper_bound_verified", + "task": "The q=373 residual tail-prime component is certified; attack q=379 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=373 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q389_progression_atom", + "status": "done_q389_tail_progression_upper_bound_verified", + "task": "The q=389 residual tail-prime component is certified; attack q=397 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=389 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q409_progression_atom", + "status": "done_q409_tail_progression_upper_bound_verified", + "task": "The q=409 residual tail-prime component is certified; attack q=419 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=409 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q431_progression_atom", + "status": "done_q431_tail_progression_upper_bound_verified", + "task": "The q=431 residual tail-prime component is certified; attack q=433 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=431 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q439_progression_atom", + "status": "done_q439_tail_progression_upper_bound_verified", + "task": "The q=439 residual tail-prime component is certified; attack q=443 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=439 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q443_progression_atom", + "status": "done_q443_tail_progression_upper_bound_verified", + "task": "The q=443 residual tail-prime component is certified; attack q=449 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=443 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q461_progression_atom", + "status": "done_q461_tail_progression_upper_bound_verified", + "task": "The q=461 residual tail-prime component is certified; attack q=463 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=461 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q479_progression_atom", + "status": "done_q479_tail_progression_upper_bound_verified", + "task": "The q=479 residual tail-prime component is certified; attack q=487 next as a two-sided residual tail-prime CRT floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=479 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=499 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=521 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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floor-bound.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The q=569 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": 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"p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_weakest_p13_dmax_tail_q587_progression_atom", + "status": "done_q587_tail_progression_upper_bound_verified", + "task": "The q=587 residual tail-prime component is certified; lift the bounded q>=587 zero-floor profile before any aggregate 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becomes the next deterministic packet.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift", + "status": 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"/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "status": "done_window_relaxed_fallback_menu_emitted", + "task": "The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "A symbolic expanded fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully expanded-menu-blocked row becomes the next deterministic packet.", + "packetAtomId": null, + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift", + "status": "highest", + "task": "Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.", + "packetAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md" + }, + { + "stepId": "start_singleton_p13_profile", + "status": "done_successor_packets_emitted", + "task": "Attack the singleton p13 split outP2=99|out25=14|smaller=side7 first to determine whether it is a real symbolic class or an under-split boundary artifact.", + "source": "split_core_atomization_plan", + "command": null, + "completionRule": "The singleton split either gets a persistence atom or emits a sharper split key.", + "packetAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "packetJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "packetMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "manifestJsonPath": null, + "manifestMarkdownPath": null + }, + { + "stepId": "structural_verifier_import_audit", + "status": "high", + "task": "Use the structural-verifier import audit: status blocked, blockers sawhney_handoff_not_claimed_at_1e7, base_exchange_mask_covers_both_principal_sides.", + "source": "external_structural_verifier_audit", + "command": "erdos number-theory dispatch 848 --apply --action structural_verifier_audit" + }, + { + "stepId": "base_side_scout", + "status": "high", + "task": "Use the base-side scout: status counterexample_to_global_7_side_domination_found over 1..200; max side18-minus-side7 is 1.", + "source": "structural_base_side_scout", + "command": "erdos number-theory dispatch 848 --apply --action base_side_scout --base-side-max 2000" + }, + { + "stepId": "structural_two_side_scout", + "status": "ready", + "task": "Use the two-sided structural scout: status side_specific_bounds_pass_but_union_bound_fails over 7307..7600; union failures 64 repaired by the full mixed-base verifier.", + "source": "structural_two_side_scout", + "command": "erdos number-theory dispatch 848 --apply --action structural_two_side_scout --structural-min 7307 --structural-max 7600" + }, + { + "stepId": "mixed_base_failure_scout", + "status": "ready", + "task": "Use the mixed-base failure scout: status sampled_union_failures_repaired_by_mixed_base_clique; analyzed 8 union-failure rows with 0 mixed-base failures.", + "source": "mixed_base_failure_scout", + "command": "erdos number-theory dispatch 848 --apply --action mixed_base_failure_scout --mixed-base-max-rows 40" + }, + { + "stepId": "full_mixed_base_structural_verifier", + "status": "ready", + "task": "Use the full mixed-base structural verifier: status bounded_full_mixed_base_structural_verifier_certified over 7307..7600; exact threatening-outsider checks 1733, mixed failures 0.", + "source": "full_mixed_base_structural_verifier", + "command": "erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min 7307 --structural-max 7600" + }, + { + "stepId": "structural_lift_miner", + "status": "ready", + "task": "Use the structural lift miner: status structural_lift_obligation_packet_ready; mined 64 exact mixed rows; next theorem lane formalize_cross_side_matching_bound_then_exact_prime_margin_lift.", + "source": "structural_lift_miner", + "command": "erdos number-theory dispatch 848 --apply --action structural_lift_miner" + }, + { + "stepId": "regime_b_endpoint_verifier_backend", + "status": "high", + "task": "Continue the active endpoint-monotonicity exact verifier beyond 1..40500 (1621 endpoint checks cover 40500 rows; compression 24.98x).", + "source": "exact_breakpoint_certificate", + "command": "erdos number-theory dispatch 848 --apply --action exact_followup_rollout --exact-chunks 5 --exact-chunk-size 1000 --endpoint-monotonicity" + } + ], + "commands": { + "problemShow": "erdos problem show 848", + "problemArtifacts": "erdos problem artifacts 848", + "taskList": "erdos problem task-list 848", + "taskListRefresh": "erdos problem task-list-refresh 848", + "taskListRun": "erdos problem task-list-run 848 --passes 10", + "orpModeList": "orp mode list --json", + "granularBreakdown": "orp mode breakdown granular-breakdown --topic \"problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound\" --json", + "granularNudge": "orp mode nudge granular-breakdown --json", + "theoremLoop": "erdos problem theorem-loop 848", + "claimPass": "erdos problem claim-pass 848", + "formalization": "erdos problem formalization 848", + "formalizationWork": "erdos problem formalization-work 848", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848", + "taskListJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LIST.json", + "taskListMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LIST.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.json", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.json", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION_WORK.json", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml", + "exactBreakpointScoutJsonPath": 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"structuralLiftChecklistJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json", + "structuralLiftChecklistMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json" + } +} diff --git a/packs/number-theory/problems/848/TASK_LIST.md b/packs/number-theory/problems/848/TASK_LIST.md new file mode 100644 index 0000000..1b2676c --- /dev/null +++ b/packs/number-theory/problems/848/TASK_LIST.md @@ -0,0 +1,683 @@ +# Erdos Problem #848 Task List + +This task list is the canonical research-loop surface for the problem. It gives one reusable execution rule, one templated loop, the current active tasks, and the next steps discovered from the current theorem/search/verifier state. + +## Current State + +- Task list mode: `bridge_backed`. +- Active route: `finite_check_gap_closure`. +- Current claim surface: `bridge_backed_frontier_support`. +- Route summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. +- Next honest move: Decide whether to extend exact verified coverage beyond `40500` or switch method class. +- Latest verified interval: `1..40500` + +## Execution Rule + +- Stance: `concrete_execution` +- Summary: Treat the task list as a concrete research loop for problem 848: execute the highest-value task itself, not wrapper prose about the task. +- After each completed step: Cross off the completed task. +- After each completed step: Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary. +- After each completed step: Use ORP granular breakdown when the next step is broad or confusing: orp mode nudge granular-breakdown --json +- After each completed step: Use the smallest relevant ORP mode overlay when it simplifies the work: simplification for bloat, systems for cross-surface consequences, bold generation for new candidates, and sleek-progressive for clearer handoff shape. +- After each completed step: Invent the next highest-value step from the updated evidence rather than following a stale fixed script. +- After each completed step: Append that next step to the task list and refresh the canonical task-list artifacts. +- Repetition protocol: To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass. +- Long-horizon note: This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan. + +## ORP Granular Breakdown + +- Status: `core_loop_enabled` +- Mode id: `granular-breakdown` +- Topic: problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound +- Activation phrase: Break it down until it can move. +- Invocation rule: Use the full breakdown before executing a complex theorem/search packet; use the nudge card whenever the agent or user is confused, the target feels too broad, or the next action is not deterministic. +- Full breakdown: `orp mode breakdown granular-breakdown --topic "problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound" --json` +- Nudge: `orp mode nudge granular-breakdown --json` +- Loop integration: Run the full breakdown after the theorem/search surfaces are audited and before executing the current work packet. +- Loop integration: Write operationally important decompositions into TASK_LIST, FORMALIZATION_WORK, or a dedicated checklist artifact rather than leaving them in chat. +- Loop integration: Use the nudge card for quick reorientation when a step becomes blurry during implementation. +- Loop integration: Compress the breakdown back into one active target and one verification command before continuing. +- Durable artifact rule: If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state. + +## ORP Mode Overlay Palette + +- Status: `core_loop_palette_enabled` +- Source command: `orp mode list --json` +- Default mode id: `granular-breakdown` +- Selection rule: Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default. +- Durable when operational: `yes` +- Overlay `granular-breakdown` (core_decomposition_loop): The work is broad, confusing, theorem-heavy, or needs a durable dependency ladder before execution. | placement: Before execute_current_work_packet and whenever the active target becomes fuzzy. | command: `orp mode breakdown granular-breakdown --topic "problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound" --json` | output: Boundary, lanes, subclaims, atomic obligations, dependency ladder, active target, durable checklist, and next verification. +- Overlay `ruthless-simplification` (compression_and_signal_filter): A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision. | placement: After granular decomposition, before committing a plan to TASK_LIST, and before final summaries. | command: `orp mode nudge ruthless-simplification --json` | output: One core sentence, one surviving move, and a list of noise to delete or defer. +- Overlay `systems-constellation` (dependency_and_downstream_effects): A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow. | placement: Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow. | command: `orp mode nudge systems-constellation --json` | output: Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision. +- Overlay `bold-concept-generation` (candidate_generation_when_stuck): The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions. | placement: After a falsifier, before launching broad compute, or when inventing the next symbolic construction. | command: `orp mode nudge bold-concept-generation --json` | output: Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment. +- Overlay `sleek-minimal-progressive` (fresh_lens_and_low_friction_motion): The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up. | placement: When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation. | command: `orp mode nudge sleek-minimal-progressive --json` | output: One subtraction, one tasteful surprise, and one concrete next move that keeps momentum. + +## Agent Flow + +- Status: `ready` +- Audience: `agent` +- Operating rule: Read this object first; execute the primary next action unless a guardrail blocks it or the task list is stale. +- Primary next action: `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift` [highest] Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row. +- Default agent action: `execute_primary_next_action` +- Mode selection: Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default. +- Granular nudge: `orp mode nudge granular-breakdown --json` +- Situational overlay `ruthless-simplification`: A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision. | command: `orp mode nudge ruthless-simplification --json` +- Situational overlay `systems-constellation`: A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow. | command: `orp mode nudge systems-constellation --json` +- Situational overlay `bold-concept-generation`: The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions. | command: `orp mode nudge bold-concept-generation --json` +- Situational overlay `sleek-minimal-progressive`: The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up. | command: `orp mode nudge sleek-minimal-progressive --json` +- Agent guardrail: Do not run paid or remote compute unless the frontier configuration explicitly enables that paid rung. +- Agent guardrail: Prefer local/free compute before opt-in paid compute. +- Agent guardrail: Do not treat bounded search evidence as an all-N proof without a theorem-facing handoff. +- Agent guardrail: Do not run every ORP mode by default. +- Agent guardrail: Persist operationally important changes into canonical artifacts rather than chat-only state. +- Refresh after material progress: `erdos problem task-list-refresh 848` + +## Finite-Gap Strategy + +- Verdict: `exact_endpoint_rollout_is_not_a_sole_all_N_closure_strategy` +- Operational threshold: `2.64 x 10^17` (external_public_claim) +- Remaining rows to operational threshold: `263,999,999,999,959,500` +- Projected endpoint checks to operational threshold: `10,566,518,518,516,898` +- Recommended mode: `hybrid_threshold_audit_plus_structural_verifier` +- Guidance: Continue endpoint rollouts only as bounded base expansion and regression evidence. +- Guidance: Do not wait for direct endpoint checks to close the imported finite gap. +- Guidance: Prioritize auditing the imported threshold handoff or proving a stronger structural verifier lane. +- Guidance: Use GPU/frontier sweeps to generate structural candidates and counterexamples, not as a substitute for the all-N handoff proof. + +## Split-Core Atomization Plan + +- Plan id: `p848_split_core_atomization_master_plan_v1` +- Status: `active` +- North star: Make the D2/D3 matching lower-bound proof deterministic by turning every split-core persistence claim into replayable vertex, edge, congruence, matching, and K-envelope atoms. +- Deterministic rule: No split may be promoted from bounded witness support to theorem support until every layer below has a pass/fail checker and every failure emits a smaller successor atom. +- Active parent obligation: `D2_p13_matching_lower_bound` +- Target obligation: `D4_matching_bound_implies_sMaxMixed_bound` +- Split atoms: `5` +- D2 split count: `3` +- D3 split count: `2` +- Packet directory: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS` +- Packet manifest JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json` +- Packet manifest markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md` +- Packet files present: `yes` +- Successor packet count: `29` +- First packet refinement conditions: `10` +- Verified successor families: `29` +- Successor packet files present: `yes` +- All materialized successor families verified: `yes` +- First packet edge certificate: `literal_edge_obstruction_certificate_verified` +- First packet edge persistence: `literal_constant_edge_persistence_verified` +- Edge-persistent packet count: `5` +- First packet matching/K certificate: `literal_matching_sampled_k_envelope_verified` +- Matching/K packet count: `5` +- First packet split-discharge readiness: `split_discharge_readiness_candidate` +- Split-discharge ready packet count: `3` +- P13 row-universe coverage: `bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder` +- P13 row-universe first missing atom: `D2_p13_slack_dominance_symbolic_lift` +- P13 slack-dominance lift: `bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed` +- P13 slack-dominance first lemma: `D2_p13_non_tight_side_count_slack_floor_lift` +- Side-count floor packet count: `2` +- First side-count floor packet: `D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7` +- First side-count structural margin lemma: `D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18` +- First side-count moving-term subatom: `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Next undischarged p13 packet: `(none)` +- First packet to attack: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- First successor packet to attack: `D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1` +- First unverified successor packet to attack: `(none)` +- Row-universe coverage candidate: `D2_p13_row_universe_split_coverage` [bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder] +- Row-universe coverage scope: `bounded_p13_threat_rows_tight_splits_plus_slack_dominated_remainder`, tight witnesses `12` / bounded p13 threats `1285` +- Bounded p13 row strata: `52` total, `96` rows in emitted tight strata, `1189` / `1189` outside rows slack-dominated +- Bounded p13 slack floor: tight min `19`, outside min `21`, additional split rows `0` +- Row-universe emitted missing atom: `D2_p13_slack_dominance_symbolic_lift` +- Slack-dominance symbolic lift candidate: `D2_p13_slack_dominance_symbolic_lift` [bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed] +- Slack-dominance formula replay: `1189` rows across `49` strata, target floor `20`, observed min `21` +- Slack-dominance first open lemma: `D2_p13_non_tight_side_count_slack_floor_lift` +- Most confusing question: Are the common matching pairs literal fixed vertices, or formulaic residue-family vertices that move with N? +- Why it matters: This determines whether the proof obligation is fixed vertex presence across a split, or extraction of a parameterized vertex formula before edge persistence can be proved. +- First place to attack: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Layer `A0_input_universe_freeze` [done_bounded]: Freeze the exact threatening-outsider row universe, prime lanes, and K(N,x) formula used by D1. | output: A row-universe manifest keyed by prime, N, outsider, side counts, K(N,x), actual matching, and smaller-side size. +- Layer `A1_split_profile_inventory` [done_bounded]: Freeze the p13 and p17 split keys and attach each bounded split-core witness packet to a parent D-lane obligation. | output: One split atom per residue/smaller-side profile. +- Layer `A2_full_common_core_pair_export` [done]: Export the full common matching core for each split, not only a pair sample. | output: For every split atom, a complete ordered list of common matching pairs with left/right values and residues modulo 25, p, and p^2. +- Layer `A3_vertex_presence_atoms` [next]: Prove every left/right vertex used by the split core is present on the correct compatible side for every row in the split. | output: One pass/fail vertex-presence certificate per split-core vertex family. +- Layer `A4_edge_obstruction_atoms` [next]: For every selected pair, identify the exact reason the cross edge is missing. | output: One obstruction certificate per pair, preferably a square-divisor witness or explicit modular contradiction. +- Layer `A5_congruence_persistence_atoms` [done_literal]: Prove each edge obstruction is implied by the split congruence assumptions, not by accidental sampled N values. | output: A symbolic congruence proof per obstruction family. +- Layer `A6_matching_disjointness_atoms` [done_literal]: Prove the exported pairs form a matching by checking left and right uniqueness. | output: A deterministic disjointness certificate per split core. +- Layer `A7_K_envelope_atoms` [done_sampled_envelope]: Prove the symbolic core size is always at least the required K(N,x) throughout the split. | output: One K-envelope inequality certificate per split. +- Layer `A8_split_discharge_atoms` [p13_readiness_complete_p17_pending]: Promote each split from bounded support to a symbolic split lemma only after all lower atoms pass. | output: One theorem-facing split lemma per split key. +- Layer `A9_prime_lane_promotion` [p13_ready_for_D2_promotion]: Promote D2 once all p13 split lemmas pass, and promote D3 once all p17 split lemmas pass. | output: D2_p13_matching_lower_bound and D3_p17_matching_lower_bound can feed D4 without bounded-only caveats. +- Split atom `D2.1_persist_outP2=70_out25=9_smaller=side7` [high_p13_active_lane, needs_symbolic_persistence_proof]: p=13, split=outP2=70|out25=9|smaller=side7, witnesses=6, core=108, K=[88,89] +- Split atom packet `p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7`: JSON `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.json`, markdown `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md` +- Split atom `D2.2_persist_outP2=99_out25=6_smaller=side18` [high_p13_active_lane, needs_symbolic_persistence_proof]: p=13, split=outP2=99|out25=6|smaller=side18, witnesses=5, core=105, K=[85,85] +- Split atom packet `p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18`: JSON `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json`, markdown `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md` +- Split atom `D2.3_persist_outP2=99_out25=14_smaller=side7` [highest_singleton_profile, needs_symbolic_persistence_proof]: p=13, split=outP2=99|out25=14|smaller=side7, witnesses=1, core=108, K=[88,88] +- Split atom packet `p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7`: JSON `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json`, markdown `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md` +- Split atom `D3.1_persist_outP2=38_out25=23_smaller=side7` [supporting_p17_companion_lane, needs_symbolic_persistence_proof]: p=17, split=outP2=38|out25=23|smaller=side7, witnesses=10, core=109, K=[12,14] +- Split atom packet `p848_split_atom_packet_D3_1_persist_outP2_38_out25_23_smaller_side7`: JSON `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.json`, markdown `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.md` +- Split atom `D3.2_persist_outP2=251_out25=1_smaller=side18` [supporting_p17_companion_lane, needs_symbolic_persistence_proof]: p=17, split=outP2=251|out25=1|smaller=side18, witnesses=2, core=106, K=[10,11] +- Split atom packet `p848_split_atom_packet_D3_2_persist_outP2_251_out25_1_smaller_side18`: JSON `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.json`, markdown `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.md` +- Adjacent layer `B1_split_coverage_universe` [needed]: The split-core proof should not silently assume every future threatening row belongs to the current split keys. | focus: Create a checker that partitions every bounded threatening row by the split key and emits new split obligations whenever a refreshed verifier discovers a new key. +- Adjacent layer `B2_vertex_formula_extraction` [needed_if_vertices_move]: If core vertices are not literal constants across N, we need formulas for the moving vertex families before edge persistence is meaningful. | focus: Mine affine/residue formulas for common-core left/right vertices and verify them against every sampled witness row. +- Adjacent layer `B3_obstruction_witness_normal_form` [needed]: Edge persistence becomes deterministic only when every missing edge has a normalized obstruction witness. | focus: Normalize each missing edge into product-plus-one divisibility, square-witness, or explicit incompatibility schema. +- Adjacent layer `B4_all_N_handoff_guard` [needed_later]: Even after split cores are symbolic, the final 848 decision still needs a clean handoff from D2/D3/D4 into the all-N threshold route. | focus: Keep this separate from split-core work; do not let final threshold or endpoint-regime logic pollute the matching-core proof. +- Atomization task `implement_full_common_core_pair_export` [done]: Extend the matching-pattern miner so every split profile exports the full common matching core, not only commonMatchingPairSample. | completion: Each split profile has commonMatchingPairs.length === commonMatchingPairCount for p13 and p17. +- Atomization task `emit_split_atom_packets` [done]: Generate one atom packet per split with inputs, common pairs, K envelope, required lower-bound range, and falsifier boundary. | completion: The task list points at concrete split atom IDs instead of one broad D2/D3 persistence phrase. +- Atomization task `materialize_square_residue_successor_packets` [done]: Materialize square-residue successor packets for every p13 split profile so D2 can be discharged profile-by-profile. | completion: The packet manifest lists verified successor packet files for every p13 refinement condition. +- Atomization task `attack_top_square_residue_successor` [done_symbolic_family_verified]: Attack successor D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1: prove the 145 affected vertex-presence atoms as a symbolic square-residue subfamily. | completion: The successor packet is promoted to a symbolic vertex-family lemma or emits a still smaller deterministic obstruction. +- Atomization task `materialize_remaining_square_residue_successor_packets` [blocked_by_successor_family_proofs]: Materialize the remaining square-residue successor packets; 29 of 10 refinement conditions currently have packet files. | completion: Every refinement condition from the singleton p13 packet has a successor packet file and symbolic family check. +- Atomization task `emit_singleton_edge_obstruction_certificate` [done_literal_edge_certificate_verified]: Emit the literal edge-obstruction certificate for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7, proving every exported cross-edge obstruction has a checked squarefree product-plus-one certificate. | completion: The first packet manifest reports literal_edge_obstruction_certificate_verified for the singleton p13 packet. +- Atomization task `promote_singleton_edge_congruence_persistence` [done_literal_edge_persistence_verified]: Promote the singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from literal edge-obstruction certificates into A5 congruence-persistence families. | completion: Each edge-obstruction family is either proved from the split hypotheses or emits a sharper deterministic successor atom. +- Atomization task `promote_singleton_matching_disjointness_and_k_envelope` [done_literal_matching_sampled_k_verified]: Promote singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 through A6 matching disjointness and A7 K-envelope checks. | completion: The literal matching pairs are pairwise disjoint and the common-core count dominates the required K-envelope without bounded-only overclaim. +- Atomization task `assemble_singleton_split_discharge_readiness` [done_split_discharge_readiness_candidate]: Assemble split-discharge readiness for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from verified vertex successors, edge persistence, matching disjointness, and sampled K-envelope certificates. | completion: The packet either becomes a theorem-facing split lemma candidate with explicit all-N handoff gaps, or emits the first missing lower atom. +- Atomization task `attack_next_p13_split_profile` [done_p13_split_readiness_candidates]: All p13 split profiles have split-discharge readiness candidates; promote the D2 p13 lane through the explicit all-N handoff gaps next. | completion: D2 promotion either discharges the row-universe and symbolic-K handoff gaps or emits the first missing all-N atom. +- Atomization task `promote_d2_p13_all_n_handoff` [done_bounded_row_universe_stratified]: Bounded p13 row-universe stratification is audited; D2_p13_slack_dominance_symbolic_lift is now the symbolic all-N lift before D2 can be promoted. | completion: The D2 p13 lane either closes row-universe coverage and symbolic K(N,x), or emits the first missing all-N atom. +- Atomization task `attack_d2_p13_row_universe_stratification_lift` [done_bounded_slack_stratification_audited]: Lift the bounded p=13 row stratification into a symbolic theorem: the 49 non-tight residue/side strata remain slack-dominated above the tight split floor for all future rows, or the first failing stratum emits a new deterministic split packet. | completion: Every bounded p13 threat row is either assigned to a split profile, proved slack-dominated outside the tight split packet, or emitted as a new deterministic split atom. +- Atomization task `prove_d2_p13_slack_dominance_symbolic_lift` [done_bounded_formula_reduction_emitted]: Slack dominance reduced to D2_p13_non_tight_side_count_slack_floor_lift; prove the side-count floor next. | completion: The 49 non-tight p13 residue/side strata either get a symbolic slack-dominance proof, or the first failing stratum emits a deterministic successor split atom. +- Atomization task `prove_d2_p13_non_tight_side_count_slack_floor_lift` [done_weakest_side_count_atoms_emitted]: Weakest side-count floor atom packets are emitted; attack D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7 next. | completion: Either prove max(side7, side18) <= strictBaseThreshold - 1 - targetSlack for all non-tight p13 rows, or emit the weakest failing residue/side stratum as a deterministic atom. +- Atomization task `attack_weakest_p13_side_count_floor_atom` [done_structural_margin_decomposition_emitted]: Attack weakest p13 side-count floor atom D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7: prove its side-count inequality or split the first failing term. | completion: The weakest side-count floor packet either becomes a symbolic side-count lemma or emits a sharper deterministic sub-atom. +- Atomization task `prove_weakest_p13_structural_margin_atom` [done_moving_term_subatoms_emitted]: Prove structural margin lemma D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18 for outP2=70|out25=23|smaller=side7, or emit the first moving-term sub-atom. | completion: The structural margin inequality either gets a symbolic bound for candidateSize, vMax, dMax, rGreater, and the larger side count, or emits the first moving term as a sharper atom. +- Atomization task `prove_weakest_p13_dmax_bound_atom` [done_constant_bound_falsified_successor_atom_emitted]: The original dMax constant-bound atom is closed by a bounded falsifier and successor growth profile; continue with the current downstream moving-term atom. | completion: The dMax subatom either proves the uniform same-prime degree bound used by the structural margin, or emits the sharper term family that controls dMax. +- Atomization task `attack_weakest_p13_dmax_growth_atom` [done_dmax_growth_tail_profile_closed]: The dMax growth tail profile is closed through q>=587 for outP2=70|out25=23|smaller=side7; attack the residual dynamic margin next. | completion: The dMax growth atom either proves a symbolic envelope for the same-prime degree term or emits the first residue/floor-function sub-split controlling the degree growth. +- Atomization task `prove_weakest_p13_dmax_q2_progression_atom` [blocked_by_dmax_growth_profile]: Wait for the dMax growth profile to emit its first square-divisor progression atom. | completion: The q=2 progression contribution is bounded by a floor-function with exclusions, or the first unresolved exclusion class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q3_progression_atom` [blocked_by_q2_progression_certificate]: Wait for the q=2 progression proof to emit the q=3 square-divisor progression atom. | completion: The q=3 progression contribution is bounded by CRT floor-functions, or the first unresolved q=3 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q5_progression_atom` [blocked_by_q3_progression_certificate]: Wait for the q=3 progression proof to emit the q=5 square-divisor progression atom. | completion: The q=5 progression contribution is bounded by CRT floor-functions, or the first unresolved q=5 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q7_progression_atom` [blocked_by_q5_progression_certificate]: Wait for the q=5 progression proof to emit the q=7 square-divisor progression atom. | completion: The q=7 progression contribution is bounded by CRT floor-functions, or the first unresolved q=7 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q11_progression_atom` [blocked_by_q7_progression_certificate]: Wait for the q=7 progression proof to emit the q=11 square-divisor progression atom. | completion: The q=11 progression contribution is bounded by CRT floor-functions, or the first unresolved q=11 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q19_progression_atom` [blocked_by_q11_progression_certificate]: Wait for the q=11 progression proof to emit the q=19 square-divisor progression atom. | completion: The q=19 progression contribution is bounded by CRT floor-functions, or the first unresolved q=19 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q23_progression_atom` [blocked_by_q19_progression_certificate]: Wait for the q=19 progression proof to emit the q=23 square-divisor progression atom. | completion: The q=23 progression contribution is bounded by CRT floor-functions, or the first unresolved q=23 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q31_progression_atom` [blocked_by_q23_progression_certificate]: Wait for the q=23 progression proof to emit the q=31 square-divisor progression atom. | completion: The q=31 progression contribution is bounded by CRT floor-functions, or the first unresolved q=31 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_q251_progression_atom` [done_q251_progression_upper_bound_verified]: The q=251 dMax progression upper-bound certificate is present; attack the tail/recombination envelope next. | completion: The q=251 progression contribution is bounded by CRT floor-functions, or the first unresolved q=251 exclusion/overlap class becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_recombination_atom` [done_tail_scaffold_q13_residue_exclusion_verified]: The tail/recombination scaffold excludes q=13 by split residue; attack the first unresolved tail prime q=17 next. | completion: The verified q-components plus a tail estimate imply the required symbolic dMax growth envelope, or the first unresolved tail range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q17_progression_atom` [done_q17_tail_progression_upper_bound_verified]: The q=17 tail-prime upper-bound certificate is present; attack the plus-side q=19 tail complement next. | completion: The q=17 tail progression contribution is bounded by CRT floor functions for both same-prime witnesses, or the next unresolved tail prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q19_plus_progression_atom` [done_q19_plus_tail_progression_upper_bound_verified]: The plus-side q=19 tail complement is certified; backfill the earlier minus-side q=11 complement next. | completion: The plus-side q=19 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q11_minus_progression_atom` [done_q11_minus_tail_progression_upper_bound_verified]: The minus-side q=11 tail complement is certified; attack the plus-side q=23 complement next. | completion: The minus-side q=11 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q23_plus_progression_atom` [done_q23_plus_tail_progression_upper_bound_verified]: The plus-side q=23 tail complement is certified; attack the minus-side q=31 complement next. | completion: The plus-side q=23 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q31_minus_progression_atom` [done_q31_minus_tail_progression_upper_bound_verified]: The minus-side q=31 tail complement is certified; attack the minus-side q=251 complement next. | completion: The minus-side q=31 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q251_minus_progression_atom` [done_q251_minus_tail_progression_upper_bound_verified]: The minus-side q=251 tail complement is certified; attack the first remaining non-observed q=29 tail prime next. | completion: The minus-side q=251 tail contribution is bounded by its CRT floor function, or the next unresolved tail range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q29_progression_atom` [done_q29_tail_progression_upper_bound_verified]: The q=29 residual tail-prime component is certified; attack q=37 next, starting with the plus-side witness-divisibility exclusion. | completion: The q=29 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q37_progression_atom` [done_q37_tail_progression_upper_bound_verified]: The q=37 residual tail-prime component is certified; attack q=41 next as the first two-sided residual tail-prime CRT floor-bound. | completion: The q=37 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q41_progression_atom` [done_q41_tail_progression_upper_bound_verified]: The q=41 residual tail-prime component is certified; attack q=43 next, starting with the plus-side witness-divisibility exclusion. | completion: The q=41 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q43_progression_atom` [done_q43_tail_progression_upper_bound_verified]: The q=43 residual tail-prime component is certified; attack q=47 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=43 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q47_progression_atom` [done_q47_tail_progression_upper_bound_verified]: The q=47 residual tail-prime component is certified; attack q=53 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=47 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q53_progression_atom` [done_q53_tail_progression_upper_bound_verified]: The q=53 residual tail-prime component is certified; attack q=59 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=53 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q59_progression_atom` [done_q59_tail_progression_upper_bound_verified]: The q=59 residual tail-prime component is certified; attack q=61 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=59 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q61_progression_atom` [done_q61_tail_progression_upper_bound_verified]: The q=61 residual tail-prime component is certified; attack q=67 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=61 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q67_progression_atom` [done_q67_tail_progression_upper_bound_verified]: The q=67 residual tail-prime component is certified; attack q=71 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=67 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q71_progression_atom` [done_q71_tail_progression_upper_bound_verified]: The q=71 residual tail-prime component is certified; attack q=73 next, starting with the minus-side witness-divisibility exclusion. | completion: The q=71 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q73_progression_atom` [done_q73_tail_progression_upper_bound_verified]: The q=73 residual tail-prime component is certified; attack q=79 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=73 tail contribution is bounded by the plus-side CRT floor function and minus-side exclusion, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q79_progression_atom` [done_q79_tail_progression_upper_bound_verified]: The q=79 residual tail-prime component is certified; attack q=83 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=79 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q83_progression_atom` [done_q83_tail_progression_upper_bound_verified]: The q=83 residual tail-prime component is certified; attack q=89 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=83 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q89_progression_atom` [done_q89_tail_progression_upper_bound_verified]: The q=89 residual tail-prime component is certified; attack q=97 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=89 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q97_progression_atom` [done_q97_tail_progression_upper_bound_verified]: The q=97 residual tail-prime component is certified; attack q=101 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=97 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q101_progression_atom` [done_q101_tail_progression_upper_bound_verified]: The q=101 residual tail-prime component is certified; attack q=103 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=101 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q103_progression_atom` [done_q103_tail_progression_upper_bound_verified]: The q=103 residual tail-prime component is certified; attack q=107 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=103 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q107_progression_atom` [done_q107_tail_progression_upper_bound_verified]: The q=107 residual tail-prime component is certified; attack q=109 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=107 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q109_progression_atom` [done_q109_tail_progression_upper_bound_verified]: The q=109 residual tail-prime component is certified; attack q=113 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=109 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q113_progression_atom` [done_q113_tail_progression_upper_bound_verified]: The q=113 residual tail-prime component is certified; attack q=127 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=113 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q127_progression_atom` [done_q127_tail_progression_upper_bound_verified]: The q=127 residual tail-prime component is certified; attack q=131 next, combining the minus-side witness-divisibility exclusion with the plus-side CRT floor bound. | completion: The q=127 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q131_progression_atom` [done_q131_tail_progression_upper_bound_verified]: The q=131 residual tail-prime component is certified; attack q=137 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=131 tail contribution is bounded by the minus-side exclusion and plus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q137_progression_atom` [done_q137_tail_progression_upper_bound_verified]: The q=137 residual tail-prime component is certified; attack q=139 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=137 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q139_progression_atom` [done_q139_tail_progression_upper_bound_verified]: The q=139 residual tail-prime component is certified; attack q=149 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=139 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q149_progression_atom` [done_q149_tail_progression_upper_bound_verified]: The q=149 residual tail-prime component is certified; attack q=151 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=149 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q151_progression_atom` [done_q151_tail_progression_upper_bound_verified]: The q=151 residual tail-prime component is certified; attack q=157 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=151 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q157_progression_atom` [done_q157_tail_progression_upper_bound_verified]: The q=157 residual tail-prime component is certified; attack q=163 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=157 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q163_progression_atom` [done_q163_tail_progression_upper_bound_verified]: The q=163 residual tail-prime component is certified; attack q=167 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=163 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q167_progression_atom` [done_q167_tail_progression_upper_bound_verified]: The q=167 residual tail-prime component is certified; attack q=173 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=167 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q173_progression_atom` [done_q173_tail_progression_upper_bound_verified]: The q=173 residual tail-prime component is certified; attack q=179 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=173 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q179_progression_atom` [done_q179_tail_progression_upper_bound_verified]: The q=179 residual tail-prime component is certified; attack q=181 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=179 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q181_progression_atom` [done_q181_tail_progression_upper_bound_verified]: The q=181 residual tail-prime component is certified; attack q=191 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=181 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q191_progression_atom` [done_q191_tail_progression_upper_bound_verified]: The q=191 residual tail-prime component is certified; attack q=193 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=191 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q193_progression_atom` [done_q193_tail_progression_upper_bound_verified]: The q=193 residual tail-prime component is certified; attack q=197 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=193 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q197_progression_atom` [done_q197_tail_progression_upper_bound_verified]: The q=197 residual tail-prime component is certified; attack q=199 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=197 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q199_progression_atom` [done_q199_tail_progression_upper_bound_verified]: The q=199 residual tail-prime component is certified; attack q=211 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=199 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q211_progression_atom` [done_q211_tail_progression_upper_bound_verified]: The q=211 residual tail-prime component is certified; attack q=223 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=211 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q223_progression_atom` [done_q223_tail_progression_upper_bound_verified]: The q=223 residual tail-prime component is certified; attack q=227 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=223 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q227_progression_atom` [done_q227_tail_progression_upper_bound_verified]: The q=227 residual tail-prime component is certified; attack q=229 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=227 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q229_progression_atom` [done_q229_tail_progression_upper_bound_verified]: The q=229 residual tail-prime component is certified; attack q=233 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=229 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q233_progression_atom` [done_q233_tail_progression_upper_bound_verified]: The q=233 residual tail-prime component is certified; attack q=239 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=233 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q239_progression_atom` [done_q239_tail_progression_upper_bound_verified]: The q=239 residual tail-prime component is certified; attack q=241 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=239 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q241_progression_atom` [done_q241_tail_progression_upper_bound_verified]: The q=241 residual tail-prime component is certified; q=251 is already covered, so attack q=257 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=241 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q257_progression_atom` [done_q257_tail_progression_upper_bound_verified]: The q=257 residual tail-prime component is certified; attack q=263 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=257 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q263_progression_atom` [done_q263_tail_progression_upper_bound_verified]: The q=263 residual tail-prime component is certified; attack q=269 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=263 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q269_progression_atom` [done_q269_tail_progression_upper_bound_verified]: The q=269 residual tail-prime component is certified; attack q=271 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=269 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q271_progression_atom` [done_q271_tail_progression_upper_bound_verified]: The q=271 residual tail-prime component is certified; attack q=277 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=271 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q277_progression_atom` [done_q277_tail_progression_upper_bound_verified]: The q=277 residual tail-prime component is certified; attack q=281 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=277 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q281_progression_atom` [done_q281_tail_progression_upper_bound_verified]: The q=281 residual tail-prime component is certified; attack q=283 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=281 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q283_progression_atom` [done_q283_tail_progression_upper_bound_verified]: The q=283 residual tail-prime component is certified; attack q=293 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=283 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q293_progression_atom` [done_q293_tail_progression_upper_bound_verified]: The q=293 residual tail-prime component is certified; attack q=307 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=293 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q307_progression_atom` [done_q307_tail_progression_upper_bound_verified]: The q=307 residual tail-prime component is certified; attack q=311 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=307 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q311_progression_atom` [done_q311_tail_progression_upper_bound_verified]: The q=311 residual tail-prime component is certified; attack q=313 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=311 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q313_progression_atom` [done_q313_tail_progression_upper_bound_verified]: The q=313 residual tail-prime component is certified; attack q=317 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=313 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q317_progression_atom` [done_q317_tail_progression_upper_bound_verified]: The q=317 residual tail-prime component is certified; attack q=331 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=317 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q331_progression_atom` [done_q331_tail_progression_upper_bound_verified]: The q=331 residual tail-prime component is certified; attack q=337 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=331 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q337_progression_atom` [done_q337_tail_progression_upper_bound_verified]: The q=337 residual tail-prime component is certified; attack q=347 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=337 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q347_progression_atom` [done_q347_tail_progression_upper_bound_verified]: The q=347 residual tail-prime component is certified; attack q=349 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=347 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q349_progression_atom` [done_q349_tail_progression_upper_bound_verified]: The q=349 residual tail-prime component is certified; attack q=353 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=349 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q353_progression_atom` [done_q353_tail_progression_upper_bound_verified]: The q=353 residual tail-prime component is certified; attack q=359 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=353 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q359_progression_atom` [done_q359_tail_progression_upper_bound_verified]: The q=359 residual tail-prime component is certified; attack q=367 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=359 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q367_progression_atom` [done_q367_tail_progression_upper_bound_verified]: The q=367 residual tail-prime component is certified; attack q=373 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=367 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q373_progression_atom` [done_q373_tail_progression_upper_bound_verified]: The q=373 residual tail-prime component is certified; attack q=379 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=373 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q379_progression_atom` [done_q379_tail_progression_upper_bound_verified]: The q=379 residual tail-prime component is certified; attack q=383 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=379 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q383_progression_atom` [done_q383_tail_progression_upper_bound_verified]: The q=383 residual tail-prime component is certified; attack q=389 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=383 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q389_progression_atom` [done_q389_tail_progression_upper_bound_verified]: The q=389 residual tail-prime component is certified; attack q=397 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=389 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q397_progression_atom` [done_q397_tail_progression_upper_bound_verified]: The q=397 residual tail-prime component is certified; attack q=401 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=397 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q401_progression_atom` [done_q401_tail_progression_upper_bound_verified]: The q=401 residual tail-prime component is certified; attack q=409 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=401 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q409_progression_atom` [done_q409_tail_progression_upper_bound_verified]: The q=409 residual tail-prime component is certified; attack q=419 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=409 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q419_progression_atom` [done_q419_tail_progression_upper_bound_verified]: The q=419 residual tail-prime component is certified; attack q=421 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=419 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q421_progression_atom` [done_q421_tail_progression_upper_bound_verified]: The q=421 residual tail-prime component is certified; attack q=431 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=421 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q431_progression_atom` [done_q431_tail_progression_upper_bound_verified]: The q=431 residual tail-prime component is certified; attack q=433 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=431 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q433_progression_atom` [done_q433_tail_progression_upper_bound_verified]: The q=433 residual tail-prime component is certified; attack q=439 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=433 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q439_progression_atom` [done_q439_tail_progression_upper_bound_verified]: The q=439 residual tail-prime component is certified; attack q=443 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=439 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q443_progression_atom` [done_q443_tail_progression_upper_bound_verified]: The q=443 residual tail-prime component is certified; attack q=449 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=443 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q449_progression_atom` [done_q449_tail_progression_upper_bound_verified]: The q=449 residual tail-prime component is certified; attack q=457 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=449 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q457_progression_atom` [done_q457_tail_progression_upper_bound_verified]: The q=457 residual tail-prime component is certified; attack q=461 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=457 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q461_progression_atom` [done_q461_tail_progression_upper_bound_verified]: The q=461 residual tail-prime component is certified; attack q=463 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=461 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q463_progression_atom` [done_q463_tail_progression_upper_bound_verified]: The q=463 residual tail-prime component is certified; attack q=467 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=463 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q467_progression_atom` [done_q467_tail_progression_upper_bound_verified]: The q=467 residual tail-prime component is certified; attack q=479 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=467 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q479_progression_atom` [done_q479_tail_progression_upper_bound_verified]: The q=479 residual tail-prime component is certified; attack q=487 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=479 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q487_progression_atom` [done_q487_tail_progression_upper_bound_verified]: The q=487 residual tail-prime component is certified; attack q=491 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=487 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q491_progression_atom` [done_q491_tail_progression_upper_bound_verified]: The q=491 residual tail-prime component is certified; attack q=499 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=491 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q499_progression_atom` [done_q499_tail_progression_upper_bound_verified]: The q=499 residual tail-prime component is certified; attack q=503 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=499 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q503_progression_atom` [done_q503_tail_progression_upper_bound_verified]: The q=503 residual tail-prime component is certified; attack q=509 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=503 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q509_progression_atom` [done_q509_tail_progression_upper_bound_verified]: The q=509 residual tail-prime component is certified; attack q=521 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=509 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q521_progression_atom` [done_q521_tail_progression_upper_bound_verified]: The q=521 residual tail-prime component is certified; attack q=523 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=521 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q523_progression_atom` [done_q523_tail_progression_upper_bound_verified]: The q=523 residual tail-prime component is certified; attack q=541 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=523 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q541_progression_atom` [done_q541_tail_progression_upper_bound_verified]: The q=541 residual tail-prime component is certified; attack q=547 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=541 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q547_progression_atom` [done_q547_tail_progression_upper_bound_verified]: The q=547 residual tail-prime component is certified; attack q=557 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=547 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q557_progression_atom` [done_q557_tail_progression_upper_bound_verified]: The q=557 residual tail-prime component is certified; attack q=563 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=557 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q563_progression_atom` [done_q563_tail_progression_upper_bound_verified]: The q=563 residual tail-prime component is certified; attack q=569 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=563 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q569_progression_atom` [done_q569_tail_progression_upper_bound_verified]: The q=569 residual tail-prime component is certified; attack q=571 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=569 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q571_progression_atom` [done_q571_tail_progression_upper_bound_verified]: The q=571 residual tail-prime component is certified; attack q=577 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=571 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q577_progression_atom` [done_q577_tail_progression_upper_bound_verified]: The q=577 residual tail-prime component is certified; attack q=587 next as a two-sided residual tail-prime CRT floor-bound. | completion: The q=577 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_weakest_p13_dmax_tail_q587_progression_atom` [done_q587_tail_progression_upper_bound_verified]: The q=587 residual tail-prime component is certified; lift the bounded q>=587 zero-floor profile before any aggregate dMax tail claim. | completion: The q=587 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom. +- Atomization task `prove_p13_dmax_tail_q_ge_587_parametric_zero_floor_lift` [done_q_ge_587_bounded_zero_floor_lift_verified]: The q>=587 bounded zero-floor lift is verified; attack the residual dynamic margin next. | completion: The q>=587 tail profile is converted into a theorem-facing aggregate lemma, or the first concrete exceptional prime/range is emitted. +- Atomization task `prove_p13_side18_residual_dynamic_margin_atom` [done_exact_mixed_symbolic_lift_decomposed]: The exact mixed-margin symbolic lift is decomposed; prove the matching-injection sublemma next. | completion: The side18 residual dynamic margin is proved symbolically, or the first exact moving-count/rGreater obstruction becomes the next atom. +- Atomization task `prove_p13_side18_residual_dynamic_margin_symbolic_lift` [done_symbolic_lift_falsified_exact_mixed_decomposition_emitted]: The false side18 threshold lift has been replaced by an exact mixed-margin decomposition; prove the matching injection next. | completion: The side18 threshold inequality is proved symbolically for this split, or the first exact obstruction becomes a sharper side-count/rGreater successor atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_symbolic_lift` [done_symbolic_lift_decomposed_first_sublemma_emitted]: The exact mixed-margin symbolic lift is reduced to matching-injection plus margin-floor sublemmas; prove matching injection first. | completion: The exact mixed-margin successor is proved symbolically for the outsider-6323 family, or the first residue/root-universe obstruction becomes the next deterministic atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection` [done_q17_residual_window_relaxed_fallback_menu_lift_emitted]: The q17 residual p13-expanded fallback menu is falsified and repaired only after relaxing the local window; prove the window-relaxed fallback selector next. | completion: The matching injection saturates the side7-compatible set for this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A parametric insertion/replacement rule saturates side7 for every future row in this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A finite direct/replacement augmenting-path menu saturates side7 for every future event row, or the first event outside the menu becomes the next deterministic atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: The delta -1089 branch is proved and merged into the menu, or the first future row requiring another direct delta or longer augmenting path becomes the next deterministic atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: The delta -39 branch is proved and merged into the menu, or the first future row requiring another direct delta or longer augmenting path becomes the next deterministic atom. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A residue/block delta-selection theorem saturates side7 without adding singleton delta siblings, or the first uncovered event row becomes the next obstruction packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A residue/mod-square selector produces a side18-compatible direct endpoint for every future side7 event row, or the first uncovered event row becomes the next obstruction packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: The selected four-slot endpoint is a squarefree missing-cross edge for every future side7 row, or the first square-divisor exception becomes a bounded replacement-path packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A symbolic replacement menu handles the selected endpoint square-divisor exceptions without adding singleton deltas, or the first uncovered replacement row becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A symbolic finite-window lift covers all selected-cross exceptions without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A symbolic right-compatibility escape selector replaces the finite-window miss family without adding singleton delta siblings, or the first row with no bounded side18 squarefree repair becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A symbolic small-prime CRT selector handles the right-compatibility escape rows, or the first finite-window miss outside that selector becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A symbolic cross-squarefree fallback selector handles the p=7 endpoint cross-bad rows, or the first finite-window miss outside that fallback rule becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift` [blocked_by_bounded_matching_profile]: Wait for the bounded matching-injection profile to identify the parametric insertion target. | completion: A symbolic finite endpoint-menu lift covers all p=7 endpoint cross-bad rows without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift` [done_q17_residual_window_relaxed_fallback_menu_lift_emitted]: The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed selector target. | completion: A symbolic sieve/hitting lemma proves cross-squarefree endpoint existence for the menu, or the first fully cross-blocked row becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift` [done_q17_residual_window_relaxed_fallback_menu_emitted]: The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed fallback selector. | completion: A symbolic p7-shift plus q17 residual lemma proves cross-squarefree endpoint existence for the menu, or the first q17 residual cross-bad row becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift` [done_window_relaxed_fallback_menu_emitted]: The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu. | completion: A symbolic fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully fallback-blocked row becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift` [done_window_relaxed_fallback_menu_emitted]: The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu. | completion: A symbolic expanded fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully expanded-menu-blocked row becomes the next deterministic packet. +- Atomization task `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift` [highest]: Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row. | completion: A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet. +- Atomization task `start_singleton_p13_profile` [done_successor_packets_emitted]: Attack the singleton p13 split outP2=99|out25=14|smaller=side7 first to determine whether it is a real symbolic class or an under-split boundary artifact. | completion: The singleton split either gets a persistence atom or emits a sharper split key. + +## Structural Verifier Audit + +- Status: `blocked` +- Conclusion: The external verifier is useful as an idea source, but it is blocked from canonical promotion. +- Blockers: `sawhney_handoff_not_claimed_at_1e7, base_exchange_mask_covers_both_principal_sides` +- Next action: Keep the external computation in EXTERNAL_VERIFICATION_LEDGER as blocked, not promoted. +- Next action: Patch or independently reimplement the structural verifier with both base sides covered. +- Next action: Replace the false 10^7 Sawhney handoff with a repo-audited explicit threshold before any all-N claim. +- Next action: Port only the outsider-clique inequality shape into a repo-owned structural verifier lane. + +## Base-Side Scout + +- Status: `counterexample_to_global_7_side_domination_found` +- Interval: `1..200` +- Max side18-minus-side7: `1` +- Side18 global exceedance found: `yes` +- First side18 exceedance: `{"N":143,"maxSide7":2,"maxSide18":3,"maxSide7Outsider":41,"maxSide18Outsider":117,"maxSide18Minus7":1,"maxPerOutsider18Minus7":1,"maxPerOutsider7Minus18":1,"perOutsider18Winner":{"outsider":117,"side7":2,"side18":3,"delta18Minus7":1},"perOutsider7Winner":{"outsider":38,"side7":1,"side18":0,"delta7Minus18":1}}` +- Boundary: This scout compares principal-base compatibility counts on a finite interval only. It does not prove all-N base-side domination. + +## Two-Sided Structural Scout + +- Status: `side_specific_bounds_pass_but_union_bound_fails` +- Assessed range: `7307..7600` +- Union checks pass: `no` +- Union failures: `64` +- First union failure: `{"N":7307,"p":13,"p2":169,"rawPlus":43,"rawMinus":43,"vMax":43,"activePlus":40,"activeMinus":39,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":110,"sMaxSide18Witness":1789,"sMaxUnion":218,"sMaxUnionWitness":1789,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":293,"side7CandidateSize":293,"side18CandidateSize":292,"side7Bound":272,"side18Bound":271,"unionBound":379,"side7Margin":21,"side18Margin":22,"unionMargin":-86,"side7Pass":true,"side18Pass":true,"unionPass":false}` +- Worst union row: `{"N":7552,"p":13,"p2":169,"rawPlus":45,"rawMinus":45,"vMax":45,"activePlus":42,"activeMinus":41,"sMaxSide7":113,"sMaxSide7Witness":4831,"sMaxSide18":114,"sMaxSide18Witness":1789,"sMaxUnion":225,"sMaxUnionWitness":1789,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":103,"candidateSize":302,"side7CandidateSize":302,"side18CandidateSize":302,"side7Bound":279,"side18Bound":280,"unionBound":391,"side7Margin":23,"side18Margin":22,"unionMargin":-89,"side7Pass":true,"side18Pass":true,"unionPass":false}` +- Boundary: The union-base bound is safe but intentionally loose: it allows every compatible element from both principal sides even though a real clique may not be able to mix them. + +## Mixed-Base Failure Scout + +- Status: `sampled_union_failures_repaired_by_mixed_base_clique` +- Analyzed rows: `8` +- Mixed failures: `0` +- All analyzed rows pass mixed bound: `yes` +- Minimum mixed margin: `22` +- Worst mixed row: `{"source":"first_union_failure","N":7307,"p":13,"outsider":1789,"candidateSize":293,"sMaxSide7":111,"sMaxSide18":110,"sMaxUnion":218,"mixedBaseCliqueSize":110,"mixedBaseSide7Count":0,"mixedBaseSide18Count":110,"mixedBaseCliqueMatchesSingleSide":true,"mixedBound":271,"mixedMargin":22,"mixedPass":true,"originalUnionMargin":-86,"improvementOverUnion":108,"vMax":43,"dMax":18,"rGreater":100,"exampleMixedBaseClique":[43,68,143,243,268,293,343,443,518,543,643,743,843,943,968,1043,1143,1193,1243,1343,1418,1443,1468,1543,1643,1743,1843,1868,1943,2043,2093,2143,2243,2318,2343,2443,2543,2643,2693,2743,2768,2843,2918,2943,2993,3043,3143,3218,3243,3343,3443,3543,3643,3668,3743,3768,3843,3893,3918,3943,4043,4068,4118,4143,4243,4343,4443,4493,4543,4568,4618,4643,4743,4793,4843,4943,5018,5043,5143,5243,5343,5443,5468,5543,5643,5693,5743,5843,5918,5943,6043,6143,6243,6293,6343,6368,6418,6443,6543,6593,6643,6668,6743,6818,6843,6943,7043,7143,7243,7268]}` +- Boundary: This scout exactly solves the mixed-base clique on selected union-failure rows from the two-sided structural scout. It does not yet certify every structural breakpoint. + +## Full Mixed-Base Structural Verifier + +- Status: `bounded_full_mixed_base_structural_verifier_certified` +- Assessed range: `7307..7600` +- All mixed checks pass: `yes` +- Mixed failures: `0` +- Threatening outsider checks: `1733` +- Minimum certified margin: `20` +- Worst exact mixed row: `{"N":7343,"p":13,"p2":169,"rawPlus":44,"rawMinus":43,"vMax":44,"activePlus":41,"activeMinus":39,"activeOutsiderCount":80,"sMaxSide7":111,"sMaxSide7Witness":4831,"sMaxSide18":112,"sMaxSide18Witness":5309,"sMaxUnion":220,"sMaxUnionWitness":5309,"dMax":18,"dMaxWitness":{"side":"plus","value":1591},"rGreater":100,"candidateSize":294,"side7CandidateSize":294,"side18CandidateSize":294,"side7Bound":273,"side18Bound":274,"unionBound":382,"strictBaseThreshold":132,"side7Margin":21,"side18Margin":20,"unionMargin":-88,"side7Pass":true,"side18Pass":true,"unionPass":false,"certificateMode":"exact_mixed_base","threateningOutsiderCount":40,"exactMixedCheckCount":40,"sMaxMixed":112,"sMaxMixedWitness":5309,"mixedBound":274,"mixedMargin":20,"mixedPass":true,"maxImprovementOverUnion":109,"worstThreat":{"outsider":5309,"unionCount":220,"mixedBaseCliqueSize":112,"matchingSizeInMissingCrossGraph":108,"compatibleSide7Count":108,"compatibleSide18Count":112,"mixedCliqueSide7Count":0,"mixedCliqueSide18Count":112,"exampleMixedBaseClique":[43,118,143,243,268,343,368,443,543,568,643,718,743,793,843,943,1018,1043,1068,1143,1243,1318,1343,1443,1468,1493,1543,1618,1643,1693,1743,1843,1918,1943,2043,2143,2243,2343,2368,2443,2543,2593,2643,2718,2743,2818,2843,2943,3043,3143,3243,3268,3343,3443,3493,3543,3643,3718,3743,3843,3943,4043,4143,4168,4243,4343,4393,4443,4543,4618,4643,4743,4843,4943,5043,5068,5143,5168,5243,5293,5343,5443,5518,5543,5643,5718,5743,5843,5943,5968,6043,6143,6193,6243,6343,6393,6418,6443,6543,6643,6743,6768,6843,6868,6943,7043,7093,7143,7168,7243,7318,7343]},"threatMatchingSummary":{"threatCount":40,"minRequiredMatchingLowerBound":29,"maxRequiredMatchingLowerBound":89,"minActualMatching":79,"maxActualMatching":109,"minMatchingSlack":19,"allThreatsMeetRequiredLowerBound":true,"allThreatsSaturateSmallerSide":true,"tightestThreats":[{"outsider":5309,"outsiderMod25":9,"compatibleSide7Count":108,"compatibleSide18Count":112,"requiredMatchingLowerBound":89,"matchingSizeInMissingCrossGraph":108,"matchingSlack":19,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":1789,"outsiderMod25":14,"compatibleSide7Count":108,"compatibleSide18Count":111,"requiredMatchingLowerBound":88,"matchingSizeInMissingCrossGraph":108,"matchingSlack":20,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":4831,"outsiderMod25":6,"compatibleSide7Count":111,"compatibleSide18Count":105,"requiredMatchingLowerBound":85,"matchingSizeInMissingCrossGraph":105,"matchingSlack":20,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side7"},{"outsider":3281,"outsiderMod25":6,"compatibleSide7Count":108,"compatibleSide18Count":110,"requiredMatchingLowerBound":87,"matchingSizeInMissingCrossGraph":108,"matchingSlack":21,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"},{"outsider":6323,"outsiderMod25":23,"compatibleSide7Count":105,"compatibleSide18Count":110,"requiredMatchingLowerBound":84,"matchingSizeInMissingCrossGraph":105,"matchingSlack":21,"saturatesSmallerSide":true,"dominantMixedCliqueSide":"side18"}]}}` +- Boundary: Every witness-prime block and structural breakpoint in the assessed range is certified either by the safe union bound or by exact mixed-base clique checks for every threatening active outsider. + +## Structural Lift Miner + +- Status: `structural_lift_obligation_packet_ready` +- Mined exact rows: `64` +- Coverage complete: `yes` +- Primary exact primes: `13, 17` +- Next theorem lane: `formalize_cross_side_matching_bound_then_exact_prime_margin_lift` +- Obligation `p848_cross_side_matching_bound` [critical, bounded_evidence_ready]: For each threatening outsider, the missing cross-edge graph between the 7 mod 25 and 18 mod 25 compatible base sides has a matching large enough to force mixedCliqueSize below the strict base threshold. +- Obligation `p848_exact_prime_margin_lift` [critical, bounded_evidence_ready]: For the exact-mixed witness-prime families 13, 17, prove candidateSize > sMaxMixed + vMax + dMax + rGreater either eventually or by a finite periodic residue split. +- Obligation `p848_union_bound_tail_lift` [high, bounded_evidence_ready]: Prove that every non-exact witness-prime block is certified by the safe union bound past the base interval, with only finitely many exceptional rows delegated to exact verification. +- Obligation `p848_top_repeating_family_lift` [high, bounded_evidence_ready]: Use family p=17|Nmod25=7|d=minus|clique=side7|outMod25=1 as the first symbolic family to formalize. +- Recommended next: `mine_matching_pattern_witnesses` [critical] The active D2 atom needs a symbolic matching construction, and the matching-pattern miner extracts actual tight-row missing-cross pairs without bloating the verifier artifact. | command: `erdos number-theory dispatch 848 --apply --action matching_pattern_miner --matching-pattern-prime 13` +- Recommended next: `formalize_cross_side_matching_bound` [critical] The full verifier succeeds exactly because mixed-base cliques are much smaller than the safe union overcount; this is the theorem-shaped repair mechanism. | command: `erdos problem formalization-work-refresh 848` +- Recommended next: `formalize_exact_prime_margin_lift` [critical] The mined rows identify which witness-prime blocks still need symbolic margin control after the union-bound rows are separated. | command: `erdos problem formalization 848` +- Recommended next: `extend_structural_range_after_lift_target` [high] Once the first symbolic family is named, extend the bounded verifier beyond 7307..7600 to falsify or strengthen the family before claiming a lift. | command: `erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min 7307 --structural-max 15200` +- Boundary: This miner extracts proof obligations from a bounded structural verifier. It does not certify any N outside the source verifier range. + +## Structural Lift Reference Backlog + +- Status: `active` +- North star: Turn the bounded mixed-base structural verifier into an all-N proof lane by proving the cross-side matching reduction, then the p=13 and p=17 margin lifts, while keeping exact finite coverage separate. +- Current packet: `D_matching_lower_bounds` +- First actionable step: `D2_p13_matching_lower_bound` +- Target step: `D4_matching_bound_implies_sMaxMixed_bound` +- Completion rule: Each step is complete only when it has a statement, hypotheses, proof sketch or proof artifact, falsifier boundary, dependencies, and the next downstream step updated. +- Reference next: `prove_p13_matching_lower_bound` [critical] Prove the symbolic p=13 lower bound that explains why maxMatching(H_{x,N}) always reaches the D1-extracted K(N,x) target in the tightest current exact-mixed family. | command: `erdos problem formalization-work-refresh 848` +- Reference next: `regression_check_C6_against_verifier` [high] Keep the discharged C6 mixed-clique matching formula regression-checked against representative full-verifier rows. | command: `erdos number-theory dispatch 848 --apply --action structural_lift_miner` +- Reference next: `extract_p13_residue_matching_pattern` [high] For the top p=13 families, extract the residue-block pattern behind the smaller-side-saturating matchings so D2 can become a symbolic construction rather than bounded evidence. | command: `erdos number-theory dispatch 848 --apply --action structural_lift_miner` +- Boundary: This checklist records a proof plan and dependencies. It does not certify any new N by itself. + +## Template Loop + +- `freeze_current_state`: Freeze the current north star and active theorem packet | Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 848` +- `audit_theorem_surfaces`: Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 848` +- `verify_canonical_inputs`: Verify canonical bridge inputs against the latest harvested compute artifacts | Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos number-theory bridge-refresh 848` +- `verify_primary_structural_hook`: Verify the primary structural hook remains canonical | Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 848` +- `verify_verifier_boundary`: Verify the current exact/verifier boundary and next target | Verify that the certified interval 1..40500 and the next verifier target remain current across the pack surfaces. | completion: The interval work queue or verifier boundary packet still matches the theorem-facing status. | command: `erdos number-theory dispatch 848` +- `apply_granular_breakdown`: Apply ORP granular breakdown before execution | Run ORP granular breakdown on the active topic `problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound` and compress it into one active target plus one verification command. | completion: The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification. | command: `orp mode breakdown granular-breakdown --topic "problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound" --json` +- `execute_current_work_packet`: Explain the 282 First-Failure Mechanism | Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. | command: `erdos problem formalization-work 848` +- `refresh_and_rerank`: Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 848` + +## Current Objective + +- Formalization id: `p848_282_alignment_formalization_v1` +- Focus id: `formalize_282_alignment` +- Title: Formalize the 282 Obstruction Alignment +- Active work id: `p848_282_first_failure_mechanism_packet_v1` +- Active work title: Explain the 282 First-Failure Mechanism +- Active work status: `in_progress` + +## Current Tasks + +- `freeze_current_state` [ready] Freeze the current north star and active theorem packet | Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 848` +- `audit_theorem_surfaces` [ready] Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 848` +- `verify_canonical_inputs` [ready] Verify canonical bridge inputs against the latest harvested compute artifacts | Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos number-theory bridge-refresh 848` +- `verify_primary_structural_hook` [ready] Verify the primary structural hook remains canonical | Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 848` +- `verify_verifier_boundary` [ready] Verify the current exact/verifier boundary and next target | Verify that the certified interval 1..40500 and the next verifier target remain current across the pack surfaces. | completion: The interval work queue or verifier boundary packet still matches the theorem-facing status. | command: `erdos number-theory dispatch 848` +- `apply_granular_breakdown` [ready] Apply ORP granular breakdown before execution | Run ORP granular breakdown on the active topic `problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound` and compress it into one active target plus one verification command. | completion: The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification. | command: `orp mode breakdown granular-breakdown --topic "problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound" --json` +- `execute_current_work_packet` [in_progress] Explain the 282 First-Failure Mechanism | Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class. | The live 137720141 / 282 obstruction packet is checked at finite-menu scope; the remaining theorem work is the narrower symbolic-lift boundary. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. | command: `erdos problem formalization-work 848` +- `discharge_first_remaining_gap` [ready] Discharge the first remaining gap in the active theorem packet | Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. | This is the sharpest unresolved statement already named by the active theorem-work packet. | completion: The first remaining gap is either resolved or replaced by a more precise successor gap. | command: `erdos problem formalization-work-refresh 848` +- `refresh_and_rerank` [ready] Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 848` + +## Completed Anchors + +- `completed_anchor_1` [done] The family-menu boundary agrees with the tracked-tail boundary: the earliest 282-failing family row is also representative 137720141. +- `completed_anchor_2` [done] The extra witness has been isolated: 841 belongs to the 282 repair row, not to the six defining tuple moduli of the shared-prefix class. +- `completed_anchor_3` [done] The witness boundary is locally frozen: no earlier family-menu row gives tail 282 residue 0 modulo 841. +- `completed_anchor_4` [done] The representative residue is structurally derived: the tuple-row CRT projects the shared-prefix obstruction class to 504 mod 841. +- `completed_anchor_5` [done] The congruence boundary is isolated: residue class 504 mod 841 is the failure class for tracked tail 282 and no other tracked coprime tail. +- `completed_anchor_6` [done] The row-index boundary is isolated: within the shared-prefix row progression, tracked anchor 282 is the only tracked anchor whose 841 witness class starts at row index 0. +- `completed_anchor_7` [done] The row-start derivation is explicit: the boundary representative already lies on the 282 witness class modulo 841, so the row equation reduces to t ≡ 0 (mod 841). +- `completed_anchor_8` [done] The menu-level first-occurrence boundary is isolated: 137720141 is the first family-menu representative in the 282 witness class 504 mod 841, so no earlier menu row can fail via witness 841 on that same congruence class. +- `completed_anchor_9` [done] The mechanism falsifier boundary is explicit: a lower representative in residue class 504 mod 841, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment would all break this packet. +- `completed_anchor_10` [done] The 132-row lift is explicit: adding the 132 row forces the tuple-row CRT class from residue 400 mod 841 to the boundary residue 504 mod 841 via k ≡ 147 (mod 289). +- `completed_anchor_11` [done] The activation boundary is explicit: before anchor 132 no tuple-row CRT step lands on any tracked failure residue mod 841, anchor 132 creates the unique tracked 282 match at residue 504, and anchor 182 preserves that same unique match. +- `completed_anchor_12` [done] The 132-activation pattern is reusable on the current finite menu: 17 failing witness rows first activate their own failing tracked tail at anchor 132. +- `completed_anchor_13` [done] The finite-menu 132-activation pattern has been promoted into lemma schema p848_finite_menu_132_target_activation_schema_v1 with hypotheses, conclusion, falsifier boundary, and 17 row certificates. +- `completed_anchor_14` [done] The 17 finite-menu 132-activation row certificates replay successfully in checker p848_132_activation_row_certificate_checker_v1. +- `completed_anchor_15` [done] The 132-row lift to residue 504 mod 841 is proved from tuple-row CRT equations by checker p848_132_lift_crt_checker_v1. +- `completed_anchor_16` [done] The activation schema lift decision is explicit: finite_menu_certificate_not_universal_yet; next theorem pass is formalize_top_repair_class_mechanism. +- `completed_anchor_17` [done] The checked 132 activation schema has been lifted into symbolic CRT hypothesis packet p848_132_activation_symbolic_lift_candidate_v1; the next obligation is domain closure, not merely packet construction. +- `completed_anchor_18` [done] The broad domain-closure overclaim is ruled out at the current evidence boundary: The finite symbolic-lift survey splits across 8 failing anchors and 12 witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem. +- `completed_anchor_19` [done] The recommended anchor_832_witness_529 closure lane has been executed at finite repeated-group scope: 3 raw rows pass checker p848_832_529_anchor_witness_domain_closure_checker_v1. +- `completed_anchor_20` [done] The single-profile symbolic closure over anchor_832_witness_529 is falsified by the finite evidence split into 2 pre-132 residue profiles. +- `completed_anchor_21` [done] The anchor_832_witness_529 anchor-182 preservation step is explained: every checked row has lift parameter 0 at anchor 182. +- `completed_anchor_22` [done] The repeated pre132_7_1_32_224_57_229_82_412 sublane is closed as a finite duplicate final-anchor variant, not a new symbolic family. +- `completed_anchor_23` [done] Structural atom C1_same_side_base_clique is discharged: same-side principal base residues force a 25 divisor of u*v+1, so each same-side component is a clique. +- `completed_anchor_24` [done] Structural atom C2_two_cliques_plus_cross_edges is discharged by checker p848_C2_two_cliques_plus_cross_edges_checker_v1: the mixed-base graph is two cliques plus arbitrary cross edges. +- `completed_anchor_25` [done] Structural atom C3_missing_cross_graph_definition is discharged by checker p848_C3_missing_cross_graph_definition_checker_v1: H_{x,N} records exactly the missing cross edges between the two clique sides. +- `completed_anchor_26` [done] Structural atom C4_clique_to_vertex_cover_duality is discharged by checker p848_C4_clique_to_vertex_cover_duality_checker_v1: clique complements are exactly vertex covers of H_{x,N}. +- `completed_anchor_27` [done] Structural atom C5_konig_matching_reduction is discharged by checker p848_C5_konig_matching_reduction_checker_v1: Konig's theorem applies because H_{x,N} is finite bipartite. +- `completed_anchor_28` [done] Structural atom C6_mixed_clique_matching_formula is discharged by checker p848_C6_mixed_clique_matching_formula_checker_v1: sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}). +- `completed_anchor_29` [done] Structural atom D1_residue_block_matching_injection is discharged at bounded extraction scope by checker p848_D1_matching_saturation_bound_checker_v1: every current exact mixed-base threatening outsider meets K(N,x) and saturates the smaller compatible side. +- `completed_anchor_30` [done] D2 split-core witness extraction is discharged at bounded pattern scope by checker p848_D2_p13_split_core_witness_checker_v1: each p=13 split common core reaches the sampled K(N,x) target. +- `completed_anchor_31` [done] D3 split-core witness extraction is discharged at bounded pattern scope by checker p848_D3_p17_split_core_witness_checker_v1: each p=17 split common core reaches the sampled K(N,x) target. +- `completed_anchor_32` [done] The top repair-class mechanism packet p848_top_repair_class_mechanism_packet_v1 is seeded with shared metrics, nearest contrasts, common missed-family boundary, and falsifier conditions. +- `completed_anchor_33` [done] The finite-menu +2 repaired-predicted-family separation is discharged: 432->242, 782->242, 832->242 versus 332->240, 382->240, 1232->240. +- `completed_anchor_34` [done] The common missed-family replay is explicit: 9 top-tie shared missed predicted family rows were replayed directly from the family menu. +- `completed_anchor_35` [done] The finite-menu +2 separation has been lifted into mod-50 lane-index congruences: 74 exchange rows all pass the bad-m-class certificate. +- `completed_anchor_36` [done] The mod-50 bad-lane congruence has been generalized into symbolic schema p848_mod50_bad_lane_symbolic_schema_v1; 74 finite witness instances replay with 0 failures. +- `completed_anchor_37` [done] The strict 782 > 1232 handoff is connected to the symbolic mod-50 schema by checker p848_782_1232_strict_handoff_checker_v1; it is certified as finite-menu guidance, not all-N closure. +- `completed_anchor_38` [done] The 182 row preserves the boundary residue: the 132-lifted class already satisfies 137720141 ≡ 119 (mod 121), so the final anchor adds no further correction modulo 841. + +## Next Needed Steps + +- `gap_1` [next] Prove structural-lift atom D2_p13_matching_lower_bound: For p=13 threatening rows, maxMatching(H_{x,N}) is at least the required matching bound extracted from the margin inequality. | source: formalization_work | command: `erdos problem formalization-work-refresh 848` +- `gap_2` [next] Advance the same atomic packet toward target D4_matching_bound_implies_sMaxMixed_bound: If maxMatching(H_{x,N}) >= K(N), then sMixed(x,N) <= |L| + |R| - K(N). | source: formalization_work | command: `erdos problem formalization-work-refresh 848` +- `gap_3` [next] Decide and run the next post-40500 verification lane using local CPU and opt-in local 4090 compute only. | source: formalization_work | command: `erdos problem formalization-work-refresh 848` +- `formalize_282_alignment` [high] The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141. | source: theorem_formalization | command: `erdos problem formalization 848` +- `formalize_top_repair_cluster` [high] Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000. | source: theorem_formalization | command: `erdos problem formalization 848` +- `decide_post_40500_verification_lane` [high] The canonical exact base currently ends at 1..40500. The next verification move is still open. | source: exact_verifier | command: `erdos number-theory dispatch 848` +- `model_repair_pool_growth` [medium] Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849. | source: theorem_formalization | command: `erdos problem formalization 848` +- `finite_gap_strategy_handoff` [high] Use the finite-gap strategy readout: endpoint rollout is useful, but exact-only closure would still require about 10,566,518,518,516,898 endpoint checks to reach the imported 2.64 x 10^17 handoff. | source: finite_gap_strategy | command: `erdos problem task-list-refresh 848` +- `implement_full_common_core_pair_export` [done] Extend the matching-pattern miner so every split profile exports the full common matching core, not only commonMatchingPairSample. | source: split_core_atomization_plan | command: `erdos problem task-list-refresh 848` +- `emit_split_atom_packets` [done] Generate one atom packet per split with inputs, common pairs, K envelope, required lower-bound range, and falsifier boundary. | source: split_core_atomization_plan | command: `erdos problem task-list-refresh 848` +- `materialize_square_residue_successor_packets` [done] Materialize square-residue successor packets for every p13 split profile so D2 can be discharged profile-by-profile. | source: split_core_atomization_plan | command: `erdos problem task-list-refresh 848` +- `attack_top_square_residue_successor` [done_symbolic_family_verified] Attack successor D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1: prove the 145 affected vertex-presence atoms as a symbolic square-residue subfamily. | source: split_core_atomization_plan +- `materialize_remaining_square_residue_successor_packets` [blocked_by_successor_family_proofs] Materialize the remaining square-residue successor packets; 29 of 10 refinement conditions currently have packet files. | source: split_core_atomization_plan +- `emit_singleton_edge_obstruction_certificate` [done_literal_edge_certificate_verified] Emit the literal edge-obstruction certificate for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7, proving every exported cross-edge obstruction has a checked squarefree product-plus-one certificate. | source: split_core_atomization_plan | command: `erdos problem task-list-refresh 848` +- `promote_singleton_edge_congruence_persistence` [done_literal_edge_persistence_verified] Promote the singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from literal edge-obstruction certificates into A5 congruence-persistence families. | source: split_core_atomization_plan +- `promote_singleton_matching_disjointness_and_k_envelope` [done_literal_matching_sampled_k_verified] Promote singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 through A6 matching disjointness and A7 K-envelope checks. | source: split_core_atomization_plan +- `assemble_singleton_split_discharge_readiness` [done_split_discharge_readiness_candidate] Assemble split-discharge readiness for singleton p13 packet D2.3_persist_outP2=99_out25=14_smaller=side7 from verified vertex successors, edge persistence, matching disjointness, and sampled K-envelope certificates. | source: split_core_atomization_plan +- `attack_next_p13_split_profile` [done_p13_split_readiness_candidates] All p13 split profiles have split-discharge readiness candidates; promote the D2 p13 lane through the explicit all-N handoff gaps next. | source: split_core_atomization_plan +- `promote_d2_p13_all_n_handoff` [done_bounded_row_universe_stratified] Bounded p13 row-universe stratification is audited; D2_p13_slack_dominance_symbolic_lift is now the symbolic all-N lift before D2 can be promoted. | source: split_core_atomization_plan +- `attack_d2_p13_row_universe_stratification_lift` [done_bounded_slack_stratification_audited] Lift the bounded p=13 row stratification into a symbolic theorem: the 49 non-tight residue/side strata remain slack-dominated above the tight split floor for all future rows, or the first failing stratum emits a new deterministic split packet. | source: split_core_atomization_plan +- `prove_d2_p13_slack_dominance_symbolic_lift` [done_bounded_formula_reduction_emitted] Slack dominance reduced to D2_p13_non_tight_side_count_slack_floor_lift; prove the side-count floor next. | source: split_core_atomization_plan +- `prove_d2_p13_non_tight_side_count_slack_floor_lift` [done_weakest_side_count_atoms_emitted] Weakest side-count floor atom packets are emitted; attack D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7 next. | source: split_core_atomization_plan +- `attack_weakest_p13_side_count_floor_atom` [done_structural_margin_decomposition_emitted] Attack weakest p13 side-count floor atom D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7: prove its side-count inequality or split the first failing term. | source: split_core_atomization_plan +- `prove_weakest_p13_structural_margin_atom` [done_moving_term_subatoms_emitted] Prove structural margin lemma D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18 for outP2=70|out25=23|smaller=side7, or emit the first moving-term sub-atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_bound_atom` [done_constant_bound_falsified_successor_atom_emitted] The original dMax constant-bound atom is closed by a bounded falsifier and successor growth profile; continue with the current downstream moving-term atom. | source: split_core_atomization_plan +- `attack_weakest_p13_dmax_growth_atom` [done_dmax_growth_tail_profile_closed] The dMax growth tail profile is closed through q>=587 for outP2=70|out25=23|smaller=side7; attack the residual dynamic margin next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q2_progression_atom` [blocked_by_dmax_growth_profile] Wait for the dMax growth profile to emit its first square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q3_progression_atom` [blocked_by_q2_progression_certificate] Wait for the q=2 progression proof to emit the q=3 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q5_progression_atom` [blocked_by_q3_progression_certificate] Wait for the q=3 progression proof to emit the q=5 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q7_progression_atom` [blocked_by_q5_progression_certificate] Wait for the q=5 progression proof to emit the q=7 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q11_progression_atom` [blocked_by_q7_progression_certificate] Wait for the q=7 progression proof to emit the q=11 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q19_progression_atom` [blocked_by_q11_progression_certificate] Wait for the q=11 progression proof to emit the q=19 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q23_progression_atom` [blocked_by_q19_progression_certificate] Wait for the q=19 progression proof to emit the q=23 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q31_progression_atom` [blocked_by_q23_progression_certificate] Wait for the q=23 progression proof to emit the q=31 square-divisor progression atom. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_q251_progression_atom` [done_q251_progression_upper_bound_verified] The q=251 dMax progression upper-bound certificate is present; attack the tail/recombination envelope next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_recombination_atom` [done_tail_scaffold_q13_residue_exclusion_verified] The tail/recombination scaffold excludes q=13 by split residue; attack the first unresolved tail prime q=17 next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q17_progression_atom` [done_q17_tail_progression_upper_bound_verified] The q=17 tail-prime upper-bound certificate is present; attack the plus-side q=19 tail complement next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q19_plus_progression_atom` [done_q19_plus_tail_progression_upper_bound_verified] The plus-side q=19 tail complement is certified; backfill the earlier minus-side q=11 complement next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q11_minus_progression_atom` [done_q11_minus_tail_progression_upper_bound_verified] The minus-side q=11 tail complement is certified; attack the plus-side q=23 complement next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q23_plus_progression_atom` [done_q23_plus_tail_progression_upper_bound_verified] The plus-side q=23 tail complement is certified; attack the minus-side q=31 complement next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q31_minus_progression_atom` [done_q31_minus_tail_progression_upper_bound_verified] The minus-side q=31 tail complement is certified; attack the minus-side q=251 complement next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q251_minus_progression_atom` [done_q251_minus_tail_progression_upper_bound_verified] The minus-side q=251 tail complement is certified; attack the first remaining non-observed q=29 tail prime next. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q29_progression_atom` [done_q29_tail_progression_upper_bound_verified] The q=29 residual tail-prime component is certified; attack q=37 next, starting with the plus-side witness-divisibility exclusion. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q37_progression_atom` [done_q37_tail_progression_upper_bound_verified] The q=37 residual tail-prime component is certified; attack q=41 next as the first two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q41_progression_atom` [done_q41_tail_progression_upper_bound_verified] The q=41 residual tail-prime component is certified; attack q=43 next, starting with the plus-side witness-divisibility exclusion. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q43_progression_atom` [done_q43_tail_progression_upper_bound_verified] The q=43 residual tail-prime component is certified; attack q=47 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q47_progression_atom` [done_q47_tail_progression_upper_bound_verified] The q=47 residual tail-prime component is certified; attack q=53 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q53_progression_atom` [done_q53_tail_progression_upper_bound_verified] The q=53 residual tail-prime component is certified; attack q=59 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q59_progression_atom` [done_q59_tail_progression_upper_bound_verified] The q=59 residual tail-prime component is certified; attack q=61 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q61_progression_atom` [done_q61_tail_progression_upper_bound_verified] The q=61 residual tail-prime component is certified; attack q=67 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q67_progression_atom` [done_q67_tail_progression_upper_bound_verified] The q=67 residual tail-prime component is certified; attack q=71 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q71_progression_atom` [done_q71_tail_progression_upper_bound_verified] The q=71 residual tail-prime component is certified; attack q=73 next, starting with the minus-side witness-divisibility exclusion. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q73_progression_atom` [done_q73_tail_progression_upper_bound_verified] The q=73 residual tail-prime component is certified; attack q=79 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q79_progression_atom` [done_q79_tail_progression_upper_bound_verified] The q=79 residual tail-prime component is certified; attack q=83 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q83_progression_atom` [done_q83_tail_progression_upper_bound_verified] The q=83 residual tail-prime component is certified; attack q=89 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q89_progression_atom` [done_q89_tail_progression_upper_bound_verified] The q=89 residual tail-prime component is certified; attack q=97 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q97_progression_atom` [done_q97_tail_progression_upper_bound_verified] The q=97 residual tail-prime component is certified; attack q=101 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q101_progression_atom` [done_q101_tail_progression_upper_bound_verified] The q=101 residual tail-prime component is certified; attack q=103 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q103_progression_atom` [done_q103_tail_progression_upper_bound_verified] The q=103 residual tail-prime component is certified; attack q=107 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q107_progression_atom` [done_q107_tail_progression_upper_bound_verified] The q=107 residual tail-prime component is certified; attack q=109 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q109_progression_atom` [done_q109_tail_progression_upper_bound_verified] The q=109 residual tail-prime component is certified; attack q=113 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q113_progression_atom` [done_q113_tail_progression_upper_bound_verified] The q=113 residual tail-prime component is certified; attack q=127 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q127_progression_atom` [done_q127_tail_progression_upper_bound_verified] The q=127 residual tail-prime component is certified; attack q=131 next, combining the minus-side witness-divisibility exclusion with the plus-side CRT floor bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q131_progression_atom` [done_q131_tail_progression_upper_bound_verified] The q=131 residual tail-prime component is certified; attack q=137 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q137_progression_atom` [done_q137_tail_progression_upper_bound_verified] The q=137 residual tail-prime component is certified; attack q=139 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q139_progression_atom` [done_q139_tail_progression_upper_bound_verified] The q=139 residual tail-prime component is certified; attack q=149 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q149_progression_atom` [done_q149_tail_progression_upper_bound_verified] The q=149 residual tail-prime component is certified; attack q=151 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q151_progression_atom` [done_q151_tail_progression_upper_bound_verified] The q=151 residual tail-prime component is certified; attack q=157 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q157_progression_atom` [done_q157_tail_progression_upper_bound_verified] The q=157 residual tail-prime component is certified; attack q=163 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q163_progression_atom` [done_q163_tail_progression_upper_bound_verified] The q=163 residual tail-prime component is certified; attack q=167 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q167_progression_atom` [done_q167_tail_progression_upper_bound_verified] The q=167 residual tail-prime component is certified; attack q=173 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q173_progression_atom` [done_q173_tail_progression_upper_bound_verified] The q=173 residual tail-prime component is certified; attack q=179 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q179_progression_atom` [done_q179_tail_progression_upper_bound_verified] The q=179 residual tail-prime component is certified; attack q=181 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q181_progression_atom` [done_q181_tail_progression_upper_bound_verified] The q=181 residual tail-prime component is certified; attack q=191 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q191_progression_atom` [done_q191_tail_progression_upper_bound_verified] The q=191 residual tail-prime component is certified; attack q=193 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q193_progression_atom` [done_q193_tail_progression_upper_bound_verified] The q=193 residual tail-prime component is certified; attack q=197 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q197_progression_atom` [done_q197_tail_progression_upper_bound_verified] The q=197 residual tail-prime component is certified; attack q=199 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q199_progression_atom` [done_q199_tail_progression_upper_bound_verified] The q=199 residual tail-prime component is certified; attack q=211 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q211_progression_atom` [done_q211_tail_progression_upper_bound_verified] The q=211 residual tail-prime component is certified; attack q=223 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q223_progression_atom` [done_q223_tail_progression_upper_bound_verified] The q=223 residual tail-prime component is certified; attack q=227 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q227_progression_atom` [done_q227_tail_progression_upper_bound_verified] The q=227 residual tail-prime component is certified; attack q=229 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q229_progression_atom` [done_q229_tail_progression_upper_bound_verified] The q=229 residual tail-prime component is certified; attack q=233 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q233_progression_atom` [done_q233_tail_progression_upper_bound_verified] The q=233 residual tail-prime component is certified; attack q=239 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q239_progression_atom` [done_q239_tail_progression_upper_bound_verified] The q=239 residual tail-prime component is certified; attack q=241 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q241_progression_atom` [done_q241_tail_progression_upper_bound_verified] The q=241 residual tail-prime component is certified; q=251 is already covered, so attack q=257 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q257_progression_atom` [done_q257_tail_progression_upper_bound_verified] The q=257 residual tail-prime component is certified; attack q=263 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q263_progression_atom` [done_q263_tail_progression_upper_bound_verified] The q=263 residual tail-prime component is certified; attack q=269 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q269_progression_atom` [done_q269_tail_progression_upper_bound_verified] The q=269 residual tail-prime component is certified; attack q=271 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q271_progression_atom` [done_q271_tail_progression_upper_bound_verified] The q=271 residual tail-prime component is certified; attack q=277 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q277_progression_atom` [done_q277_tail_progression_upper_bound_verified] The q=277 residual tail-prime component is certified; attack q=281 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q281_progression_atom` [done_q281_tail_progression_upper_bound_verified] The q=281 residual tail-prime component is certified; attack q=283 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q283_progression_atom` [done_q283_tail_progression_upper_bound_verified] The q=283 residual tail-prime component is certified; attack q=293 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q293_progression_atom` [done_q293_tail_progression_upper_bound_verified] The q=293 residual tail-prime component is certified; attack q=307 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q307_progression_atom` [done_q307_tail_progression_upper_bound_verified] The q=307 residual tail-prime component is certified; attack q=311 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q311_progression_atom` [done_q311_tail_progression_upper_bound_verified] The q=311 residual tail-prime component is certified; attack q=313 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q313_progression_atom` [done_q313_tail_progression_upper_bound_verified] The q=313 residual tail-prime component is certified; attack q=317 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q317_progression_atom` [done_q317_tail_progression_upper_bound_verified] The q=317 residual tail-prime component is certified; attack q=331 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q331_progression_atom` [done_q331_tail_progression_upper_bound_verified] The q=331 residual tail-prime component is certified; attack q=337 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q337_progression_atom` [done_q337_tail_progression_upper_bound_verified] The q=337 residual tail-prime component is certified; attack q=347 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q347_progression_atom` [done_q347_tail_progression_upper_bound_verified] The q=347 residual tail-prime component is certified; attack q=349 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q349_progression_atom` [done_q349_tail_progression_upper_bound_verified] The q=349 residual tail-prime component is certified; attack q=353 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q353_progression_atom` [done_q353_tail_progression_upper_bound_verified] The q=353 residual tail-prime component is certified; attack q=359 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q359_progression_atom` [done_q359_tail_progression_upper_bound_verified] The q=359 residual tail-prime component is certified; attack q=367 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q367_progression_atom` [done_q367_tail_progression_upper_bound_verified] The q=367 residual tail-prime component is certified; attack q=373 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q373_progression_atom` [done_q373_tail_progression_upper_bound_verified] The q=373 residual tail-prime component is certified; attack q=379 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q379_progression_atom` [done_q379_tail_progression_upper_bound_verified] The q=379 residual tail-prime component is certified; attack q=383 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q383_progression_atom` [done_q383_tail_progression_upper_bound_verified] The q=383 residual tail-prime component is certified; attack q=389 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q389_progression_atom` [done_q389_tail_progression_upper_bound_verified] The q=389 residual tail-prime component is certified; attack q=397 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q397_progression_atom` [done_q397_tail_progression_upper_bound_verified] The q=397 residual tail-prime component is certified; attack q=401 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q401_progression_atom` [done_q401_tail_progression_upper_bound_verified] The q=401 residual tail-prime component is certified; attack q=409 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q409_progression_atom` [done_q409_tail_progression_upper_bound_verified] The q=409 residual tail-prime component is certified; attack q=419 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q419_progression_atom` [done_q419_tail_progression_upper_bound_verified] The q=419 residual tail-prime component is certified; attack q=421 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q421_progression_atom` [done_q421_tail_progression_upper_bound_verified] The q=421 residual tail-prime component is certified; attack q=431 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q431_progression_atom` [done_q431_tail_progression_upper_bound_verified] The q=431 residual tail-prime component is certified; attack q=433 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q433_progression_atom` [done_q433_tail_progression_upper_bound_verified] The q=433 residual tail-prime component is certified; attack q=439 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q439_progression_atom` [done_q439_tail_progression_upper_bound_verified] The q=439 residual tail-prime component is certified; attack q=443 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q443_progression_atom` [done_q443_tail_progression_upper_bound_verified] The q=443 residual tail-prime component is certified; attack q=449 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q449_progression_atom` [done_q449_tail_progression_upper_bound_verified] The q=449 residual tail-prime component is certified; attack q=457 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q457_progression_atom` [done_q457_tail_progression_upper_bound_verified] The q=457 residual tail-prime component is certified; attack q=461 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q461_progression_atom` [done_q461_tail_progression_upper_bound_verified] The q=461 residual tail-prime component is certified; attack q=463 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q463_progression_atom` [done_q463_tail_progression_upper_bound_verified] The q=463 residual tail-prime component is certified; attack q=467 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q467_progression_atom` [done_q467_tail_progression_upper_bound_verified] The q=467 residual tail-prime component is certified; attack q=479 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q479_progression_atom` [done_q479_tail_progression_upper_bound_verified] The q=479 residual tail-prime component is certified; attack q=487 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q487_progression_atom` [done_q487_tail_progression_upper_bound_verified] The q=487 residual tail-prime component is certified; attack q=491 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q491_progression_atom` [done_q491_tail_progression_upper_bound_verified] The q=491 residual tail-prime component is certified; attack q=499 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q499_progression_atom` [done_q499_tail_progression_upper_bound_verified] The q=499 residual tail-prime component is certified; attack q=503 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q503_progression_atom` [done_q503_tail_progression_upper_bound_verified] The q=503 residual tail-prime component is certified; attack q=509 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q509_progression_atom` [done_q509_tail_progression_upper_bound_verified] The q=509 residual tail-prime component is certified; attack q=521 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q521_progression_atom` [done_q521_tail_progression_upper_bound_verified] The q=521 residual tail-prime component is certified; attack q=523 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q523_progression_atom` [done_q523_tail_progression_upper_bound_verified] The q=523 residual tail-prime component is certified; attack q=541 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q541_progression_atom` [done_q541_tail_progression_upper_bound_verified] The q=541 residual tail-prime component is certified; attack q=547 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q547_progression_atom` [done_q547_tail_progression_upper_bound_verified] The q=547 residual tail-prime component is certified; attack q=557 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q557_progression_atom` [done_q557_tail_progression_upper_bound_verified] The q=557 residual tail-prime component is certified; attack q=563 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q563_progression_atom` [done_q563_tail_progression_upper_bound_verified] The q=563 residual tail-prime component is certified; attack q=569 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q569_progression_atom` [done_q569_tail_progression_upper_bound_verified] The q=569 residual tail-prime component is certified; attack q=571 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q571_progression_atom` [done_q571_tail_progression_upper_bound_verified] The q=571 residual tail-prime component is certified; attack q=577 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q577_progression_atom` [done_q577_tail_progression_upper_bound_verified] The q=577 residual tail-prime component is certified; attack q=587 next as a two-sided residual tail-prime CRT floor-bound. | source: split_core_atomization_plan +- `prove_weakest_p13_dmax_tail_q587_progression_atom` [done_q587_tail_progression_upper_bound_verified] The q=587 residual tail-prime component is certified; lift the bounded q>=587 zero-floor profile before any aggregate dMax tail claim. | source: split_core_atomization_plan +- `prove_p13_dmax_tail_q_ge_587_parametric_zero_floor_lift` [done_q_ge_587_bounded_zero_floor_lift_verified] The q>=587 bounded zero-floor lift is verified; attack the residual dynamic margin next. | source: split_core_atomization_plan +- `prove_p13_side18_residual_dynamic_margin_atom` [done_exact_mixed_symbolic_lift_decomposed] The exact mixed-margin symbolic lift is decomposed; prove the matching-injection sublemma next. | source: split_core_atomization_plan +- `prove_p13_side18_residual_dynamic_margin_symbolic_lift` [done_symbolic_lift_falsified_exact_mixed_decomposition_emitted] The false side18 threshold lift has been replaced by an exact mixed-margin decomposition; prove the matching injection next. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_symbolic_lift` [done_symbolic_lift_decomposed_first_sublemma_emitted] The exact mixed-margin symbolic lift is reduced to matching-injection plus margin-floor sublemmas; prove matching injection first. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection` [done_q17_residual_window_relaxed_fallback_menu_lift_emitted] The q17 residual p13-expanded fallback menu is falsified and repaired only after relaxing the local window; prove the window-relaxed fallback selector next. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift` [blocked_by_bounded_matching_profile] Wait for the bounded matching-injection profile to identify the parametric insertion target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift` [done_q17_residual_window_relaxed_fallback_menu_lift_emitted] The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed selector target. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift` [done_q17_residual_window_relaxed_fallback_menu_emitted] The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed fallback selector. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift` [done_window_relaxed_fallback_menu_emitted] The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift` [done_window_relaxed_fallback_menu_emitted] The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu. | source: split_core_atomization_plan +- `prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift` [highest] Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row. | source: split_core_atomization_plan +- `start_singleton_p13_profile` [done_successor_packets_emitted] Attack the singleton p13 split outP2=99|out25=14|smaller=side7 first to determine whether it is a real symbolic class or an under-split boundary artifact. | source: split_core_atomization_plan +- `structural_verifier_import_audit` [high] Use the structural-verifier import audit: status blocked, blockers sawhney_handoff_not_claimed_at_1e7, base_exchange_mask_covers_both_principal_sides. | source: external_structural_verifier_audit | command: `erdos number-theory dispatch 848 --apply --action structural_verifier_audit` +- `base_side_scout` [high] Use the base-side scout: status counterexample_to_global_7_side_domination_found over 1..200; max side18-minus-side7 is 1. | source: structural_base_side_scout | command: `erdos number-theory dispatch 848 --apply --action base_side_scout --base-side-max 2000` +- `structural_two_side_scout` [ready] Use the two-sided structural scout: status side_specific_bounds_pass_but_union_bound_fails over 7307..7600; union failures 64 repaired by the full mixed-base verifier. | source: structural_two_side_scout | command: `erdos number-theory dispatch 848 --apply --action structural_two_side_scout --structural-min 7307 --structural-max 7600` +- `mixed_base_failure_scout` [ready] Use the mixed-base failure scout: status sampled_union_failures_repaired_by_mixed_base_clique; analyzed 8 union-failure rows with 0 mixed-base failures. | source: mixed_base_failure_scout | command: `erdos number-theory dispatch 848 --apply --action mixed_base_failure_scout --mixed-base-max-rows 40` +- `full_mixed_base_structural_verifier` [ready] Use the full mixed-base structural verifier: status bounded_full_mixed_base_structural_verifier_certified over 7307..7600; exact threatening-outsider checks 1733, mixed failures 0. | source: full_mixed_base_structural_verifier | command: `erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min 7307 --structural-max 7600` +- `structural_lift_miner` [ready] Use the structural lift miner: status structural_lift_obligation_packet_ready; mined 64 exact mixed rows; next theorem lane formalize_cross_side_matching_bound_then_exact_prime_margin_lift. | source: structural_lift_miner | command: `erdos number-theory dispatch 848 --apply --action structural_lift_miner` +- `regime_b_endpoint_verifier_backend` [high] Continue the active endpoint-monotonicity exact verifier beyond 1..40500 (1621 endpoint checks cover 40500 rows; compression 24.98x). | source: exact_breakpoint_certificate | command: `erdos number-theory dispatch 848 --apply --action exact_followup_rollout --exact-chunks 5 --exact-chunk-size 1000 --endpoint-monotonicity` + +## Commands + +- Problem surface: `erdos problem show 848` +- Problem artifacts: `erdos problem artifacts 848` +- Task list: `erdos problem task-list 848` +- Task list refresh: `erdos problem task-list-refresh 848` +- Task list run: `erdos problem task-list-run 848 --passes 10` +- ORP mode list: `orp mode list --json` +- ORP granular breakdown: `orp mode breakdown granular-breakdown --topic "problem 848 | Explain the 282 First-Failure Mechanism | active atom D2_p13_matching_lower_bound | target D4_matching_bound_implies_sMaxMixed_bound" --json` +- ORP granular nudge: `orp mode nudge granular-breakdown --json` +- Theorem loop: `erdos problem theorem-loop 848` +- Claim pass: `erdos problem claim-pass 848` +- Formalization: `erdos problem formalization 848` +- Formalization work: `erdos problem formalization-work 848` +- Source refresh: `erdos number-theory bridge-refresh 848` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848` +- taskListJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LIST.json` +- taskListMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LIST.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/CLAIM_PASS.json` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION.json` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FORMALIZATION_WORK.json` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/INTERVAL_WORK_QUEUE.yaml` +- exactBreakpointScoutJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/EXACT_BREAKPOINT_SCOUT.json` +- exactBreakpointCertificateJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/EXACT_BREAKPOINT_CERTIFICATE.json` +- externalStructuralVerifierAuditJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json` +- externalStructuralVerifierAuditMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md` +- baseSideScoutJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/BASE_SIDE_SCOUT.json` +- baseSideScoutMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/BASE_SIDE_SCOUT.md` +- structuralTwoSideScoutJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json` +- structuralTwoSideScoutMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.md` +- mixedBaseFailureScoutJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.json` +- mixedBaseFailureScoutMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/MIXED_BASE_FAILURE_SCOUT.md` +- fullMixedBaseStructuralVerifierJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json` +- fullMixedBaseStructuralVerifierMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md` +- structuralLiftMinerJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.json` +- structuralLiftMinerMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_MINER.md` +- structuralLiftChecklistJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.json` +- structuralLiftChecklistMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/STRUCTURAL_LIFT_CHECKLIST.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json` diff --git a/packs/number-theory/problems/848/TASK_LOOP_RUN.json b/packs/number-theory/problems/848/TASK_LOOP_RUN.json new file mode 100644 index 0000000..af42ce1 --- /dev/null +++ b/packs/number-theory/problems/848/TASK_LOOP_RUN.json @@ -0,0 +1,4548 @@ +{ + "ok": true, + "schema": "erdos.problem_task_loop_run/1", + "generatedAt": "2026-04-10T08:45:22.100Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "requestedPasses": 250, + "executedPasses": 250, + "stopOnConvergence": false, + "stopReason": "requested_pass_limit_reached", + "converged": true, + "convergedAtPass": 2, + "currentState": { + "activeRoute": "finite_check_gap_closure", + "currentClaimSurface": "bridge_backed_frontier_support", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `11300` or switch method class.", + "latestVerifiedInterval": "1..11300" + }, + "currentObjective": { + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "title": "Formalize the 282 Obstruction Alignment", + "activeWorkId": "p848_282_first_failure_mechanism_packet_v1", + "activeWorkTitle": "Explain the 282 First-Failure Mechanism", + "activeWorkStatus": "in_progress" + }, + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.", + "command": "erdos problem formalization-work-refresh 848" + }, + "passes": [ + { + "passNumber": 1, + "changed": true, + "activeRoute": "finite_check_gap_closure", + "latestVerifiedInterval": "1..11300", + "currentClaimSurface": "bridge_backed_frontier_support", + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "activeWorkId": 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The next verification move is still open.\",\"source\":\"exact_verifier\"},{\"stepId\":\"model_repair_pool_growth\",\"status\":\"medium\",\"task\":\"Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 247, + "changed": false, + "activeRoute": "finite_check_gap_closure", + "latestVerifiedInterval": "1..11300", + "currentClaimSurface": "bridge_backed_frontier_support", + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "activeWorkId": "p848_282_first_failure_mechanism_packet_v1", + "activeWorkStatus": "in_progress", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.", + "command": "erdos problem formalization-work-refresh 848" + }, + "fingerprint": "{\"activeRoute\":\"finite_check_gap_closure\",\"currentClaimSurface\":\"bridge_backed_frontier_support\",\"nextHonestMove\":\"Decide whether to extend exact verified coverage beyond `11300` or switch method class.\",\"latestVerifiedInterval\":\"1..11300\",\"currentObjective\":{\"formalizationId\":\"p848_282_alignment_formalization_v1\",\"focusId\":\"formalize_282_alignment\",\"activeWorkId\":\"p848_282_first_failure_mechanism_packet_v1\",\"activeWorkStatus\":\"in_progress\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical bridge inputs against the latest harvested compute artifacts\",\"task\":\"Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the primary structural hook remains canonical\",\"task\":\"Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current exact/verifier boundary and next target\",\"task\":\"Verify that the certified interval 1..11300 and the next verifier target remain current across the pack surfaces.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"in_progress\",\"title\":\"Explain the 282 First-Failure Mechanism\",\"task\":\"Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\"},{\"taskId\":\"refresh_and_rerank\",\"status\":\"ready\",\"title\":\"Refresh the task list and rerank the next step\",\"task\":\"Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"Decide whether the 132-row lift to residue 504 mod 841 is a reusable obstruction-family pattern or a packet-specific accident.\",\"source\":\"formalization_work\"},{\"stepId\":\"formalize_282_alignment\",\"status\":\"high\",\"task\":\"The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"formalize_top_repair_cluster\",\"status\":\"high\",\"task\":\"Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"decide_post_11300_verification_lane\",\"status\":\"high\",\"task\":\"The canonical exact base currently ends at 1..11300. The next verification move is still open.\",\"source\":\"exact_verifier\"},{\"stepId\":\"model_repair_pool_growth\",\"status\":\"medium\",\"task\":\"Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 248, + "changed": false, + "activeRoute": "finite_check_gap_closure", + "latestVerifiedInterval": "1..11300", + "currentClaimSurface": "bridge_backed_frontier_support", + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "activeWorkId": "p848_282_first_failure_mechanism_packet_v1", + "activeWorkStatus": "in_progress", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.", + "command": "erdos problem formalization-work-refresh 848" + }, + "fingerprint": "{\"activeRoute\":\"finite_check_gap_closure\",\"currentClaimSurface\":\"bridge_backed_frontier_support\",\"nextHonestMove\":\"Decide whether to extend exact verified coverage beyond `11300` or switch method class.\",\"latestVerifiedInterval\":\"1..11300\",\"currentObjective\":{\"formalizationId\":\"p848_282_alignment_formalization_v1\",\"focusId\":\"formalize_282_alignment\",\"activeWorkId\":\"p848_282_first_failure_mechanism_packet_v1\",\"activeWorkStatus\":\"in_progress\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical bridge inputs against the latest harvested compute artifacts\",\"task\":\"Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the primary structural hook remains canonical\",\"task\":\"Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current exact/verifier boundary and next target\",\"task\":\"Verify that the certified interval 1..11300 and the next verifier target remain current across the pack surfaces.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"in_progress\",\"title\":\"Explain the 282 First-Failure Mechanism\",\"task\":\"Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\"},{\"taskId\":\"refresh_and_rerank\",\"status\":\"ready\",\"title\":\"Refresh the task list and rerank the next step\",\"task\":\"Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"Decide whether the 132-row lift to residue 504 mod 841 is a reusable obstruction-family pattern or a packet-specific accident.\",\"source\":\"formalization_work\"},{\"stepId\":\"formalize_282_alignment\",\"status\":\"high\",\"task\":\"The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"formalize_top_repair_cluster\",\"status\":\"high\",\"task\":\"Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"decide_post_11300_verification_lane\",\"status\":\"high\",\"task\":\"The canonical exact base currently ends at 1..11300. The next verification move is still open.\",\"source\":\"exact_verifier\"},{\"stepId\":\"model_repair_pool_growth\",\"status\":\"medium\",\"task\":\"Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 249, + "changed": false, + "activeRoute": "finite_check_gap_closure", + "latestVerifiedInterval": "1..11300", + "currentClaimSurface": "bridge_backed_frontier_support", + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "activeWorkId": "p848_282_first_failure_mechanism_packet_v1", + "activeWorkStatus": "in_progress", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.", + "command": "erdos problem formalization-work-refresh 848" + }, + "fingerprint": "{\"activeRoute\":\"finite_check_gap_closure\",\"currentClaimSurface\":\"bridge_backed_frontier_support\",\"nextHonestMove\":\"Decide whether to extend exact verified coverage beyond `11300` or switch method class.\",\"latestVerifiedInterval\":\"1..11300\",\"currentObjective\":{\"formalizationId\":\"p848_282_alignment_formalization_v1\",\"focusId\":\"formalize_282_alignment\",\"activeWorkId\":\"p848_282_first_failure_mechanism_packet_v1\",\"activeWorkStatus\":\"in_progress\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical bridge inputs against the latest harvested compute artifacts\",\"task\":\"Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the primary structural hook remains canonical\",\"task\":\"Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current exact/verifier boundary and next target\",\"task\":\"Verify that the certified interval 1..11300 and the next verifier target remain current across the pack surfaces.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"in_progress\",\"title\":\"Explain the 282 First-Failure Mechanism\",\"task\":\"Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\"},{\"taskId\":\"refresh_and_rerank\",\"status\":\"ready\",\"title\":\"Refresh the task list and rerank the next step\",\"task\":\"Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"Decide whether the 132-row lift to residue 504 mod 841 is a reusable obstruction-family pattern or a packet-specific accident.\",\"source\":\"formalization_work\"},{\"stepId\":\"formalize_282_alignment\",\"status\":\"high\",\"task\":\"The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"formalize_top_repair_cluster\",\"status\":\"high\",\"task\":\"Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"decide_post_11300_verification_lane\",\"status\":\"high\",\"task\":\"The canonical exact base currently ends at 1..11300. The next verification move is still open.\",\"source\":\"exact_verifier\"},{\"stepId\":\"model_repair_pool_growth\",\"status\":\"medium\",\"task\":\"Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.\",\"source\":\"theorem_formalization\"}]}" + }, + { + "passNumber": 250, + "changed": false, + "activeRoute": "finite_check_gap_closure", + "latestVerifiedInterval": "1..11300", + "currentClaimSurface": "bridge_backed_frontier_support", + "formalizationId": "p848_282_alignment_formalization_v1", + "focusId": "formalize_282_alignment", + "activeWorkId": "p848_282_first_failure_mechanism_packet_v1", + "activeWorkStatus": "in_progress", + "highestValueStep": { + "source": "formalization_work", + "stepId": "gap_1", + "task": "Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.", + "command": "erdos problem formalization-work-refresh 848" + }, + "fingerprint": "{\"activeRoute\":\"finite_check_gap_closure\",\"currentClaimSurface\":\"bridge_backed_frontier_support\",\"nextHonestMove\":\"Decide whether to extend exact verified coverage beyond `11300` or switch method class.\",\"latestVerifiedInterval\":\"1..11300\",\"currentObjective\":{\"formalizationId\":\"p848_282_alignment_formalization_v1\",\"focusId\":\"formalize_282_alignment\",\"activeWorkId\":\"p848_282_first_failure_mechanism_packet_v1\",\"activeWorkStatus\":\"in_progress\"},\"currentTasks\":[{\"taskId\":\"freeze_current_state\",\"status\":\"ready\",\"title\":\"Freeze the current north star and active theorem packet\",\"task\":\"Freeze the current route `finite_check_gap_closure`, claim surface `bridge_backed_frontier_support`, and active theorem packet before widening the search.\"},{\"taskId\":\"audit_theorem_surfaces\",\"status\":\"ready\",\"title\":\"Audit theorem, claim, and formalization surfaces for consistency\",\"task\":\"Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.\"},{\"taskId\":\"verify_canonical_inputs\",\"status\":\"ready\",\"title\":\"Verify canonical bridge inputs against the latest harvested compute artifacts\",\"task\":\"Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.\"},{\"taskId\":\"verify_primary_structural_hook\",\"status\":\"ready\",\"title\":\"Verify the primary structural hook remains canonical\",\"task\":\"Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.\"},{\"taskId\":\"verify_verifier_boundary\",\"status\":\"ready\",\"title\":\"Verify the current exact/verifier boundary and next target\",\"task\":\"Verify that the certified interval 1..11300 and the next verifier target remain current across the pack surfaces.\"},{\"taskId\":\"execute_current_work_packet\",\"status\":\"in_progress\",\"title\":\"Explain the 282 First-Failure Mechanism\",\"task\":\"Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.\"},{\"taskId\":\"discharge_first_remaining_gap\",\"status\":\"ready\",\"title\":\"Discharge the first remaining gap in the active theorem packet\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\"},{\"taskId\":\"refresh_and_rerank\",\"status\":\"ready\",\"title\":\"Refresh the task list and rerank the next step\",\"task\":\"Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.\"}],\"nextNeededSteps\":[{\"stepId\":\"gap_1\",\"status\":\"next\",\"task\":\"Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence.\",\"source\":\"formalization_work\"},{\"stepId\":\"gap_2\",\"status\":\"next\",\"task\":\"Decide whether the 132-row lift to residue 504 mod 841 is a reusable obstruction-family pattern or a packet-specific accident.\",\"source\":\"formalization_work\"},{\"stepId\":\"formalize_282_alignment\",\"status\":\"high\",\"task\":\"The bridge matches shared-prefix representative 137720141 with tracked tail 282 first failure 137720141.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"formalize_top_repair_cluster\",\"status\":\"high\",\"task\":\"Top cluster 432, 782, 832 shares repaired-known=26, repaired-predicted=242, clean-through=250075000.\",\"source\":\"theorem_formalization\"},{\"stepId\":\"decide_post_11300_verification_lane\",\"status\":\"high\",\"task\":\"The canonical exact base currently ends at 1..11300. The next verification move is still open.\",\"source\":\"exact_verifier\"},{\"stepId\":\"model_repair_pool_growth\",\"status\":\"medium\",\"task\":\"Recent bridge packets introduced new square moduli: 1369, 841, 17161, 1849.\",\"source\":\"theorem_formalization\"}]}" + } + ], + "commands": { + "taskList": "erdos problem task-list 848", + "taskListRefresh": "erdos problem task-list-refresh 848", + "rerun": "erdos problem task-list-run 848 --passes 250" + }, + "sources": { + "taskListJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LIST.json", + "taskListMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LIST.md", + "taskLoopRunJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LOOP_RUN.json", + "taskLoopRunMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/TASK_LOOP_RUN.md" + } +} diff --git a/packs/number-theory/problems/848/TASK_LOOP_RUN.md b/packs/number-theory/problems/848/TASK_LOOP_RUN.md new file mode 100644 index 0000000..f4c32a4 --- /dev/null +++ b/packs/number-theory/problems/848/TASK_LOOP_RUN.md @@ -0,0 +1,266 @@ +# Erdos Problem #848 Task Loop Run + +- Problem id: `848` +- Requested passes: `250` +- Executed passes: `250` +- Stop reason: `requested_pass_limit_reached` +- Converged: `yes` +- Converged at pass: `2` +- Active route: `finite_check_gap_closure` +- Current claim surface: `bridge_backed_frontier_support` +- Latest verified interval: `1..11300` +- Highest-value next step: `gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Highest-value command: `erdos problem formalization-work-refresh 848` + +## Passes + +- Pass 1: changed=`yes` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 2: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 3: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 4: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 5: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 6: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 7: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 8: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 9: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 10: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 11: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 12: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 13: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 14: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 15: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 16: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 17: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 18: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 19: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 20: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 21: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 22: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 23: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 24: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 25: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 26: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 27: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 28: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 29: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 30: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 31: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 32: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 33: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 34: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 35: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 36: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 37: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 38: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 39: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 40: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 41: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 42: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 43: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 44: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 45: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 46: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 47: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 48: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 49: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 50: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 51: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 52: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 53: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 54: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 55: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 56: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 57: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 58: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 59: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 60: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 61: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 62: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 63: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 64: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 65: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 66: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 67: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 68: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 69: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 70: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 71: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 72: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 73: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 74: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 75: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 76: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 77: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 78: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 79: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 80: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 81: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 82: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 83: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 84: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 85: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 86: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 87: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 88: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 89: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 90: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 91: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 92: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 93: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 94: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 95: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 96: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 97: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 98: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 99: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 100: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 101: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 102: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 103: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 104: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 105: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 106: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 107: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 108: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 109: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 110: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 111: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 112: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 113: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 114: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 115: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 116: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 117: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 118: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 119: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 120: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 121: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 122: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 123: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 124: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 125: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 126: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 127: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 128: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 129: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 130: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 131: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 132: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 133: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 134: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 135: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 136: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 137: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 138: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 139: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 140: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 141: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 142: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 143: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 144: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 145: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 146: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 147: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 148: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 149: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 150: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 151: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 152: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 153: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 154: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 155: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 156: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 157: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 158: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 159: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 160: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 161: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 162: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 163: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 164: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 165: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 166: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 167: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 168: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 169: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 170: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 171: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 172: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 173: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 174: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 175: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 176: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 177: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 178: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 179: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 180: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 181: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 182: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 183: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 184: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 185: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 186: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 187: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 188: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 189: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 190: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 191: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 192: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 193: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 194: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 195: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 196: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 197: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 198: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 199: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 200: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 201: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 202: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 203: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 204: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 205: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 206: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 207: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 208: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 209: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 210: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 211: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 212: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 213: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 214: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 215: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 216: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 217: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 218: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 219: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 220: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 221: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 222: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 223: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 224: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 225: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 226: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 227: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 228: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 229: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 230: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 231: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 232: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 233: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 234: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 235: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 236: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 237: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 238: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 239: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 240: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 241: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 242: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 243: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 244: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 245: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 246: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 247: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 248: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 249: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. +- Pass 250: changed=`no` | active work=`p848_282_first_failure_mechanism_packet_v1` | next=`gap_1` | Show whether the 132-activation sequence should be described as a controlled interaction between the shared-prefix class and the 282 repair congruence rather than as a packet-specific coincidence. diff --git a/packs/number-theory/problems/848/THEOREM_LOOP.json b/packs/number-theory/problems/848/THEOREM_LOOP.json new file mode 100644 index 0000000..7aa00f5 --- /dev/null +++ b/packs/number-theory/problems/848/THEOREM_LOOP.json @@ -0,0 +1,125 @@ +{ + "schema": "erdos.problem_theorem_loop/1", + "generatedAt": "2026-04-14T11:45:57.590Z", + "problemId": "848", + "displayName": "Erdos Problem #848", + "title": "Squarefree ab+1 Extremal Set Problem", + "cluster": "number-theory", + "sourceKind": "search_theorem_bridge", + "theoremLoopMode": "bridge_backed", + "activeRoute": "finite_check_gap_closure", + "theoremModule": null, + "currentState": { + "siteStatus": "decidable", + "repoStatus": "active", + "openProblem": false, + "routeBreakthrough": true, + "problemSolved": false, + "currentClaimSurface": "bridge_backed_frontier_support", + "routeSummary": "Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims.", + "nextHonestMove": "Decide whether to extend exact verified coverage beyond `40500` or switch method class." + }, + "theoremHooks": [ + { + "hook_id": "next_unmatched_equals_282_failure", + "status": "supported", + "note": "" + }, + { + "hook_id": "completed_tail_vs_search_leader_split", + "status": "supported", + "note": "" + }, + { + "hook_id": "repair_pool_not_closed", + "status": "supported", + "note": "" + }, + { + "hook_id": "top_repair_class_cluster", + "status": "supported", + "note": "" + } + ], + "theoremAgenda": [ + { + "item_id": "choose_next_finite_gap_move", + "status": "ready", + "task": "Choose the next finite-gap closure move and keep the theorem-facing claim surface honest.", + "why": "Decide whether to extend exact verified coverage beyond `40500` or switch method class." + }, + { + "item_id": "explain_next_unmatched_alignment", + "status": "ready", + "task": "Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`.", + "why": "If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class." + }, + { + "item_id": "explain_completed_vs_search_leader_split", + "status": "ready", + "task": "Explain why completed structured tail `332` differs from current family-aware leader `432`.", + "why": "That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class." + }, + { + "item_id": "model_repair_pool_growth", + "status": "ready", + "task": "Model the repaired square-modulus pool as a growing family rather than treating it as already closed.", + "why": "Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure." + }, + { + "item_id": "characterize_top_repair_cluster", + "status": "ready", + "task": "Characterize what the top repair cluster `432, 782, 832` shares structurally.", + "why": "If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction." + } + ], + "currentBridgeState": { + "shared_prefix_failure_count": 24, + "latest_shared_prefix_failure": 136702637, + "family_menu_count": 280, + "known_family_matches": 25, + "next_unmatched_representative": 137720141, + "next_unmatched_matches_282_failure": true, + "strongest_completed_structured_tail": { + "continuation": 332, + "clean_through": 250000000 + }, + "current_family_aware_leader": { + "continuation": 432, + "repaired_known_packets": 26, + "repaired_predicted_families": 242, + "effective_clean_through": 250075000 + }, + "top_gpu_tie_class": [ + 432, + 782, + 832 + ], + "recent_pool_expansion_moduli": [ + 1369, + 841, + 17161, + 1849 + ] + }, + "commands": { + "problemShow": "erdos problem show 848", + "problemArtifacts": "erdos problem artifacts 848", + "theoremLoop": "erdos problem theorem-loop 848", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 848", + "clusterStatus": "erdos number-theory status 848", + "clusterFrontier": "erdos number-theory frontier 848", + "sourceRefresh": "erdos number-theory bridge-refresh 848" + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md", + "contextPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/context.yaml", + "routePacketPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/ROUTE_PACKET.yaml", + "frontierNotePath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FRONTIER_NOTE.md", + "opsDetailsPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/OPS_DETAILS.yaml", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md" + } +} diff --git a/packs/number-theory/problems/848/THEOREM_LOOP.md b/packs/number-theory/problems/848/THEOREM_LOOP.md new file mode 100644 index 0000000..55aa0fb --- /dev/null +++ b/packs/number-theory/problems/848/THEOREM_LOOP.md @@ -0,0 +1,60 @@ +# Erdos Problem #848 Theorem Loop + +This theorem loop is generated from a richer search/theorem bridge, then exposed through a generic product-wide theorem-loop surface. + +## Current State + +- Theorem loop mode: `bridge_backed`. +- Active route: `finite_check_gap_closure`. +- Current claim surface: `bridge_backed_frontier_support`. +- Repo status: `active`; site status: `decidable`. +- Route breakthrough: `yes`. +- Problem solved: `no`. +- Open problem: `no`. +- Theorem module: `(none)`. +- Route summary: Convert the sufficiently-large-N theorem into a complete all-N resolution without overstating what is already closed or confusing imported thresholds with repo-owned claims. +- Next honest move: Decide whether to extend exact verified coverage beyond `40500` or switch method class. + +## Theorem Hooks + +- `next_unmatched_equals_282_failure`: supported +- `completed_tail_vs_search_leader_split`: supported +- `repair_pool_not_closed`: supported +- `top_repair_class_cluster`: supported + +## Theorem Agenda + +- `choose_next_finite_gap_move`: ready | Choose the next finite-gap closure move and keep the theorem-facing claim surface honest. | Decide whether to extend exact verified coverage beyond `40500` or switch method class. +- `explain_next_unmatched_alignment`: ready | Explain structurally why shared-prefix representative `137720141` aligns with the first failure of tail `282`. | If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class. +- `explain_completed_vs_search_leader_split`: ready | Explain why completed structured tail `332` differs from current family-aware leader `432`. | That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class. +- `model_repair_pool_growth`: ready | Model the repaired square-modulus pool as a growing family rather than treating it as already closed. | Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure. +- `characterize_top_repair_cluster`: ready | Characterize what the top repair cluster `432, 782, 832` shares structurally. | If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction. + +## Bridge State + +- Shared-prefix failures frozen: `24` through `(unknown)`. +- Strongest completed structured tail: `332` through `250000000`. +- Current family-aware leader: `432`. +- Next unmatched representative: `137720141`. + +## Commands + +- Problem surface: `erdos problem show 848` +- Canonical theorem loop: `erdos problem theorem-loop 848` +- Refresh theorem loop: `erdos problem theorem-loop-refresh 848` +- Problem artifacts: `erdos problem artifacts 848` +- Cluster status: `erdos number-theory status 848` +- Cluster frontier: `erdos number-theory frontier 848` +- Source refresh: `erdos number-theory bridge-refresh 848` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/THEOREM_LOOP.md` +- contextPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/context.yaml` +- routePacketPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/ROUTE_PACKET.yaml` +- frontierNotePath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FRONTIER_NOTE.md` +- opsDetailsPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/OPS_DETAILS.yaml` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md` diff --git a/packs/number-theory/problems/848/compute/problem848_base_side_scout.mjs b/packs/number-theory/problems/848/compute/problem848_base_side_scout.mjs new file mode 100644 index 0000000..7d294d8 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_base_side_scout.mjs @@ -0,0 +1,270 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { + max: 2000, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--max') { + args.max = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!Number.isInteger(args.max) || args.max < 1) { + throw new Error('--max must be a positive integer'); + } + return args; +} + +function primeSieve(max) { + const composite = new Uint8Array(max + 1); + const primes = []; + for (let n = 2; n <= max; n += 1) { + if (composite[n]) continue; + primes.push(n); + if (n * n > max) continue; + for (let multiple = n * n; multiple <= max; multiple += n) { + composite[multiple] = 1; + } + } + return primes; +} + +function isNonSquarefree(value, primeSquares) { + for (const square of primeSquares) { + if (square > value) break; + if (value % square === 0) return true; + } + return false; +} + +function residueValues(max, residue) { + const values = []; + for (let n = residue; n <= max; n += 25) { + if (n >= 1) values.push(n); + } + return values; +} + +function upperBound(values, maxValue) { + let low = 0; + let high = values.length; + while (low < high) { + const mid = (low + high) >>> 1; + if (values[mid] <= maxValue) { + low = mid + 1; + } else { + high = mid; + } + } + return low; +} + +function buildCompatibilityLists(outsiders, baseValues, primeSquares) { + const byOutsider = new Map(); + for (const outsider of outsiders) { + const compatible = []; + for (const base of baseValues) { + if (isNonSquarefree(outsider * base + 1, primeSquares)) { + compatible.push(base); + } + } + byOutsider.set(outsider, compatible); + } + return byOutsider; +} + +function summarizeSideAtN(N, outsiders, side7ByOutsider, side18ByOutsider) { + let maxSide7 = 0; + let maxSide18 = 0; + let maxSide7Outsider = null; + let maxSide18Outsider = null; + let maxPerOutsider18Minus7 = -Infinity; + let maxPerOutsider7Minus18 = -Infinity; + let perOutsider18Winner = null; + let perOutsider7Winner = null; + + for (const outsider of outsiders) { + if (outsider > N) break; + const side7 = upperBound(side7ByOutsider.get(outsider) ?? [], N); + const side18 = upperBound(side18ByOutsider.get(outsider) ?? [], N); + if (side7 > maxSide7) { + maxSide7 = side7; + maxSide7Outsider = outsider; + } + if (side18 > maxSide18) { + maxSide18 = side18; + maxSide18Outsider = outsider; + } + const delta18 = side18 - side7; + const delta7 = side7 - side18; + if (delta18 > maxPerOutsider18Minus7) { + maxPerOutsider18Minus7 = delta18; + perOutsider18Winner = { outsider, side7, side18, delta18Minus7: delta18 }; + } + if (delta7 > maxPerOutsider7Minus18) { + maxPerOutsider7Minus18 = delta7; + perOutsider7Winner = { outsider, side7, side18, delta7Minus18: delta7 }; + } + } + + return { + N, + maxSide7, + maxSide18, + maxSide7Outsider, + maxSide18Outsider, + maxSide18Minus7: maxSide18 - maxSide7, + maxPerOutsider18Minus7, + maxPerOutsider7Minus18, + perOutsider18Winner, + perOutsider7Winner, + }; +} + +function analyze(maxN) { + const primeSquares = primeSieve(Math.ceil(Math.sqrt(maxN * maxN + 1))) + .map((prime) => prime * prime); + const side7Values = residueValues(maxN, 7); + const side18Values = residueValues(maxN, 18); + const outsiders = []; + for (let n = 1; n <= maxN; n += 1) { + const residue = n % 25; + if (residue === 7 || residue === 18) continue; + if (isNonSquarefree(n * n + 1, primeSquares)) outsiders.push(n); + } + + const side7ByOutsider = buildCompatibilityLists(outsiders, side7Values, primeSquares); + const side18ByOutsider = buildCompatibilityLists(outsiders, side18Values, primeSquares); + const rows = []; + let globalMaxSide18Minus7 = -Infinity; + let globalMaxPerOutsider18Minus7 = -Infinity; + let firstNWithSide18MaxExceedingSide7 = null; + let firstNWithPerOutsider18ExceedingSide7 = null; + let strongestSide18MaxRow = null; + let strongestPerOutsider18Row = null; + + for (let N = 1; N <= maxN; N += 1) { + const row = summarizeSideAtN(N, outsiders, side7ByOutsider, side18ByOutsider); + rows.push(row); + if (row.maxSide18Minus7 > globalMaxSide18Minus7) { + globalMaxSide18Minus7 = row.maxSide18Minus7; + strongestSide18MaxRow = row; + } + if (row.maxPerOutsider18Minus7 > globalMaxPerOutsider18Minus7) { + globalMaxPerOutsider18Minus7 = row.maxPerOutsider18Minus7; + strongestPerOutsider18Row = row; + } + if (firstNWithSide18MaxExceedingSide7 === null && row.maxSide18 > row.maxSide7) { + firstNWithSide18MaxExceedingSide7 = row; + } + if ( + firstNWithPerOutsider18ExceedingSide7 === null + && row.maxPerOutsider18Minus7 > 0 + ) { + firstNWithPerOutsider18ExceedingSide7 = row; + } + } + + const maxSide18ExceedsSide7 = firstNWithSide18MaxExceedingSide7 !== null; + const perOutsiderSide18ExceedsSide7 = firstNWithPerOutsider18ExceedingSide7 !== null; + return { + schema: 'erdos.number_theory.p848_base_side_scout/1', + generatedAt: new Date().toISOString(), + problemId: '848', + method: 'bounded_base_side_compatibility_scout', + parameters: { + maxN, + }, + status: maxSide18ExceedsSide7 + ? 'counterexample_to_global_7_side_domination_found' + : perOutsiderSide18ExceedsSide7 + ? 'per_outsider_18_side_can_exceed_7_side_but_global_smax_ok' + : 'bounded_7_side_dominates_18_side', + summary: { + interval: `1..${maxN}`, + outsiderCount: outsiders.length, + side7CountAtMax: side7Values.length, + side18CountAtMax: side18Values.length, + globalMaxSide18Minus7, + globalMaxPerOutsider18Minus7, + maxSide18ExceedsSide7, + perOutsiderSide18ExceedsSide7, + }, + strongestSide18MaxRow, + strongestPerOutsider18Row, + firstNWithSide18MaxExceedingSide7, + firstNWithPerOutsider18ExceedingSide7, + rows, + boundary: { + claimLevel: 'bounded_scout_not_proof', + note: 'This scout compares principal-base compatibility counts on a finite interval only. It does not prove all-N base-side domination.', + nextUse: maxSide18ExceedsSide7 + ? 'A one-sided 7 mod 25 base mask is not safe on this bounded scout; a two-sided structural verifier is needed.' + : 'Use this as evidence while seeking either a two-sided verifier or a theorem proving 7-side domination.', + }, + }; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 Base-Side Scout', + '', + `- Generated: ${packet.generatedAt}`, + `- Method: \`${packet.method}\``, + `- Status: \`${packet.status}\``, + `- Interval: \`${packet.summary.interval}\``, + `- Outsiders checked: \`${packet.summary.outsiderCount}\``, + `- Global max side18-minus-side7: \`${packet.summary.globalMaxSide18Minus7}\``, + `- Max per-outsider side18-minus-side7: \`${packet.summary.globalMaxPerOutsider18Minus7}\``, + '', + '## Strongest Rows', + '', + `- Strongest global side-18 row: \`${JSON.stringify(packet.strongestSide18MaxRow)}\``, + `- Strongest per-outsider side-18 row: \`${JSON.stringify(packet.strongestPerOutsider18Row)}\``, + `- First global side-18 exceedance: \`${JSON.stringify(packet.firstNWithSide18MaxExceedingSide7)}\``, + `- First per-outsider side-18 exceedance: \`${JSON.stringify(packet.firstNWithPerOutsider18ExceedingSide7)}\``, + '', + '## Boundary', + '', + `- Claim level: \`${packet.boundary.claimLevel}\``, + `- ${packet.boundary.note}`, + `- Next use: ${packet.boundary.nextUse}`, + '', + ]; + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = analyze(args.max); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify({ + status: packet.status, + interval: packet.summary.interval, + outsiderCount: packet.summary.outsiderCount, + globalMaxSide18Minus7: packet.summary.globalMaxSide18Minus7, + maxSide18ExceedsSide7: packet.summary.maxSide18ExceedsSide7, +}, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_breakpoint_certificate.mjs b/packs/number-theory/problems/848/compute/problem848_breakpoint_certificate.mjs new file mode 100644 index 0000000..73cd9b0 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_breakpoint_certificate.mjs @@ -0,0 +1,148 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { results: null, jsonOutput: null }; + for (let i = 0; i < argv.length; i += 1) { + const token = argv[i]; + if (token === '--results') { + args.results = argv[++i]; + } else if (token === '--json-output') { + args.jsonOutput = argv[++i]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + if (!args.results) { + throw new Error('--results is required'); + } + return args; +} + +function candidateSize(row) { + return Math.max(Number(row.residue7Size), Number(row.residue18Size)); +} + +function candidateClass(row) { + if (row.residue7Size > row.residue18Size) return '7_mod_25'; + if (row.residue18Size > row.residue7Size) return '18_mod_25'; + return '7_or_18_mod_25'; +} + +function buildCandidatePlateaus(rows) { + const plateaus = []; + let current = null; + for (const row of rows) { + const size = candidateSize(row); + if (!current || current.candidateSize !== size || row.N !== current.endN + 1) { + if (current) plateaus.push(current); + current = { + startN: row.N, + endN: row.N, + candidateSize: size, + candidateClassAtEnd: candidateClass(row), + }; + } else { + current.endN = row.N; + current.candidateClassAtEnd = candidateClass(row); + } + } + if (current) plateaus.push(current); + return plateaus; +} + +function countBy(values) { + return Object.fromEntries([...new Set(values)] + .sort((left, right) => Number(left) - Number(right)) + .map((value) => [String(value), values.filter((candidate) => candidate === value).length])); +} + +function validateRows(rows) { + const failures = []; + for (let index = 0; index < rows.length; index += 1) { + const row = rows[index]; + if (row.N !== index + 1) failures.push({ index, N: row.N, reason: 'not_sorted_contiguous_from_one' }); + if (candidateSize(row) !== Number(row.maxCliqueSize)) failures.push({ index, N: row.N, reason: 'candidate_size_not_maximum' }); + if (row.candidateAchievesMaximum !== true) failures.push({ index, N: row.N, reason: 'candidate_flag_false' }); + } + return failures; +} + +function buildCertificate(resultsPath) { + const payload = JSON.parse(fs.readFileSync(resultsPath, 'utf8')); + const rows = Array.isArray(payload.results) ? payload.results : []; + const rowFailures = validateRows(rows); + const rowByN = new Map(rows.map((row) => [row.N, row])); + const plateaus = buildCandidatePlateaus(rows); + const endpointChecks = plateaus.map((plateau) => { + const endpoint = rowByN.get(plateau.endN); + const endpointCandidateSize = endpoint ? candidateSize(endpoint) : null; + const endpointExact = endpoint + && endpoint.candidateAchievesMaximum === true + && Number(endpoint.maxCliqueSize) === endpointCandidateSize + && endpointCandidateSize === plateau.candidateSize; + return { + startN: plateau.startN, + endN: plateau.endN, + length: plateau.endN - plateau.startN + 1, + candidateSize: plateau.candidateSize, + endpointN: plateau.endN, + endpointMaxCliqueSize: endpoint?.maxCliqueSize ?? null, + endpointCandidateSize, + endpointCertified: Boolean(endpointExact), + inferredRows: plateau.endN - plateau.startN + 1, + candidateClassAtEnd: plateau.candidateClassAtEnd, + }; + }); + const failedEndpointChecks = endpointChecks.filter((check) => !check.endpointCertified); + const plateauLengths = endpointChecks.map((check) => check.length); + const interval = payload.summary?.interval ?? (rows.length > 0 ? `${rows[0].N}..${rows.at(-1).N}` : null); + const status = rowFailures.length === 0 && failedEndpointChecks.length === 0 + ? 'certified_from_endpoint_monotonicity' + : 'failed'; + + return { + generatedAt: new Date().toISOString(), + method: 'candidate_plateau_endpoint_monotonicity', + problemId: '848', + sourceResultsPath: path.resolve(resultsPath), + status, + summary: { + interval, + rowCount: rows.length, + endpointCheckCount: endpointChecks.length, + compressionRatio: rows.length > 0 ? rows.length / endpointChecks.length : null, + allRowsAlreadyExact: rowFailures.length === 0, + allEndpointChecksCertified: failedEndpointChecks.length === 0, + plateauLengthFrequency: countBy(plateauLengths), + }, + lemma: { + name: 'candidate_size_plateau_endpoint_monotonicity', + statement: 'For a candidate-size plateau [L,R], if the exact verifier proves omega(G_R) equals the constant candidate size C, then every N in [L,R] has omega(G_N)=C.', + proofSketch: [ + 'The graph G_N is an induced subgraph of G_R for every N <= R, so omega(G_N) <= omega(G_R).', + 'The candidate residue class has constant size C throughout the plateau, so omega(G_N) >= C for every N in [L,R].', + 'The endpoint exact check gives omega(G_R)=C, hence C <= omega(G_N) <= C throughout the plateau.', + ], + scopeBoundary: 'This certificate compresses exact checks inside the certified interval. It does not certify any endpoint that has not itself been exactly checked.', + }, + endpointChecks, + failedEndpointChecks, + rowFailures: rowFailures.slice(0, 50), + }; +} + +const args = parseArgs(process.argv.slice(2)); +const certificate = buildCertificate(args.results); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(certificate, null, 2)}\n`); +} + +console.log(JSON.stringify({ + status: certificate.status, + ...certificate.summary, +}, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_endpoint_menu_compiler.mjs b/packs/number-theory/problems/848/compute/problem848_endpoint_menu_compiler.mjs new file mode 100644 index 0000000..7dbecb0 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_endpoint_menu_compiler.mjs @@ -0,0 +1,1020 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; +import { fileURLToPath } from 'node:url'; + +const scriptDir = path.dirname(fileURLToPath(import.meta.url)); +const problemDir = path.resolve(scriptDir, '..'); + +const DEFAULT_PREDECESSOR_PROOF = path.join( + problemDir, + 'SPLIT_ATOM_PACKETS', + 'DYNAMIC_MARGIN_PROOFS', + 'D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json', +); + +function parseArgs(argv) { + const args = { + predecessorProof: DEFAULT_PREDECESSOR_PROOF, + primes: [23, 31], + fallbackPrimes: [37, 41, 61], + outsider: 6323, + residue: null, + modulus: null, + start: null, + end: null, + window: null, + windowGrid: null, + availabilityProfile: false, + expandedWindow: 10000, + maxSquarePrime: null, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--predecessor-proof') { + args.predecessorProof = argv[++index]; + } else if (token === '--primes') { + args.primes = parsePrimeList(argv[++index]); + } else if (token === '--fallback-primes') { + args.fallbackPrimes = parsePrimeList(argv[++index]); + } else if (token === '--outsider') { + args.outsider = Number(argv[++index]); + } else if (token === '--residue') { + args.residue = Number(argv[++index]); + } else if (token === '--modulus') { + args.modulus = Number(argv[++index]); + } else if (token === '--start') { + args.start = Number(argv[++index]); + } else if (token === '--end') { + args.end = Number(argv[++index]); + } else if (token === '--window') { + args.window = Number(argv[++index]); + } else if (token === '--window-grid') { + args.windowGrid = parseIntegerList(argv[++index]); + } else if (token === '--availability-profile') { + args.availabilityProfile = true; + } else if (token === '--expanded-window') { + args.expandedWindow = Number(argv[++index]); + } else if (token === '--max-square-prime') { + args.maxSquarePrime = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else if (token === '--help' || token === '-h') { + printHelp(); + process.exit(0); + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!Number.isInteger(args.outsider) || args.outsider < 1) { + throw new Error('--outsider must be a positive integer'); + } + for (const [label, primes] of [['--primes', args.primes], ['--fallback-primes', args.fallbackPrimes]]) { + if (!Array.isArray(primes) || primes.some((prime) => !Number.isInteger(prime) || prime < 2)) { + throw new Error(`${label} must be a comma-separated list of primes`); + } + } + if (args.residue !== null && !Number.isInteger(args.residue)) { + throw new Error('--residue must be an integer'); + } + if (args.modulus !== null && (!Number.isInteger(args.modulus) || args.modulus < 1)) { + throw new Error('--modulus must be a positive integer'); + } + if (args.start !== null && (!Number.isInteger(args.start) || args.start < 1)) { + throw new Error('--start must be a positive integer'); + } + if (args.end !== null && (!Number.isInteger(args.end) || args.end < 1)) { + throw new Error('--end must be a positive integer'); + } + if (args.start !== null && args.end !== null && args.start > args.end) { + throw new Error('--start must be <= --end'); + } + if (args.window !== null && (!Number.isInteger(args.window) || args.window < 1)) { + throw new Error('--window must be a positive integer'); + } + if (args.windowGrid !== null && ( + !Array.isArray(args.windowGrid) + || args.windowGrid.length === 0 + || args.windowGrid.some((value) => !Number.isInteger(value) || value < 1) + )) { + throw new Error('--window-grid must be a comma-separated list of positive integers'); + } + if (!Number.isInteger(args.expandedWindow) || args.expandedWindow < 1) { + throw new Error('--expanded-window must be a positive integer'); + } + if (args.maxSquarePrime !== null && (!Number.isInteger(args.maxSquarePrime) || args.maxSquarePrime < 2)) { + throw new Error('--max-square-prime must be an integer >= 2'); + } + + return args; +} + +function printHelp() { + console.log(`Usage: node problem848_endpoint_menu_compiler.mjs [options] + +Compile a deterministic endpoint-menu selector profile for Problem 848. + +Options: + --predecessor-proof Seed proof JSON to read defaults from + --primes Primary menu primes, e.g. 23,31 + --fallback-primes Backup menu primes, e.g. 37,41,61 + --outsider Outsider coefficient (default: 6323) + --residue Residual left residue; defaults from proof + --modulus Residual left modulus; defaults from proof + --start First left value to scan + --end Last left value to scan + --window Endpoint window; defaults from next subatom + --window-grid Profile several endpoint windows, e.g. 25000,28500,35000 + --availability-profile Emit modular window-availability rules instead of squarefree coverage + --expanded-window Smaller predecessor window (default: 10000) + --max-square-prime Square-divisor scan prime limit + --json-output Write JSON packet + --markdown-output Write Markdown summary +`); +} + +function parsePrimeList(value) { + if (!value) return []; + return value.split(',').map((part) => Number(part.trim())).filter((part) => Number.isFinite(part)); +} + +function parseIntegerList(value) { + if (!value) return []; + return value.split(',').map((part) => Number(part.trim())).filter((part) => Number.isFinite(part)); +} + +function readJson(filePath) { + return JSON.parse(fs.readFileSync(filePath, 'utf8')); +} + +function positiveModulo(value, modulus) { + const bigModulus = BigInt(modulus); + const residue = BigInt(value) % bigModulus; + return residue < 0n ? residue + bigModulus : residue; +} + +function gcdExtended(a, b) { + let oldR = BigInt(a); + let r = BigInt(b); + let oldS = 1n; + let s = 0n; + + while (r !== 0n) { + const quotient = oldR / r; + [oldR, r] = [r, oldR - quotient * r]; + [oldS, s] = [s, oldS - quotient * s]; + } + + return { gcd: oldR < 0n ? -oldR : oldR, coefficient: oldS }; +} + +function modularInverse(value, modulus) { + const normalized = positiveModulo(value, modulus); + const { gcd, coefficient } = gcdExtended(normalized, BigInt(modulus)); + if (gcd !== 1n) { + throw new Error(`${value} has no inverse modulo ${modulus}`); + } + return positiveModulo(coefficient, modulus); +} + +function primeSieve(max) { + const composite = new Uint8Array(max + 1); + const primes = []; + for (let value = 2; value <= max; value += 1) { + if (composite[value]) continue; + primes.push(value); + if (value * value > max) continue; + for (let multiple = value * value; multiple <= max; multiple += value) { + composite[multiple] = 1; + } + } + return primes; +} + +function gcdNumber(a, b) { + let left = Math.abs(Number(a)); + let right = Math.abs(Number(b)); + while (right !== 0) { + [left, right] = [right, left % right]; + } + return left; +} + +function firstSquareDivisor(value, primes) { + const n = BigInt(value); + for (const prime of primes) { + const square = BigInt(prime) * BigInt(prime); + if (square > n) break; + if (n % square === 0n) { + return { prime, square: prime * prime }; + } + } + return null; +} + +function compileEndpointFormula({ prime, outsider }) { + const primeSquare = prime * prime; + const modulus = BigInt(primeSquare); + const denominator = BigInt(25 * outsider); + const inverse = modularInverse(denominator, modulus); + const leftCoefficient = positiveModulo(BigInt(outsider) * inverse, modulus); + const constant = positiveModulo((1n - 14n * BigInt(outsider)) * inverse, modulus); + const maxDelta = -14; + const minDelta = -14 - 25 * (primeSquare - 1); + + return { + prime, + primeSquare, + kFormula: { + leftCoefficient: Number(leftCoefficient), + constant: Number(constant), + modulus: primeSquare, + text: `k_${prime}(left) = (${leftCoefficient}*left + ${constant}) mod ${primeSquare}`, + }, + deltaRange: { + min: minDelta, + max: maxDelta, + }, + universallyWithinWindows: { + 10000: Math.abs(minDelta) <= 10000, + 25000: Math.abs(minDelta) <= 25000, + }, + }; +} + +function endpointForLeft({ left, formula, outsider }) { + const k = Number(positiveModulo( + BigInt(formula.kFormula.leftCoefficient) * BigInt(left) + BigInt(formula.kFormula.constant), + formula.primeSquare, + )); + const delta = -14 - 25 * k; + const right = left + delta; + const outsiderCompatibilityResidue = Number(positiveModulo(BigInt(outsider) * BigInt(right) + 1n, formula.primeSquare)); + const crossProductPlusOne = BigInt(left) * BigInt(right) + 1n; + return { + prime: formula.prime, + k, + delta, + right, + rightMod25: Number(positiveModulo(right, 25)), + withinWindow: null, + compatibilityModPrimeSquare: outsiderCompatibilityResidue, + crossProductPlusOne: crossProductPlusOne.toString(), + }; +} + +function evaluateEndpoint({ left, formula, outsider, window, squarePrimes }) { + const endpoint = endpointForLeft({ left, formula, outsider }); + const squareWitness = firstSquareDivisor(endpoint.crossProductPlusOne, squarePrimes); + const checkedSquarePrimeLimit = squarePrimes.at(-1) ?? null; + const exactSquarefree = checkedSquarePrimeLimit !== null + && BigInt(checkedSquarePrimeLimit) * BigInt(checkedSquarePrimeLimit) >= BigInt(endpoint.crossProductPlusOne); + const squarefreeStatus = squareWitness + ? 'non_squarefree' + : exactSquarefree + ? 'exact_squarefree' + : 'no_checked_square_divisor'; + return { + ...endpoint, + withinWindow: endpoint.delta <= -14 && endpoint.delta >= -window, + checkedSquarePrimeLimit, + squareDivisorPrime: squareWitness?.prime ?? null, + squareDivisor: squareWitness?.square ?? null, + squarefree: exactSquarefree && squareWitness === null, + squarefreeStatus, + profileUsable: squareWitness === null, + }; +} + +function alignStartToResidue(start, residue, modulus) { + const offset = Number(positiveModulo(BigInt(residue) - BigInt(start), modulus)); + return start + offset; +} + +function makeCountMap(values) { + const counts = new Map(); + for (const value of values) { + counts.set(value, (counts.get(value) ?? 0) + 1); + } + return [...counts.entries()] + .map(([key, count]) => ({ key, count })) + .sort((left, right) => right.count - left.count || Number(left.key) - Number(right.key)); +} + +function maxKForWindow(window) { + return Math.floor((window - 14) / 25); +} + +function windowFromMaxK(maxK) { + return 14 + 25 * maxK; +} + +function resolveProfileDefaults(args) { + const predecessor = readJson(args.predecessorProof); + const residualClass = { + residue: args.residue ?? predecessor.residualClass?.residue, + modulus: args.modulus ?? predecessor.residualClass?.modulus, + }; + if (!Number.isInteger(residualClass.residue) || !Number.isInteger(residualClass.modulus)) { + throw new Error('Residual class is required; pass --residue and --modulus or use a predecessor proof with residualClass'); + } + + const targetWindow = args.window ?? predecessor.nextSubatom?.seedEscapeWindow ?? 25000; + const firstBlockedLeft = predecessor.firstFullyExpandedMenuBlockedRow?.left ?? null; + const start = args.start ?? firstBlockedLeft ?? residualClass.residue; + const end = args.end ?? start; + return { + predecessor, + residualClass, + targetWindow, + firstBlockedLeft, + start, + end, + }; +} + +function compileAvailabilityRule({ formula, residualClass, window }) { + const primeSquare = formula.primeSquare; + const maxK = maxKForWindow(window); + const base = Number(positiveModulo( + BigInt(formula.kFormula.leftCoefficient) * BigInt(residualClass.residue) + BigInt(formula.kFormula.constant), + primeSquare, + )); + const step = Number(positiveModulo( + BigInt(formula.kFormula.leftCoefficient) * BigInt(residualClass.modulus), + primeSquare, + )); + const stepGcd = gcdNumber(step, primeSquare); + const period = primeSquare / stepGcd; + const availableTResidues = []; + let availableCount = 0; + let firstUnavailableTResidue = null; + + for (let tResidue = 0; tResidue < period; tResidue += 1) { + const k = Number(positiveModulo(BigInt(base) + BigInt(step) * BigInt(tResidue), primeSquare)); + const available = k <= maxK; + if (available) { + availableCount += 1; + if (availableTResidues.length < 16) { + availableTResidues.push({ tResidue, k }); + } + } else if (firstUnavailableTResidue === null) { + firstUnavailableTResidue = { tResidue, k }; + } + } + + return { + window, + maxK, + minimalWindowForMaxK: maxK < 0 ? null : windowFromMaxK(maxK), + criterion: `within window ${window} iff k_${formula.prime}(left) <= ${maxK}`, + leftParameterization: `left = ${residualClass.residue} + ${residualClass.modulus}*t`, + kFormulaInT: `k_${formula.prime}(t) = (${step}*t + ${base}) mod ${primeSquare}`, + tPeriod: period, + stepGcdWithPrimeSquare: stepGcd, + availableResidueCount: availableCount, + unavailableResidueCount: period - availableCount, + density: availableCount / period, + universallyWithinWindow: availableCount === period, + firstAvailableTResidues: availableTResidues, + firstUnavailableTResidue, + }; +} + +function compileAvailabilityProfile(args) { + const defaults = resolveProfileDefaults(args); + const windows = [...new Set(args.windowGrid ?? [defaults.targetWindow])].sort((left, right) => left - right); + const primaryFormulas = args.primes.map((prime) => compileEndpointFormula({ prime, outsider: args.outsider })); + const fallbackFormulas = args.fallbackPrimes.map((prime) => compileEndpointFormula({ prime, outsider: args.outsider })); + const allFormulas = [...primaryFormulas, ...fallbackFormulas]; + const firstLeft = alignStartToResidue(defaults.start, defaults.residualClass.residue, defaults.residualClass.modulus); + const witnessRows = []; + const maxWitnessRows = 25; + + for ( + let left = firstLeft; + left <= defaults.end && witnessRows.length < maxWitnessRows; + left += defaults.residualClass.modulus + ) { + witnessRows.push({ + left, + leftModResidualClass: Number(positiveModulo(left, defaults.residualClass.modulus)), + endpoints: allFormulas.map((formula) => { + const endpoint = endpointForLeft({ left, formula, outsider: args.outsider }); + return { + prime: endpoint.prime, + k: endpoint.k, + delta: endpoint.delta, + right: endpoint.right, + rightMod25: endpoint.rightMod25, + compatibilityModPrimeSquare: endpoint.compatibilityModPrimeSquare, + withinWindows: Object.fromEntries(windows.map((window) => [window, endpoint.delta <= -14 && endpoint.delta >= -window])), + }; + }), + }); + } + + return { + schema: 'erdos.number_theory.p848_endpoint_availability_profile/1', + generatedAt: new Date().toISOString(), + problemId: '848', + target: { + description: 'q17 residual window-relaxed fallback endpoint-menu availability profile', + predecessorProof: args.predecessorProof, + outsider: args.outsider, + residualClass: defaults.residualClass, + start: firstLeft, + end: defaults.end, + witnessRowCount: witnessRows.length, + windows, + }, + interpretation: { + endpointWindowCriterion: 'Because delta=-14-25*k, an endpoint is inside window W exactly when k <= floor((W-14)/25).', + provesSquarefreeHitting: false, + provesCollisionFreeMatching: false, + warning: 'This profile proves modular endpoint availability only. Squarefree hitting and matching remain separate layers.', + }, + primaryMenu: { + primeSet: args.primes, + }, + fallbackMenu: { + primeSet: args.fallbackPrimes, + }, + formulasByPrime: Object.fromEntries(allFormulas.map((formula) => [ + formula.prime, + { + ...formula, + availabilityByWindow: windows.map((window) => compileAvailabilityRule({ + formula, + residualClass: defaults.residualClass, + window, + })), + }, + ])), + witnessRows, + nextTheoremOptions: [ + { + id: 'availability_residue_cover', + status: 'ready', + statement: 'Use the k-threshold rules to split endpoint availability into finite t-residue strata before proving squarefree hitting.', + }, + { + id: 'window_legality_threshold', + status: 'ready', + statement: `The candidate windows have thresholds ${windows.map((window) => `${window}->k<=${maxKForWindow(window)}`).join(', ')}; prove which threshold is theorem-legal.`, + }, + ], + }; +} + +function compileProfile(args) { + const { + residualClass, + targetWindow, + firstBlockedLeft, + start, + end, + } = resolveProfileDefaults(args); + const maxSquarePrime = args.maxSquarePrime ?? Math.ceil(Math.sqrt(Number(BigInt(end) * BigInt(end) + 1n))); + const squarePrimes = primeSieve(maxSquarePrime); + const primaryFormulas = args.primes.map((prime) => compileEndpointFormula({ prime, outsider: args.outsider })); + const fallbackFormulas = args.fallbackPrimes.map((prime) => compileEndpointFormula({ prime, outsider: args.outsider })); + const allFormulas = [...primaryFormulas, ...fallbackFormulas]; + const firstLeft = alignStartToResidue(start, residualClass.residue, residualClass.modulus); + const rows = []; + const primaryCoveredRows = []; + const allCoveredRows = []; + const primaryMisses = []; + const allMisses = []; + + for (let left = firstLeft; left <= end; left += residualClass.modulus) { + const primaryEndpoints = primaryFormulas.map((formula) => evaluateEndpoint({ + left, + formula, + outsider: args.outsider, + window: targetWindow, + squarePrimes, + })); + const fallbackEndpoints = fallbackFormulas.map((formula) => evaluateEndpoint({ + left, + formula, + outsider: args.outsider, + window: targetWindow, + squarePrimes, + })); + const allEndpoints = [...primaryEndpoints, ...fallbackEndpoints]; + const firstPrimarySquarefree = primaryEndpoints.find((endpoint) => endpoint.withinWindow && endpoint.profileUsable) ?? null; + const firstAnySquarefree = allEndpoints.find((endpoint) => endpoint.withinWindow && endpoint.profileUsable) ?? null; + const row = { + left, + leftModResidualClass: Number(positiveModulo(left, residualClass.modulus)), + primaryEndpoints, + fallbackEndpoints, + firstPrimarySquarefree, + firstAnySquarefree, + primaryCovered: Boolean(firstPrimarySquarefree), + allCovered: Boolean(firstAnySquarefree), + }; + rows.push(row); + if (row.primaryCovered) { + primaryCoveredRows.push(row); + } else { + primaryMisses.push(row); + } + if (row.allCovered) { + allCoveredRows.push(row); + } else { + allMisses.push(row); + } + } + + const primaryCoverPrimes = primaryCoveredRows.map((row) => row.firstPrimarySquarefree.prime); + const allCoverPrimes = allCoveredRows.map((row) => row.firstAnySquarefree.prime); + const exactForPrimaryCoveredEndpoints = primaryCoveredRows.length > 0 + && primaryCoveredRows.every((row) => row.firstPrimarySquarefree?.squarefreeStatus === 'exact_squarefree'); + const exactForAllCoveredEndpoints = allCoveredRows.length > 0 + && allCoveredRows.every((row) => row.firstAnySquarefree?.squarefreeStatus === 'exact_squarefree'); + const checkedPrimeLimit = squarePrimes.at(-1) ?? null; + const primaryFormulasByPrime = Object.fromEntries(primaryFormulas.map((formula) => [formula.prime, formula])); + const fallbackFormulasByPrime = Object.fromEntries(fallbackFormulas.map((formula) => [formula.prime, formula])); + const squareCheckInterpretation = allCoveredRows.length === 0 + ? 'No full-menu covered endpoint was selected in this profile; inspect candidate square-divisor statuses and window availability.' + : exactForAllCoveredEndpoints + ? 'Every covered endpoint selected by the full menu is exactly squarefree-certified.' + : 'Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof.'; + + return { + schema: 'erdos.number_theory.p848_endpoint_menu_compiler/1', + generatedAt: new Date().toISOString(), + problemId: '848', + target: { + description: 'q17 residual window-relaxed fallback endpoint-menu selector', + predecessorProof: args.predecessorProof, + outsider: args.outsider, + residualClass, + start: firstLeft, + end, + rowCount: rows.length, + targetWindow, + predecessorWindow: args.expandedWindow, + squareCheck: { + checkedPrimeLimit, + exactForPrimaryCoveredEndpoints, + exactForAllCoveredEndpoints, + interpretation: squareCheckInterpretation, + }, + }, + endpointRule: { + statement: 'For each menu prime p, choose k_p(left) modulo p^2 so p^2 divides outsider*(left - 14 - 25*k_p(left)) + 1, then set right_p(left)=left-14-25*k_p(left).', + invariant: 'Every compiled endpoint has right congruent to 18 mod 25 and is outsider-compatible by construction.', + }, + primaryMenu: { + primeSet: args.primes, + formulasByPrime: primaryFormulasByPrime, + universalWindowAvailability: primaryFormulas.every((formula) => Math.abs(formula.deltaRange.min) <= targetWindow), + }, + fallbackMenu: { + primeSet: args.fallbackPrimes, + formulasByPrime: fallbackFormulasByPrime, + universalWindowAvailability: fallbackFormulas.every((formula) => Math.abs(formula.deltaRange.min) <= targetWindow), + }, + allMenu: { + primeSet: allFormulas.map((formula) => formula.prime), + formulasByPrime: Object.fromEntries(allFormulas.map((formula) => [formula.prime, formula])), + }, + coverage: { + primaryCovered: primaryCoveredRows.length, + primaryMisses: primaryMisses.length, + allCovered: allCoveredRows.length, + allMisses: allMisses.length, + firstPrimaryMiss: primaryMisses[0] ?? null, + firstAllMiss: allMisses[0] ?? null, + primaryCoverPrimeCounts: makeCountMap(primaryCoverPrimes), + allCoverPrimeCounts: makeCountMap(allCoverPrimes), + }, + seedCheck: firstBlockedLeft === null + ? null + : rows.find((row) => row.left === firstBlockedLeft) ?? null, + rowSamples: { + firstRows: rows.slice(0, 5), + primaryMisses: primaryMisses.slice(0, 5), + allMisses: allMisses.slice(0, 5), + }, + claims: { + provesAllN: false, + provesCollisionFreeMatching: false, + provesEndpointFormulas: true, + provesUniversalWindowAvailabilityForPrimaryMenu: primaryFormulas.every((formula) => Math.abs(formula.deltaRange.min) <= targetWindow), + provesBoundedPrimaryMenuCoverage: primaryMisses.length === 0 && exactForPrimaryCoveredEndpoints, + provesBoundedAllMenuCoverage: allMisses.length === 0 && exactForAllCoveredEndpoints, + screensBoundedPrimaryMenuCoverage: primaryMisses.length === 0, + screensBoundedAllMenuCoverage: allMisses.length === 0, + }, + nextTheoremOptions: buildNextTheoremOptions({ + targetWindow, + primaryMisses, + allMisses, + primaryFormulas, + fallbackFormulas, + }), + }; +} + +function summarizeEndpoint(endpoint) { + if (!endpoint) return null; + return { + prime: endpoint.prime, + k: endpoint.k, + delta: endpoint.delta, + right: endpoint.right, + withinWindow: endpoint.withinWindow, + squarefreeStatus: endpoint.squarefreeStatus, + squareDivisorPrime: endpoint.squareDivisorPrime, + squareDivisor: endpoint.squareDivisor, + checkedSquarePrimeLimit: endpoint.checkedSquarePrimeLimit, + }; +} + +function summarizeMissRow(row) { + if (!row) return null; + const endpoints = [...(row.primaryEndpoints ?? []), ...(row.fallbackEndpoints ?? [])]; + const usableWithinWindow = endpoints + .filter((endpoint) => endpoint.withinWindow && endpoint.profileUsable) + .sort((left, right) => Math.abs(left.delta) - Math.abs(right.delta)); + const usableOutsideWindow = endpoints + .filter((endpoint) => !endpoint.withinWindow && endpoint.profileUsable) + .sort((left, right) => Math.abs(left.delta) - Math.abs(right.delta)); + const blockedWithinWindow = endpoints + .filter((endpoint) => endpoint.withinWindow && !endpoint.profileUsable) + .sort((left, right) => Math.abs(left.delta) - Math.abs(right.delta)); + + return { + left: row.left, + leftModResidualClass: row.leftModResidualClass, + usableWithinWindow: usableWithinWindow.slice(0, 5).map(summarizeEndpoint), + nearestUsableOutsideWindow: usableOutsideWindow.slice(0, 5).map(summarizeEndpoint), + blockedWithinWindow: blockedWithinWindow.slice(0, 5).map(summarizeEndpoint), + }; +} + +function summarizeProfileForWindow(packet) { + return { + window: packet.target.targetWindow, + rowCount: packet.target.rowCount, + squareCheck: packet.target.squareCheck, + primaryCovered: packet.coverage.primaryCovered, + primaryMisses: packet.coverage.primaryMisses, + allCovered: packet.coverage.allCovered, + allMisses: packet.coverage.allMisses, + firstPrimaryMiss: summarizeMissRow(packet.coverage.firstPrimaryMiss), + firstAllMiss: summarizeMissRow(packet.coverage.firstAllMiss), + primaryCoverPrimeCounts: packet.coverage.primaryCoverPrimeCounts, + allCoverPrimeCounts: packet.coverage.allCoverPrimeCounts, + claims: { + provesBoundedPrimaryMenuCoverage: packet.claims.provesBoundedPrimaryMenuCoverage, + provesBoundedAllMenuCoverage: packet.claims.provesBoundedAllMenuCoverage, + screensBoundedPrimaryMenuCoverage: packet.claims.screensBoundedPrimaryMenuCoverage, + screensBoundedAllMenuCoverage: packet.claims.screensBoundedAllMenuCoverage, + }, + }; +} + +function compileWindowGrid(args) { + const windows = [...new Set(args.windowGrid)].sort((left, right) => left - right); + const profiles = windows.map((window) => compileProfile({ + ...args, + window, + windowGrid: null, + jsonOutput: null, + markdownOutput: null, + })); + const summaries = profiles.map(summarizeProfileForWindow); + const firstScreenPrimaryCovered = summaries.find((summary) => summary.primaryMisses === 0) ?? null; + const firstScreenAllCovered = summaries.find((summary) => summary.allMisses === 0) ?? null; + const firstProvedPrimaryCovered = summaries.find((summary) => summary.claims.provesBoundedPrimaryMenuCoverage) ?? null; + const firstProvedAllCovered = summaries.find((summary) => summary.claims.provesBoundedAllMenuCoverage) ?? null; + const baseline = profiles[0]; + const gridHasCoveredEndpoints = profiles.some((profile) => profile.coverage.allCovered > 0); + const gridCoveredEndpointsExact = gridHasCoveredEndpoints + && profiles.every((profile) => profile.coverage.allCovered === 0 || profile.target.squareCheck.exactForAllCoveredEndpoints); + const gridSquareCheckInterpretation = !gridHasCoveredEndpoints + ? 'No full-menu covered endpoint was selected in any profiled window; inspect candidate square-divisor statuses and window availability.' + : gridCoveredEndpointsExact + ? 'Every covered endpoint selected by each profiled full menu is exactly squarefree-certified.' + : 'Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof.'; + + return { + schema: 'erdos.number_theory.p848_endpoint_window_grid/1', + generatedAt: new Date().toISOString(), + problemId: '848', + target: { + description: `${baseline.target.description} window grid`, + predecessorProof: args.predecessorProof, + outsider: args.outsider, + residualClass: baseline.target.residualClass, + start: baseline.target.start, + end: baseline.target.end, + rowCount: baseline.target.rowCount, + windows, + squareCheck: gridSquareCheckInterpretation, + }, + primaryMenu: baseline.primaryMenu.primeSet, + fallbackMenu: baseline.fallbackMenu.primeSet, + firstScreenPrimaryCoveredWindow: firstScreenPrimaryCovered?.window ?? null, + firstScreenAllCoveredWindow: firstScreenAllCovered?.window ?? null, + firstProvedPrimaryCoveredWindow: firstProvedPrimaryCovered?.window ?? null, + firstProvedAllCoveredWindow: firstProvedAllCovered?.window ?? null, + summaries, + interpretation: { + windowGridProvesAllN: false, + warning: 'A window grid is a bounded selector profile. It can identify the next theorem boundary but does not prove all-N coverage or matching by itself.', + }, + nextTheoremOptions: buildWindowGridNextTheoremOptions({ summaries }), + }; +} + +function buildWindowGridNextTheoremOptions({ summaries }) { + const options = []; + const firstAllCovered = summaries.find((summary) => summary.allMisses === 0) ?? null; + const finalSummary = summaries.at(-1) ?? null; + if (firstAllCovered) { + options.push({ + id: 'window_relaxation_candidate', + status: 'candidate', + statement: `The full menu first covers the bounded scan at window=${firstAllCovered.window}; decide whether that relaxation is theorem-legal or requires a replacement-path handoff.`, + }); + } + if (finalSummary?.allMisses > 0) { + options.push({ + id: 'window_grid_first_remaining_miss', + status: 'needed', + statement: `Even the largest profiled window=${finalSummary.window} has first full-menu miss left=${finalSummary.firstAllMiss?.left}; inspect that row before adding more primes or windows.`, + }); + } + options.push({ + id: 'availability_strata_lift', + status: 'needed', + statement: 'Convert the observed window thresholds into residue-class availability strata rather than continuing a row-by-row staircase.', + }); + return options; +} + +function buildNextTheoremOptions({ targetWindow, primaryMisses, allMisses, primaryFormulas, fallbackFormulas }) { + const options = []; + if (primaryFormulas.every((formula) => Math.abs(formula.deltaRange.min) <= targetWindow)) { + options.push({ + id: 'primary_menu_universal_window_lemma', + status: 'ready', + statement: `Every primary endpoint prime stays inside the ${targetWindow}-window by its delta range.`, + }); + } + if (primaryMisses.length === 0) { + options.push({ + id: 'primary_menu_squarefree_hitting_lemma', + status: 'candidate', + statement: 'The primary menu alone covers the bounded scan; attempt a symbolic squarefree-hitting lemma for the primary menu.', + }); + } else { + options.push({ + id: 'primary_menu_first_miss', + status: 'needed', + statement: `The primary menu misses at left=${primaryMisses[0].left}; inspect this miss before adding more abstraction.`, + }); + } + if (allMisses.length === 0) { + options.push({ + id: 'full_menu_squarefree_hitting_lemma', + status: 'candidate', + statement: 'The full menu covers the bounded scan; try to prove a symbolic finite-menu squarefree-hitting lemma.', + }); + } else { + options.push({ + id: 'full_menu_first_miss', + status: 'needed', + statement: `The full menu misses at left=${allMisses[0].left}; emit this row as the next deterministic obstruction.`, + }); + } + if (fallbackFormulas.some((formula) => Math.abs(formula.deltaRange.min) > targetWindow)) { + options.push({ + id: 'fallback_window_availability_split', + status: 'optional', + statement: 'Some fallback primes are not universally inside the window; split fallback usage into availability residues before relying on them symbolically.', + }); + } + return options; +} + +function renderMarkdown(packet) { + const lines = []; + lines.push(`# Problem 848 Endpoint Menu Compiler`); + lines.push(''); + lines.push(`- Target: \`${packet.target.description}\``); + lines.push(`- Residual class: \`left ≡ ${packet.target.residualClass.residue} mod ${packet.target.residualClass.modulus}\``); + lines.push(`- Scan: \`${packet.target.start}..${packet.target.end}\` over \`${packet.target.rowCount}\` residual rows`); + lines.push(`- Window: \`${packet.target.targetWindow}\``); + lines.push(`- Square check: \`${packet.target.squareCheck.interpretation}\``); + lines.push(`- Primary menu: \`${packet.primaryMenu.primeSet.join(',')}\``); + lines.push(`- Fallback menu: \`${packet.fallbackMenu.primeSet.join(',') || '(none)'}\``); + lines.push(''); + lines.push(`## Endpoint Formulas`); + lines.push(''); + for (const formula of Object.values(packet.allMenu.formulasByPrime)) { + lines.push(`- p=${formula.prime}: \`${formula.kFormula.text}\`; delta range \`${formula.deltaRange.min}..${formula.deltaRange.max}\`; within ${packet.target.targetWindow}: \`${Math.abs(formula.deltaRange.min) <= packet.target.targetWindow}\``); + } + lines.push(''); + lines.push(`## Coverage`); + lines.push(''); + lines.push(`- Primary covered: \`${packet.coverage.primaryCovered}/${packet.target.rowCount}\``); + lines.push(`- Full menu covered: \`${packet.coverage.allCovered}/${packet.target.rowCount}\``); + lines.push(`- First primary miss: \`${packet.coverage.firstPrimaryMiss?.left ?? '(none)'}\``); + lines.push(`- First full-menu miss: \`${packet.coverage.firstAllMiss?.left ?? '(none)'}\``); + lines.push(`- Primary cover prime counts: \`${JSON.stringify(packet.coverage.primaryCoverPrimeCounts)}\``); + lines.push(`- Full cover prime counts: \`${JSON.stringify(packet.coverage.allCoverPrimeCounts)}\``); + lines.push(''); + const firstAllMissSummary = summarizeMissRow(packet.coverage.firstAllMiss); + if (firstAllMissSummary) { + lines.push(`## First Full-Menu Miss Detail`); + lines.push(''); + lines.push(`- Left: \`${firstAllMissSummary.left}\``); + lines.push(`- Left residual: \`${firstAllMissSummary.leftModResidualClass}\``); + if (firstAllMissSummary.blockedWithinWindow.length > 0) { + lines.push(`- Blocked within-window endpoints: \`${JSON.stringify(firstAllMissSummary.blockedWithinWindow)}\``); + } + if (firstAllMissSummary.nearestUsableOutsideWindow.length > 0) { + lines.push(`- Nearest unblocked outside-window endpoints: \`${JSON.stringify(firstAllMissSummary.nearestUsableOutsideWindow)}\``); + } + lines.push(''); + } + lines.push(`## Next Theorem Options`); + lines.push(''); + for (const option of packet.nextTheoremOptions) { + lines.push(`- \`${option.id}\` [${option.status}]: ${option.statement}`); + } + lines.push(''); + lines.push(`## Boundary`); + lines.push(''); + lines.push('- This compiler proves endpoint formulas and bounded coverage profiles only.'); + lines.push('- It does not prove all-N squarefree hitting or collision-free matching by itself.'); + lines.push(''); + return `${lines.join('\n')}\n`; +} + +function renderWindowGridMarkdown(packet) { + const lines = []; + lines.push(`# Problem 848 Endpoint Window Grid`); + lines.push(''); + lines.push(`- Target: \`${packet.target.description}\``); + lines.push(`- Residual class: \`left ≡ ${packet.target.residualClass.residue} mod ${packet.target.residualClass.modulus}\``); + lines.push(`- Scan: \`${packet.target.start}..${packet.target.end}\` over \`${packet.target.rowCount}\` residual rows`); + lines.push(`- Windows: \`${packet.target.windows.join(',')}\``); + lines.push(`- Square check: \`${packet.target.squareCheck}\``); + lines.push(`- Primary menu: \`${packet.primaryMenu.join(',')}\``); + lines.push(`- Fallback menu: \`${packet.fallbackMenu.join(',') || '(none)'}\``); + lines.push(`- First screen primary-covered window: \`${packet.firstScreenPrimaryCoveredWindow ?? '(none)'}\``); + lines.push(`- First screen full-menu-covered window: \`${packet.firstScreenAllCoveredWindow ?? '(none)'}\``); + lines.push(''); + lines.push(`## Coverage By Window`); + lines.push(''); + for (const summary of packet.summaries) { + lines.push(`- window=${summary.window}: primary \`${summary.primaryCovered}/${summary.rowCount}\`, full \`${summary.allCovered}/${summary.rowCount}\`, first primary miss \`${summary.firstPrimaryMiss?.left ?? '(none)'}\`, first full miss \`${summary.firstAllMiss?.left ?? '(none)'}\``); + const nearest = summary.firstAllMiss?.nearestUsableOutsideWindow?.[0] ?? null; + if (nearest) { + lines.push(`- window=${summary.window} nearest unblocked outside-window endpoint for first full miss: p=${nearest.prime}, delta=${nearest.delta}, right=${nearest.right}, status=${nearest.squarefreeStatus}`); + } + } + lines.push(''); + lines.push(`## Next Theorem Options`); + lines.push(''); + for (const option of packet.nextTheoremOptions) { + lines.push(`- \`${option.id}\` [${option.status}]: ${option.statement}`); + } + lines.push(''); + lines.push(`## Boundary`); + lines.push(''); + lines.push(`- ${packet.interpretation.warning}`); + lines.push(''); + return `${lines.join('\n')}\n`; +} + +function renderAvailabilityMarkdown(packet) { + const lines = []; + lines.push(`# Problem 848 Endpoint Availability Profile`); + lines.push(''); + lines.push(`- Target: \`${packet.target.description}\``); + lines.push(`- Residual class: \`left ≡ ${packet.target.residualClass.residue} mod ${packet.target.residualClass.modulus}\``); + lines.push(`- Windows: \`${packet.target.windows.join(',')}\``); + lines.push(`- Primary menu: \`${packet.primaryMenu.primeSet.join(',')}\``); + lines.push(`- Fallback menu: \`${packet.fallbackMenu.primeSet.join(',') || '(none)'}\``); + lines.push(''); + lines.push(`## Window Thresholds`); + lines.push(''); + for (const window of packet.target.windows) { + lines.push(`- window=${window}: endpoint is available iff \`k <= ${maxKForWindow(window)}\`; minimal exact threshold window is \`${windowFromMaxK(maxKForWindow(window))}\``); + } + lines.push(''); + lines.push(`## Availability By Prime`); + lines.push(''); + for (const formula of Object.values(packet.formulasByPrime)) { + lines.push(`- p=${formula.prime}: \`${formula.kFormula.text}\``); + for (const rule of formula.availabilityByWindow) { + lines.push(`- p=${formula.prime}, window=${rule.window}: \`${rule.kFormulaInT}\`, t-period \`${rule.tPeriod}\`, available \`${rule.availableResidueCount}/${rule.tPeriod}\`, universal \`${rule.universallyWithinWindow}\``); + } + } + if (packet.witnessRows.length > 0) { + lines.push(''); + lines.push(`## Witness Rows`); + lines.push(''); + for (const row of packet.witnessRows.slice(0, 5)) { + const endpoints = row.endpoints + .map((endpoint) => `p=${endpoint.prime}: k=${endpoint.k}, delta=${endpoint.delta}, windows=${JSON.stringify(endpoint.withinWindows)}`) + .join('; '); + lines.push(`- left=${row.left}: ${endpoints}`); + } + } + lines.push(''); + lines.push(`## Next Theorem Options`); + lines.push(''); + for (const option of packet.nextTheoremOptions) { + lines.push(`- \`${option.id}\` [${option.status}]: ${option.statement}`); + } + lines.push(''); + lines.push(`## Boundary`); + lines.push(''); + lines.push(`- ${packet.interpretation.warning}`); + lines.push(''); + return `${lines.join('\n')}\n`; +} + +function writeOutput(filePath, content) { + fs.mkdirSync(path.dirname(filePath), { recursive: true }); + fs.writeFileSync(filePath, content); +} + +function main() { + const args = parseArgs(process.argv.slice(2)); + const packet = args.availabilityProfile + ? compileAvailabilityProfile(args) + : args.windowGrid + ? compileWindowGrid(args) + : compileProfile(args); + const json = JSON.stringify(packet, null, 2); + if (args.jsonOutput) { + writeOutput(args.jsonOutput, `${json}\n`); + } + if (args.markdownOutput) { + writeOutput( + args.markdownOutput, + args.availabilityProfile + ? renderAvailabilityMarkdown(packet) + : args.windowGrid + ? renderWindowGridMarkdown(packet) + : renderMarkdown(packet), + ); + } + if (!args.jsonOutput && !args.markdownOutput) { + console.log(json); + } else { + const isAvailabilityProfile = packet.schema === 'erdos.number_theory.p848_endpoint_availability_profile/1'; + const isWindowGrid = packet.schema === 'erdos.number_theory.p848_endpoint_window_grid/1'; + console.log(JSON.stringify(isAvailabilityProfile + ? { + ok: true, + jsonOutput: args.jsonOutput, + markdownOutput: args.markdownOutput, + windows: packet.target.windows, + witnessRowCount: packet.target.witnessRowCount, + } + : isWindowGrid + ? { + ok: true, + jsonOutput: args.jsonOutput, + markdownOutput: args.markdownOutput, + firstScreenPrimaryCoveredWindow: packet.firstScreenPrimaryCoveredWindow, + firstScreenAllCoveredWindow: packet.firstScreenAllCoveredWindow, + firstProvedPrimaryCoveredWindow: packet.firstProvedPrimaryCoveredWindow, + firstProvedAllCoveredWindow: packet.firstProvedAllCoveredWindow, + largestWindow: packet.target.windows.at(-1), + largestWindowAllMisses: packet.summaries.at(-1)?.allMisses ?? null, + } + : { + ok: true, + jsonOutput: args.jsonOutput, + markdownOutput: args.markdownOutput, + primaryCovered: packet.coverage.primaryCovered, + primaryMisses: packet.coverage.primaryMisses, + allCovered: packet.coverage.allCovered, + allMisses: packet.coverage.allMisses, + firstPrimaryMiss: packet.coverage.firstPrimaryMiss?.left ?? null, + firstAllMiss: packet.coverage.firstAllMiss?.left ?? null, + }, null, 2)); + } +} + +main(); diff --git a/packs/number-theory/problems/848/compute/problem848_exact_breakpoint_scout.mjs b/packs/number-theory/problems/848/compute/problem848_exact_breakpoint_scout.mjs new file mode 100644 index 0000000..416549f --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_exact_breakpoint_scout.mjs @@ -0,0 +1,140 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { results: null, jsonOutput: null }; + for (let i = 0; i < argv.length; i += 1) { + const token = argv[i]; + if (token === '--results') { + args.results = argv[++i]; + } else if (token === '--json-output') { + args.jsonOutput = argv[++i]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + if (!args.results) { + throw new Error('--results is required'); + } + return args; +} + +function exampleClass(row) { + if (row.exampleMatchesResidue7 && row.exampleMatchesResidue18) return '7_or_18'; + if (row.exampleMatchesResidue7) return '7'; + if (row.exampleMatchesResidue18) return '18'; + return 'other'; +} + +function rowSignature(row) { + return [ + row.maxCliqueSize, + row.residue7Size, + row.residue18Size, + exampleClass(row), + ].join('/'); +} + +function pushPlateau(plateaus, current) { + if (!current) return; + plateaus.push({ + startN: current.startN, + endN: current.endN, + length: current.endN - current.startN + 1, + signature: current.signature, + maxCliqueSize: current.maxCliqueSize, + residue7Size: current.residue7Size, + residue18Size: current.residue18Size, + exampleClass: current.exampleClass, + }); +} + +function buildPlateaus(rows) { + const plateaus = []; + let current = null; + for (const row of rows) { + const signature = rowSignature(row); + if (!current || current.signature !== signature || row.N !== current.endN + 1) { + pushPlateau(plateaus, current); + current = { + startN: row.N, + endN: row.N, + signature, + maxCliqueSize: row.maxCliqueSize, + residue7Size: row.residue7Size, + residue18Size: row.residue18Size, + exampleClass: exampleClass(row), + }; + } else { + current.endN = row.N; + } + } + pushPlateau(plateaus, current); + return plateaus; +} + +function countBy(values) { + return Object.fromEntries([...new Set(values)] + .sort((left, right) => Number(left) - Number(right)) + .map((value) => [String(value), values.filter((candidate) => candidate === value).length])); +} + +function analyze(resultsPath) { + const payload = JSON.parse(fs.readFileSync(resultsPath, 'utf8')); + const rows = Array.isArray(payload.results) ? payload.results : []; + const seen = new Set(); + let duplicateCount = 0; + let sorted = true; + let previousN = 0; + for (const row of rows) { + if (seen.has(row.N)) duplicateCount += 1; + seen.add(row.N); + if (row.N !== previousN + 1) sorted = false; + previousN = row.N; + } + + const plateaus = buildPlateaus(rows); + const breakpointNs = plateaus.slice(1).map((plateau) => plateau.startN); + const breakpointGaps = breakpointNs.map((value, index) => ( + index === 0 ? value - plateaus[0].startN : value - breakpointNs[index - 1] + )); + + return { + generatedAt: new Date().toISOString(), + method: 'exact_rows_breakpoint_scout', + problemId: '848', + sourceResultsPath: path.resolve(resultsPath), + sourceSummary: payload.summary ?? null, + summary: { + interval: payload.summary?.interval ?? (rows.length > 0 ? `${rows[0].N}..${rows.at(-1).N}` : null), + rowCount: rows.length, + uniqueNCount: seen.size, + duplicateCount, + sortedContiguousFromOne: sorted && rows[0]?.N === 1, + allCandidateAchievesMaximum: rows.every((row) => row.candidateAchievesMaximum === true), + allExampleCliquesMatchCandidateClass: rows.every((row) => row.exampleMatchesResidue7 || row.exampleMatchesResidue18), + plateauCount: plateaus.length, + breakpointCount: breakpointNs.length, + breakpointGapFrequency: countBy(breakpointGaps), + }, + plateaus, + breakpointNs, + boundary: { + claimLevel: 'scout_not_proof', + note: 'This artifact summarizes already-certified exact rows. It does not prove coverage between unchecked rows or replace a Regime B monotonicity/breakpoint lemma.', + nextUse: 'Use the plateau and breakpoint pattern to propose a structured-breakpoint certificate with an explicit monotonicity justification.', + }, + }; +} + +const args = parseArgs(process.argv.slice(2)); +const packet = analyze(args.results); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +console.log(JSON.stringify(packet.summary, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_external_structural_audit.mjs b/packs/number-theory/problems/848/compute/problem848_external_structural_audit.mjs new file mode 100644 index 0000000..332b3f9 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_external_structural_audit.mjs @@ -0,0 +1,354 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { + sourceDir: process.env.P848_EXTERNAL_SOURCE_DIR ?? '/tmp/hjyuh-erdos-848', + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--source-dir') { + args.sourceDir = argv[++index]; + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + return args; +} + +function walkFiles(rootDir) { + const files = []; + const stack = [rootDir]; + while (stack.length > 0) { + const current = stack.pop(); + const entries = fs.readdirSync(current, { withFileTypes: true }); + for (const entry of entries) { + if (entry.name === '.git' || entry.name === 'node_modules') { + continue; + } + const entryPath = path.join(current, entry.name); + if (entry.isDirectory()) { + stack.push(entryPath); + } else if (entry.isFile()) { + files.push(entryPath); + } + } + } + return files.sort(); +} + +function readText(filePath) { + try { + return fs.readFileSync(filePath, 'utf8'); + } catch { + return ''; + } +} + +function relativePath(rootDir, filePath) { + return path.relative(rootDir, filePath).replaceAll(path.sep, '/'); +} + +function findLineHits(rootDir, filePath, patterns) { + const lines = readText(filePath).split(/\r?\n/); + const hits = []; + for (let index = 0; index < lines.length; index += 1) { + const line = lines[index]; + if (patterns.some((pattern) => pattern.test(line))) { + hits.push({ + file: relativePath(rootDir, filePath), + line: index + 1, + text: line.trim().slice(0, 240), + }); + } + } + return hits; +} + +function hasAny(text, patterns) { + return patterns.some((pattern) => pattern.test(text)); +} + +function buildCheck({ checkId, status, severity, summary, evidence = [], recommendation }) { + return { + checkId, + status, + severity, + summary, + evidence, + recommendation, + }; +} + +function analyzeSource(sourceDir) { + const sourceRoot = path.resolve(sourceDir); + const sourceExists = fs.existsSync(sourceRoot) && fs.statSync(sourceRoot).isDirectory(); + if (!sourceExists) { + return { + schema: 'erdos.number_theory.p848_external_structural_verifier_audit/1', + generatedAt: new Date().toISOString(), + problemId: '848', + sourceDir: sourceRoot, + sourceAvailable: false, + status: 'source_unavailable', + conclusion: 'No external verifier source tree was available to audit.', + summary: { + sourceFileCount: 0, + markdownFileCount: 0, + cppFileCount: 0, + blockerCount: 1, + warningCount: 0, + supportCount: 0, + }, + checks: [ + buildCheck({ + checkId: 'external_source_tree_available', + status: 'failed', + severity: 'blocker', + summary: `Expected an external verifier source tree at ${sourceRoot}.`, + recommendation: 'Clone or copy the external verifier source before trying to absorb its structural ideas.', + }), + ], + nextActions: [ + 'Provide an external verifier source tree, then rerun this audit.', + 'Do not promote external finite coverage unless the verifier source and certificate are both present.', + ], + honestyBoundary: 'This audit only evaluates structural import readiness. It does not certify the external computation or solve Problem 848.', + }; + } + + const files = walkFiles(sourceRoot); + const markdownFiles = files.filter((file) => /\.md$/i.test(file)); + const cppFiles = files.filter((file) => /\.(cc|cpp|cxx|hpp|h)$/i.test(file)); + const certificateFiles = files.filter((file) => /certificate.*\.(tsv|csv|json)$/i.test(file)); + const allMarkdownText = markdownFiles.map(readText).join('\n'); + const allCppText = cppFiles.map(readText).join('\n'); + + const sawHandoffHits = markdownFiles.flatMap((file) => findLineHits(sourceRoot, file, [ + /Sawhney/i, + /10\^7|10000000/i, + /N\s*>\s*10/i, + ])).filter((hit) => /Sawhney|10\^7|10000000|N\s*>\s*10/i.test(hit.text)); + const claimsTenMillionSawhneyHandoff = /Sawhney/i.test(allMarkdownText) + && /(10\^7|10\^⁷|10000000|N\s*[>≥]\s*10)/i.test(allMarkdownText) + && /(all positive integers|for all N|N\s*>\s*10\^?7|N\s*>\s*10000000)/i.test(allMarkdownText); + + const baseResidueBothPresent = hasAny(allCppText, [ + /r\s*==\s*7\s*\|\|\s*r\s*==\s*18/, + /r\s*==\s*18\s*\|\|\s*r\s*==\s*7/, + ]); + const baseSevenMaskPresent = hasAny(allCppText, [ + /7LL\s*\*\s*x\s*\+\s*1/, + /7\s*\+\s*25\s*\*\s*m/, + /7LL\s*\+\s*25LL\s*\*/, + /for\s*\([^)]*m[^)]*\)\s*[^;{]*7\s*\+\s*25/, + ]); + const baseEighteenMaskPresent = hasAny(allCppText, [ + /18LL\s*\*\s*x\s*\+\s*1/, + /18\s*\+\s*25\s*\*\s*m/, + /18LL\s*\+\s*25LL\s*\*/, + /for\s*\([^)]*m[^)]*\)\s*[^;{]*18\s*\+\s*25/, + ]); + const baseMaskHits = cppFiles.flatMap((file) => findLineHits(sourceRoot, file, [ + /7LL\s*\*\s*x\s*\+\s*1/, + /18LL\s*\*\s*x\s*\+\s*1/, + /7LL\s*\+\s*25LL\s*\*/, + /18LL\s*\+\s*25LL\s*\*/, + /r\s*==\s*7\s*\|\|\s*r\s*==\s*18/, + ])); + + const inequalityPresent = hasAny(allMarkdownText, [ + /s_max/i, + /R_\{>p\}/, + /outsider-clique/i, + /Verification Inequality/i, + ]); + const breakpointClaimPresent = hasAny(allMarkdownText, [ + /breakpoints/i, + /zero failures/i, + /margin/i, + ]); + const cppVerifierPresent = cppFiles.some((file) => /848.*verifier|verifier.*848/i.test(relativePath(sourceRoot, file))); + + const checks = [ + buildCheck({ + checkId: 'external_source_tree_available', + status: 'passed', + severity: 'support', + summary: `Audited ${files.length} files under ${sourceRoot}.`, + evidence: [{ file: '.', line: null, text: sourceRoot }], + recommendation: 'Keep this source tree pinned by URL and commit before any promotion.', + }), + buildCheck({ + checkId: 'sawhney_handoff_not_claimed_at_1e7', + status: claimsTenMillionSawhneyHandoff ? 'failed' : 'passed', + severity: claimsTenMillionSawhneyHandoff ? 'blocker' : 'support', + summary: claimsTenMillionSawhneyHandoff + ? 'The external writeup appears to claim that Sawhney handles N > 10^7.' + : 'No direct Sawhney handoff at 10^7 was detected in the scanned markdown.', + evidence: sawHandoffHits.slice(0, 12), + recommendation: claimsTenMillionSawhneyHandoff + ? 'Replace the 10^7 handoff with a repo-audited explicit threshold or mark the claim external-only.' + : 'Keep scanning for threshold language whenever the external source changes.', + }), + buildCheck({ + checkId: 'base_exchange_mask_covers_both_principal_sides', + status: baseSevenMaskPresent && !baseEighteenMaskPresent ? 'failed' : 'passed', + severity: baseSevenMaskPresent && !baseEighteenMaskPresent ? 'blocker' : 'support', + summary: baseSevenMaskPresent && !baseEighteenMaskPresent + ? 'The verifier appears to build base-exchange masks for the 7 mod 25 side without a parallel 18 mod 25 mask.' + : 'The scanned verifier did not expose a one-sided 7 mod 25 base-mask pattern.', + evidence: baseMaskHits.slice(0, 12), + recommendation: baseSevenMaskPresent && !baseEighteenMaskPresent + ? 'Either add a separate 18 mod 25 mask audit, or supply a proof that the 7-side mask dominates the 18-side case for every outsider and N.' + : 'If relying on symmetry rather than explicit masks, record the symmetry lemma next to the verifier certificate.', + }), + buildCheck({ + checkId: 'both_base_residues_are_excluded_from_outsider_pool', + status: baseResidueBothPresent ? 'passed' : 'warning', + severity: baseResidueBothPresent ? 'support' : 'warning', + summary: baseResidueBothPresent + ? 'The verifier source explicitly recognizes both 7 and 18 mod 25 as principal base residues.' + : 'The scan did not find an explicit 7-or-18 base residue predicate.', + evidence: baseMaskHits.filter((hit) => /r\s*==\s*7|r\s*==\s*18/.test(hit.text)).slice(0, 6), + recommendation: 'Keep outsider-pool exclusion separate from base-exchange mask coverage; both are required for promotion.', + }), + buildCheck({ + checkId: 'outsider_clique_inequality_is_documented', + status: inequalityPresent ? 'passed' : 'warning', + severity: inequalityPresent ? 'support' : 'warning', + summary: inequalityPresent + ? 'The external writeup documents an outsider-clique style inequality.' + : 'The scan did not find the outsider-clique inequality in markdown.', + evidence: markdownFiles.flatMap((file) => findLineHits(sourceRoot, file, [/s_max/i, /R_\{>p\}/, /outsider-clique/i])).slice(0, 8), + recommendation: 'Treat this as a structural idea source until the inequality is ported into repo-owned definitions and tests.', + }), + buildCheck({ + checkId: 'finite_certificate_surface_present', + status: certificateFiles.length > 0 && breakpointClaimPresent && cppVerifierPresent ? 'passed' : 'warning', + severity: certificateFiles.length > 0 && breakpointClaimPresent && cppVerifierPresent ? 'support' : 'warning', + summary: certificateFiles.length > 0 && breakpointClaimPresent && cppVerifierPresent + ? 'The source includes verifier code, certificate-like output, and breakpoint/margin claims.' + : 'The scan did not find a complete verifier/certificate/writeup surface.', + evidence: [ + ...certificateFiles.slice(0, 5).map((file) => ({ file: relativePath(sourceRoot, file), line: null, text: 'certificate-like artifact' })), + ...cppFiles.filter((file) => /848.*verifier|verifier.*848/i.test(relativePath(sourceRoot, file))).slice(0, 5) + .map((file) => ({ file: relativePath(sourceRoot, file), line: null, text: 'verifier source' })), + ], + recommendation: 'Require a repo-owned certificate schema before importing any interval coverage.', + }), + ]; + + const blockerCount = checks.filter((check) => check.severity === 'blocker' && check.status === 'failed').length; + const warningCount = checks.filter((check) => check.severity === 'warning').length; + const supportCount = checks.filter((check) => check.severity === 'support' && check.status === 'passed').length; + const status = blockerCount > 0 ? 'blocked' : warningCount > 0 ? 'needs_review' : 'passed_for_structural_reuse'; + + return { + schema: 'erdos.number_theory.p848_external_structural_verifier_audit/1', + generatedAt: new Date().toISOString(), + problemId: '848', + sourceDir: sourceRoot, + sourceAvailable: true, + status, + conclusion: blockerCount > 0 + ? 'The external verifier is useful as an idea source, but it is blocked from canonical promotion.' + : 'No blocker was detected by the structural import audit; this still does not certify the computation.', + summary: { + sourceFileCount: files.length, + markdownFileCount: markdownFiles.length, + cppFileCount: cppFiles.length, + certificateLikeFileCount: certificateFiles.length, + blockerCount, + warningCount, + supportCount, + baseSevenMaskPresent, + baseEighteenMaskPresent, + baseResidueBothPresent, + claimsTenMillionSawhneyHandoff, + }, + checks, + nextActions: blockerCount > 0 + ? [ + 'Keep the external computation in EXTERNAL_VERIFICATION_LEDGER as blocked, not promoted.', + 'Patch or independently reimplement the structural verifier with both base sides covered.', + 'Replace the false 10^7 Sawhney handoff with a repo-audited explicit threshold before any all-N claim.', + 'Port only the outsider-clique inequality shape into a repo-owned structural verifier lane.', + ] + : [ + 'Port the structural verifier into the repo-owned certificate spec.', + 'Run the verifier under reproducible CI or supervised local compute before promoting coverage.', + 'Keep the asymptotic threshold handoff separate from bounded finite certificates.', + ], + honestyBoundary: 'This audit only evaluates structural import readiness. It does not certify the external computation or solve Problem 848.', + }; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 External Structural Verifier Audit', + '', + `- Generated: ${packet.generatedAt}`, + `- Source dir: \`${packet.sourceDir}\``, + `- Status: \`${packet.status}\``, + `- Conclusion: ${packet.conclusion}`, + '', + '## Summary', + '', + ]; + + for (const [key, value] of Object.entries(packet.summary ?? {})) { + lines.push(`- ${key}: \`${value}\``); + } + + lines.push('', '## Checks', ''); + for (const check of packet.checks ?? []) { + lines.push(`- \`${check.checkId}\` [${check.status}/${check.severity}] ${check.summary}`); + if (check.recommendation) { + lines.push(`- Recommendation: ${check.recommendation}`); + } + for (const hit of check.evidence ?? []) { + const lineLabel = hit.line ? `:${hit.line}` : ''; + lines.push(`- Evidence: \`${hit.file}${lineLabel}\` ${hit.text ?? ''}`); + } + } + + lines.push('', '## Next Actions', ''); + for (const action of packet.nextActions ?? []) { + lines.push(`- ${action}`); + } + + lines.push('', '## Boundary', ''); + lines.push(`- ${packet.honestyBoundary}`); + lines.push(''); + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = analyzeSource(args.sourceDir); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify({ + status: packet.status, + blockerCount: packet.summary?.blockerCount ?? 0, + warningCount: packet.summary?.warningCount ?? 0, + sourceAvailable: packet.sourceAvailable, +}, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_full_mixed_base_structural_verifier.mjs b/packs/number-theory/problems/848/compute/problem848_full_mixed_base_structural_verifier.mjs new file mode 100644 index 0000000..500da4b --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_full_mixed_base_structural_verifier.mjs @@ -0,0 +1,933 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { + max: 10000, + minStructuralN: 7307, + rowSampleLimit: 200, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--max') { + args.max = Number(argv[++index]); + } else if (token === '--min-structural-n') { + args.minStructuralN = Number(argv[++index]); + } else if (token === '--row-sample-limit') { + args.rowSampleLimit = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!Number.isInteger(args.max) || args.max < 1) { + throw new Error('--max must be a positive integer'); + } + if (!Number.isInteger(args.minStructuralN) || args.minStructuralN < 1) { + throw new Error('--min-structural-n must be a positive integer'); + } + if (args.minStructuralN > args.max) { + throw new Error('--min-structural-n must be <= --max'); + } + if (!Number.isInteger(args.rowSampleLimit) || args.rowSampleLimit < 1) { + throw new Error('--row-sample-limit must be a positive integer'); + } + return args; +} + +function positiveModulo(value, modulus) { + const residue = value % modulus; + return residue < 0 ? residue + modulus : residue; +} + +function modInverse(value, modulus) { + let oldR = positiveModulo(value, modulus); + let r = modulus; + let oldS = 1; + let s = 0; + while (r !== 0) { + const quotient = Math.floor(oldR / r); + [oldR, r] = [r, oldR - quotient * r]; + [oldS, s] = [s, oldS - quotient * s]; + } + if (oldR !== 1) return null; + return positiveModulo(oldS, modulus); +} + +function primeSieve(max) { + const composite = new Uint8Array(max + 1); + const primes = []; + for (let n = 2; n <= max; n += 1) { + if (composite[n]) continue; + primes.push(n); + if (n * n > max) continue; + for (let multiple = n * n; multiple <= max; multiple += n) { + composite[multiple] = 1; + } + } + return primes; +} + +function isBaseResidue(value) { + const residue = positiveModulo(value, 25); + return residue === 7 || residue === 18; +} + +function isNonSquarefree(value, primeSquares) { + for (const square of primeSquares) { + if (square > value) break; + if (value % square === 0) return true; + } + return false; +} + +function residueValues(max, residue, modulus = 25) { + const values = []; + for (let value = residue; value <= max; value += modulus) { + if (value >= 1) values.push(value); + } + return values; +} + +function upperBound(values, maxValue) { + let low = 0; + let high = values.length; + while (low < high) { + const mid = (low + high) >>> 1; + if (values[mid] <= maxValue) { + low = mid + 1; + } else { + high = mid; + } + } + return low; +} + +function henselRootPrimeSquare(p) { + let rootModP = null; + for (let residue = 1; residue < p; residue += 1) { + if ((residue * residue + 1) % p === 0) { + rootModP = residue; + break; + } + } + if (rootModP === null) { + throw new Error(`No root for p=${p}`); + } + const p2 = p * p; + const t = Math.floor((rootModP * rootModP + 1) / p) % p; + const inverse = modInverse((2 * rootModP) % p, p); + if (inverse === null) { + throw new Error(`Hensel inverse failed for p=${p}`); + } + let k = (-t * inverse) % p; + if (k < 0) k += p; + let root = (rootModP + k * p) % p2; + if (root <= 0) root += p2; + if ((root * root + 1) % p2 !== 0) { + throw new Error(`Hensel root verification failed for p=${p}`); + } + return { + p, + p2, + rPlus: root, + rMinus: p2 - root, + }; +} + +function buildRootInfos(maxN) { + return primeSieve(Math.floor(Math.sqrt(maxN)) + 5) + .filter((prime) => prime >= 13 && prime % 4 === 1 && prime * prime <= maxN) + .map(henselRootPrimeSquare); +} + +function rootProgression(residue, modulus, maxN) { + const values = []; + for (let value = residue; value <= maxN; value += modulus) { + if (value >= 1) values.push(value); + } + return values; +} + +function classifyLeastWitness(value, roots) { + for (let index = 0; index < roots.length; index += 1) { + const root = roots[index]; + const residue = positiveModulo(value, root.p2); + if (residue === root.rPlus) { + return { index, sign: 'plus', p: root.p }; + } + if (residue === root.rMinus) { + return { index, sign: 'minus', p: root.p }; + } + } + return null; +} + +function compatibleValues(value, candidates, primeSquares) { + return candidates.filter((candidate) => isNonSquarefree(value * candidate + 1, primeSquares)); +} + +function maxPrefixCompatibility(values, compatibleByValue, activeN) { + let max = 0; + let witness = null; + for (const value of values) { + if (value > activeN) break; + const count = upperBound(compatibleByValue.get(value) ?? [], activeN); + if (count > max) { + max = count; + witness = value; + } + } + return { max, witness }; +} + +function hopcroftKarp(leftCount, rightCount, adjacency) { + const pairLeft = new Int32Array(leftCount).fill(-1); + const pairRight = new Int32Array(rightCount).fill(-1); + const distance = new Int32Array(leftCount); + let matching = 0; + + function bfs() { + const queue = []; + let foundFreeRight = false; + for (let left = 0; left < leftCount; left += 1) { + if (pairLeft[left] === -1) { + distance[left] = 0; + queue.push(left); + } else { + distance[left] = -1; + } + } + for (let cursor = 0; cursor < queue.length; cursor += 1) { + const left = queue[cursor]; + for (const right of adjacency[left]) { + const nextLeft = pairRight[right]; + if (nextLeft === -1) { + foundFreeRight = true; + } else if (distance[nextLeft] === -1) { + distance[nextLeft] = distance[left] + 1; + queue.push(nextLeft); + } + } + } + return foundFreeRight; + } + + function dfs(left) { + for (const right of adjacency[left]) { + const nextLeft = pairRight[right]; + if (nextLeft === -1 || (distance[nextLeft] === distance[left] + 1 && dfs(nextLeft))) { + pairLeft[left] = right; + pairRight[right] = left; + return true; + } + } + distance[left] = -1; + return false; + } + + while (bfs()) { + for (let left = 0; left < leftCount; left += 1) { + if (pairLeft[left] === -1 && dfs(left)) { + matching += 1; + } + } + } + + return { matching, pairLeft, pairRight }; +} + +function buildBaseCrossCompatibility(side7Values, side18Values, primeSquares) { + const side7IndexByValue = new Map(side7Values.map((value, index) => [value, index])); + const side18IndexByValue = new Map(side18Values.map((value, index) => [value, index])); + const side18Count = side18Values.length; + const compatible = new Uint8Array(side7Values.length * side18Count); + for (let left = 0; left < side7Values.length; left += 1) { + for (let right = 0; right < side18Values.length; right += 1) { + if (isNonSquarefree(side7Values[left] * side18Values[right] + 1, primeSquares)) { + compatible[left * side18Count + right] = 1; + } + } + } + return { + side7IndexByValue, + side18IndexByValue, + side18Count, + compatible, + }; +} + +function maximumCoBipartiteClique(side7, side18, crossCompatibility) { + const missingCrossEdges = side7.map(() => []); + const side7GlobalIndices = side7.map((value) => crossCompatibility.side7IndexByValue.get(value)); + const side18GlobalIndices = side18.map((value) => crossCompatibility.side18IndexByValue.get(value)); + for (let left = 0; left < side7.length; left += 1) { + for (let right = 0; right < side18.length; right += 1) { + const compatibleIndex = side7GlobalIndices[left] * crossCompatibility.side18Count + side18GlobalIndices[right]; + if (!crossCompatibility.compatible[compatibleIndex]) { + missingCrossEdges[left].push(right); + } + } + } + + const { matching, pairLeft, pairRight } = hopcroftKarp(side7.length, side18.length, missingCrossEdges); + const visitedLeft = new Uint8Array(side7.length); + const visitedRight = new Uint8Array(side18.length); + const queue = []; + for (let left = 0; left < side7.length; left += 1) { + if (pairLeft[left] === -1) { + visitedLeft[left] = 1; + queue.push({ side: 'left', index: left }); + } + } + + for (let cursor = 0; cursor < queue.length; cursor += 1) { + const entry = queue[cursor]; + if (entry.side === 'left') { + for (const right of missingCrossEdges[entry.index]) { + if (pairLeft[entry.index] === right || visitedRight[right]) continue; + visitedRight[right] = 1; + queue.push({ side: 'right', index: right }); + } + } else { + const left = pairRight[entry.index]; + if (left !== -1 && !visitedLeft[left]) { + visitedLeft[left] = 1; + queue.push({ side: 'left', index: left }); + } + } + } + + const cliqueSide7 = []; + const cliqueSide18 = []; + for (let left = 0; left < side7.length; left += 1) { + if (visitedLeft[left]) cliqueSide7.push(side7[left]); + } + for (let right = 0; right < side18.length; right += 1) { + if (!visitedRight[right]) cliqueSide18.push(side18[right]); + } + + return { + cliqueSize: side7.length + side18.length - matching, + matchingSize: matching, + side7Count: side7.length, + side18Count: side18.length, + cliqueSide7Count: cliqueSide7.length, + cliqueSide18Count: cliqueSide18.length, + exampleClique: [...cliqueSide7, ...cliqueSide18].sort((left, right) => left - right), + }; +} + +function buildBlock(root, rootIndex, roots, maxN, baseSides, primeSquares) { + const rawPlusValues = rootProgression(root.rPlus, root.p2, maxN); + const rawMinusValues = rootProgression(root.rMinus, root.p2, maxN); + const plusValues = rawPlusValues.filter((value) => { + if (isBaseResidue(value)) return false; + const witness = classifyLeastWitness(value, roots); + return witness?.index === rootIndex && witness.sign === 'plus'; + }); + const minusValues = rawMinusValues.filter((value) => { + if (isBaseResidue(value)) return false; + const witness = classifyLeastWitness(value, roots); + return witness?.index === rootIndex && witness.sign === 'minus'; + }); + const outsiderValues = [...plusValues, ...minusValues].sort((left, right) => left - right); + const side7CompatibleByValue = new Map(); + const side18CompatibleByValue = new Map(); + const unionCompatibleByValue = new Map(); + + for (const value of outsiderValues) { + const side7 = compatibleValues(value, baseSides.side7Values, primeSquares); + const side18 = compatibleValues(value, baseSides.side18Values, primeSquares); + side7CompatibleByValue.set(value, side7); + side18CompatibleByValue.set(value, side18); + unionCompatibleByValue.set(value, [...side7, ...side18].sort((left, right) => left - right)); + } + + const plusToMinus = new Map(plusValues.map((value) => [value, []])); + const minusToPlus = new Map(minusValues.map((value) => [value, []])); + for (const plus of plusValues) { + for (const minus of minusValues) { + if (!isNonSquarefree(plus * minus + 1, primeSquares)) continue; + plusToMinus.get(plus).push(minus); + minusToPlus.get(minus).push(plus); + } + } + + return { + root, + rootIndex, + rawPlusValues, + rawMinusValues, + plusValues, + minusValues, + outsiderValues, + side7CompatibleByValue, + side18CompatibleByValue, + unionCompatibleByValue, + plusToMinus, + minusToPlus, + }; +} + +function evaluateStructuralRow(block, higherRootEventValues, baseSides, activeN) { + const rawPlus = upperBound(block.rawPlusValues, activeN); + const rawMinus = upperBound(block.rawMinusValues, activeN); + const vMax = Math.max(rawPlus, rawMinus); + const s7 = maxPrefixCompatibility(block.outsiderValues, block.side7CompatibleByValue, activeN); + const s18 = maxPrefixCompatibility(block.outsiderValues, block.side18CompatibleByValue, activeN); + const sUnion = maxPrefixCompatibility(block.outsiderValues, block.unionCompatibleByValue, activeN); + const activePlus = upperBound(block.plusValues, activeN); + const activeMinus = upperBound(block.minusValues, activeN); + let dMax = 0; + let dWitness = null; + + for (const plus of block.plusValues.slice(0, activePlus)) { + const degree = upperBound(block.plusToMinus.get(plus) ?? [], activeN); + if (degree > dMax) { + dMax = degree; + dWitness = { side: 'plus', value: plus }; + } + } + for (const minus of block.minusValues.slice(0, activeMinus)) { + const degree = upperBound(block.minusToPlus.get(minus) ?? [], activeN); + if (degree > dMax) { + dMax = degree; + dWitness = { side: 'minus', value: minus }; + } + } + + const rGreater = upperBound(higherRootEventValues, activeN); + const side7CandidateSize = upperBound(baseSides.side7Values, activeN); + const side18CandidateSize = upperBound(baseSides.side18Values, activeN); + const candidateSize = Math.max(side7CandidateSize, side18CandidateSize); + const side7Bound = s7.max + vMax + dMax + rGreater; + const side18Bound = s18.max + vMax + dMax + rGreater; + const unionBound = sUnion.max + vMax + dMax + rGreater; + const strictBaseThreshold = candidateSize - vMax - dMax - rGreater; + + return { + N: activeN, + p: block.root.p, + p2: block.root.p2, + rawPlus, + rawMinus, + vMax, + activePlus, + activeMinus, + activeOutsiderCount: activePlus + activeMinus, + sMaxSide7: s7.max, + sMaxSide7Witness: s7.witness, + sMaxSide18: s18.max, + sMaxSide18Witness: s18.witness, + sMaxUnion: sUnion.max, + sMaxUnionWitness: sUnion.witness, + dMax, + dMaxWitness: dWitness, + rGreater, + candidateSize, + side7CandidateSize, + side18CandidateSize, + side7Bound, + side18Bound, + unionBound, + strictBaseThreshold, + side7Margin: candidateSize - side7Bound, + side18Margin: candidateSize - side18Bound, + unionMargin: candidateSize - unionBound, + side7Pass: side7Bound < candidateSize, + side18Pass: side18Bound < candidateSize, + unionPass: unionBound < candidateSize, + }; +} + +function exactMixedForOutsider(block, activeN, outsider, crossCompatibility) { + const side7Compatible = block.side7CompatibleByValue.get(outsider) ?? []; + const side18Compatible = block.side18CompatibleByValue.get(outsider) ?? []; + const side7 = side7Compatible.slice(0, upperBound(side7Compatible, activeN)); + const side18 = side18Compatible.slice(0, upperBound(side18Compatible, activeN)); + return maximumCoBipartiteClique(side7, side18, crossCompatibility); +} + +function evaluateMixedRow(block, row, crossCompatibility) { + if (row.unionPass) { + return { + ...row, + certificateMode: 'union_bound', + threateningOutsiderCount: 0, + exactMixedCheckCount: 0, + sMaxMixed: null, + sMaxMixedWitness: null, + mixedBound: row.unionBound, + mixedMargin: row.unionMargin, + mixedPass: true, + maxImprovementOverUnion: 0, + threatSummaries: [], + }; + } + + const threatening = []; + for (const outsider of block.outsiderValues) { + if (outsider > row.N) break; + const unionCount = upperBound(block.unionCompatibleByValue.get(outsider) ?? [], row.N); + if (unionCount >= row.strictBaseThreshold) { + threatening.push({ outsider, unionCount }); + } + } + + let sMaxMixed = 0; + let sMaxMixedWitness = null; + let worstThreat = null; + let maxImprovementOverUnion = 0; + const threatSummaries = []; + for (const threat of threatening) { + const mixed = exactMixedForOutsider(block, row.N, threat.outsider, crossCompatibility); + const improvement = threat.unionCount - mixed.cliqueSize; + const requiredMatchingLowerBound = mixed.side7Count + mixed.side18Count - row.strictBaseThreshold + 1; + const smallerSideSize = Math.min(mixed.side7Count, mixed.side18Count); + threatSummaries.push({ + outsider: threat.outsider, + outsiderMod25: positiveModulo(threat.outsider, 25), + unionCount: threat.unionCount, + mixedBaseCliqueSize: mixed.cliqueSize, + matchingSizeInMissingCrossGraph: mixed.matchingSize, + compatibleSide7Count: mixed.side7Count, + compatibleSide18Count: mixed.side18Count, + requiredMatchingLowerBound, + matchingSlack: mixed.matchingSize - requiredMatchingLowerBound, + smallerSideSize, + saturatesSmallerSide: mixed.matchingSize === smallerSideSize, + mixedCliqueSide7Count: mixed.cliqueSide7Count, + mixedCliqueSide18Count: mixed.cliqueSide18Count, + dominantMixedCliqueSide: mixed.cliqueSide7Count > mixed.cliqueSide18Count + ? 'side7' + : mixed.cliqueSide18Count > mixed.cliqueSide7Count + ? 'side18' + : 'tie', + }); + if (mixed.cliqueSize > sMaxMixed) { + sMaxMixed = mixed.cliqueSize; + sMaxMixedWitness = threat.outsider; + worstThreat = { + outsider: threat.outsider, + unionCount: threat.unionCount, + mixedBaseCliqueSize: mixed.cliqueSize, + matchingSizeInMissingCrossGraph: mixed.matchingSize, + compatibleSide7Count: mixed.side7Count, + compatibleSide18Count: mixed.side18Count, + mixedCliqueSide7Count: mixed.cliqueSide7Count, + mixedCliqueSide18Count: mixed.cliqueSide18Count, + exampleMixedBaseClique: mixed.exampleClique, + }; + } + if (improvement > maxImprovementOverUnion) { + maxImprovementOverUnion = improvement; + } + } + + const mixedBound = sMaxMixed + row.vMax + row.dMax + row.rGreater; + const mixedMargin = row.candidateSize - mixedBound; + return { + ...row, + certificateMode: 'exact_mixed_base', + threateningOutsiderCount: threatening.length, + exactMixedCheckCount: threatening.length, + sMaxMixed, + sMaxMixedWitness, + mixedBound, + mixedMargin, + mixedPass: mixedBound < row.candidateSize, + maxImprovementOverUnion, + threatSummaries, + worstThreat, + }; +} + +function dominantMixedCliqueSide(row) { + const side7 = row.worstThreat?.mixedCliqueSide7Count ?? 0; + const side18 = row.worstThreat?.mixedCliqueSide18Count ?? 0; + if (side7 > side18) return 'side7'; + if (side18 > side7) return 'side18'; + if (side7 === 0 && side18 === 0) return 'none'; + return 'tie'; +} + +function compactLiftMiningRow(row) { + const worstThreat = row.worstThreat ?? null; + return { + N: row.N, + certificateMode: row.certificateMode, + nMod25: positiveModulo(row.N, 25), + p: row.p, + p2: row.p2, + rawPlus: row.rawPlus, + rawMinus: row.rawMinus, + vMax: row.vMax, + activePlus: row.activePlus, + activeMinus: row.activeMinus, + activeOutsiderCount: row.activeOutsiderCount, + dMax: row.dMax, + dMaxWitnessSide: row.dMaxWitness?.side ?? null, + dMaxWitnessValue: row.dMaxWitness?.value ?? null, + rGreater: row.rGreater, + candidateSize: row.candidateSize, + strictBaseThreshold: row.strictBaseThreshold, + side7Margin: row.side7Margin, + side18Margin: row.side18Margin, + unionMargin: row.unionMargin, + mixedMargin: row.mixedMargin, + sMaxMixed: row.sMaxMixed, + sMaxMixedWitness: row.sMaxMixedWitness, + sMaxMixedWitnessMod25: row.sMaxMixedWitness === null || row.sMaxMixedWitness === undefined + ? null + : positiveModulo(row.sMaxMixedWitness, 25), + threateningOutsiderCount: row.threateningOutsiderCount, + maxImprovementOverUnion: row.maxImprovementOverUnion, + worstOutsider: worstThreat?.outsider ?? null, + worstOutsiderMod25: worstThreat?.outsider === null || worstThreat?.outsider === undefined + ? null + : positiveModulo(worstThreat.outsider, 25), + worstUnionCount: worstThreat?.unionCount ?? null, + worstMixedCliqueSize: worstThreat?.mixedBaseCliqueSize ?? null, + matchingSizeInMissingCrossGraph: worstThreat?.matchingSizeInMissingCrossGraph ?? null, + compatibleSide7Count: worstThreat?.compatibleSide7Count ?? null, + compatibleSide18Count: worstThreat?.compatibleSide18Count ?? null, + mixedCliqueSide7Count: worstThreat?.mixedCliqueSide7Count ?? null, + mixedCliqueSide18Count: worstThreat?.mixedCliqueSide18Count ?? null, + threatMatchingSummary: summarizeThreatMatching(row), + dominantMixedCliqueSide: dominantMixedCliqueSide(row), + }; +} + +function summarizeThreatMatching(row) { + const threats = row.threatSummaries ?? []; + if (threats.length === 0) { + return null; + } + const minRequiredMatchingLowerBound = Math.min(...threats.map((threat) => threat.requiredMatchingLowerBound)); + const maxRequiredMatchingLowerBound = Math.max(...threats.map((threat) => threat.requiredMatchingLowerBound)); + const minActualMatching = Math.min(...threats.map((threat) => threat.matchingSizeInMissingCrossGraph)); + const maxActualMatching = Math.max(...threats.map((threat) => threat.matchingSizeInMissingCrossGraph)); + const minMatchingSlack = Math.min(...threats.map((threat) => threat.matchingSlack)); + const tightestThreats = [...threats] + .sort((left, right) => left.matchingSlack - right.matchingSlack || left.outsider - right.outsider) + .slice(0, 5) + .map((threat) => ({ + outsider: threat.outsider, + outsiderMod25: threat.outsiderMod25, + compatibleSide7Count: threat.compatibleSide7Count, + compatibleSide18Count: threat.compatibleSide18Count, + requiredMatchingLowerBound: threat.requiredMatchingLowerBound, + matchingSizeInMissingCrossGraph: threat.matchingSizeInMissingCrossGraph, + matchingSlack: threat.matchingSlack, + saturatesSmallerSide: threat.saturatesSmallerSide, + dominantMixedCliqueSide: threat.dominantMixedCliqueSide, + })); + + return { + threatCount: threats.length, + minRequiredMatchingLowerBound, + maxRequiredMatchingLowerBound, + minActualMatching, + maxActualMatching, + minMatchingSlack, + allThreatsMeetRequiredLowerBound: threats.every((threat) => threat.matchingSlack >= 0), + allThreatsSaturateSmallerSide: threats.every((threat) => threat.saturatesSmallerSide), + tightestThreats, + }; +} + +function compactThreatMiningRows(row) { + return (row.threatSummaries ?? []).map((threat) => ({ + N: row.N, + certificateMode: row.certificateMode, + nMod25: positiveModulo(row.N, 25), + p: row.p, + p2: row.p2, + outsider: threat.outsider, + outsiderMod25: threat.outsiderMod25, + activePlus: row.activePlus, + activeMinus: row.activeMinus, + activeOutsiderCount: row.activeOutsiderCount, + dMax: row.dMax, + dMaxWitnessSide: row.dMaxWitness?.side ?? null, + dMaxWitnessValue: row.dMaxWitness?.value ?? null, + rGreater: row.rGreater, + candidateSize: row.candidateSize, + strictBaseThreshold: row.strictBaseThreshold, + unionCount: threat.unionCount, + mixedBaseCliqueSize: threat.mixedBaseCliqueSize, + matchingSizeInMissingCrossGraph: threat.matchingSizeInMissingCrossGraph, + compatibleSide7Count: threat.compatibleSide7Count, + compatibleSide18Count: threat.compatibleSide18Count, + requiredMatchingLowerBound: threat.requiredMatchingLowerBound, + matchingSlack: threat.matchingSlack, + smallerSideSize: threat.smallerSideSize, + saturatesSmallerSide: threat.saturatesSmallerSide, + mixedCliqueSide7Count: threat.mixedCliqueSide7Count, + mixedCliqueSide18Count: threat.mixedCliqueSide18Count, + dominantMixedCliqueSide: threat.dominantMixedCliqueSide, + })); +} + +function stripThreatSummaries(row) { + if (!row) { + return row; + } + const { threatSummaries, ...compactRow } = row; + if (threatSummaries?.length > 0) { + compactRow.threatMatchingSummary = summarizeThreatMatching(row); + } + return compactRow; +} + +function betterWorst(left, right, key) { + if (!left) return right; + if (!right) return left; + if (right[key] < left[key]) return right; + if (right[key] === left[key] && right.N < left.N) return right; + return left; +} + +function analyze(maxN, minStructuralN, rowSampleLimit) { + const roots = buildRootInfos(maxN); + const primes = primeSieve(maxN); + const primeSquares = primes.map((prime) => prime * prime); + const side7Values = residueValues(maxN, 7); + const side18Values = residueValues(maxN, 18); + const baseSides = { side7Values, side18Values }; + const crossCompatibility = buildBaseCrossCompatibility(side7Values, side18Values, primeSquares); + const globalRootEvents = []; + for (let rootIndex = 0; rootIndex < roots.length; rootIndex += 1) { + const root = roots[rootIndex]; + for (const value of rootProgression(root.rPlus, root.p2, maxN)) { + globalRootEvents.push({ n: value, rootIndex, p: root.p, sign: 'plus' }); + } + for (const value of rootProgression(root.rMinus, root.p2, maxN)) { + globalRootEvents.push({ n: value, rootIndex, p: root.p, sign: 'minus' }); + } + } + globalRootEvents.sort((left, right) => left.n - right.n || left.rootIndex - right.rootIndex); + + const breakpoints = [ + minStructuralN, + maxN, + ...side7Values, + ...side18Values, + ...globalRootEvents.map((event) => event.n), + ] + .filter((value) => value >= minStructuralN && value <= maxN) + .sort((left, right) => left - right) + .filter((value, index, values) => index === 0 || value !== values[index - 1]); + + const higherRootEventsByIndex = roots.map((_, rootIndex) => globalRootEvents + .filter((event) => event.rootIndex > rootIndex) + .map((event) => event.n) + .sort((left, right) => left - right)); + + const blockSummaries = []; + const exactRowsSample = []; + const failureRowsSample = []; + const liftMiningRows = []; + const threatLiftMiningRows = []; + let checkCount = 0; + let unionCertifiedRowCount = 0; + let exactMixedRowCount = 0; + let threateningOutsiderCheckCount = 0; + let mixedFailureCount = 0; + let firstMixedFailure = null; + let worstCertifiedRow = null; + let worstExactMixedRow = null; + let maxThreateningOutsidersInRow = 0; + let maxImprovementOverUnion = 0; + + for (let rootIndex = 0; rootIndex < roots.length; rootIndex += 1) { + const block = buildBlock(roots[rootIndex], rootIndex, roots, maxN, baseSides, primeSquares); + let blockUnionCertifiedRowCount = 0; + let blockExactMixedRowCount = 0; + let blockThreateningOutsiderCheckCount = 0; + let blockMixedFailureCount = 0; + let blockWorstCertifiedRow = null; + + for (const activeN of breakpoints) { + const structuralRow = evaluateStructuralRow(block, higherRootEventsByIndex[rootIndex], baseSides, activeN); + const mixedRow = evaluateMixedRow(block, structuralRow, crossCompatibility); + checkCount += 1; + if (mixedRow.certificateMode === 'union_bound') { + unionCertifiedRowCount += 1; + blockUnionCertifiedRowCount += 1; + } else { + exactMixedRowCount += 1; + blockExactMixedRowCount += 1; + threateningOutsiderCheckCount += mixedRow.exactMixedCheckCount; + blockThreateningOutsiderCheckCount += mixedRow.exactMixedCheckCount; + maxThreateningOutsidersInRow = Math.max(maxThreateningOutsidersInRow, mixedRow.threateningOutsiderCount); + maxImprovementOverUnion = Math.max(maxImprovementOverUnion, mixedRow.maxImprovementOverUnion); + worstExactMixedRow = betterWorst(worstExactMixedRow, mixedRow, 'mixedMargin'); + liftMiningRows.push(compactLiftMiningRow(mixedRow)); + threatLiftMiningRows.push(...compactThreatMiningRows(mixedRow)); + if (exactRowsSample.length < rowSampleLimit) { + exactRowsSample.push(mixedRow); + } + } + worstCertifiedRow = betterWorst(worstCertifiedRow, mixedRow, 'mixedMargin'); + blockWorstCertifiedRow = betterWorst(blockWorstCertifiedRow, mixedRow, 'mixedMargin'); + if (!mixedRow.mixedPass) { + mixedFailureCount += 1; + blockMixedFailureCount += 1; + firstMixedFailure ??= mixedRow; + if (failureRowsSample.length < rowSampleLimit) { + failureRowsSample.push(mixedRow); + } + } + } + + blockSummaries.push({ + p: block.root.p, + p2: block.root.p2, + rPlus: block.root.rPlus, + rMinus: block.root.rMinus, + rawPlusCountAtMax: block.rawPlusValues.length, + rawMinusCountAtMax: block.rawMinusValues.length, + leastWitnessPlusCountAtMax: block.plusValues.length, + leastWitnessMinusCountAtMax: block.minusValues.length, + unionCertifiedRowCount: blockUnionCertifiedRowCount, + exactMixedRowCount: blockExactMixedRowCount, + threateningOutsiderCheckCount: blockThreateningOutsiderCheckCount, + mixedFailureCount: blockMixedFailureCount, + worstCertifiedRow: blockWorstCertifiedRow, + }); + } + + const allMixedChecksPass = mixedFailureCount === 0; + const status = allMixedChecksPass + ? 'bounded_full_mixed_base_structural_verifier_certified' + : 'bounded_full_mixed_base_structural_verifier_has_failures'; + + return { + schema: 'erdos.number_theory.p848_full_mixed_base_structural_verifier/1', + generatedAt: new Date().toISOString(), + problemId: '848', + method: 'bounded_outsider_clique_full_mixed_base_structural_verifier', + status, + parameters: { + maxN, + minStructuralN, + rowSampleLimit, + assessedRange: `${minStructuralN}..${maxN}`, + }, + summary: { + assessedRange: `${minStructuralN}..${maxN}`, + witnessBlockCount: roots.length, + breakpointCount: breakpoints.length, + checkCount, + globalRootEventCount: globalRootEvents.length, + side7BaseCountAtMax: side7Values.length, + side18BaseCountAtMax: side18Values.length, + unionCertifiedRowCount, + exactMixedRowCount, + threateningOutsiderCheckCount, + mixedFailureCount, + allMixedChecksPass, + minCertifiedMargin: worstCertifiedRow?.mixedMargin ?? null, + minExactMixedMargin: worstExactMixedRow?.mixedMargin ?? null, + maxThreateningOutsidersInRow, + maxImprovementOverUnion, + liftMiningRowCount: liftMiningRows.length, + threatLiftMiningRowCount: threatLiftMiningRows.length, + }, + firstMixedFailure: stripThreatSummaries(firstMixedFailure), + worstCertifiedRow: stripThreatSummaries(worstCertifiedRow), + worstExactMixedRow: stripThreatSummaries(worstExactMixedRow), + blockSummaries: blockSummaries.map((block) => ({ + ...block, + worstCertifiedRow: stripThreatSummaries(block.worstCertifiedRow), + })), + exactRowsSample: exactRowsSample.map(stripThreatSummaries), + liftMiningRows, + threatLiftMiningRows, + failureRowsSample: failureRowsSample.map(stripThreatSummaries), + boundary: { + claimLevel: 'bounded_structural_certificate_not_all_N_proof', + proofObligation: 'Every witness-prime block and structural breakpoint in the assessed range is certified either by the safe union bound or by exact mixed-base clique checks for every threatening active outsider.', + cliqueReduction: 'For a fixed outsider, the compatible base graph is two cliques, one on 7 mod 25 and one on 18 mod 25. Its maximum clique equals total compatible base vertices minus a maximum matching in the bipartite graph of missing cross-edges.', + promotionRule: 'Promote bounded structural coverage only when allMixedChecksPass is true for the full assessed range and all artifact parameters match the intended handoff range.', + nextUse: allMixedChecksPass + ? 'Use this as the repo-owned bounded structural certificate and extend the assessed range or lift the finite-block argument.' + : 'Inspect the first mixed failure before extending or lifting the structural verifier.', + }, + }; +} + +function renderRow(row) { + return row ? JSON.stringify(row) : '(none)'; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 Full Mixed-Base Structural Verifier', + '', + `- Generated: ${packet.generatedAt}`, + `- Method: \`${packet.method}\``, + `- Status: \`${packet.status}\``, + `- Assessed range: \`${packet.summary.assessedRange}\``, + `- Witness blocks: \`${packet.summary.witnessBlockCount}\``, + `- Breakpoints: \`${packet.summary.breakpointCount}\``, + `- Structural rows checked: \`${packet.summary.checkCount}\``, + `- Rows certified by union bound: \`${packet.summary.unionCertifiedRowCount}\``, + `- Rows requiring exact mixed-base checks: \`${packet.summary.exactMixedRowCount}\``, + `- Compact lift-mining rows: \`${packet.summary.liftMiningRowCount ?? '(unknown)'}\``, + `- Compact threatening-outsider rows: \`${packet.summary.threatLiftMiningRowCount ?? '(unknown)'}\``, + `- Threatening outsider checks: \`${packet.summary.threateningOutsiderCheckCount}\``, + '', + '## Pass/Fail Summary', + '', + `- All mixed checks pass: \`${packet.summary.allMixedChecksPass ? 'yes' : 'no'}\``, + `- Mixed failures: \`${packet.summary.mixedFailureCount}\``, + `- Minimum certified margin: \`${packet.summary.minCertifiedMargin ?? '(none)'}\``, + `- Minimum exact mixed margin: \`${packet.summary.minExactMixedMargin ?? '(none)'}\``, + `- Max threatening outsiders in one row: \`${packet.summary.maxThreateningOutsidersInRow}\``, + `- Max improvement over union: \`${packet.summary.maxImprovementOverUnion}\``, + '', + '## Key Rows', + '', + `- First mixed failure: \`${renderRow(packet.firstMixedFailure)}\``, + `- Worst certified row: \`${renderRow(packet.worstCertifiedRow)}\``, + `- Worst exact mixed row: \`${renderRow(packet.worstExactMixedRow)}\``, + '', + '## Boundary', + '', + `- Claim level: \`${packet.boundary.claimLevel}\``, + `- Proof obligation: ${packet.boundary.proofObligation}`, + `- Clique reduction: ${packet.boundary.cliqueReduction}`, + `- Promotion rule: ${packet.boundary.promotionRule}`, + `- Next use: ${packet.boundary.nextUse}`, + '', + ]; + + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = analyze(args.max, args.minStructuralN, args.rowSampleLimit); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify(packet.summary, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_matching_pattern_miner.mjs b/packs/number-theory/problems/848/compute/problem848_matching_pattern_miner.mjs new file mode 100644 index 0000000..3ea0649 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_matching_pattern_miner.mjs @@ -0,0 +1,570 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; +import { fileURLToPath } from 'node:url'; + +const scriptDir = path.dirname(fileURLToPath(import.meta.url)); +const problemDir = path.resolve(scriptDir, '..'); + +function parseArgs(argv) { + const args = { + verifierJson: path.join(problemDir, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json'), + prime: 13, + topRows: 12, + pairSampleLimit: 24, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--verifier-json') { + args.verifierJson = argv[++index]; + } else if (token === '--prime') { + args.prime = Number(argv[++index]); + } else if (token === '--top-rows') { + args.topRows = Number(argv[++index]); + } else if (token === '--pair-sample-limit') { + args.pairSampleLimit = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!args.verifierJson) { + throw new Error('--verifier-json is required'); + } + if (!Number.isInteger(args.prime) || args.prime < 2) { + throw new Error('--prime must be a prime integer'); + } + if (!Number.isInteger(args.topRows) || args.topRows < 1) { + throw new Error('--top-rows must be a positive integer'); + } + if (!Number.isInteger(args.pairSampleLimit) || args.pairSampleLimit < 1) { + throw new Error('--pair-sample-limit must be a positive integer'); + } + return args; +} + +function positiveModulo(value, modulus) { + const residue = Number(value) % modulus; + return residue < 0 ? residue + modulus : residue; +} + +function readJson(filePath) { + return JSON.parse(fs.readFileSync(filePath, 'utf8')); +} + +function primeSieve(max) { + const composite = new Uint8Array(max + 1); + const primes = []; + for (let n = 2; n <= max; n += 1) { + if (composite[n]) continue; + primes.push(n); + if (n * n > max) continue; + for (let multiple = n * n; multiple <= max; multiple += n) { + composite[multiple] = 1; + } + } + return primes; +} + +function residueValues(max, residue, modulus = 25) { + const values = []; + for (let value = residue; value <= max; value += modulus) { + if (value >= 1) values.push(value); + } + return values; +} + +function isNonSquarefree(value, primeSquares) { + for (const square of primeSquares) { + if (square > value) break; + if (value % square === 0) return true; + } + return false; +} + +function compatibleValues(outsider, candidates, activeN, primeSquares) { + const values = []; + for (const candidate of candidates) { + if (candidate > activeN) break; + if (isNonSquarefree(outsider * candidate + 1, primeSquares)) { + values.push(candidate); + } + } + return values; +} + +function hopcroftKarp(leftCount, rightCount, adjacency) { + const pairLeft = new Int32Array(leftCount).fill(-1); + const pairRight = new Int32Array(rightCount).fill(-1); + const distance = new Int32Array(leftCount); + let matching = 0; + + function bfs() { + const queue = []; + let foundFreeRight = false; + for (let left = 0; left < leftCount; left += 1) { + if (pairLeft[left] === -1) { + distance[left] = 0; + queue.push(left); + } else { + distance[left] = -1; + } + } + for (let cursor = 0; cursor < queue.length; cursor += 1) { + const left = queue[cursor]; + for (const right of adjacency[left]) { + const nextLeft = pairRight[right]; + if (nextLeft === -1) { + foundFreeRight = true; + } else if (distance[nextLeft] === -1) { + distance[nextLeft] = distance[left] + 1; + queue.push(nextLeft); + } + } + } + return foundFreeRight; + } + + function dfs(left) { + for (const right of adjacency[left]) { + const nextLeft = pairRight[right]; + if (nextLeft === -1 || (distance[nextLeft] === distance[left] + 1 && dfs(nextLeft))) { + pairLeft[left] = right; + pairRight[right] = left; + return true; + } + } + distance[left] = -1; + return false; + } + + while (bfs()) { + for (let left = 0; left < leftCount; left += 1) { + if (pairLeft[left] === -1 && dfs(left)) { + matching += 1; + } + } + } + + return { matching, pairLeft, pairRight }; +} + +function countBy(values, keyFn) { + const counts = new Map(); + for (const value of values) { + const key = keyFn(value); + counts.set(key, (counts.get(key) ?? 0) + 1); + } + return [...counts.entries()] + .map(([key, count]) => ({ key, count })) + .sort((left, right) => right.count - left.count || String(left.key).localeCompare(String(right.key))); +} + +function minValue(values) { + return values.length === 0 ? null : Math.min(...values); +} + +function maxValue(values) { + return values.length === 0 ? null : Math.max(...values); +} + +function buildMissingCrossGraph(side7, side18, primeSquares) { + const adjacency = side7.map(() => []); + let missingCrossEdgeCount = 0; + let compatibleCrossEdgeCount = 0; + + for (let left = 0; left < side7.length; left += 1) { + for (let right = 0; right < side18.length; right += 1) { + if (isNonSquarefree(side7[left] * side18[right] + 1, primeSquares)) { + compatibleCrossEdgeCount += 1; + } else { + adjacency[left].push(right); + missingCrossEdgeCount += 1; + } + } + } + + return { + adjacency, + missingCrossEdgeCount, + compatibleCrossEdgeCount, + }; +} + +function compactPair(leftValue, rightValue, p, p2) { + return { + leftValue, + rightValue, + leftMod25: positiveModulo(leftValue, 25), + rightMod25: positiveModulo(rightValue, 25), + leftModP2: positiveModulo(leftValue, p2), + rightModP2: positiveModulo(rightValue, p2), + leftModP: positiveModulo(leftValue, p), + rightModP: positiveModulo(rightValue, p), + productPlusOneModP2: positiveModulo(leftValue * rightValue + 1, p2), + }; +} + +function buildMatchingWitness(row, baseSides, primeSquares, pairSampleLimit) { + const p = Number(row.p); + const p2 = p * p; + const side7 = compatibleValues(Number(row.outsider), baseSides.side7Values, Number(row.N), primeSquares); + const side18 = compatibleValues(Number(row.outsider), baseSides.side18Values, Number(row.N), primeSquares); + const graph = buildMissingCrossGraph(side7, side18, primeSquares); + const matching = hopcroftKarp(side7.length, side18.length, graph.adjacency); + const pairs = []; + for (let left = 0; left < matching.pairLeft.length; left += 1) { + const right = matching.pairLeft[left]; + if (right !== -1) { + pairs.push(compactPair(side7[left], side18[right], p, p2)); + } + } + pairs.sort((left, right) => left.leftValue - right.leftValue || left.rightValue - right.rightValue); + + const smallerSide = side7.length <= side18.length ? 'side7' : 'side18'; + const largerSide = smallerSide === 'side7' ? 'side18' : 'side7'; + const smallerSideSize = Math.min(side7.length, side18.length); + const largerSideSize = Math.max(side7.length, side18.length); + const requiredMatchingLowerBound = Number(row.requiredMatchingLowerBound); + const matchingSlack = matching.matching - requiredMatchingLowerBound; + const matchedLeftValues = new Set(pairs.map((pair) => pair.leftValue)); + const matchedRightValues = new Set(pairs.map((pair) => pair.rightValue)); + const matchedSmallerSideValues = smallerSide === 'side7' + ? side7.filter((value) => matchedLeftValues.has(value)) + : side18.filter((value) => matchedRightValues.has(value)); + const unmatchedLargerSideValues = largerSide === 'side7' + ? side7.filter((value) => !matchedLeftValues.has(value)) + : side18.filter((value) => !matchedRightValues.has(value)); + + return { + N: Number(row.N), + p, + p2, + outsider: Number(row.outsider), + outsiderMod25: positiveModulo(row.outsider, 25), + outsiderModP2: positiveModulo(row.outsider, p2), + strictBaseThreshold: Number(row.strictBaseThreshold), + requiredMatchingLowerBound, + verifierMatchingSize: Number(row.matchingSizeInMissingCrossGraph), + reconstructedMatchingSize: matching.matching, + verifierAndReconstructionAgree: matching.matching === Number(row.matchingSizeInMissingCrossGraph), + matchingSlack, + side7Count: side7.length, + side18Count: side18.length, + smallerSide, + largerSide, + smallerSideSize, + largerSideSize, + saturatesSmallerSide: matching.matching === smallerSideSize, + matchedSmallerSideCount: matchedSmallerSideValues.length, + unmatchedSmallerSideCount: smallerSideSize - matchedSmallerSideValues.length, + unmatchedLargerSideCount: largerSideSize - matching.matching, + missingCrossEdgeCount: graph.missingCrossEdgeCount, + compatibleCrossEdgeCount: graph.compatibleCrossEdgeCount, + matchingPairResidueProfiles: { + modulo25: countBy(pairs, (pair) => `${pair.leftMod25}:${pair.rightMod25}`), + moduloP: countBy(pairs, (pair) => `${pair.leftModP}:${pair.rightModP}`), + moduloP2: countBy(pairs, (pair) => `${pair.leftModP2}:${pair.rightModP2}`).slice(0, 24), + productPlusOneModuloP2: countBy(pairs, (pair) => pair.productPlusOneModP2).slice(0, 24), + }, + matchedSmallerSideResidues: { + modulo25: countBy(matchedSmallerSideValues, (value) => positiveModulo(value, 25)), + moduloP: countBy(matchedSmallerSideValues, (value) => positiveModulo(value, p)), + moduloP2: countBy(matchedSmallerSideValues, (value) => positiveModulo(value, p2)).slice(0, 24), + }, + unmatchedLargerSideResidues: { + modulo25: countBy(unmatchedLargerSideValues, (value) => positiveModulo(value, 25)), + moduloP: countBy(unmatchedLargerSideValues, (value) => positiveModulo(value, p)), + moduloP2: countBy(unmatchedLargerSideValues, (value) => positiveModulo(value, p2)).slice(0, 24), + }, + matchingPairsForMining: pairs, + matchingPairSample: pairs.slice(0, pairSampleLimit), + }; +} + +function chooseTargetRows(verifier, prime, topRows) { + return (verifier.threatLiftMiningRows ?? []) + .filter((row) => row?.certificateMode === 'exact_mixed_base') + .filter((row) => Number(row.p) === prime) + .sort((left, right) => ( + Number(left.matchingSlack) - Number(right.matchingSlack) + || Number(right.requiredMatchingLowerBound) - Number(left.requiredMatchingLowerBound) + || Number(left.N) - Number(right.N) + || Number(left.outsider) - Number(right.outsider) + )) + .slice(0, topRows); +} + +function summarizeWitnesses(witnesses) { + return { + witnessRowCount: witnesses.length, + allReconstructedMatchesAgree: witnesses.every((witness) => witness.verifierAndReconstructionAgree), + allWitnessesMeetRequiredMatchingLowerBound: witnesses.every((witness) => witness.reconstructedMatchingSize >= witness.requiredMatchingLowerBound), + allWitnessesSaturateSmallerSide: witnesses.every((witness) => witness.saturatesSmallerSide), + minRequiredMatchingLowerBound: minValue(witnesses.map((witness) => witness.requiredMatchingLowerBound).filter(Number.isFinite)), + maxRequiredMatchingLowerBound: maxValue(witnesses.map((witness) => witness.requiredMatchingLowerBound).filter(Number.isFinite)), + minReconstructedMatchingSize: minValue(witnesses.map((witness) => witness.reconstructedMatchingSize).filter(Number.isFinite)), + maxReconstructedMatchingSize: maxValue(witnesses.map((witness) => witness.reconstructedMatchingSize).filter(Number.isFinite)), + minMatchingSlack: minValue(witnesses.map((witness) => witness.matchingSlack).filter(Number.isFinite)), + saturatedSideDistribution: countBy(witnesses, (witness) => witness.smallerSide), + outsiderMod25Distribution: countBy(witnesses, (witness) => witness.outsiderMod25), + outsiderModP2Distribution: countBy(witnesses, (witness) => witness.outsiderModP2), + }; +} + +function pairKey(pair) { + return `${pair.leftValue}:${pair.rightValue}`; +} + +function commonPairsForWitnesses(witnesses) { + if (witnesses.length === 0) { + return []; + } + const commonPairKeys = witnesses.slice(1).reduce((commonKeys, witness) => { + const rowKeys = new Set((witness.matchingPairsForMining ?? []).map(pairKey)); + return new Set([...commonKeys].filter((key) => rowKeys.has(key))); + }, new Set((witnesses[0]?.matchingPairsForMining ?? []).map(pairKey))); + const pairByKey = new Map(); + for (const pair of witnesses.flatMap((witness) => witness.matchingPairsForMining ?? [])) { + pairByKey.set(pairKey(pair), pair); + } + return [...commonPairKeys] + .map((key) => pairByKey.get(key)) + .filter(Boolean) + .sort((left, right) => left.leftValue - right.leftValue || left.rightValue - right.rightValue); +} + +function groupBy(values, keyFn) { + const groups = new Map(); + for (const value of values) { + const key = keyFn(value); + const group = groups.get(key) ?? []; + group.push(value); + groups.set(key, group); + } + return groups; +} + +function buildPatternSummary(witnesses, pairSampleLimit) { + const allPairs = witnesses.flatMap((witness) => witness.matchingPairsForMining ?? []); + const p2 = witnesses[0]?.p2 ?? 1; + const commonPairs = commonPairsForWitnesses(witnesses); + const groupedByOutsider = countBy(witnesses, (witness) => `${witness.outsiderModP2}:${witness.outsiderMod25}`); + const splitProfiles = [...groupBy( + witnesses, + (witness) => `outP2=${witness.outsiderModP2}|out25=${witness.outsiderMod25}|smaller=${witness.smallerSide}`, + ).entries()].map(([groupKey, groupWitnesses]) => { + const groupPairs = groupWitnesses.flatMap((witness) => witness.matchingPairsForMining ?? []); + const groupCommonPairs = commonPairsForWitnesses(groupWitnesses); + const minRequiredMatchingLowerBound = minValue(groupWitnesses + .map((witness) => witness.requiredMatchingLowerBound) + .filter(Number.isFinite)); + const maxRequiredMatchingLowerBound = maxValue(groupWitnesses + .map((witness) => witness.requiredMatchingLowerBound) + .filter(Number.isFinite)); + const minReconstructedMatchingSize = minValue(groupWitnesses + .map((witness) => witness.reconstructedMatchingSize) + .filter(Number.isFinite)); + const maxReconstructedMatchingSize = maxValue(groupWitnesses + .map((witness) => witness.reconstructedMatchingSize) + .filter(Number.isFinite)); + const minSmallerSideSize = minValue(groupWitnesses + .map((witness) => witness.smallerSideSize) + .filter(Number.isFinite)); + const maxSmallerSideSize = maxValue(groupWitnesses + .map((witness) => witness.smallerSideSize) + .filter(Number.isFinite)); + return { + groupKey, + witnessCount: groupWitnesses.length, + minN: minValue(groupWitnesses.map((witness) => witness.N)), + maxN: maxValue(groupWitnesses.map((witness) => witness.N)), + minRequiredMatchingLowerBound, + maxRequiredMatchingLowerBound, + minReconstructedMatchingSize, + maxReconstructedMatchingSize, + minSmallerSideSize, + maxSmallerSideSize, + minMatchingSlack: minValue(groupWitnesses.map((witness) => witness.matchingSlack).filter(Number.isFinite)), + commonMatchingPairCount: groupCommonPairs.length, + commonCoreMeetsMaxRequiredBound: Number.isFinite(maxRequiredMatchingLowerBound) + && groupCommonPairs.length >= maxRequiredMatchingLowerBound, + commonCoreSaturatesMinSmallerSide: Number.isFinite(minSmallerSideSize) + && groupCommonPairs.length >= minSmallerSideSize, + commonMatchingPairs: groupCommonPairs, + commonMatchingPairExportComplete: true, + commonMatchingPairSample: groupCommonPairs.slice(0, pairSampleLimit), + rightMinusLeftModuloP2Distribution: countBy(groupPairs, (pair) => positiveModulo(pair.rightValue - pair.leftValue, p2)).slice(0, 12), + }; + }).sort((left, right) => ( + right.witnessCount - left.witnessCount + || left.minMatchingSlack - right.minMatchingSlack + || left.groupKey.localeCompare(right.groupKey) + )); + + return { + totalWitnessMatchingPairs: allPairs.length, + commonMatchingPairCountAcrossWitnesses: commonPairs.length, + commonMatchingPairsAcrossWitnesses: commonPairs, + commonMatchingPairExportCompleteAcrossWitnesses: true, + commonMatchingPairSample: commonPairs.slice(0, pairSampleLimit), + outsiderResidueGroups: groupedByOutsider, + splitProfiles, + allSplitCommonCoresMeetMaxRequiredBound: splitProfiles.every((profile) => profile.commonCoreMeetsMaxRequiredBound), + allSplitCommonCoresSaturateMinSmallerSide: splitProfiles.every((profile) => profile.commonCoreSaturatesMinSmallerSide), + rightMinusLeftDistribution: countBy(allPairs, (pair) => pair.rightValue - pair.leftValue).slice(0, 24), + rightMinusLeftModuloP2Distribution: countBy(allPairs, (pair) => positiveModulo(pair.rightValue - pair.leftValue, p2)).slice(0, 24), + productPlusOneModuloP2Distribution: countBy(allPairs, (pair) => pair.productPlusOneModP2).slice(0, 24), + proofHeuristic: commonPairs.length > 0 + ? 'The tight-row witnesses share a nonempty stable matching core. Try proving saturation by extending this stable core across residue blocks, then handle boundary insertions separately.' + : 'The tight-row witnesses do not share one common matching core; split the symbolic construction by outsider residue and saturated side.', + }; +} + +function mine(args) { + const verifier = readJson(args.verifierJson); + const maxN = Number(verifier.parameters?.maxN ?? verifier.summary?.assessedRange?.split('..')?.[1] ?? 0); + if (!Number.isInteger(maxN) || maxN < 1) { + throw new Error('Could not infer maxN from verifier artifact'); + } + const primes = primeSieve(maxN); + const primeSquares = primes.map((prime) => prime * prime); + const baseSides = { + side7Values: residueValues(maxN, 7), + side18Values: residueValues(maxN, 18), + }; + const targetRows = chooseTargetRows(verifier, args.prime, args.topRows); + const rawWitnesses = targetRows.map((row) => buildMatchingWitness( + row, + baseSides, + primeSquares, + args.pairSampleLimit, + )); + const patternSummary = buildPatternSummary(rawWitnesses, args.pairSampleLimit); + const witnesses = rawWitnesses.map(({ matchingPairsForMining, ...witness }) => witness); + const summary = summarizeWitnesses(witnesses); + const status = witnesses.length === 0 + ? 'matching_pattern_miner_no_target_rows' + : summary.allReconstructedMatchesAgree + && summary.allWitnessesMeetRequiredMatchingLowerBound + && summary.allWitnessesSaturateSmallerSide + ? 'matching_pattern_witness_packet_ready' + : 'matching_pattern_witness_packet_has_failures'; + + return { + schema: 'erdos.number_theory.p848_matching_pattern_miner/1', + generatedAt: new Date().toISOString(), + problemId: '848', + method: 'bounded_missing_cross_matching_pattern_mining', + status, + parameters: { + verifierJsonPath: path.resolve(args.verifierJson), + targetPrime: args.prime, + topRows: args.topRows, + pairSampleLimit: args.pairSampleLimit, + sourceAssessedRange: verifier.summary?.assessedRange ?? verifier.parameters?.assessedRange ?? null, + }, + sourceVerifier: { + status: verifier.status ?? null, + assessedRange: verifier.summary?.assessedRange ?? verifier.parameters?.assessedRange ?? null, + threatLiftMiningRowCount: verifier.summary?.threatLiftMiningRowCount ?? verifier.threatLiftMiningRows?.length ?? null, + }, + summary, + patternSummary, + witnesses, + symbolicUse: { + activeAtom: args.prime === 13 ? 'D2_p13_matching_lower_bound' : args.prime === 17 ? 'D3_p17_matching_lower_bound' : null, + constructionTarget: 'Replace Hopcroft-Karp replay with a residue/block injection that saturates the smaller compatible side of H_{x,N}.', + proofHint: 'Each witness records actual missing-cross matching pairs. A human/prover lane should look for a residue-parametric injection from the smaller compatible side into squarefree cross pairs.', + nextExtractor: 'Generalize from these tight-row pair residues into a symbolic side-saturation lemma, then rerun this miner for any newly tight prime family.', + }, + boundary: { + claimLevel: 'bounded_pattern_witness_not_symbolic_proof', + note: 'This artifact reconstructs matching witnesses for selected bounded threat rows. It does not certify rows outside the source verifier range and does not prove the all-N matching lemma.', + promotionRule: 'Promote D2/D3 only after the observed matching pattern is replaced by a symbolic construction and checked against the structural-lift atom.', + }, + }; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 Matching Pattern Miner', + '', + `- Generated: ${packet.generatedAt}`, + `- Method: \`${packet.method}\``, + `- Status: \`${packet.status}\``, + `- Target prime: \`${packet.parameters.targetPrime}\``, + `- Source range: \`${packet.parameters.sourceAssessedRange ?? '(unknown)'}\``, + `- Witness rows: \`${packet.summary.witnessRowCount}\``, + `- Reconstructed matches agree: \`${packet.summary.allReconstructedMatchesAgree ? 'yes' : 'no'}\``, + `- Saturates smaller side: \`${packet.summary.allWitnessesSaturateSmallerSide ? 'yes' : 'no'}\``, + `- K range: \`${packet.summary.minRequiredMatchingLowerBound ?? '(unknown)'}..${packet.summary.maxRequiredMatchingLowerBound ?? '(unknown)'}\``, + `- Matching range: \`${packet.summary.minReconstructedMatchingSize ?? '(unknown)'}..${packet.summary.maxReconstructedMatchingSize ?? '(unknown)'}\``, + `- Minimum slack: \`${packet.summary.minMatchingSlack ?? '(unknown)'}\``, + `- Common matching core across witnesses: \`${packet.patternSummary.commonMatchingPairCountAcrossWitnesses}\``, + '', + '## Pattern Summary', + '', + `- Total witness matching pairs: \`${packet.patternSummary.totalWitnessMatchingPairs}\``, + `- Outsider residue groups: \`${JSON.stringify(packet.patternSummary.outsiderResidueGroups)}\``, + `- Top right-left deltas: \`${JSON.stringify(packet.patternSummary.rightMinusLeftDistribution.slice(0, 8))}\``, + `- Top product+1 residues mod p^2: \`${JSON.stringify(packet.patternSummary.productPlusOneModuloP2Distribution.slice(0, 8))}\``, + `- Proof heuristic: ${packet.patternSummary.proofHeuristic}`, + '', + '## Split Profiles', + '', + ]; + + for (const profile of packet.patternSummary.splitProfiles.slice(0, 8)) { + lines.push(`- \`${profile.groupKey}\`: witnesses ${profile.witnessCount}, N ${profile.minN}..${profile.maxN}, K ${profile.minRequiredMatchingLowerBound}..${profile.maxRequiredMatchingLowerBound}, min slack ${profile.minMatchingSlack}, common pairs ${profile.commonMatchingPairCount}, full core exported ${profile.commonMatchingPairExportComplete ? 'yes' : 'no'}, core >= max K ${profile.commonCoreMeetsMaxRequiredBound ? 'yes' : 'no'}`); + } + + lines.push( + '', + '## Witness Rows', + '', + ); + + for (const witness of packet.witnesses) { + lines.push(`- N=${witness.N}, outsider=${witness.outsider}, K=${witness.requiredMatchingLowerBound}, matching=${witness.reconstructedMatchingSize}, slack=${witness.matchingSlack}, smaller=${witness.smallerSide}, unmatched larger=${witness.unmatchedLargerSideCount}`); + } + + lines.push('', '## Tightest Pair Samples', ''); + for (const witness of packet.witnesses.slice(0, 3)) { + lines.push(`- N=${witness.N}, outsider=${witness.outsider}: ${JSON.stringify(witness.matchingPairSample.slice(0, 8))}`); + } + + lines.push('', '## Symbolic Use', ''); + lines.push(`- Active atom: \`${packet.symbolicUse.activeAtom ?? '(generic)'}\``); + lines.push(`- Construction target: ${packet.symbolicUse.constructionTarget}`); + lines.push(`- Proof hint: ${packet.symbolicUse.proofHint}`); + lines.push('', '## Boundary', ''); + lines.push(`- Claim level: \`${packet.boundary.claimLevel}\``); + lines.push(`- Note: ${packet.boundary.note}`); + lines.push(`- Promotion rule: ${packet.boundary.promotionRule}`); + lines.push(''); + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = mine(args); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify(packet.summary, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_mixed_base_failure_scout.mjs b/packs/number-theory/problems/848/compute/problem848_mixed_base_failure_scout.mjs new file mode 100644 index 0000000..346e0e0 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_mixed_base_failure_scout.mjs @@ -0,0 +1,332 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { + structuralJson: path.resolve('packs/number-theory/problems/848/STRUCTURAL_TWO_SIDE_SCOUT.json'), + maxRows: 40, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--structural-json') { + args.structuralJson = path.resolve(argv[++index]); + } else if (token === '--max-rows') { + args.maxRows = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!Number.isInteger(args.maxRows) || args.maxRows < 1) { + throw new Error('--max-rows must be a positive integer'); + } + return args; +} + +function primeSieve(max) { + const composite = new Uint8Array(max + 1); + const primes = []; + for (let n = 2; n <= max; n += 1) { + if (composite[n]) continue; + primes.push(n); + if (n * n > max) continue; + for (let multiple = n * n; multiple <= max; multiple += n) { + composite[multiple] = 1; + } + } + return primes; +} + +function isNonSquarefree(value, primeSquares) { + for (const square of primeSquares) { + if (square > value) break; + if (value % square === 0) return true; + } + return false; +} + +function residueValues(max, residue) { + const values = []; + for (let value = residue; value <= max; value += 25) { + if (value >= 1) values.push(value); + } + return values; +} + +function upperBound(values, maxValue) { + let low = 0; + let high = values.length; + while (low < high) { + const mid = (low + high) >>> 1; + if (values[mid] <= maxValue) { + low = mid + 1; + } else { + high = mid; + } + } + return low; +} + +function sameSortedSet(left, right) { + if (left.length !== right.length) return false; + const a = [...left].sort((x, y) => x - y); + const b = [...right].sort((x, y) => x - y); + return a.every((value, index) => value === b[index]); +} + +function setBit(bits, index) { + bits[index >>> 5] |= 1 << (index & 31); +} + +function hasBit(bits, index) { + return (bits[index >>> 5] & (1 << (index & 31))) !== 0; +} + +function maximumClique(vertices, adjacency, seedCliqueValues = []) { + const indexByValue = new Map(vertices.map((value, index) => [value, index])); + const seedClique = seedCliqueValues + .map((value) => indexByValue.get(value)) + .filter((index) => index !== undefined); + let best = seedClique; + const degrees = adjacency.map((bits) => { + let degree = 0; + for (let index = 0; index < vertices.length; index += 1) { + if (hasBit(bits, index)) degree += 1; + } + return degree; + }); + + function adjacent(left, right) { + return hasBit(adjacency[left], right); + } + + function colorSort(candidates) { + let uncolored = [...candidates].sort((left, right) => degrees[right] - degrees[left]); + const ordered = []; + const colors = []; + let color = 0; + while (uncolored.length > 0) { + color += 1; + let colorable = [...uncolored]; + while (colorable.length > 0) { + const vertex = colorable[0]; + ordered.push(vertex); + colors.push(color); + uncolored = uncolored.filter((candidate) => candidate !== vertex); + colorable = colorable.filter( + (candidate) => candidate !== vertex && !adjacent(vertex, candidate), + ); + } + } + return { ordered, colors }; + } + + function expand(clique, candidates) { + if (candidates.length === 0) { + if (clique.length > best.length) best = clique; + return; + } + const { ordered, colors } = colorSort(candidates); + for (let index = ordered.length - 1; index >= 0; index -= 1) { + if (clique.length + colors[index] <= best.length) return; + const vertex = ordered[index]; + const nextCandidates = []; + for (let next = 0; next < index; next += 1) { + const candidate = ordered[next]; + if (adjacent(vertex, candidate)) nextCandidates.push(candidate); + } + expand([...clique, vertex], nextCandidates); + } + } + + expand([], Array.from({ length: vertices.length }, (_, index) => index)); + return best.map((index) => vertices[index]).sort((left, right) => left - right); +} + +function buildMixedBaseGraph(N, outsider, primeSquares) { + const side7 = residueValues(N, 7).filter((value) => isNonSquarefree(outsider * value + 1, primeSquares)); + const side18 = residueValues(N, 18).filter((value) => isNonSquarefree(outsider * value + 1, primeSquares)); + const vertices = [...side7, ...side18].sort((left, right) => left - right); + const sideByValue = new Map([ + ...side7.map((value) => [value, 7]), + ...side18.map((value) => [value, 18]), + ]); + const wordCount = Math.ceil(vertices.length / 32); + const adjacency = Array.from({ length: vertices.length }, () => new Uint32Array(wordCount)); + + for (let left = 0; left < vertices.length; left += 1) { + for (let right = left + 1; right < vertices.length; right += 1) { + const samePrincipalSide = sideByValue.get(vertices[left]) === sideByValue.get(vertices[right]); + if (samePrincipalSide || isNonSquarefree(vertices[left] * vertices[right] + 1, primeSquares)) { + setBit(adjacency[left], right); + setBit(adjacency[right], left); + } + } + } + + return { + vertices, + side7, + side18, + adjacency, + }; +} + +function collectRows(structuralScout, maxRows) { + const rows = []; + const seen = new Set(); + function add(row, source) { + if (!row?.N || !row?.p || !row?.sMaxUnionWitness) return; + const key = `${row.N}:${row.p}:${row.sMaxUnionWitness}`; + if (seen.has(key)) return; + seen.add(key); + rows.push({ ...row, source }); + } + + add(structuralScout.firstFailures?.union, 'first_union_failure'); + add(structuralScout.worstRows?.union, 'worst_union_row'); + for (const block of structuralScout.blockSummaries ?? []) { + add(block.firstUnionFailure, `block_${block.p}_first_union_failure`); + add(block.worstUnionRow, `block_${block.p}_worst_union_row`); + } + for (const row of structuralScout.failureRowsSample ?? []) { + add(row, 'failure_sample'); + if (rows.length >= maxRows) break; + } + return rows.slice(0, maxRows); +} + +function analyze(structuralJson, maxRows) { + const structuralScout = JSON.parse(fs.readFileSync(structuralJson, 'utf8')); + const maxN = Number(structuralScout.parameters?.maxN ?? 0); + if (!Number.isInteger(maxN) || maxN < 1) { + throw new Error('Structural scout is missing parameters.maxN'); + } + const primeSquares = primeSieve(maxN).map((prime) => prime * prime); + const rows = collectRows(structuralScout, maxRows); + const analyses = rows.map((row) => { + const graph = buildMixedBaseGraph(row.N, row.sMaxUnionWitness, primeSquares); + const sideSeed = graph.side7.length >= graph.side18.length ? graph.side7 : graph.side18; + const clique = maximumClique(graph.vertices, graph.adjacency, sideSeed); + const side7Members = clique.filter((value) => value % 25 === 7); + const side18Members = clique.filter((value) => value % 25 === 18); + const mixedBound = clique.length + row.vMax + row.dMax + row.rGreater; + const mixedMargin = row.candidateSize - mixedBound; + return { + source: row.source, + N: row.N, + p: row.p, + outsider: row.sMaxUnionWitness, + candidateSize: row.candidateSize, + sMaxSide7: row.sMaxSide7, + sMaxSide18: row.sMaxSide18, + sMaxUnion: row.sMaxUnion, + mixedBaseCliqueSize: clique.length, + mixedBaseSide7Count: side7Members.length, + mixedBaseSide18Count: side18Members.length, + mixedBaseCliqueMatchesSingleSide: sameSortedSet(clique, graph.side7) || sameSortedSet(clique, graph.side18), + mixedBound, + mixedMargin, + mixedPass: mixedBound < row.candidateSize, + originalUnionMargin: row.unionMargin, + improvementOverUnion: row.sMaxUnion - clique.length, + vMax: row.vMax, + dMax: row.dMax, + rGreater: row.rGreater, + exampleMixedBaseClique: clique, + }; + }); + + const failingAnalyses = analyses.filter((row) => !row.mixedPass); + const status = analyses.length === 0 + ? 'no_union_failures_to_analyze' + : failingAnalyses.length === 0 + ? 'sampled_union_failures_repaired_by_mixed_base_clique' + : 'mixed_base_clique_still_fails_sampled_rows'; + + return { + schema: 'erdos.number_theory.p848_mixed_base_failure_scout/1', + generatedAt: new Date().toISOString(), + problemId: '848', + method: 'exact_mixed_base_clique_on_structural_union_failures', + status, + sourceStructuralJson: structuralJson, + parameters: { + maxRows, + structuralAssessedRange: structuralScout.summary?.assessedRange ?? null, + structuralStatus: structuralScout.status ?? null, + }, + summary: { + analyzedRowCount: analyses.length, + mixedPassCount: analyses.filter((row) => row.mixedPass).length, + mixedFailureCount: failingAnalyses.length, + allAnalyzedRowsMixedPass: failingAnalyses.length === 0, + minMixedMargin: analyses.reduce((minimum, row) => Math.min(minimum, row.mixedMargin), Infinity), + maxImprovementOverUnion: analyses.reduce((maximum, row) => Math.max(maximum, row.improvementOverUnion), 0), + }, + firstMixedFailure: failingAnalyses[0] ?? null, + worstMixedRow: analyses.reduce((worst, row) => { + if (!worst || row.mixedMargin < worst.mixedMargin) return row; + return worst; + }, null), + analyses, + boundary: { + claimLevel: 'sampled_failure_scout_not_full_structural_certificate', + note: 'This scout exactly solves the mixed-base clique on selected union-failure rows from the two-sided structural scout. It does not yet certify every structural breakpoint.', + nextUse: failingAnalyses.length === 0 + ? 'Promote this into the full two-sided structural verifier by replacing the union-base overcount with the exact mixed-base clique bound at every breakpoint.' + : 'Inspect the remaining mixed-base failures before trying to promote a mixed-base lemma.', + }, + }; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 Mixed-Base Failure Scout', + '', + `- Generated: ${packet.generatedAt}`, + `- Method: \`${packet.method}\``, + `- Status: \`${packet.status}\``, + `- Source structural scout: \`${packet.sourceStructuralJson}\``, + `- Analyzed rows: \`${packet.summary.analyzedRowCount}\``, + `- Mixed failures: \`${packet.summary.mixedFailureCount}\``, + `- Minimum mixed margin: \`${Number.isFinite(packet.summary.minMixedMargin) ? packet.summary.minMixedMargin : '(none)'}\``, + `- Max improvement over union: \`${packet.summary.maxImprovementOverUnion}\``, + '', + '## Worst Mixed Row', + '', + `- \`${packet.worstMixedRow ? JSON.stringify(packet.worstMixedRow) : '(none)'}\``, + '', + '## Boundary', + '', + `- Claim level: \`${packet.boundary.claimLevel}\``, + `- ${packet.boundary.note}`, + `- Next use: ${packet.boundary.nextUse}`, + '', + ]; + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = analyze(args.structuralJson, args.maxRows); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify(packet.summary, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_structural_lift_miner.mjs b/packs/number-theory/problems/848/compute/problem848_structural_lift_miner.mjs new file mode 100644 index 0000000..2b2a986 --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_structural_lift_miner.mjs @@ -0,0 +1,548 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; +import { fileURLToPath } from 'node:url'; + +const scriptDir = path.dirname(fileURLToPath(import.meta.url)); +const problemDir = path.resolve(scriptDir, '..'); + +function parseArgs(argv) { + const args = { + verifierJson: path.join(problemDir, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json'), + topRows: 12, + familyLimit: 20, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--verifier-json') { + args.verifierJson = argv[++index]; + } else if (token === '--top-rows') { + args.topRows = Number(argv[++index]); + } else if (token === '--family-limit') { + args.familyLimit = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!args.verifierJson) { + throw new Error('--verifier-json is required'); + } + if (!Number.isInteger(args.topRows) || args.topRows < 1) { + throw new Error('--top-rows must be a positive integer'); + } + if (!Number.isInteger(args.familyLimit) || args.familyLimit < 1) { + throw new Error('--family-limit must be a positive integer'); + } + return args; +} + +function positiveModulo(value, modulus) { + const residue = Number(value) % modulus; + return residue < 0 ? residue + modulus : residue; +} + +function readJson(filePath) { + return JSON.parse(fs.readFileSync(filePath, 'utf8')); +} + +function average(values) { + if (values.length === 0) return null; + return values.reduce((sum, value) => sum + value, 0) / values.length; +} + +function minValue(values) { + return values.length === 0 ? null : Math.min(...values); +} + +function maxValue(values) { + return values.length === 0 ? null : Math.max(...values); +} + +function countBy(values, keyFn) { + const counts = new Map(); + for (const value of values) { + const key = keyFn(value); + counts.set(key, (counts.get(key) ?? 0) + 1); + } + return [...counts.entries()] + .map(([key, count]) => ({ key, count })) + .sort((left, right) => right.count - left.count || String(left.key).localeCompare(String(right.key))); +} + +function groupBy(values, keyFn) { + const groups = new Map(); + for (const value of values) { + const key = keyFn(value); + const group = groups.get(key) ?? []; + group.push(value); + groups.set(key, group); + } + return groups; +} + +function dominantMixedCliqueSide(row) { + const side7 = row.mixedCliqueSide7Count ?? row.worstThreat?.mixedCliqueSide7Count ?? 0; + const side18 = row.mixedCliqueSide18Count ?? row.worstThreat?.mixedCliqueSide18Count ?? 0; + if (side7 > side18) return 'side7'; + if (side18 > side7) return 'side18'; + if (side7 === 0 && side18 === 0) return 'none'; + return 'tie'; +} + +function compactFromVerifierRow(row) { + const worstThreat = row.worstThreat ?? null; + const sMaxMixedWitness = row.sMaxMixedWitness ?? worstThreat?.outsider ?? null; + const worstOutsider = worstThreat?.outsider ?? row.worstOutsider ?? null; + return { + N: row.N, + certificateMode: row.certificateMode ?? null, + nMod25: row.nMod25 ?? positiveModulo(row.N, 25), + p: row.p, + p2: row.p2, + rawPlus: row.rawPlus, + rawMinus: row.rawMinus, + vMax: row.vMax, + activePlus: row.activePlus, + activeMinus: row.activeMinus, + activeOutsiderCount: row.activeOutsiderCount, + dMax: row.dMax, + dMaxWitnessSide: row.dMaxWitnessSide ?? row.dMaxWitness?.side ?? null, + dMaxWitnessValue: row.dMaxWitnessValue ?? row.dMaxWitness?.value ?? null, + rGreater: row.rGreater, + candidateSize: row.candidateSize, + strictBaseThreshold: row.strictBaseThreshold, + side7Margin: row.side7Margin, + side18Margin: row.side18Margin, + unionMargin: row.unionMargin, + mixedMargin: row.mixedMargin, + sMaxMixed: row.sMaxMixed, + sMaxMixedWitness, + sMaxMixedWitnessMod25: row.sMaxMixedWitnessMod25 ?? (sMaxMixedWitness === null ? null : positiveModulo(sMaxMixedWitness, 25)), + threateningOutsiderCount: row.threateningOutsiderCount, + maxImprovementOverUnion: row.maxImprovementOverUnion, + worstOutsider, + worstOutsiderMod25: row.worstOutsiderMod25 ?? (worstOutsider === null ? null : positiveModulo(worstOutsider, 25)), + worstUnionCount: row.worstUnionCount ?? worstThreat?.unionCount ?? null, + worstMixedCliqueSize: row.worstMixedCliqueSize ?? worstThreat?.mixedBaseCliqueSize ?? null, + matchingSizeInMissingCrossGraph: row.matchingSizeInMissingCrossGraph ?? worstThreat?.matchingSizeInMissingCrossGraph ?? null, + compatibleSide7Count: row.compatibleSide7Count ?? worstThreat?.compatibleSide7Count ?? null, + compatibleSide18Count: row.compatibleSide18Count ?? worstThreat?.compatibleSide18Count ?? null, + mixedCliqueSide7Count: row.mixedCliqueSide7Count ?? worstThreat?.mixedCliqueSide7Count ?? null, + mixedCliqueSide18Count: row.mixedCliqueSide18Count ?? worstThreat?.mixedCliqueSide18Count ?? null, + dominantMixedCliqueSide: row.dominantMixedCliqueSide ?? dominantMixedCliqueSide(row), + }; +} + +function rowKey(row) { + return [ + row.p, + row.N, + row.worstOutsider ?? row.sMaxMixedWitness ?? 'none', + row.mixedMargin ?? 'none', + row.unionMargin ?? 'none', + ].join(':'); +} + +function collectLiftRows(verifier) { + const candidates = []; + if (Array.isArray(verifier.liftMiningRows)) { + candidates.push(...verifier.liftMiningRows); + } + if (Array.isArray(verifier.exactRowsSample)) { + candidates.push(...verifier.exactRowsSample); + } + for (const row of [ + verifier.worstCertifiedRow, + verifier.worstExactMixedRow, + ...(verifier.blockSummaries ?? []).map((block) => block.worstCertifiedRow), + ]) { + if (row) candidates.push(row); + } + + const seen = new Set(); + const rows = []; + for (const candidate of candidates) { + const row = compactFromVerifierRow(candidate); + if (row.N === undefined || row.p === undefined || row.mixedMargin === undefined || row.certificateMode === 'union_bound') { + continue; + } + const key = rowKey(row); + if (seen.has(key)) continue; + seen.add(key); + rows.push(row); + } + return rows.sort((left, right) => left.N - right.N || left.p - right.p); +} + +function rowFamilyKey(row) { + return [ + `p=${row.p}`, + `Nmod25=${row.nMod25}`, + `d=${row.dMaxWitnessSide ?? 'none'}`, + `clique=${row.dominantMixedCliqueSide ?? 'none'}`, + `outMod25=${row.worstOutsiderMod25 ?? row.sMaxMixedWitnessMod25 ?? 'none'}`, + ].join('|'); +} + +function summarizeRows(rows) { + return { + count: rows.length, + firstN: minValue(rows.map((row) => row.N)), + lastN: maxValue(rows.map((row) => row.N)), + minMixedMargin: minValue(rows.map((row) => row.mixedMargin).filter(Number.isFinite)), + maxMixedMargin: maxValue(rows.map((row) => row.mixedMargin).filter(Number.isFinite)), + averageMixedMargin: average(rows.map((row) => row.mixedMargin).filter(Number.isFinite)), + minUnionMargin: minValue(rows.map((row) => row.unionMargin).filter(Number.isFinite)), + maxThreateningOutsiders: maxValue(rows.map((row) => row.threateningOutsiderCount).filter(Number.isFinite)), + maxImprovementOverUnion: maxValue(rows.map((row) => row.maxImprovementOverUnion).filter(Number.isFinite)), + }; +} + +function buildPrimeProfiles(rows) { + return [...groupBy(rows, (row) => row.p).entries()] + .map(([p, primeRows]) => { + const sorted = [...primeRows].sort((left, right) => left.N - right.N); + const first = sorted[0] ?? null; + const last = sorted[sorted.length - 1] ?? null; + const marginSlopePerN = first && last && last.N !== first.N + ? (last.mixedMargin - first.mixedMargin) / (last.N - first.N) + : null; + return { + p: Number(p), + p2: first?.p2 ?? null, + ...summarizeRows(sorted), + marginDeltaAcrossMinedRows: first && last ? last.mixedMargin - first.mixedMargin : null, + approximateMarginSlopePerN: marginSlopePerN, + nMod25Distribution: countBy(sorted, (row) => row.nMod25), + dMaxWitnessSideDistribution: countBy(sorted, (row) => row.dMaxWitnessSide ?? 'none'), + dominantMixedCliqueSideDistribution: countBy(sorted, (row) => row.dominantMixedCliqueSide ?? 'none'), + worstOutsiderMod25Distribution: countBy(sorted, (row) => row.worstOutsiderMod25 ?? 'none'), + }; + }) + .sort((left, right) => right.count - left.count || left.p - right.p); +} + +function buildFamilySummaries(rows, familyLimit) { + return [...groupBy(rows, rowFamilyKey).entries()] + .map(([familyKey, familyRows]) => { + const sorted = [...familyRows].sort((left, right) => left.mixedMargin - right.mixedMargin || left.N - right.N); + return { + familyKey, + ...summarizeRows(sorted), + representativeRows: sorted.slice(0, 3), + }; + }) + .sort((left, right) => right.count - left.count || left.minMixedMargin - right.minMixedMargin || left.familyKey.localeCompare(right.familyKey)) + .slice(0, familyLimit); +} + +function buildThreatMatchingProfiles(threatRows) { + return [...groupBy(threatRows, (row) => row.p).entries()] + .map(([p, rows]) => { + const sorted = [...rows].sort((left, right) => left.matchingSlack - right.matchingSlack || left.N - right.N || left.outsider - right.outsider); + return { + p: Number(p), + threatRowCount: rows.length, + structuralRowCount: new Set(rows.map((row) => `${row.N}:${row.p}`)).size, + firstN: minValue(rows.map((row) => row.N)), + lastN: maxValue(rows.map((row) => row.N)), + minRequiredMatchingLowerBound: minValue(rows.map((row) => row.requiredMatchingLowerBound).filter(Number.isFinite)), + maxRequiredMatchingLowerBound: maxValue(rows.map((row) => row.requiredMatchingLowerBound).filter(Number.isFinite)), + minActualMatching: minValue(rows.map((row) => row.matchingSizeInMissingCrossGraph).filter(Number.isFinite)), + maxActualMatching: maxValue(rows.map((row) => row.matchingSizeInMissingCrossGraph).filter(Number.isFinite)), + minMatchingSlack: minValue(rows.map((row) => row.matchingSlack).filter(Number.isFinite)), + allThreatsMeetRequiredLowerBound: rows.every((row) => Number(row.matchingSlack) >= 0), + allThreatsSaturateSmallerSide: rows.every((row) => row.saturatesSmallerSide === true), + outsiderMod25Distribution: countBy(rows, (row) => row.outsiderMod25 ?? 'none'), + dominantMixedCliqueSideDistribution: countBy(rows, (row) => row.dominantMixedCliqueSide ?? 'none'), + tightestThreats: sorted.slice(0, 8), + }; + }) + .sort((left, right) => right.threatRowCount - left.threatRowCount || left.p - right.p); +} + +function buildLiftObligations(rows, verifier, primeProfiles, familySummaries, threatMatchingProfiles) { + const topExactPrimes = primeProfiles.slice(0, 4).map((profile) => profile.p); + const topFamily = familySummaries[0] ?? null; + const minMixedMargin = minValue(rows.map((row) => row.mixedMargin).filter(Number.isFinite)); + const minUnionMargin = verifier.summary?.minCertifiedMargin ?? null; + const minThreatMatchingSlack = minValue(threatMatchingProfiles + .map((profile) => profile.minMatchingSlack) + .filter(Number.isFinite)); + + return [ + { + obligationId: 'p848_cross_side_matching_bound', + priority: 'critical', + status: 'bounded_evidence_ready', + statementTemplate: 'For each threatening outsider, the missing cross-edge graph between the 7 mod 25 and 18 mod 25 compatible base sides has a matching large enough to force mixedCliqueSize below the strict base threshold.', + currentEvidence: { + assessedRange: verifier.summary?.assessedRange ?? null, + threateningOutsiderCheckCount: verifier.summary?.threateningOutsiderCheckCount ?? null, + compactThreatMiningRowCount: verifier.summary?.threatLiftMiningRowCount ?? null, + maxImprovementOverUnion: verifier.summary?.maxImprovementOverUnion ?? null, + minMixedMargin, + minThreatMatchingSlack, + threatMatchingProfiles: threatMatchingProfiles.slice(0, 4), + }, + proofUse: 'This is the exact step that turns the computational co-bipartite clique repair into a reusable lemma.', + }, + { + obligationId: 'p848_exact_prime_margin_lift', + priority: 'critical', + status: topExactPrimes.length > 0 ? 'bounded_evidence_ready' : 'blocked_no_exact_rows', + statementTemplate: `For the exact-mixed witness-prime families ${topExactPrimes.length > 0 ? topExactPrimes.join(', ') : '(none)'}, prove candidateSize > sMaxMixed + vMax + dMax + rGreater either eventually or by a finite periodic residue split.`, + currentEvidence: { + exactPrimeProfiles: primeProfiles.slice(0, 4), + }, + proofUse: 'This is the likely all-N lift of the hardest bounded structural rows.', + }, + { + obligationId: 'p848_union_bound_tail_lift', + priority: 'high', + status: 'bounded_evidence_ready', + statementTemplate: 'Prove that every non-exact witness-prime block is certified by the safe union bound past the base interval, with only finitely many exceptional rows delegated to exact verification.', + currentEvidence: { + unionCertifiedRowCount: verifier.summary?.unionCertifiedRowCount ?? null, + exactMixedRowCount: verifier.summary?.exactMixedRowCount ?? null, + minCertifiedMargin: minUnionMargin, + }, + proofUse: 'This separates the easy tail from the p-specific exact mixed-base obligations.', + }, + { + obligationId: 'p848_top_repeating_family_lift', + priority: topFamily ? 'high' : 'medium', + status: topFamily ? 'bounded_evidence_ready' : 'blocked_no_family', + statementTemplate: topFamily + ? `Use family ${topFamily.familyKey} as the first symbolic family to formalize.` + : 'Pick the first repeated exact mixed-base row family once mined rows exist.', + currentEvidence: topFamily, + proofUse: 'A repeated row family is the best handhold for converting the verifier into a theorem packet.', + }, + ]; +} + +function buildRecommendedNextSteps(rows, verifier, coverageComplete) { + const exactMixedRowCount = verifier.summary?.exactMixedRowCount ?? null; + const minedRowCount = rows.length; + const assessedRange = verifier.summary?.assessedRange ?? verifier.parameters?.assessedRange ?? null; + const maxN = verifier.parameters?.maxN ?? null; + const minStructuralN = verifier.parameters?.minStructuralN ?? null; + + const steps = [ + { + stepId: 'mine_matching_pattern_witnesses', + priority: 'critical', + command: 'erdos number-theory dispatch 848 --apply --action matching_pattern_miner --matching-pattern-prime 13', + why: 'The active D2 atom needs a symbolic matching construction, and the matching-pattern miner extracts actual tight-row missing-cross pairs without bloating the verifier artifact.', + }, + { + stepId: 'formalize_cross_side_matching_bound', + priority: 'critical', + command: 'erdos problem formalization-work-refresh 848', + why: 'The full verifier succeeds exactly because mixed-base cliques are much smaller than the safe union overcount; this is the theorem-shaped repair mechanism.', + }, + { + stepId: 'formalize_exact_prime_margin_lift', + priority: 'critical', + command: 'erdos problem formalization 848', + why: 'The mined rows identify which witness-prime blocks still need symbolic margin control after the union-bound rows are separated.', + }, + { + stepId: 'extend_structural_range_after_lift_target', + priority: 'high', + command: maxN && minStructuralN + ? `erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --structural-min ${minStructuralN} --structural-max ${Math.max(maxN + 5000, maxN * 2)}` + : 'erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier', + why: `Once the first symbolic family is named, extend the bounded verifier beyond ${assessedRange ?? 'the current range'} to falsify or strengthen the family before claiming a lift.`, + }, + ]; + + if (!coverageComplete) { + steps.unshift({ + stepId: 'refresh_full_verifier_compact_rows', + priority: 'critical', + command: exactMixedRowCount + ? `erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier --full-mixed-row-sample-limit ${Math.max(exactMixedRowCount, 200)}` + : 'erdos number-theory dispatch 848 --apply --action full_mixed_base_structural_verifier', + why: `The miner saw ${minedRowCount} rows but the verifier reports ${exactMixedRowCount ?? '(unknown)'} exact mixed rows; refresh the full verifier so compact lift-mining rows cover the exact row set.`, + }); + } + + return steps; +} + +function mine(args) { + const verifier = readJson(args.verifierJson); + const rows = collectLiftRows(verifier); + const threatRows = Array.isArray(verifier.threatLiftMiningRows) ? verifier.threatLiftMiningRows : []; + const exactMixedRowCount = verifier.summary?.exactMixedRowCount ?? null; + const compactRowCount = verifier.summary?.liftMiningRowCount ?? verifier.liftMiningRows?.length ?? null; + const coverageComplete = exactMixedRowCount !== null && rows.length >= exactMixedRowCount; + const primeProfiles = buildPrimeProfiles(rows); + const familySummaries = buildFamilySummaries(rows, args.familyLimit); + const threatMatchingProfiles = buildThreatMatchingProfiles(threatRows); + const worstRowsByMargin = [...rows] + .sort((left, right) => left.mixedMargin - right.mixedMargin || left.N - right.N || left.p - right.p) + .slice(0, args.topRows); + const worstRowsByThreatCount = [...rows] + .sort((left, right) => (right.threateningOutsiderCount ?? 0) - (left.threateningOutsiderCount ?? 0) || left.mixedMargin - right.mixedMargin) + .slice(0, args.topRows); + const worstRowsByUnionRepair = [...rows] + .sort((left, right) => (right.maxImprovementOverUnion ?? 0) - (left.maxImprovementOverUnion ?? 0) || left.mixedMargin - right.mixedMargin) + .slice(0, args.topRows); + + const status = rows.length === 0 + ? 'structural_lift_miner_no_exact_rows' + : coverageComplete + ? 'structural_lift_obligation_packet_ready' + : 'sampled_structural_lift_obligation_packet_ready'; + + return { + schema: 'erdos.number_theory.p848_structural_lift_miner/1', + generatedAt: new Date().toISOString(), + problemId: '848', + method: 'mixed_base_structural_lift_pattern_mining', + status, + parameters: { + verifierJsonPath: path.resolve(args.verifierJson), + topRows: args.topRows, + familyLimit: args.familyLimit, + }, + sourceVerifier: { + status: verifier.status ?? null, + method: verifier.method ?? null, + assessedRange: verifier.summary?.assessedRange ?? verifier.parameters?.assessedRange ?? null, + exactMixedRowCount, + compactLiftMiningRowCount: compactRowCount, + compactThreatMiningRowCount: verifier.summary?.threatLiftMiningRowCount ?? threatRows.length, + minedExactRowCount: rows.length, + coverageComplete, + }, + summary: { + assessedRange: verifier.summary?.assessedRange ?? verifier.parameters?.assessedRange ?? null, + exactMixedRowCount, + minedExactRowCount: rows.length, + threatMiningRowCount: threatRows.length, + coverageComplete, + exactPrimeCount: primeProfiles.length, + primaryExactPrimes: primeProfiles.slice(0, 6).map((profile) => profile.p), + topFamilyCount: familySummaries.length, + minMixedMargin: minValue(rows.map((row) => row.mixedMargin).filter(Number.isFinite)), + minUnionMargin: minValue(rows.map((row) => row.unionMargin).filter(Number.isFinite)), + minThreatMatchingSlack: minValue(threatMatchingProfiles.map((profile) => profile.minMatchingSlack).filter(Number.isFinite)), + maxThreateningOutsidersInRow: maxValue(rows.map((row) => row.threateningOutsiderCount).filter(Number.isFinite)), + maxImprovementOverUnion: maxValue(rows.map((row) => row.maxImprovementOverUnion).filter(Number.isFinite)), + nextTheoremLane: rows.length > 0 + ? 'formalize_cross_side_matching_bound_then_exact_prime_margin_lift' + : 'refresh_full_mixed_base_structural_verifier', + }, + periodicityHints: { + nMod25Distribution: countBy(rows, (row) => row.nMod25), + dMaxWitnessSideDistribution: countBy(rows, (row) => row.dMaxWitnessSide ?? 'none'), + dominantMixedCliqueSideDistribution: countBy(rows, (row) => row.dominantMixedCliqueSide ?? 'none'), + worstOutsiderMod25Distribution: countBy(rows, (row) => row.worstOutsiderMod25 ?? 'none'), + }, + primeProfiles, + threatMatchingProfiles, + familySummaries, + worstRows: { + byMixedMargin: worstRowsByMargin, + byThreateningOutsiderCount: worstRowsByThreatCount, + byUnionRepair: worstRowsByUnionRepair, + }, + liftObligations: buildLiftObligations(rows, verifier, primeProfiles, familySummaries, threatMatchingProfiles), + recommendedNextSteps: buildRecommendedNextSteps(rows, verifier, coverageComplete), + boundary: { + claimLevel: 'theorem_obligation_packet_not_all_N_proof', + note: 'This miner extracts proof obligations from a bounded structural verifier. It does not certify any N outside the source verifier range.', + promotionRule: 'Use this packet to choose and formalize symbolic lemmas. Promote all-N closure only after those lemmas are independently proved and linked to the finite exact base.', + }, + }; +} + +function renderRow(row) { + return row ? JSON.stringify(row) : '(none)'; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 Structural Lift Miner', + '', + `- Generated: ${packet.generatedAt}`, + `- Method: \`${packet.method}\``, + `- Status: \`${packet.status}\``, + `- Source verifier status: \`${packet.sourceVerifier.status ?? '(unknown)'}\``, + `- Assessed range: \`${packet.summary.assessedRange ?? '(unknown)'}\``, + `- Exact mixed rows reported: \`${packet.summary.exactMixedRowCount ?? '(unknown)'}\``, + `- Exact mixed rows mined: \`${packet.summary.minedExactRowCount}\``, + `- Threatening-outsider rows mined: \`${packet.summary.threatMiningRowCount ?? '(unknown)'}\``, + `- Coverage complete: \`${packet.summary.coverageComplete ? 'yes' : 'no'}\``, + `- Primary exact primes: \`${packet.summary.primaryExactPrimes.join(', ') || '(none)'}\``, + `- Minimum mixed margin: \`${packet.summary.minMixedMargin ?? '(unknown)'}\``, + `- Minimum threat matching slack: \`${packet.summary.minThreatMatchingSlack ?? '(unknown)'}\``, + '', + '## Prime Profiles', + '', + ]; + + for (const profile of packet.primeProfiles.slice(0, 8)) { + lines.push(`- p=${profile.p}: rows ${profile.count}, N ${profile.firstN}..${profile.lastN}, min margin ${profile.minMixedMargin}, margin delta ${profile.marginDeltaAcrossMinedRows}`); + } + + lines.push('', '## Threat Matching Profiles', ''); + for (const profile of packet.threatMatchingProfiles.slice(0, 8)) { + lines.push(`- p=${profile.p}: threats ${profile.threatRowCount}, rows ${profile.structuralRowCount}, K ${profile.minRequiredMatchingLowerBound}..${profile.maxRequiredMatchingLowerBound}, matching ${profile.minActualMatching}..${profile.maxActualMatching}, min slack ${profile.minMatchingSlack}, saturates smaller side ${profile.allThreatsSaturateSmallerSide ? 'yes' : 'no'}`); + } + + lines.push('', '## Top Families', ''); + for (const family of packet.familySummaries.slice(0, 10)) { + lines.push(`- \`${family.familyKey}\`: rows ${family.count}, N ${family.firstN}..${family.lastN}, min margin ${family.minMixedMargin}, max union repair ${family.maxImprovementOverUnion}`); + } + + lines.push('', '## Worst Rows', ''); + for (const row of packet.worstRows.byMixedMargin.slice(0, 8)) { + lines.push(`- ${renderRow(row)}`); + } + + lines.push('', '## Lift Obligations', ''); + for (const obligation of packet.liftObligations) { + lines.push(`- \`${obligation.obligationId}\` [${obligation.priority}, ${obligation.status}]: ${obligation.statementTemplate}`); + } + + lines.push('', '## Recommended Next Steps', ''); + for (const step of packet.recommendedNextSteps) { + lines.push(`- \`${step.stepId}\` [${step.priority}]: ${step.why} | command: \`${step.command}\``); + } + + lines.push('', '## Boundary', ''); + lines.push(`- Claim level: \`${packet.boundary.claimLevel}\``); + lines.push(`- Note: ${packet.boundary.note}`); + lines.push(`- Promotion rule: ${packet.boundary.promotionRule}`); + lines.push(''); + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = mine(args); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify(packet.summary, null, 2)); diff --git a/packs/number-theory/problems/848/compute/problem848_structural_two_side_scout.mjs b/packs/number-theory/problems/848/compute/problem848_structural_two_side_scout.mjs new file mode 100644 index 0000000..2ffe13a --- /dev/null +++ b/packs/number-theory/problems/848/compute/problem848_structural_two_side_scout.mjs @@ -0,0 +1,528 @@ +#!/usr/bin/env node + +import fs from 'node:fs'; +import path from 'node:path'; + +function parseArgs(argv) { + const args = { + max: 10000, + minStructuralN: 7307, + jsonOutput: null, + markdownOutput: null, + }; + + for (let index = 0; index < argv.length; index += 1) { + const token = argv[index]; + if (token === '--max') { + args.max = Number(argv[++index]); + } else if (token === '--min-structural-n') { + args.minStructuralN = Number(argv[++index]); + } else if (token === '--json-output') { + args.jsonOutput = argv[++index]; + } else if (token === '--markdown-output') { + args.markdownOutput = argv[++index]; + } else { + throw new Error(`Unknown argument: ${token}`); + } + } + + if (!Number.isInteger(args.max) || args.max < 1) { + throw new Error('--max must be a positive integer'); + } + if (!Number.isInteger(args.minStructuralN) || args.minStructuralN < 1) { + throw new Error('--min-structural-n must be a positive integer'); + } + if (args.minStructuralN > args.max) { + throw new Error('--min-structural-n must be <= --max'); + } + return args; +} + +function positiveModulo(value, modulus) { + const residue = value % modulus; + return residue < 0 ? residue + modulus : residue; +} + +function modInverse(value, modulus) { + let oldR = positiveModulo(value, modulus); + let r = modulus; + let oldS = 1; + let s = 0; + while (r !== 0) { + const quotient = Math.floor(oldR / r); + [oldR, r] = [r, oldR - quotient * r]; + [oldS, s] = [s, oldS - quotient * s]; + } + if (oldR !== 1) return null; + return positiveModulo(oldS, modulus); +} + +function primeSieve(max) { + const composite = new Uint8Array(max + 1); + const primes = []; + for (let n = 2; n <= max; n += 1) { + if (composite[n]) continue; + primes.push(n); + if (n * n > max) continue; + for (let multiple = n * n; multiple <= max; multiple += n) { + composite[multiple] = 1; + } + } + return primes; +} + +function isBaseResidue(value) { + const residue = positiveModulo(value, 25); + return residue === 7 || residue === 18; +} + +function isNonSquarefree(value, primeSquares) { + for (const square of primeSquares) { + if (square > value) break; + if (value % square === 0) return true; + } + return false; +} + +function residueValues(max, residue, modulus = 25) { + const values = []; + for (let value = residue; value <= max; value += modulus) { + if (value >= 1) values.push(value); + } + return values; +} + +function upperBound(values, maxValue) { + let low = 0; + let high = values.length; + while (low < high) { + const mid = (low + high) >>> 1; + if (values[mid] <= maxValue) { + low = mid + 1; + } else { + high = mid; + } + } + return low; +} + +function henselRootPrimeSquare(p) { + let rootModP = null; + for (let residue = 1; residue < p; residue += 1) { + if ((residue * residue + 1) % p === 0) { + rootModP = residue; + break; + } + } + if (rootModP === null) { + throw new Error(`No root for p=${p}`); + } + const p2 = p * p; + const t = Math.floor((rootModP * rootModP + 1) / p) % p; + const inverse = modInverse((2 * rootModP) % p, p); + if (inverse === null) { + throw new Error(`Hensel inverse failed for p=${p}`); + } + let k = (-t * inverse) % p; + if (k < 0) k += p; + let root = (rootModP + k * p) % p2; + if (root <= 0) root += p2; + if ((root * root + 1) % p2 !== 0) { + throw new Error(`Hensel root verification failed for p=${p}`); + } + return { + p, + p2, + rPlus: root, + rMinus: p2 - root, + }; +} + +function buildRootInfos(maxN) { + return primeSieve(Math.floor(Math.sqrt(maxN)) + 5) + .filter((prime) => prime >= 13 && prime % 4 === 1 && prime * prime <= maxN) + .map(henselRootPrimeSquare); +} + +function rootProgression(residue, modulus, maxN) { + const values = []; + for (let value = residue; value <= maxN; value += modulus) { + if (value >= 1) values.push(value); + } + return values; +} + +function classifyLeastWitness(value, roots) { + for (let index = 0; index < roots.length; index += 1) { + const root = roots[index]; + const residue = positiveModulo(value, root.p2); + if (residue === root.rPlus) { + return { index, sign: 'plus', p: root.p }; + } + if (residue === root.rMinus) { + return { index, sign: 'minus', p: root.p }; + } + } + return null; +} + +function compatibleValues(value, candidates, primeSquares) { + return candidates.filter((candidate) => isNonSquarefree(value * candidate + 1, primeSquares)); +} + +function maxPrefixCompatibility(values, compatibleByValue, activeN) { + let max = 0; + let witness = null; + for (const value of values) { + if (value > activeN) break; + const count = upperBound(compatibleByValue.get(value) ?? [], activeN); + if (count > max) { + max = count; + witness = value; + } + } + return { max, witness }; +} + +function buildBlock(root, rootIndex, roots, maxN, baseSides, primeSquares) { + const rawPlusValues = rootProgression(root.rPlus, root.p2, maxN); + const rawMinusValues = rootProgression(root.rMinus, root.p2, maxN); + const plusValues = rawPlusValues.filter((value) => { + if (isBaseResidue(value)) return false; + const witness = classifyLeastWitness(value, roots); + return witness?.index === rootIndex && witness.sign === 'plus'; + }); + const minusValues = rawMinusValues.filter((value) => { + if (isBaseResidue(value)) return false; + const witness = classifyLeastWitness(value, roots); + return witness?.index === rootIndex && witness.sign === 'minus'; + }); + const outsiderValues = [...plusValues, ...minusValues].sort((left, right) => left - right); + const side7CompatibleByValue = new Map(); + const side18CompatibleByValue = new Map(); + const unionCompatibleByValue = new Map(); + + for (const value of outsiderValues) { + const side7 = compatibleValues(value, baseSides.side7Values, primeSquares); + const side18 = compatibleValues(value, baseSides.side18Values, primeSquares); + side7CompatibleByValue.set(value, side7); + side18CompatibleByValue.set(value, side18); + unionCompatibleByValue.set(value, [...side7, ...side18].sort((left, right) => left - right)); + } + + const plusToMinus = new Map(plusValues.map((value) => [value, []])); + const minusToPlus = new Map(minusValues.map((value) => [value, []])); + for (const plus of plusValues) { + for (const minus of minusValues) { + if (!isNonSquarefree(plus * minus + 1, primeSquares)) continue; + plusToMinus.get(plus).push(minus); + minusToPlus.get(minus).push(plus); + } + } + + return { + root, + rootIndex, + rawPlusValues, + rawMinusValues, + plusValues, + minusValues, + outsiderValues, + side7CompatibleByValue, + side18CompatibleByValue, + unionCompatibleByValue, + plusToMinus, + minusToPlus, + }; +} + +function evaluateBlockAtN(block, higherRootEventValues, baseSides, activeN) { + const rawPlus = upperBound(block.rawPlusValues, activeN); + const rawMinus = upperBound(block.rawMinusValues, activeN); + const vMax = Math.max(rawPlus, rawMinus); + const s7 = maxPrefixCompatibility(block.outsiderValues, block.side7CompatibleByValue, activeN); + const s18 = maxPrefixCompatibility(block.outsiderValues, block.side18CompatibleByValue, activeN); + const sUnion = maxPrefixCompatibility(block.outsiderValues, block.unionCompatibleByValue, activeN); + const activePlus = upperBound(block.plusValues, activeN); + const activeMinus = upperBound(block.minusValues, activeN); + let dMax = 0; + let dWitness = null; + + for (const plus of block.plusValues.slice(0, activePlus)) { + const degree = upperBound(block.plusToMinus.get(plus) ?? [], activeN); + if (degree > dMax) { + dMax = degree; + dWitness = { side: 'plus', value: plus }; + } + } + for (const minus of block.minusValues.slice(0, activeMinus)) { + const degree = upperBound(block.minusToPlus.get(minus) ?? [], activeN); + if (degree > dMax) { + dMax = degree; + dWitness = { side: 'minus', value: minus }; + } + } + + const rGreater = upperBound(higherRootEventValues, activeN); + const side7CandidateSize = upperBound(baseSides.side7Values, activeN); + const side18CandidateSize = upperBound(baseSides.side18Values, activeN); + const candidateSize = Math.max(side7CandidateSize, side18CandidateSize); + const side7Bound = s7.max + vMax + dMax + rGreater; + const side18Bound = s18.max + vMax + dMax + rGreater; + const unionBound = sUnion.max + vMax + dMax + rGreater; + + return { + N: activeN, + p: block.root.p, + p2: block.root.p2, + rawPlus, + rawMinus, + vMax, + activePlus, + activeMinus, + sMaxSide7: s7.max, + sMaxSide7Witness: s7.witness, + sMaxSide18: s18.max, + sMaxSide18Witness: s18.witness, + sMaxUnion: sUnion.max, + sMaxUnionWitness: sUnion.witness, + dMax, + dMaxWitness: dWitness, + rGreater, + candidateSize, + side7CandidateSize, + side18CandidateSize, + side7Bound, + side18Bound, + unionBound, + side7Margin: candidateSize - side7Bound, + side18Margin: candidateSize - side18Bound, + unionMargin: candidateSize - unionBound, + side7Pass: side7Bound < candidateSize, + side18Pass: side18Bound < candidateSize, + unionPass: unionBound < candidateSize, + }; +} + +function betterWorst(left, right, key) { + if (!left) return right; + if (!right) return left; + if (right[key] < left[key]) return right; + if (right[key] === left[key] && right.N < left.N) return right; + return left; +} + +function analyze(maxN, minStructuralN) { + const roots = buildRootInfos(maxN); + const primes = primeSieve(maxN); + const primeSquares = primes.map((prime) => prime * prime); + const side7Values = residueValues(maxN, 7); + const side18Values = residueValues(maxN, 18); + const baseSides = { side7Values, side18Values }; + const globalRootEvents = []; + for (let rootIndex = 0; rootIndex < roots.length; rootIndex += 1) { + const root = roots[rootIndex]; + for (const value of rootProgression(root.rPlus, root.p2, maxN)) { + globalRootEvents.push({ n: value, rootIndex, p: root.p, sign: 'plus' }); + } + for (const value of rootProgression(root.rMinus, root.p2, maxN)) { + globalRootEvents.push({ n: value, rootIndex, p: root.p, sign: 'minus' }); + } + } + globalRootEvents.sort((left, right) => left.n - right.n || left.rootIndex - right.rootIndex); + + const breakpoints = [ + minStructuralN, + maxN, + ...side7Values, + ...side18Values, + ...globalRootEvents.map((event) => event.n), + ] + .filter((value) => value >= minStructuralN && value <= maxN) + .sort((left, right) => left - right) + .filter((value, index, values) => index === 0 || value !== values[index - 1]); + + const higherRootEventsByIndex = roots.map((_, rootIndex) => globalRootEvents + .filter((event) => event.rootIndex > rootIndex) + .map((event) => event.n) + .sort((left, right) => left - right)); + + const blockSummaries = []; + const failureRows = []; + let checkCount = 0; + let side7FailureCount = 0; + let side18FailureCount = 0; + let unionFailureCount = 0; + let firstSide7Failure = null; + let firstSide18Failure = null; + let firstUnionFailure = null; + let worstSide7Row = null; + let worstSide18Row = null; + let worstUnionRow = null; + + for (let rootIndex = 0; rootIndex < roots.length; rootIndex += 1) { + const block = buildBlock(roots[rootIndex], rootIndex, roots, maxN, baseSides, primeSquares); + let blockWorstUnionRow = null; + let blockUnionFailureCount = 0; + let blockFirstUnionFailure = null; + + for (const activeN of breakpoints) { + const row = evaluateBlockAtN(block, higherRootEventsByIndex[rootIndex], baseSides, activeN); + checkCount += 1; + worstSide7Row = betterWorst(worstSide7Row, row, 'side7Margin'); + worstSide18Row = betterWorst(worstSide18Row, row, 'side18Margin'); + worstUnionRow = betterWorst(worstUnionRow, row, 'unionMargin'); + blockWorstUnionRow = betterWorst(blockWorstUnionRow, row, 'unionMargin'); + + if (!row.side7Pass) { + side7FailureCount += 1; + firstSide7Failure ??= row; + } + if (!row.side18Pass) { + side18FailureCount += 1; + firstSide18Failure ??= row; + } + if (!row.unionPass) { + unionFailureCount += 1; + blockUnionFailureCount += 1; + firstUnionFailure ??= row; + blockFirstUnionFailure ??= row; + if (failureRows.length < 1000) { + failureRows.push(row); + } + } + } + + blockSummaries.push({ + p: block.root.p, + p2: block.root.p2, + rPlus: block.root.rPlus, + rMinus: block.root.rMinus, + rawPlusCountAtMax: block.rawPlusValues.length, + rawMinusCountAtMax: block.rawMinusValues.length, + leastWitnessPlusCountAtMax: block.plusValues.length, + leastWitnessMinusCountAtMax: block.minusValues.length, + unionFailureCount: blockUnionFailureCount, + firstUnionFailure: blockFirstUnionFailure, + worstUnionRow: blockWorstUnionRow, + }); + } + + const allUnionChecksPass = unionFailureCount === 0; + const allSide7ChecksPass = side7FailureCount === 0; + const allSide18ChecksPass = side18FailureCount === 0; + const status = allUnionChecksPass + ? 'bounded_two_side_union_structural_bound_certified' + : allSide7ChecksPass && allSide18ChecksPass + ? 'side_specific_bounds_pass_but_union_bound_fails' + : 'bounded_two_side_structural_bound_has_failures'; + + return { + schema: 'erdos.number_theory.p848_structural_two_side_scout/1', + generatedAt: new Date().toISOString(), + problemId: '848', + method: 'bounded_outsider_clique_two_side_structural_scout', + status, + parameters: { + maxN, + minStructuralN, + assessedRange: `${minStructuralN}..${maxN}`, + }, + summary: { + assessedRange: `${minStructuralN}..${maxN}`, + witnessBlockCount: roots.length, + breakpointCount: breakpoints.length, + checkCount, + globalRootEventCount: globalRootEvents.length, + side7BaseCountAtMax: side7Values.length, + side18BaseCountAtMax: side18Values.length, + allSide7ChecksPass, + allSide18ChecksPass, + allUnionChecksPass, + side7FailureCount, + side18FailureCount, + unionFailureCount, + }, + firstFailures: { + side7: firstSide7Failure, + side18: firstSide18Failure, + union: firstUnionFailure, + }, + worstRows: { + side7: worstSide7Row, + side18: worstSide18Row, + union: worstUnionRow, + }, + blockSummaries, + failureRowsSample: failureRows, + boundary: { + claimLevel: 'bounded_scout_not_all_n_proof', + safety: 'The union-base bound is safe but intentionally loose: it allows every compatible element from both principal sides even though a real clique may not be able to mix them.', + promotionRule: 'Promote only bounded structural coverage when unionPass is true for every checked witness-prime block and structural breakpoint in the assessed range.', + nextUse: allUnionChecksPass + ? 'Use this bounded pass as the repo-owned replacement direction for the external one-sided mask.' + : 'Use the first/worst union failures to decide whether we need a sharper mixed-base lemma rather than a raw union overcount.', + }, + }; +} + +function renderRow(row) { + return row ? JSON.stringify(row) : '(none)'; +} + +function renderMarkdown(packet) { + const lines = [ + '# Problem 848 Two-Sided Structural Scout', + '', + `- Generated: ${packet.generatedAt}`, + `- Method: \`${packet.method}\``, + `- Status: \`${packet.status}\``, + `- Assessed range: \`${packet.summary.assessedRange}\``, + `- Witness blocks: \`${packet.summary.witnessBlockCount}\``, + `- Breakpoints: \`${packet.summary.breakpointCount}\``, + `- Checks: \`${packet.summary.checkCount}\``, + '', + '## Pass/Fail Summary', + '', + `- Side 7 checks pass: \`${packet.summary.allSide7ChecksPass ? 'yes' : 'no'}\` (${packet.summary.side7FailureCount} failures)`, + `- Side 18 checks pass: \`${packet.summary.allSide18ChecksPass ? 'yes' : 'no'}\` (${packet.summary.side18FailureCount} failures)`, + `- Union-base checks pass: \`${packet.summary.allUnionChecksPass ? 'yes' : 'no'}\` (${packet.summary.unionFailureCount} failures)`, + '', + '## First Failures', + '', + `- Side 7: \`${renderRow(packet.firstFailures.side7)}\``, + `- Side 18: \`${renderRow(packet.firstFailures.side18)}\``, + `- Union: \`${renderRow(packet.firstFailures.union)}\``, + '', + '## Worst Rows', + '', + `- Side 7: \`${renderRow(packet.worstRows.side7)}\``, + `- Side 18: \`${renderRow(packet.worstRows.side18)}\``, + `- Union: \`${renderRow(packet.worstRows.union)}\``, + '', + '## Boundary', + '', + `- Claim level: \`${packet.boundary.claimLevel}\``, + `- Safety: ${packet.boundary.safety}`, + `- Promotion rule: ${packet.boundary.promotionRule}`, + `- Next use: ${packet.boundary.nextUse}`, + '', + ]; + + return lines.join('\n'); +} + +const args = parseArgs(process.argv.slice(2)); +const packet = analyze(args.max, args.minStructuralN); + +if (args.jsonOutput) { + fs.mkdirSync(path.dirname(args.jsonOutput), { recursive: true }); + fs.writeFileSync(args.jsonOutput, `${JSON.stringify(packet, null, 2)}\n`); +} + +if (args.markdownOutput) { + fs.mkdirSync(path.dirname(args.markdownOutput), { recursive: true }); + fs.writeFileSync(args.markdownOutput, renderMarkdown(packet)); +} + +console.log(JSON.stringify(packet.summary, null, 2)); diff --git a/packs/sunflower/problems/857/CLAIM_LOOP.json b/packs/sunflower/problems/857/CLAIM_LOOP.json new file mode 100644 index 0000000..0a57524 --- /dev/null +++ b/packs/sunflower/problems/857/CLAIM_LOOP.json @@ -0,0 +1,183 @@ +{ + "schema": "erdos.problem_claim_loop/1", + "generatedAt": "2026-04-10T08:11:06.264Z", + "problemId": "857", + "displayName": "Erdos Problem #857", + "title": "Sunflower Conjecture", + "cluster": "sunflower", + "sourceKind": "theorem_loop_only", + "claimLoopMode": "baseline", + "currentClaimSurface": "frontier_supported_route", + "currentState": { + "theoremLoopMode": "baseline", + "activeRoute": "anchored_selector_linearization", + "nextHonestMove": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "routeSummary": "Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary.", + "sourceRefresh": null + }, + "featureExtractors": [ + { + "extractor_id": "pack_route_state", + "kind": "pack_context", + "scope": "all_problems", + "status": "ready", + "note": "Reads pack route, ticket, and atom state as the baseline theorem-search context." + }, + { + "extractor_id": "theorem_loop_snapshot", + "kind": "theorem_loop", + "scope": "all_problems", + "status": "ready", + "note": "Uses the canonical theorem-loop as the current claim-surface ledger." + }, + { + "extractor_id": "cluster_sunflower_features", + "kind": "cluster_adapter", + "scope": "sunflower", + "status": "ready", + "note": "Exposes sunflower-family route state, witness status, and compute packet context." + } + ], + "claimGenerators": [ + { + "generator_id": "baseline_route_claims", + "kind": "route_state", + "scope": "all_problems", + "status": "ready", + "note": "Promotes active routes, ready atoms, and next-honest-move records into candidate claims." + }, + { + "generator_id": "theorem_agenda_claims", + "kind": "agenda_projection", + "scope": "all_problems", + "status": "ready", + "note": "Turns theorem agenda items into explicit candidate claim tickets." + } + ], + "claimFalsifiers": [ + { + "falsifier_id": "theorem_loop_consistency_check", + "kind": "ledger_consistency", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims that overstate the current theorem-loop claim surface." + }, + { + "falsifier_id": "artifact_boundary_check", + "kind": "artifact_boundary", + "scope": "all_problems", + "status": "ready", + "note": "Rejects claims unsupported by canonical artifacts already present in the pack." + } + ], + "verifierAdapters": [ + { + "adapter_id": "canonical_artifact_reader", + "kind": "artifact_reader", + "scope": "all_problems", + "status": "ready", + "note": "Reads theorem-loop, route, and pack artifacts as verifier-facing evidence." + } + ], + "candidateClaims": [ + { + "claim_id": "promote_ready_atom", + "status": "ready", + "source": "theorem_agenda", + "summary": "Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "support": [ + "active_route_recorded", + "theorem_module_registered", + "ready_atom_present", + "frontier_note_present" + ] + }, + { + "claim_id": "stabilize_theorem_module_boundary", + "status": "ready", + "source": "theorem_agenda", + "summary": "Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary.", + "why": "The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies.", + "support": [ + "active_route_recorded", + "theorem_module_registered", + "ready_atom_present", + "frontier_note_present" + ] + }, + { + "claim_id": "tighten_active_route_claim", + "status": "ready", + "source": "theorem_agenda", + "summary": "Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "support": [ + "active_route_recorded", + "theorem_module_registered", + "ready_atom_present", + "frontier_note_present" + ] + } + ], + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `anchored_selector_linearization`." + }, + { + "hook_id": "theorem_module_registered", + "status": "supported", + "note": "A theorem module is already registered for the active route: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `T10.G3.A2`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "theoremAgenda": [ + { + "item_id": "promote_ready_atom", + "status": "ready", + "task": "Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes." + }, + { + "item_id": "stabilize_theorem_module_boundary", + "status": "ready", + "task": "Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary.", + "why": "The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies." + }, + { + "item_id": "tighten_active_route_claim", + "status": "ready", + "task": "Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes." + } + ], + "commands": { + "problemShow": "erdos problem show 857", + "problemArtifacts": "erdos problem artifacts 857", + "theoremLoop": "erdos problem theorem-loop 857", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 857", + "claimLoop": "erdos problem claim-loop 857", + "claimLoopRefresh": "erdos problem claim-loop-refresh 857", + "sourceRefresh": null + }, + "sources": { + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null, + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857" + } +} diff --git a/packs/sunflower/problems/857/CLAIM_LOOP.md b/packs/sunflower/problems/857/CLAIM_LOOP.md new file mode 100644 index 0000000..daf5239 --- /dev/null +++ b/packs/sunflower/problems/857/CLAIM_LOOP.md @@ -0,0 +1,54 @@ +# Erdos Problem #857 Claim Loop + +This claim loop generalizes theorem-search-verification work directly from the canonical theorem loop, even when no richer bridge is present yet. + +## Current State + +- Claim loop mode: `baseline`. +- Current claim surface: `frontier_supported_route`. +- Active route: `anchored_selector_linearization`. +- Route summary: Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary. +- Next honest move: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Feature Extractors + +- `pack_route_state`: ready | Reads pack route, ticket, and atom state as the baseline theorem-search context. +- `theorem_loop_snapshot`: ready | Uses the canonical theorem-loop as the current claim-surface ledger. +- `cluster_sunflower_features`: ready | Exposes sunflower-family route state, witness status, and compute packet context. + +## Claim Generators + +- `baseline_route_claims`: ready | Promotes active routes, ready atoms, and next-honest-move records into candidate claims. +- `theorem_agenda_claims`: ready | Turns theorem agenda items into explicit candidate claim tickets. + +## Claim Falsifiers + +- `theorem_loop_consistency_check`: ready | Rejects claims that overstate the current theorem-loop claim surface. +- `artifact_boundary_check`: ready | Rejects claims unsupported by canonical artifacts already present in the pack. + +## Verifier Adapters + +- `canonical_artifact_reader`: ready | Reads theorem-loop, route, and pack artifacts as verifier-facing evidence. + +## Candidate Claims + +- `promote_ready_atom`: ready | Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- `stabilize_theorem_module_boundary`: ready | Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary. | The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies. +- `tighten_active_route_claim`: ready | Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Commands + +- Problem surface: `erdos problem show 857` +- Problem artifacts: `erdos problem artifacts 857` +- Theorem loop: `erdos problem theorem-loop 857` +- Theorem refresh: `erdos problem theorem-loop-refresh 857` +- Claim loop: `erdos problem claim-loop 857` +- Claim refresh: `erdos problem claim-loop-refresh 857` + +## Sources + +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md` +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857` diff --git a/packs/sunflower/problems/857/CLAIM_PASS.json b/packs/sunflower/problems/857/CLAIM_PASS.json new file mode 100644 index 0000000..8eb1af5 --- /dev/null +++ b/packs/sunflower/problems/857/CLAIM_PASS.json @@ -0,0 +1,139 @@ +{ + "schema": "erdos.problem_claim_pass/1", + "generatedAt": "2026-04-10T08:11:06.267Z", + "problemId": "857", + "displayName": "Erdos Problem #857", + "title": "Sunflower Conjecture", + "cluster": "sunflower", + "sourceKind": "claim_loop_only", + "claimPassMode": "baseline", + "currentClaimSurface": "frontier_supported_route", + "currentState": { + "activeRoute": "anchored_selector_linearization", + "nextHonestMove": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "routeSummary": "Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary.", + "latestVerifiedInterval": null, + "sourceRefresh": null + }, + "summary": { + "hooks": { + "total": 4, + "supported": 4, + "actionable": 0, + "unresolved": 0, + "broken": 0 + }, + "claims": { + "total": 3, + "supported": 0, + "actionable": 3, + "unresolved": 0, + "broken": 0 + } + }, + "hookAssessments": [ + { + "hook_id": "active_route_recorded", + "verdict": "supported", + "status": "supported", + "evidenceClass": "route_state", + "theoremReady": false, + "rationale": "The pack records an active route, currently `anchored_selector_linearization`.", + "nextAction": "promote_route_claim" + }, + { + "hook_id": "theorem_module_registered", + "verdict": "supported", + "status": "supported", + "evidenceClass": "theorem_module", + "theoremReady": false, + "rationale": "A theorem module is already registered for the active route: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`.", + "nextAction": "stabilize_theorem_module_boundary" + }, + { + "hook_id": "ready_atom_present", + "verdict": "supported", + "status": "supported", + "evidenceClass": "ready_atom", + "theoremReady": false, + "rationale": "The live route already has a ready atom, `T10.G3.A2`, which can feed the theorem lane.", + "nextAction": "promote_ready_atom" + }, + { + "hook_id": "frontier_note_present", + "verdict": "supported", + "status": "supported", + "evidenceClass": "frontier_note", + "theoremReady": false, + "rationale": "The pack already carries a frontier note that can anchor theorem-facing updates.", + "nextAction": "anchor_frontier_note" + } + ], + "claimAssessments": [ + { + "claim_id": "promote_ready_atom", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint.", + "rationale": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "nextAction": "promote_ready_atom" + }, + { + "claim_id": "stabilize_theorem_module_boundary", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary.", + "rationale": "The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies.", + "nextAction": "stabilize_theorem_module_boundary" + }, + { + "claim_id": "tighten_active_route_claim", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit.", + "rationale": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "nextAction": "tighten_active_route_claim" + } + ], + "recommendations": [ + { + "recommendation_id": "promote_ready_atom", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "command": "erdos problem formalization 857" + } + ], + "commands": { + "problemShow": "erdos problem show 857", + "problemArtifacts": "erdos problem artifacts 857", + "theoremLoop": "erdos problem theorem-loop 857", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 857", + "claimLoop": "erdos problem claim-loop 857", + "claimLoopRefresh": "erdos problem claim-loop-refresh 857", + "claimPass": "erdos problem claim-pass 857", + "claimPassRefresh": "erdos problem claim-pass-refresh 857", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.md", + "legacyBridgeJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/SEARCH_THEOREM_BRIDGE.json", + "legacyBridgeMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/SEARCH_THEOREM_BRIDGE.md", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/INTERVAL_WORK_QUEUE.yaml" + } +} diff --git a/packs/sunflower/problems/857/CLAIM_PASS.md b/packs/sunflower/problems/857/CLAIM_PASS.md new file mode 100644 index 0000000..bb70452 --- /dev/null +++ b/packs/sunflower/problems/857/CLAIM_PASS.md @@ -0,0 +1,56 @@ +# Erdos Problem #857 Claim Pass + +This claim pass evaluates theorem-search claims against the canonical claim loop and pack-level evidence. + +## Current State + +- Claim pass mode: `baseline`. +- Current claim surface: `frontier_supported_route`. +- Active route: `anchored_selector_linearization`. +- Route summary: Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary. +- Next honest move: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- Latest verified interval: `(none)` + +## Summary + +- Hook assessments: supported `4`, unresolved `0`, broken `0`. +- Claim assessments: supported `0`, actionable `3`, unresolved `0`, broken `0`. + +## Hook Assessments + +- `active_route_recorded`: supported | The pack records an active route, currently `anchored_selector_linearization`. +- `theorem_module_registered`: supported | A theorem module is already registered for the active route: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`. +- `ready_atom_present`: supported | The live route already has a ready atom, `T10.G3.A2`, which can feed the theorem lane. +- `frontier_note_present`: supported | The pack already carries a frontier note that can anchor theorem-facing updates. + +## Claim Assessments + +- `promote_ready_atom`: actionable | Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- `stabilize_theorem_module_boundary`: actionable | Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary. | The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies. +- `tighten_active_route_claim`: actionable | Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Recommendations + +- `promote_ready_atom`: medium | theorem_formalization | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. | erdos problem formalization 857 + +## Commands + +- Problem surface: `erdos problem show 857` +- Problem artifacts: `erdos problem artifacts 857` +- Theorem loop: `erdos problem theorem-loop 857` +- Claim loop: `erdos problem claim-loop 857` +- Claim pass: `erdos problem claim-pass 857` +- Claim pass refresh: `erdos problem claim-pass-refresh 857` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.md` +- legacyBridgeJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/SEARCH_THEOREM_BRIDGE.json` +- legacyBridgeMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/SEARCH_THEOREM_BRIDGE.md` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/sunflower/problems/857/FORMALIZATION.json b/packs/sunflower/problems/857/FORMALIZATION.json new file mode 100644 index 0000000..4edc548 --- /dev/null +++ b/packs/sunflower/problems/857/FORMALIZATION.json @@ -0,0 +1,210 @@ +{ + "schema": "erdos.problem_formalization/1", + "generatedAt": "2026-04-10T08:11:06.272Z", + "problemId": "857", + "displayName": "Erdos Problem #857", + "title": "Sunflower Conjecture", + "cluster": "sunflower", + "sourceKind": "claim_pass_only", + "formalizationMode": "baseline", + "currentClaimSurface": "frontier_supported_route", + "currentState": { + "activeRoute": "anchored_selector_linearization", + "routeSummary": "Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary.", + "nextHonestMove": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "latestVerifiedInterval": null, + "sourceRefresh": null + }, + "currentTarget": { + "formalizationId": "sunflower_857_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "status": "ready", + "lane": "theorem_formalization", + "sourceRecommendationId": "promote_ready_atom", + "summary": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "statement": "Candidate formalization target: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "whyThisExists": "This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria.", + "whyNow": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "evidenceBasis": [ + "Current claim surface: frontier_supported_route.", + "Active route: anchored_selector_linearization.", + "No canonical verified interval is currently frozen." + ], + "proofObligations": [ + { + "obligationId": "state_claim_honestly", + "status": "ready", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "This keeps the formalization target narrower than the current evidence boundary.", + "dischargeWith": "Write a claim statement that is no stronger than the active claim-pass support surface." + }, + { + "obligationId": "freeze_support_artifacts", + "status": "ready", + "task": "List the exact canonical artifacts that support the claim and the artifacts that could still falsify it.", + "why": "The theorem lane should point at stable evidence, not drifting interpretation.", + "dischargeWith": "Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet." + }, + { + "obligationId": "define_promotion_boundary", + "status": "ready", + "task": "Promote the target only when its support survives the current claim-pass falsifiers.", + "why": "This prevents formalization packets from silently outrunning the rest of the loop.", + "dischargeWith": "Record explicit promotion criteria tied to current falsifiers." + } + ], + "falsifierChecks": [ + { + "checkId": "claim_pass_survival", + "status": "ready", + "task": "A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported.", + "why": "If the recommendation itself no longer survives refresh, the formalization target is stale.", + "command": "erdos problem claim-pass-refresh 857" + }, + { + "checkId": "artifact_boundary_check", + "status": "ready", + "task": "A canonical artifact boundary check shows the statement is stronger than the current pack evidence.", + "why": "The packet should fail early if it is stronger than what the pack actually certifies.", + "command": "erdos problem theorem-loop 857" + } + ], + "promotionCriteria": [ + { + "criterionId": "top_recommendation_survives", + "status": "ready", + "task": "The current target remains the top theorem-formalization recommendation after refresh." + }, + { + "criterionId": "statement_stays_narrow", + "status": "ready", + "task": "The candidate statement is narrower than or equal to the current claim-pass support surface." + }, + { + "criterionId": "obligations_are_actionable", + "status": "ready", + "task": "The remaining proof obligations are explicit enough to guide search or exact follow-up." + } + ], + "supportingCommands": [ + "erdos problem theorem-loop 857", + "erdos problem claim-pass 857", + "erdos problem claim-pass-refresh 857" + ] + }, + "summary": { + "proofObligations": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "falsifierChecks": { + "total": 2, + "ready": 2, + "inProgress": 0, + "blocked": 0, + "done": 0 + }, + "promotionCriteria": { + "total": 3, + "ready": 3, + "inProgress": 0, + "blocked": 0, + "done": 0 + } + }, + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `anchored_selector_linearization`." + }, + { + "hook_id": "theorem_module_registered", + "status": "supported", + "note": "A theorem module is already registered for the active route: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `T10.G3.A2`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "claimAssessments": [ + { + "claim_id": "promote_ready_atom", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint.", + "rationale": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "nextAction": "promote_ready_atom" + }, + { + "claim_id": "stabilize_theorem_module_boundary", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary.", + "rationale": "The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies.", + "nextAction": "stabilize_theorem_module_boundary" + }, + { + "claim_id": "tighten_active_route_claim", + "source": "theorem_agenda", + "verdict": "actionable", + "evidenceClass": "theorem_agenda", + "theoremReady": false, + "supportSatisfied": true, + "summary": "Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit.", + "rationale": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "nextAction": "tighten_active_route_claim" + } + ], + "recommendationLedger": [ + { + "recommendation_id": "promote_ready_atom", + "priority": "medium", + "lane": "theorem_formalization", + "reason": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "command": "erdos problem formalization 857" + } + ], + "commands": { + "problemShow": "erdos problem show 857", + "problemArtifacts": "erdos problem artifacts 857", + "theoremLoop": "erdos problem theorem-loop 857", + "claimLoop": "erdos problem claim-loop 857", + "claimPass": "erdos problem claim-pass 857", + "formalization": "erdos problem formalization 857", + "formalizationRefresh": "erdos problem formalization-refresh 857", + "formalizationWork": "erdos problem formalization-work 857", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 857", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md", + "claimLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.json", + "claimLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.md", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.json", + "claimPassMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.md", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null + } +} diff --git a/packs/sunflower/problems/857/FORMALIZATION.md b/packs/sunflower/problems/857/FORMALIZATION.md new file mode 100644 index 0000000..19a18b5 --- /dev/null +++ b/packs/sunflower/problems/857/FORMALIZATION.md @@ -0,0 +1,86 @@ +# Erdos Problem #857 Formalization + +This formalization packet promotes the current claim-pass recommendation into a concrete theorem-facing proof obligation anchored in canonical pack evidence. + +## Current State + +- Formalization mode: `baseline`. +- Current claim surface: `frontier_supported_route`. +- Active route: `anchored_selector_linearization`. +- Route summary: Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary. +- Next honest move: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- Latest verified interval: `(none)` + +## Current Target + +- Formalization id: `sunflower_857_promote_ready_atom_v1`. +- Focus id: `promote_ready_atom`. +- Title: Promote Ready Atom +- Status: `ready`. +- Lane: `theorem_formalization`. +- Summary: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- Candidate statement: Candidate formalization target: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- Proof obligations: ready `3` / total `3`. +- Falsifier checks: ready `2` / total `2`. +- Promotion criteria: ready `3` / total `3`. + +## Why This Exists + +This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria. + +## Why Now + +Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Evidence Basis + +- Current claim surface: frontier_supported_route. +- Active route: anchored_selector_linearization. +- No canonical verified interval is currently frozen. + +## Proof Obligations + +- `state_claim_honestly`: ready | State the candidate theorem-facing claim in pack language without overstating current support. | This keeps the formalization target narrower than the current evidence boundary. | discharge: Write a claim statement that is no stronger than the active claim-pass support surface. +- `freeze_support_artifacts`: ready | List the exact canonical artifacts that support the claim and the artifacts that could still falsify it. | The theorem lane should point at stable evidence, not drifting interpretation. | discharge: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. +- `define_promotion_boundary`: ready | Promote the target only when its support survives the current claim-pass falsifiers. | This prevents formalization packets from silently outrunning the rest of the loop. | discharge: Record explicit promotion criteria tied to current falsifiers. + +## Falsifier Checks + +- `claim_pass_survival`: ready | A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported. | If the recommendation itself no longer survives refresh, the formalization target is stale. | command: erdos problem claim-pass-refresh 857 +- `artifact_boundary_check`: ready | A canonical artifact boundary check shows the statement is stronger than the current pack evidence. | The packet should fail early if it is stronger than what the pack actually certifies. | command: erdos problem theorem-loop 857 + +## Promotion Criteria + +- `top_recommendation_survives`: ready | The current target remains the top theorem-formalization recommendation after refresh. +- `statement_stays_narrow`: ready | The candidate statement is narrower than or equal to the current claim-pass support surface. +- `obligations_are_actionable`: ready | The remaining proof obligations are explicit enough to guide search or exact follow-up. + +## Supporting Commands + +- `erdos problem theorem-loop 857` +- `erdos problem claim-pass 857` +- `erdos problem claim-pass-refresh 857` + +## Commands + +- Problem surface: `erdos problem show 857` +- Problem artifacts: `erdos problem artifacts 857` +- Theorem loop: `erdos problem theorem-loop 857` +- Claim loop: `erdos problem claim-loop 857` +- Claim pass: `erdos problem claim-pass 857` +- Formalization: `erdos problem formalization 857` +- Formalization refresh: `erdos problem formalization-refresh 857` +- Formalization work: `erdos problem formalization-work 857` +- Formalization work refresh: `erdos problem formalization-work-refresh 857` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md` +- claimLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.json` +- claimLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_LOOP.md` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.json` +- claimPassMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.md` diff --git a/packs/sunflower/problems/857/FORMALIZATION_WORK.json b/packs/sunflower/problems/857/FORMALIZATION_WORK.json new file mode 100644 index 0000000..bf3255a --- /dev/null +++ b/packs/sunflower/problems/857/FORMALIZATION_WORK.json @@ -0,0 +1,64 @@ +{ + "schema": "erdos.problem_formalization_work/1", + "generatedAt": "2026-04-10T08:11:06.278Z", + "problemId": "857", + "displayName": "Erdos Problem #857", + "title": "Sunflower Conjecture", + "cluster": "sunflower", + "sourceKind": "claim_pass_only", + "formalizationWorkMode": "baseline", + "currentClaimSurface": "frontier_supported_route", + "currentState": { + "activeRoute": "anchored_selector_linearization", + "routeSummary": "Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary.", + "nextHonestMove": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "latestVerifiedInterval": null + }, + "currentWork": { + "workId": "sunflower_857_state_claim_honestly_v1", + "focusFormalizationId": "sunflower_857_promote_ready_atom_v1", + "focusId": "state_claim_honestly", + "title": "State Claim Honestly", + "status": "ready", + "summary": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "This keeps the formalization target narrower than the current evidence boundary.", + "workingDefinition": [ + "Candidate formalization target: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes." + ], + "currentEvidence": [ + "Current claim surface: frontier_supported_route.", + "Active route: anchored_selector_linearization.", + "No canonical verified interval is currently frozen." + ], + "dischargedWork": [], + "remainingGaps": [ + "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.", + "define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers." + ], + "nextCommands": [ + "erdos problem formalization-refresh 857", + "erdos problem formalization 857" + ] + }, + "commands": { + "problemShow": "erdos problem show 857", + "problemArtifacts": "erdos problem artifacts 857", + "formalization": "erdos problem formalization 857", + "formalizationRefresh": "erdos problem formalization-refresh 857", + "formalizationWork": "erdos problem formalization-work 857", + "formalizationWorkRefresh": "erdos problem formalization-work-refresh 857", + "claimPass": "erdos problem claim-pass 857", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.json", + "formalizationWorkMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.md", + "formalizationWorkSvgPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.svg", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.json", + "formalizationMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json", + "legacyBridgeJsonPath": null + } +} diff --git a/packs/sunflower/problems/857/FORMALIZATION_WORK.md b/packs/sunflower/problems/857/FORMALIZATION_WORK.md new file mode 100644 index 0000000..39597a2 --- /dev/null +++ b/packs/sunflower/problems/857/FORMALIZATION_WORK.md @@ -0,0 +1,61 @@ +# Erdos Problem #857 Formalization Work + +This packet turns the current formalization target into one concrete work unit that can be discharged, falsified, or narrowed without losing the surrounding theorem-search context. + +## Current State + +- Formalization work mode: `baseline`. +- Current claim surface: `frontier_supported_route`. +- Active route: `anchored_selector_linearization`. +- Route summary: Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary. +- Next honest move: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- Latest verified interval: `(none)` + +## Current Work + +- Work id: `sunflower_857_state_claim_honestly_v1`. +- Focus formalization id: `sunflower_857_promote_ready_atom_v1`. +- Focus id: `state_claim_honestly`. +- Title: State Claim Honestly +- Status: `ready`. +- Summary: State the candidate theorem-facing claim in pack language without overstating current support. +- Why: This keeps the formalization target narrower than the current evidence boundary. + +## Working Definition + +- Candidate formalization target: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Current Evidence + +- Current claim surface: frontier_supported_route. +- Active route: anchored_selector_linearization. +- No canonical verified interval is currently frozen. + +## Discharged Work + + +## Remaining Gaps + +- state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. +- freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. +- define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers. + +## Commands + +- Problem surface: `erdos problem show 857` +- Problem artifacts: `erdos problem artifacts 857` +- Formalization: `erdos problem formalization 857` +- Formalization refresh: `erdos problem formalization-refresh 857` +- Formalization work: `erdos problem formalization-work 857` +- Formalization work refresh: `erdos problem formalization-work-refresh 857` +- Claim pass: `erdos problem claim-pass 857` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.json` +- formalizationWorkMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.md` +- formalizationWorkSvgPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.svg` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.json` +- formalizationMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json` diff --git a/packs/sunflower/problems/857/FORMALIZATION_WORK.svg b/packs/sunflower/problems/857/FORMALIZATION_WORK.svg new file mode 100644 index 0000000..145ea48 --- /dev/null +++ b/packs/sunflower/problems/857/FORMALIZATION_WORK.svg @@ -0,0 +1 @@ +Erdos Problem #857 formalization work diagramGeneric visual summary of the current formalization-work packet.Erdos Problem #857 Formalization WorkState Claim HonestlyStatus: ready | Route: anchored_selector_linearizationWorking DefinitionCurrent Evidence• Candidate formalization target: Prove or package• the helper stack cleanly and checkpoint the• route if the leaf closes.• Current claim surface:• frontier_supported_route.• Active route: anchored_selector_linearization.• No canonical verified interval is currently• frozen.Canonical files: /Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.json and /Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.md \ No newline at end of file diff --git a/packs/sunflower/problems/857/MULTIPLICATIVE_REORIENTATION.md b/packs/sunflower/problems/857/MULTIPLICATIVE_REORIENTATION.md new file mode 100644 index 0000000..64218cc --- /dev/null +++ b/packs/sunflower/problems/857/MULTIPLICATIVE_REORIENTATION.md @@ -0,0 +1,118 @@ +# Problem 857 Multiplicative Reorientation + +This note records a research-direction update for the weak sunflower program +around problem `857`. + +It does not replace the current public frontier packet. The canonical live route +is still `anchored_selector_linearization`, and problem `857` remains open. + +## Why this note exists + +The sunflower quartet in this repo already treats +- `857` as the weak / non-uniform sunflower core +- `536` as the natural-density LCM bridge +- `856` as the harmonic-density LCM bridge + +A recent preprint sharpens that bridge: + +- Quanyu Tang and Shengtong Zhang, "Harmonic LCM patterns and sunflower-free + capacity", arXiv:2512.20055 (2025), + . + +At the abstract level, that paper introduces the sunflower-free capacity +`mu_k^S := limsup F_k(n)^(1/n)` together with a harmonic LCM extremal function +`f_k(N)`, and gives comparison bounds between them. It also states that failure +of the Erdős-Szemerédi fixed-`k` sunflower conjecture (`mu_k^S = 2`) is +equivalent to `f_k(N) = (log N)^(1-o(1))`. + +That is enough to justify a stronger bridge posture in `erdos-problems`. + +## What we can safely adopt now + +`Verified` +- `mu_k^S` is now a useful literature-level capacity object for the weak + sunflower problem. +- Harmonic / multiplicative LCM extremal functions are not just loose analogies; + they are mathematically coupled to sunflower-free growth rates. +- Problems `536` and `856` should be treated as active bridge problems that can + influence how we prioritize `857` experiments and documentation. + +`Heuristic` +- Prime-support and squarefree representations are reasonable local search + coordinates for new `857` experiments. +- Capacity estimation, LCM growth tracking, and process-style sunflower-free + simulations are now higher-value exploratory lanes than generic family-size + maximization alone. +- The most promising local combination is prime-support optimization plus + sunflower-free process simulation. + +## What we should not overclaim + +Do not write any of the following into canonical status files unless a stronger +source or local theorem packet is added first: + +- "Problem 857 is equivalent to controlling a single LCM extremal function." +- "The sunflower conjecture is equivalent to `f_k(N)` being sub-polynomial in + `log N`." +- "The multiplicative reformulation replaces the active anchored-selector + frontier." + +The current source we have justifies comparison bounds and a specific failure-case +criterion. It does not, on its face, justify collapsing the entire `857` program +into one unconditional hard equivalence with the wording above. + +## Recommended repo posture + +Keep the current public status ladder unchanged: +- open problem +- active route +- route breakthrough +- problem solved + +Keep the current public frontier unchanged: +- active route: `anchored_selector_linearization` +- active ticket: `T10` +- next honest move: promote the helper/theorem stack into + `anchored_selector_linearization_realized` + +Add the multiplicative-capacity story as an adjacent research note: +- useful for bridge prioritization +- useful for local compute and experiment design +- not yet a replacement for the live theorem-facing route packet + +## Suggested experimental lanes + +If we open a new local scout or research lane for `857`, the most compatible +extensions are: + +1. Prime-support optimization + Build squarefree / prime-support families, track overlap structure, and score + them by both sunflower obstructions and LCM-side growth proxies. +2. Capacity estimation + Estimate local behavior of `mu_k^S`-style growth indicators and compare them + against multiplicative proxies rather than raw family size alone. +3. Process simulation + Run greedy or random sunflower-avoidance processes and record the emergent + intersection profile instead of only the terminal family size. +4. Structural classification + Cluster near-extremal families by intersection distribution, degree profile, + and multiplicative shadow. + +## Suggested artifact names + +These names fit the proposed pivot, but they should start as local research +artifacts before being promoted into canonical pack evidence: + +- `prime_support_family.json` +- `capacity_estimate.json` +- `process_simulation_trace.json` + +## Claim discipline + +When this note is used in agent handoffs: +- label literature-backed statements as `Verified` +- label bridge extrapolations as `Heuristic` +- label unproved equivalence upgrades as `Conjecture` + +That keeps the new direction visible without blurring route progress into +mathematical closure. diff --git a/packs/sunflower/problems/857/TASK_LIST.json b/packs/sunflower/problems/857/TASK_LIST.json new file mode 100644 index 0000000..67a1d7f --- /dev/null +++ b/packs/sunflower/problems/857/TASK_LIST.json @@ -0,0 +1,215 @@ +{ + "schema": "erdos.problem_task_list/1", + "generatedAt": "2026-04-10T08:11:06.289Z", + "problemId": "857", + "displayName": "Erdos Problem #857", + "title": "Sunflower Conjecture", + "cluster": "sunflower", + "sourceKind": "claim_pass_only", + "taskListMode": "baseline", + "currentState": { + "activeRoute": "anchored_selector_linearization", + "currentClaimSurface": "frontier_supported_route", + "routeSummary": "Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary.", + "nextHonestMove": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "latestVerifiedInterval": null + }, + "executionRule": { + "stance": "concrete_execution", + "summary": "Treat the task list as a concrete research loop for problem 857: execute the highest-value task itself, not wrapper prose about the task.", + "afterEachCompletion": [ + "Cross off the completed task.", + "Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary.", + "Invent the next highest-value step from the updated evidence rather than following a stale fixed script.", + "Append that next step to the task list and refresh the canonical task-list artifacts." + ], + "repetitionProtocol": "To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass.", + "lowStressLongHorizonNote": "This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan." + }, + "loopTemplate": [ + { + "stepId": "freeze_current_state", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `anchored_selector_linearization`, claim surface `frontier_supported_route`, and active theorem packet before widening the search.", + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 857" + }, + { + "stepId": "audit_theorem_surfaces", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 857" + }, + { + "stepId": "verify_canonical_inputs", + "title": "Verify canonical pack inputs against the latest route and verifier artifacts", + "task": "Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.", + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos problem theorem-loop-refresh 857" + }, + { + "stepId": "verify_primary_structural_hook", + "title": "Verify the current highest-value structural hook remains canonical", + "task": "Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.", + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 857" + }, + { + "stepId": "verify_verifier_boundary", + "title": "Verify the current verifier boundary and next target", + "task": "Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.", + "completionRule": "The verifier-facing boundary remains explicit even without a dedicated interval queue.", + "command": "erdos problem formalization 857" + }, + { + "stepId": "execute_current_work_packet", + "title": "State Claim Honestly", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work 857" + }, + { + "stepId": "refresh_and_rerank", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 857" + } + ], + "currentObjective": { + "formalizationId": "sunflower_857_promote_ready_atom_v1", + "focusId": "promote_ready_atom", + "title": "Promote Ready Atom", + "activeWorkId": "sunflower_857_state_claim_honestly_v1", + "activeWorkTitle": "State Claim Honestly", + "activeWorkStatus": "ready" + }, + "currentTasks": [ + { + "taskId": "freeze_current_state", + "status": "ready", + "title": "Freeze the current north star and active theorem packet", + "task": "Freeze the current route `anchored_selector_linearization`, claim surface `frontier_supported_route`, and active theorem packet before widening the search.", + "why": null, + "completionRule": "The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.", + "command": "erdos problem theorem-loop 857" + }, + { + "taskId": "audit_theorem_surfaces", + "status": "ready", + "title": "Audit theorem, claim, and formalization surfaces for consistency", + "task": "Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.", + "why": null, + "completionRule": "The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.", + "command": "erdos problem task-list 857" + }, + { + "taskId": "verify_canonical_inputs", + "status": "ready", + "title": "Verify canonical pack inputs against the latest route and verifier artifacts", + "task": "Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.", + "why": null, + "completionRule": "The canonical input packet for this loop remains current and trustworthy.", + "command": "erdos problem theorem-loop-refresh 857" + }, + { + "taskId": "verify_primary_structural_hook", + "status": "ready", + "title": "Verify the current highest-value structural hook remains canonical", + "task": "Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.", + "why": null, + "completionRule": "The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.", + "command": "erdos problem claim-pass-refresh 857" + }, + { + "taskId": "verify_verifier_boundary", + "status": "ready", + "title": "Verify the current verifier boundary and next target", + "task": "Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.", + "why": null, + "completionRule": "The verifier-facing boundary remains explicit even without a dedicated interval queue.", + "command": "erdos problem formalization 857" + }, + { + "taskId": "execute_current_work_packet", + "status": "ready", + "title": "State Claim Honestly", + "task": "State the candidate theorem-facing claim in pack language without overstating current support.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "completionRule": "The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "command": "erdos problem formalization-work 857" + }, + { + "taskId": "discharge_first_remaining_gap", + "status": "ready", + "title": "Discharge the first remaining gap in the active theorem packet", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "why": "This is the sharpest unresolved statement already named by the active theorem-work packet.", + "completionRule": "The first remaining gap is either resolved or replaced by a more precise successor gap.", + "command": "erdos problem formalization-work-refresh 857" + }, + { + "taskId": "refresh_and_rerank", + "status": "ready", + "title": "Refresh the task list and rerank the next step", + "task": "Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.", + "why": null, + "completionRule": "The refreshed task list records the next highest-value action instead of relying on a stale fixed script.", + "command": "erdos problem task-list-refresh 857" + } + ], + "completedAnchors": [], + "nextNeededSteps": [ + { + "stepId": "gap_1", + "status": "next", + "task": "state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 857" + }, + { + "stepId": "gap_2", + "status": "next", + "task": "freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 857" + }, + { + "stepId": "gap_3", + "status": "next", + "task": "define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers.", + "source": "formalization_work", + "command": "erdos problem formalization-work-refresh 857" + }, + { + "stepId": "promote_ready_atom", + "status": "medium", + "task": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes.", + "source": "theorem_formalization", + "command": "erdos problem formalization 857" + } + ], + "commands": { + "problemShow": "erdos problem show 857", + "problemArtifacts": "erdos problem artifacts 857", + "taskList": "erdos problem task-list 857", + "taskListRefresh": "erdos problem task-list-refresh 857", + "theoremLoop": "erdos problem theorem-loop 857", + "claimPass": "erdos problem claim-pass 857", + "formalization": "erdos problem formalization 857", + "formalizationWork": "erdos problem formalization-work 857", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857", + "taskListJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/TASK_LIST.json", + "taskListMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/TASK_LIST.md", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json", + "claimPassJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.json", + "formalizationJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.json", + "formalizationWorkJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.json", + "intervalQueuePath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/INTERVAL_WORK_QUEUE.yaml", + "legacyBridgeJsonPath": null + } +} diff --git a/packs/sunflower/problems/857/TASK_LIST.md b/packs/sunflower/problems/857/TASK_LIST.md new file mode 100644 index 0000000..5fc4e49 --- /dev/null +++ b/packs/sunflower/problems/857/TASK_LIST.md @@ -0,0 +1,85 @@ +# Erdos Problem #857 Task List + +This task list is the canonical research-loop surface for the problem. It gives one reusable execution rule, one templated loop, the current active tasks, and the next steps discovered from the current theorem/search/verifier state. + +## Current State + +- Task list mode: `baseline`. +- Active route: `anchored_selector_linearization`. +- Current claim surface: `frontier_supported_route`. +- Route summary: Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary. +- Next honest move: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- Latest verified interval: `(none)` + +## Execution Rule + +- Stance: `concrete_execution` +- Summary: Treat the task list as a concrete research loop for problem 857: execute the highest-value task itself, not wrapper prose about the task. +- After each completed step: Cross off the completed task. +- After each completed step: Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary. +- After each completed step: Invent the next highest-value step from the updated evidence rather than following a stale fixed script. +- After each completed step: Append that next step to the task list and refresh the canonical task-list artifacts. +- Repetition protocol: To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass. +- Long-horizon note: This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan. + +## Template Loop + +- `freeze_current_state`: Freeze the current north star and active theorem packet | Freeze the current route `anchored_selector_linearization`, claim surface `frontier_supported_route`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 857` +- `audit_theorem_surfaces`: Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 857` +- `verify_canonical_inputs`: Verify canonical pack inputs against the latest route and verifier artifacts | Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos problem theorem-loop-refresh 857` +- `verify_primary_structural_hook`: Verify the current highest-value structural hook remains canonical | Verify that the strongest supported structural hook still survives across the theorem and claim surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 857` +- `verify_verifier_boundary`: Verify the current verifier boundary and next target | Verify that the current verifier boundary and next target are stated honestly across the pack surfaces. | completion: The verifier-facing boundary remains explicit even without a dedicated interval queue. | command: `erdos problem formalization 857` +- `execute_current_work_packet`: State Claim Honestly | State the candidate theorem-facing claim in pack language without overstating current support. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | command: `erdos problem formalization-work 857` +- `refresh_and_rerank`: Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 857` + +## Current Objective + +- Formalization id: `sunflower_857_promote_ready_atom_v1` +- Focus id: `promote_ready_atom` +- Title: Promote Ready Atom +- Active work id: `sunflower_857_state_claim_honestly_v1` +- Active work title: State Claim Honestly +- Active work status: `ready` + +## Current Tasks + +- `freeze_current_state` [ready] Freeze the current north star and active theorem packet | Freeze the current route `anchored_selector_linearization`, claim surface `frontier_supported_route`, and active theorem packet before widening the search. | completion: The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target. | command: `erdos problem theorem-loop 857` +- `audit_theorem_surfaces` [ready] Audit theorem, claim, and formalization surfaces for consistency | Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording. | completion: The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is. | command: `erdos problem task-list 857` +- `verify_canonical_inputs` [ready] Verify canonical pack inputs against the latest route and verifier artifacts | Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts. | completion: The canonical input packet for this loop remains current and trustworthy. | command: `erdos problem theorem-loop-refresh 857` +- `verify_primary_structural_hook` [ready] Verify the current highest-value structural hook remains canonical | Verify that the strongest supported structural hook still survives across the theorem and claim surfaces. | completion: The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly. | command: `erdos problem claim-pass-refresh 857` +- `verify_verifier_boundary` [ready] Verify the current verifier boundary and next target | Verify that the current verifier boundary and next target are stated honestly across the pack surfaces. | completion: The verifier-facing boundary remains explicit even without a dedicated interval queue. | command: `erdos problem formalization 857` +- `execute_current_work_packet` [ready] State Claim Honestly | State the candidate theorem-facing claim in pack language without overstating current support. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. | completion: The first remaining gap is either discharged, narrowed, or replaced by a sharper one: state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | command: `erdos problem formalization-work 857` +- `discharge_first_remaining_gap` [ready] Discharge the first remaining gap in the active theorem packet | state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | This is the sharpest unresolved statement already named by the active theorem-work packet. | completion: The first remaining gap is either resolved or replaced by a more precise successor gap. | command: `erdos problem formalization-work-refresh 857` +- `refresh_and_rerank` [ready] Refresh the task list and rerank the next step | Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence. | completion: The refreshed task list records the next highest-value action instead of relying on a stale fixed script. | command: `erdos problem task-list-refresh 857` + +## Completed Anchors + + +## Next Needed Steps + +- `gap_1` [next] state_claim_honestly: Write a claim statement that is no stronger than the active claim-pass support surface. | source: formalization_work | command: `erdos problem formalization-work-refresh 857` +- `gap_2` [next] freeze_support_artifacts: Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet. | source: formalization_work | command: `erdos problem formalization-work-refresh 857` +- `gap_3` [next] define_promotion_boundary: Record explicit promotion criteria tied to current falsifiers. | source: formalization_work | command: `erdos problem formalization-work-refresh 857` +- `promote_ready_atom` [medium] Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. | source: theorem_formalization | command: `erdos problem formalization 857` + +## Commands + +- Problem surface: `erdos problem show 857` +- Problem artifacts: `erdos problem artifacts 857` +- Task list: `erdos problem task-list 857` +- Task list refresh: `erdos problem task-list-refresh 857` +- Theorem loop: `erdos problem theorem-loop 857` +- Claim pass: `erdos problem claim-pass 857` +- Formalization: `erdos problem formalization 857` +- Formalization work: `erdos problem formalization-work 857` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857` +- taskListJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/TASK_LIST.json` +- taskListMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/TASK_LIST.md` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json` +- claimPassJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/CLAIM_PASS.json` +- formalizationJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION.json` +- formalizationWorkJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FORMALIZATION_WORK.json` +- intervalQueuePath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/INTERVAL_WORK_QUEUE.yaml` diff --git a/packs/sunflower/problems/857/THEOREM_LOOP.json b/packs/sunflower/problems/857/THEOREM_LOOP.json new file mode 100644 index 0000000..97fa628 --- /dev/null +++ b/packs/sunflower/problems/857/THEOREM_LOOP.json @@ -0,0 +1,85 @@ +{ + "schema": "erdos.problem_theorem_loop/1", + "generatedAt": "2026-04-10T08:11:06.261Z", + "problemId": "857", + "displayName": "Erdos Problem #857", + "title": "Sunflower Conjecture", + "cluster": "sunflower", + "sourceKind": "pack_route_state", + "theoremLoopMode": "baseline", + "activeRoute": "anchored_selector_linearization", + "theoremModule": "sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean", + "currentState": { + "siteStatus": "open", + "repoStatus": "active", + "openProblem": true, + "routeBreakthrough": true, + "problemSolved": false, + "currentClaimSurface": "frontier_supported_route", + "routeSummary": "Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary.", + "nextHonestMove": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes." + }, + "theoremHooks": [ + { + "hook_id": "active_route_recorded", + "status": "supported", + "note": "The pack records an active route, currently `anchored_selector_linearization`." + }, + { + "hook_id": "theorem_module_registered", + "status": "supported", + "note": "A theorem module is already registered for the active route: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`." + }, + { + "hook_id": "ready_atom_present", + "status": "supported", + "note": "The live route already has a ready atom, `T10.G3.A2`, which can feed the theorem lane." + }, + { + "hook_id": "frontier_note_present", + "status": "supported", + "note": "The pack already carries a frontier note that can anchor theorem-facing updates." + } + ], + "theoremAgenda": [ + { + "item_id": "promote_ready_atom", + "status": "ready", + "task": "Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes." + }, + { + "item_id": "stabilize_theorem_module_boundary", + "status": "ready", + "task": "Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary.", + "why": "The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies." + }, + { + "item_id": "tighten_active_route_claim", + "status": "ready", + "task": "Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit.", + "why": "Prove or package the helper stack cleanly and checkpoint the route if the leaf closes." + } + ], + "currentBridgeState": null, + "commands": { + "problemShow": "erdos problem show 857", + "problemArtifacts": "erdos problem artifacts 857", + "theoremLoop": "erdos problem theorem-loop 857", + "theoremLoopRefresh": "erdos problem theorem-loop-refresh 857", + "clusterStatus": "erdos sunflower status 857", + "clusterFrontier": "erdos sunflower frontier 857", + "sourceRefresh": null + }, + "sources": { + "packProblemDir": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857", + "theoremLoopJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json", + "theoremLoopMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md", + "contextPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/context.yaml", + "routePacketPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/ROUTE_PACKET.yaml", + "frontierNotePath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FRONTIER_NOTE.md", + "opsDetailsPath": "/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/OPS_DETAILS.yaml", + "legacyBridgeJsonPath": null, + "legacyBridgeMarkdownPath": null + } +} diff --git a/packs/sunflower/problems/857/THEOREM_LOOP.md b/packs/sunflower/problems/857/THEOREM_LOOP.md new file mode 100644 index 0000000..9f93002 --- /dev/null +++ b/packs/sunflower/problems/857/THEOREM_LOOP.md @@ -0,0 +1,48 @@ +# Erdos Problem #857 Theorem Loop + +This note is the generic theorem-loop surface for the problem pack. It keeps theorem-facing route state visible even when no richer search bridge exists yet. + +## Current State + +- Theorem loop mode: `baseline`. +- Active route: `anchored_selector_linearization`. +- Current claim surface: `frontier_supported_route`. +- Repo status: `active`; site status: `open`. +- Route breakthrough: `yes`. +- Problem solved: `no`. +- Open problem: `yes`. +- Theorem module: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`. +- Route summary: Export the live anchored-selector helper stack into a route-facing leaf that remains honest about the open-problem boundary. +- Next honest move: Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Theorem Hooks + +- `active_route_recorded`: supported | The pack records an active route, currently `anchored_selector_linearization`. +- `theorem_module_registered`: supported | A theorem module is already registered for the active route: `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean`. +- `ready_atom_present`: supported | The live route already has a ready atom, `T10.G3.A2`, which can feed the theorem lane. +- `frontier_note_present`: supported | The pack already carries a frontier note that can anchor theorem-facing updates. + +## Theorem Agenda + +- `promote_ready_atom`: ready | Turn ready atom `T10.G3.A2` into the next theorem-facing checkpoint. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. +- `stabilize_theorem_module_boundary`: ready | Align the active route with theorem module `sunflower-coda/repo/sunflower_lean/SunflowerLean/ObstructionExport.lean` and freeze its public claim boundary. | The current claim surface is `frontier_supported_route`, so the next theorem move should sharpen what that module actually certifies. +- `tighten_active_route_claim`: ready | Compress the active route `anchored_selector_linearization` into the next honest theorem-facing claim unit. | Prove or package the helper stack cleanly and checkpoint the route if the leaf closes. + +## Commands + +- Problem surface: `erdos problem show 857` +- Canonical theorem loop: `erdos problem theorem-loop 857` +- Refresh theorem loop: `erdos problem theorem-loop-refresh 857` +- Problem artifacts: `erdos problem artifacts 857` +- Cluster status: `erdos sunflower status 857` +- Cluster frontier: `erdos sunflower frontier 857` + +## Sources + +- packProblemDir: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857` +- theoremLoopJsonPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.json` +- theoremLoopMarkdownPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/THEOREM_LOOP.md` +- contextPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/context.yaml` +- routePacketPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/ROUTE_PACKET.yaml` +- frontierNotePath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/FRONTIER_NOTE.md` +- opsDetailsPath: `/Volumes/Code_2TB/code/erdos-problems/packs/sunflower/problems/857/OPS_DETAILS.yaml` diff --git a/paper/problems/857/progress_note.typ b/paper/problems/857/progress_note.typ new file mode 100644 index 0000000..82449a7 --- /dev/null +++ b/paper/problems/857/progress_note.typ @@ -0,0 +1,353 @@ +#let ink = rgb("#16324f") +#let accent = rgb("#0f766e") +#let soft = rgb("#eef6f5") +#let soft2 = rgb("#f8fbfb") + +#set page( + paper: "us-letter", + margin: (top: 0.95in, bottom: 0.95in, left: 1.0in, right: 1.0in), + footer: context { + set text(size: 9pt, fill: luma(45%)) + align(center)[#counter(page).display("1")] + }, +) + +#set text( + font: "Libertinus Serif", + size: 11pt, + fill: luma(15%), + lang: "en", +) + +#set par( + justify: true, + leading: 0.68em, +) + +#set heading(numbering: "1.") +#show heading.where(level: 1): set text(size: 14pt, weight: "semibold", fill: ink) +#show heading.where(level: 2): set text(size: 11.6pt, weight: "semibold", fill: ink) + +#let small-note(body) = text(size: 9pt, fill: luma(42%))[#body] + +#let ref-entry(body) = block( + inset: (left: 1.35em), +)[ + #set par(hanging-indent: 1.35em, leading: 0.58em) + #body +] + +#align(center)[ + #text(size: 20pt, weight: "bold", fill: ink)[ + A Progress Note on the Weak Sunflower Problem + ] + #v(0.35em) + #text(size: 11.5pt, fill: accent)[ + Erdos Problem #857 + ] + #v(0.7em) + #text(size: 11pt)[Cody Mitchell] +] + +#v(0.45em) + +#align(center)[ + #block( + width: 96%, + inset: (x: 15pt, y: 11pt), + fill: soft2, + stroke: (paint: rgb("#d6e8e5"), thickness: 0.5pt), + radius: 5pt, + )[ + #text(size: 9.4pt, weight: "semibold", fill: ink)[Repository and CLI] + #v(0.35em) + #block(width: 100%)[ + #set par(justify: false, leading: 0.5em) + #text(size: 9pt, fill: luma(30%))[ + #text(weight: "semibold", fill: accent)[Repository URL:] https://github.com/SproutSeeds/erdos-problems + ] + #linebreak() + #text(size: 9pt, fill: luma(30%))[ + #text(weight: "semibold", fill: accent)[NPM package URL:] https://www.npmjs.com/package/erdos-problems + ] + #linebreak() + #text(size: 9pt, fill: luma(30%))[ + #text(weight: "semibold", fill: accent)[Global install:] #text(font: "Menlo", size: 8.8pt, fill: luma(26%))[npm install -g erdos-problems] + ] + #linebreak() + #text(size: 9pt, fill: luma(30%))[ + #text(weight: "semibold", fill: accent)[Local repo wiring:] #text(font: "Menlo", size: 8.8pt, fill: luma(26%))[npm link] + ] + #linebreak() + #text(size: 9pt, fill: luma(30%))[ + #text(weight: "semibold", fill: accent)[Date:] April 5, 2026. + ] + ] + ] +] + +#v(1.1em) + +#block( + inset: 13pt, + fill: soft2, + stroke: (paint: rgb("#d6e8e5"), thickness: 0.6pt), + radius: 6pt, +)[ + #text(size: 10pt, weight: "semibold", fill: ink)[Abstract.] + We study the weak sunflower problem recorded as Erdos problem $857$: determine + the growth of the minimum $m(n, k)$ such that every family of $m(n, k)$ subsets + of $[n]$ contains a $k$-sunflower. The problem remains open, and this paper does + not claim its resolution. Instead, we assemble a claim-safe progress paper + around the current public frontier represented in this repository. We isolate + the active anchored-selector linearization route, identify the strongest + closed public support layer immediately beneath it, and record the exact open + seam exposed by the current board packet. We also separate asymptotic proof + posture from finite computation: the current compute surface contains a narrow + exact packet for the question whether $M(8, 3) = 45$, marked ready for a local + scout, but this does not upgrade the status of the asymptotic problem. The + resulting document is therefore a professional progress note rather than a + solved-claim paper. +] + +#v(0.9em) + +#table( + columns: (1.2fr, 2.6fr), + inset: 7pt, + align: (left, left), + stroke: (x: none, y: (paint: rgb("#d8e4e3"), thickness: 0.5pt)), + fill: (x, y) => if y == 0 { soft } else if calc.odd(y) { white } else { soft2 }, + table.header( + text(weight: "semibold", fill: ink)[Item], + text(weight: "semibold", fill: ink)[Current public status], + ), + [Problem status], [Open. No full proof claim is made in this paper.], + [Active route], [Anchored-selector linearization], + [Strongest closed support layer], [O1a existential explicit export], + [Live ticket], [T10, with 2/5 gates and 9/15 atoms complete], + [First ready atom], [T10.G3.A2], + [Compute packet], [M(8,3) exactness lane, ready for local scout], +) + += Introduction + +The sunflower problem sits near the center of modern extremal set theory. In its +classical form, initiated by Erdos and Rado, one asks how large a family of sets +must be before a sunflower is forced to appear. Problem $857$ records the +non-uniform or weak version: for fixed $k$, determine the least $m(n, k)$ such +that every family of $m(n, k)$ subsets of $[n]$ contains a $k$-sunflower. The +public Erdos Problems page keeps this problem open and emphasizes the target +upper bound $m(n, k) <= C(k)^n$. + +This weak formulation is broader than the classical uniform sunflower lemma and +interacts with several major themes in modern combinatorics. For $k = 3$, the +problem is closely tied to cap-set-type phenomena, as emphasized by Alon, +Shpilka, and Umans, and the best asymptotic bound quoted on the public problem +page comes from Naslund and Sawin. At the same time, recent breakthroughs on the +uniform sunflower lemma by Alweiss, Lovett, Wu, and Zhang, followed by Rao and by +Bell, Chueluecha, and Warnke, have transformed the methodological background +against which any serious weak-sunflower route must be evaluated. + +The purpose of this paper is narrower than a complete solution. It converts the +current public record for problem $857$ into a mathematically legible progress +paper. The main value added here is organizational and expository: we identify +the active route, separate closed support layers from live frontier work, and +state exactly what the present public compute and formalization packets do and do +not show. This distinction matters because the repository now contains genuine +route structure, but not yet a public theorem text closing the asymptotic weak +sunflower problem. + += Problem Statement and Scope + +We write $[n] = {1, ..., n}$. A family $F$ of subsets of $[n]$ contains a +$k$-sunflower if there exist distinct sets $A_1, ..., A_k$ in $F$ such that all +pairwise intersections are equal. Equivalently, if $K$ denotes that common +intersection, then the petals $A_1 - K, ..., A_k - K$ are pairwise disjoint. + +Problem $857$ asks for the least integer $m(n, k)$ such that every family of +$m(n, k)$ subsets of $[n]$ contains a $k$-sunflower. The working normalization in +this repository is the target asymptotic shape +$m(n, k) <= C(k)^n$. + +This note is intentionally claim-safe. It makes three decisions explicit. + +- It treats the asymptotic weak sunflower problem as open. +- It treats route architecture as a mathematical object worth recording in its own + right. +- It keeps proof posture, formalization posture, and finite computation posture + separate throughout. + +That final separation is crucial. A formally organized route is not the same as a +finished proof, and a finite exact computation is not the same as asymptotic +closure. + += Literature Context + +The first layer of background is classical. Erdos and Rado introduced the +sunflower lemma and the broader fixed-petal conjectural picture. Erdos later +revisited the surrounding extremal set-theoretic landscape with Kleitman, and +the paper of Erdos and Szemeredi remains a central source for the non-uniform +weak-sunflower formulation most relevant to problem $857$. + +The second layer is the modern structural breakthrough on the uniform problem. +Alweiss, Lovett, Wu, and Zhang proved the first dramatically subfactorial general +upper bound using the spread-method viewpoint. Rao reformulated the argument via +coding ideas, and Bell, Chueluecha, and Warnke sharpened the general bound +further to the now-standard $O(p log k)$ scale in the $p$-petal, $k$-uniform +setting. Rao's later survey gives a concise entry point into how these ideas sit +within the broader sunflower story. + +The third layer is the weak-sunflower and cap-set interface. The public Erdos +Problems page for $857$ points directly to the connection observed by Alon, +Shpilka, and Umans when $k = 3$, and it quotes the Naslund-Sawin upper bound +$m(n, 3) <= (3 / 2^(2/3))^((1 + o(1)) n)$. +This remains the main asymptotic benchmark explicitly attached to the current +public statement of the problem. + += Current Public Route Architecture + +The present repository does not expose a complete theorem text for the active +leaf. Accordingly, the right mathematical object to summarize is the dependency +structure of the route itself. + +== Closed support layers + +The public route history identifies the following layers as closed public support +beneath the live frontier: + +- global family-card export +- explicit remainder export +- explicit M-remainder export +- O1a existential explicit export + +Among these, the strongest finished layer immediately below the frontier is the +O1a existential explicit export layer, which the ops packet records as +strict-closed. +This means that the current public route already has an explicit anchored +remainder package below the frontier; future work should treat that package as +input rather than re-derive it rhetorically from scratch. + +== The active frontier + +The live route is the anchored-selector linearization route. The route packet +describes its purpose as preserving the active export/compression frontier while +pushing the explicit O1a remainder package toward a genuine recurrence-facing +step. The atomic board localizes the remaining pressure inside ticket T10, which +is still open and whose gate story says that the early gates are satisfied while +the live pressure is concentrated in the G3 seam. + +The smallest honest next move has already been isolated by the public board: +T10.G3.A2, whose title says that the helper/theorem stack should be promoted into +the realized anchored-selector leaf. This is important. The current frontier is +not a vague research aspiration but a named route with a named ready atom. + +== What this route claim means + +The claim supported by the current public record is therefore modest but real. It +is not that the weak sunflower problem has been solved. It is that the weak +sunflower pack has moved past generic counting closure and now concentrates its +live pressure on a single route-facing leaf promotion. In a progress paper, that +kind of localization is mathematically meaningful because it replaces diffuse +ambition with a precise open obligation. + += Computational and Formal Evidence + +The public bundle for problem $857$ is formalization-aware, but it is not yet a +public formal proof archive for the full weak sunflower problem. The route +packets point to upstream theorem modules named ObstructionGlobalBridge.lean and +ObstructionExport.lean, which shows where formal structure is expected to +interface with the route, but the present public bundle does not expose an +end-to-end theorem chain proving the asymptotic target. + +The current compute surface is narrower still. The only packaged compute lane is +the exactness packet for the question whether $M(8, 3) = 45$, equivalently +whether a target-46 SAT instance is unsatisfiable. Its public metadata is precise: +the claim-level goal is exact, the status is "ready for local scout," the +recommendation is "cpu first," and the next honest move is to run a local scout +before any paid rung. + +Two boundaries should be kept explicit. First, even a successful exact +certification of $M(8, 3)$ would remain a finite result; it would not by itself +yield the asymptotic estimate $m(n, k) <= C(k)^n$. Second, route packets and +formalization references help organize and verify the frontier, but they do not +authorize a claim that problem $857$ is formally solved. + += Limitations and Next Steps + +The main limitation is straightforward: problem $857$ remains open. This paper +records route structure and evidence boundaries, not a completed solution. + +Near-term work is concentrated in one clearly named place. The active +anchored-selector leaf is not yet publicly closed, ticket T10 remains open, and +the board identifies T10.G3.A2 as the current dependency-satisfied atom. If one +stays faithful to the present public record, the next move is not vague: +promote the helper/theorem stack into that named leaf, checkpoint it honestly, +and only then ask whether the route merits a stronger public claim. + +Broader mathematical questions remain in view as well. One wants the correct +asymptotic growth of $m(n, k)$ for fixed $k$, a clearer understanding of how far +the strongest known $k = 3$ methods can extend, and a better account of how +uniform-sunflower spread and coding methods transfer into genuinely non-uniform +weak-sunflower settings. Those questions remain open, but the current repository +now isolates one precise frontier where further progress can be measured. + += References + +#ref-entry[ +[1] P. Erdos and R. Rado, *Intersection theorems for systems of sets*, +Journal of the London Mathematical Society 35 (1960), 85-90. +DOI: 10.1112/jlms/s1-35.1.85. +] + +#ref-entry[ +[2] P. Erdos and D. J. Kleitman, *Extremal problems among subsets of a set*, +Discrete Mathematics 8 (1974), 281-294. +DOI: 10.1016/0012-365X(74)90140-X. +] + +#ref-entry[ +[3] P. Erdos and E. Szemeredi, *Combinatorial properties of systems of sets*, +Journal of Combinatorial Theory, Series A 24 (1978), 308-313. +DOI: 10.1016/0097-3165(78)90060-2. +] + +#ref-entry[ +[4] N. Alon, A. Shpilka, and C. Umans, *On sunflowers and matrix multiplication*, +Computational Complexity 22 (2013), 219-243. +DOI: 10.1007/s00037-013-0060-1. +] + +#ref-entry[ +[5] E. Naslund and W. Sawin, *Upper bounds for sunflower-free sets*, +Forum of Mathematics, Sigma 5 (2017), e15. +DOI: 10.1017/fms.2017.12. +] + +#ref-entry[ +[6] R. Alweiss, S. Lovett, K. Wu, and J. Zhang, *Improved bounds for the sunflower +lemma*, Annals of Mathematics 194 (2021), 795-815. +DOI: 10.4007/annals.2021.194.3.5. +] + +#ref-entry[ +[7] A. Rao, *Coding for Sunflowers*, Discrete Analysis 2020:2. +DOI: 10.19086/da.11887. +] + +#ref-entry[ +[8] T. Bell, S. Chueluecha, and L. Warnke, *Note on sunflowers*, +Discrete Mathematics 344 (2021), 112367. +DOI: 10.1016/j.disc.2021.112367. +] + +#ref-entry[ +[9] A. Rao, *Sunflowers: from soil to oil*, +Bulletin of the American Mathematical Society 60 (2023), 29-38. +DOI: 10.1090/bull/1777. +] + +#ref-entry[ +[10] T. F. Bloom, *Erdos Problem #857*, https://www.erdosproblems.com/857, +accessed April 5, 2026. +] diff --git a/problems/848/FORUM_COMMENT_DRAFT.txt b/problems/848/FORUM_COMMENT_DRAFT.txt new file mode 100644 index 0000000..fa5dd96 --- /dev/null +++ b/problems/848/FORUM_COMMENT_DRAFT.txt @@ -0,0 +1,6 @@ +I’ve updated my public `erdos-problems` workspace for Problem 848 on the finite-check side. No new best `N_0` claim here; the update is mainly a bounded-verification workflow that separates imported threshold claims from repo-audited claims and requires explicit certificates for interval-coverage claims. + +More broadly, I built `erdos-problems` as an npm workspace for working on any Erdős problem against a canonical public repo. The idea is that when someone boots a problem from scratch, they inherit the current dossier, route notes, and review artifacts instead of starting from zero, and anyone can improve that shared base by contributing back to the repo. + +Repo: https://github.com/SproutSeeds/erdos-problems +npm: https://www.npmjs.com/package/erdos-problems diff --git a/research/frontier-engine/ARCHITECTURE.md b/research/frontier-engine/ARCHITECTURE.md new file mode 100644 index 0000000..eae06b7 --- /dev/null +++ b/research/frontier-engine/ARCHITECTURE.md @@ -0,0 +1,132 @@ +# Architecture + +`frontier-engine` is a verifier-guided search system. + +Its purpose is not to replace exact methods. Its purpose is to reduce the amount +of exact work that remains. + +Core loop: + +1. generate +2. classify +3. inventory +4. verify +5. learn + +## Lane posture + +`frontier-engine` should support multiple named lanes rather than one monolithic +search surface. + +Each lane should define: + +- one problem or tightly related benchmark family +- one candidate shape +- one honest finite-gap metric +- one artifact kind for downstream exact or review work + +That lets us reuse the engine while keeping the mathematical semantics of each +lane explicit. + +## Core modules + +- generator + - emits candidate structures, partial assignments, motif seeds, or cubes +- rarity + - scores how unusual a candidate is relative to the current stream +- surrogate + - predicts promise, hardness, or verifier-alignment +- inventory + - keeps the rarest and strongest candidates rather than a raw heap +- frontier + - keeps only the best and most diverse active candidates +- verifier + - exact backend such as SAT, branch-and-bound, or a certificate checker +- pipeline + - orchestrates the loop and records artifacts + +## Contract boundary + +The engine should expose the following logical objects: + +- `Candidate` + - the thing being searched +- `ScoreBundle` + - surrogate and heuristic scores +- `InventoryRecord` + - a promoted rare-structure record with rarity and signal metadata +- `FrontierItem` + - candidate plus retention metadata +- `VerificationRequest` + - exact work request +- `VerificationResult` + - exact outcome and proof-facing metadata + +## Proof posture + +The engine can support proofs, but it is not itself the proof. + +Its role is: + +- reduce entropy +- isolate hard cases +- surface strong witnesses +- package exact subproblems + +The final truth still belongs to the verifier and the mathematical record. + +## Hardware posture + +The generator and surrogate stack should be GPU-aware but hardware-adaptive. + +That means: + +- a Windows RTX 4090 rig is the first-class CUDA target during the prototype + phase +- batch sizing should depend on available VRAM +- kernels should degrade gracefully to smaller cards +- multi-GPU should be an optimization, not an assumption +- artifact formats should be device-independent + +For the first `M(8,3)` rail that now means: + +- keep a benchmark-specific search config with explicit mutation and batching + knobs +- keep the CPU scaffold and future CUDA rail on the same candidate contract +- export the same elite bundle shape no matter which runtime produced it +- treat Torch as the first device-aware backend and Triton as a later kernel + optimization step + +## Artifact flow + +Internal artifacts should include: + +- candidate ledgers +- motif catalogs +- rarity ledgers +- elite inventory snapshots +- scored frontier snapshots +- verifier task bundles +- verifier outcomes +- training snapshots for surrogate improvement + +For the first exact handoff this now also includes: + +- SAT-seed bundles containing elite family JSONs and a manifest + +Only promoted, claim-safe summaries should move into `erdos-problems`. + +## First benchmark-specific finite gap + +For the `M(8,3)` rail, a candidate is naturally a family of `46` subsets of +`[8]`. + +That suggests a benchmark-specific closeness metric: + +- `sunflower_triple_count` + +where: + +- `0` means the candidate family is already 3-sunflower-free +- smaller values mean the candidate is more SAT-worthy +- the engine can optimize this metric before exact solving diff --git a/research/frontier-engine/ERDOS_ADAPTER.md b/research/frontier-engine/ERDOS_ADAPTER.md new file mode 100644 index 0000000..d81f671 --- /dev/null +++ b/research/frontier-engine/ERDOS_ADAPTER.md @@ -0,0 +1,42 @@ +# Erdos Problems Adapter + +This document describes the boundary to `erdos-problems`. + +## What should stay outside for now + +Do not pull these directly into the packaged CLI yet: + +- Triton kernels +- GPU tuning logic +- surrogate training code +- raw experiment caches +- device-specific batching heuristics + +These belong to `frontier-engine` until the system is stable and benchmarked. + +## What may later flow into `erdos-problems` + +Only promoted, claim-safe artifacts should cross the boundary: + +- run summaries +- frontier reduction ledgers +- promoted verifier task bundles +- exact certificates or exact witness packets +- benchmark comparison notes + +## Desired eventual integration + +Once earned, the adapter can expose: + +- problem-specific frontier status +- governed local search launches +- artifact ingest into problem evidence +- exact verifier bundles tied to problem ids + +## Guardrail + +The adapter must never silently inflate: + +- search progress into solved-problem claims +- surrogate wins into exact mathematical results +- hardware throughput into proof evidence diff --git a/research/frontier-engine/HARDWARE.md b/research/frontier-engine/HARDWARE.md new file mode 100644 index 0000000..7b227fa --- /dev/null +++ b/research/frontier-engine/HARDWARE.md @@ -0,0 +1,55 @@ +# Hardware + +## Primary prototype machine + +Primary CUDA target: + +- OS: Windows +- GPU: RTX 4090 +- role: first search rail for `frontier-engine` + +## Why the 4090 is the right first target + +- strong single-card throughput +- excellent CUDA development target +- simpler than assuming a multi-GPU cluster from day one +- good fit for proving whether rarity-guided search actually reduces exact work + +## Prototype hardware rule + +The engine should earn multi-GPU complexity. + +That means: + +1. prove value on the Windows 4090 box +2. make the first benchmark reproducible there +3. only then generalize to heavier rigs or multi-GPU orchestration + +## Runtime posture + +The first runtime split now looks like this: + +- `python` + - baseline correctness path +- `torch` + - first device-aware batched backend +- `triton` + - next acceleration layer, not wired yet + +The intended Windows 4090 flow is: + +1. use the Torch backend to prove the rail shape on CUDA +2. preserve the same candidate and artifact contracts +3. only then replace hot paths with Triton kernels + +Current one-command launcher path for the 848 rail: + +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-profile-bundle research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json` + +## Legacy reference hardware + +Historical systems may have assumed heavier GPU volume, including multi-card +configurations. + +Those assumptions should be treated as scaling notes, not as design +requirements for the first modern scaffold. diff --git a/research/frontier-engine/NAMING.md b/research/frontier-engine/NAMING.md new file mode 100644 index 0000000..898bff3 --- /dev/null +++ b/research/frontier-engine/NAMING.md @@ -0,0 +1,45 @@ +# Naming + +Recommended exact name: `frontier-engine` + +Python package name: `frontier_engine` + +## Why this name + +`frontier-engine` is the best current fit because it is: + +- broad enough to cover motif generation, surrogate scoring, and verifier-guided + search +- not tied to a single problem family such as sunflower or SAT +- not too narrow around one module such as Motif Classifier +- aligned with the repo's existing language around frontiers, routes, and + honest next moves + +## Names considered + +Rejected for now: + +- `motif-classifier` + - too narrow; that is a major subsystem, not the whole engine +- `pair-surrogate` + - too narrow and too model-specific +- `trifield-searcher` + - too narrow and too experimental +- `near-sat-engine` + - too tied to one exact backend +- `constraint-frontier` + - strong candidate, but slightly colder and less adaptable than + `frontier-engine` +- `frontier-search` + - viable, but `frontier-engine` better captures the full stack rather than + only the search loop + +## Integration naming + +If later connected into `erdos-problems`, the adapter surface can use names like: + +- `erdos frontier status ` +- `erdos frontier run ` +- `erdos frontier ingest ` + +Those should not exist until the engine earns them. diff --git a/research/frontier-engine/README.md b/research/frontier-engine/README.md new file mode 100644 index 0000000..62e6f64 --- /dev/null +++ b/research/frontier-engine/README.md @@ -0,0 +1,129 @@ +# Frontier Engine + +`frontier-engine` is the standalone prototype surface for GPU-assisted, +near-exact combinatorial search. + +It is designed to sit between broad search and exact verification: + +- generate candidate structures at GPU scale +- classify them by uniqueness and rarity +- inventory the rare, high-signal structures instead of drowning in raw output +- hand a tiny elite set to an exact backend such as SAT, cube-and-conquer, or a + certificate checker + +This is the right place for systems in the spirit of: + +- Motif Classifier +- Pair Surrogate +- Trifield Searcher +- verifier-guided frontier search + +Current intended search story: + +1. a giant random number generator emits massive batches of candidate + combinations +2. a motif and rarity layer scores how structurally unusual each candidate is +3. an inventory layer keeps the rarest and highest-signal structures +4. a solver layer works only on that elite inventory + +This is the key design move: do not ask exact methods to stare at the whole +search space. Ask them to stare only at the best rare structures the GPU engine +can surface. + +## First proving ground + +The first exact proving ground should be the weak-sunflower exactness lane +around `M(8,3)`. + +That benchmark is a good fit because it has: + +- a finite exact target +- a natural SAT-facing backend +- a concrete notion of a reduced exact frontier +- an existing home in the `erdos-problems` sunflower compute surface + +## Primary hardware target + +The primary CUDA development box for the first engine build is the Windows rig +with an RTX 4090. + +That means: + +- optimize first for one strong consumer GPU +- make Windows/WSL CUDA workflows first-class during prototyping +- treat larger multi-GPU stories as later scale-up work, not as the entry cost + +## Why it lives here first + +This engine should be built and proved before it is deeply integrated into +`erdos-problems`. + +That means: + +- build it as a standalone search engine +- prove that it reduces a measurable finite gap on at least one exact benchmark +- only then connect it back into the CLI and public problem records + +`erdos-problems` should remain the mathematical record. +`frontier-engine` should remain the search engine. + +## Success criterion + +The engine is only worth integrating once it can show a real reduction in exact +work, for example: + +- fewer unresolved SAT cubes +- a smaller upper/lower bound gap +- stronger exact witnesses than random or local search +- strong correlation between surrogate ranking and verifier outcome +- a measurable improvement over naive random search because the rarity inventory + feeds the verifier better candidates + +## Layout + +- `NAMING.md`: exact naming choice and rejected alternatives +- `ARCHITECTURE.md`: system shape and core contracts +- `VISION.md`: rare-structure search loop and the intended build philosophy +- `ROADMAP.md`: build-first / prove-first milestones +- `ERDOS_ADAPTER.md`: how later integration with `erdos-problems` should work +- `pyproject.toml`: isolated Python package scaffold +- `src/frontier_engine/`: minimal engine package skeleton +- `experiments/`: future benchmark and run bundles +- `artifacts/`: future exported run artifacts + +## First runnable rail + +The current `M(8,3)` rail is no longer just a toy random sampler. + +It now has: + +- a configurable mutation-guided search loop +- runtime selection across `python`, `torch`, and `auto` +- a first-class Windows RTX 4090 search profile +- a benchmark-native warm start from the known `M(8,3) >= 45` family +- a portable JSON artifact bundle for elite candidates and verifier handoff +- a SAT-seed bundle export for exact follow-up + +Useful commands: + +- `python3 research/frontier-engine/src/frontier_engine/cli.py benchmark-plan` +- `python3 research/frontier-engine/src/frontier_engine/cli.py runtime-probe` +- `python3 research/frontier-engine/src/frontier_engine/cli.py list-lanes` +- `python3 research/frontier-engine/src/frontier_engine/cli.py show-lane p848_anchor_ladder` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run-profile research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run --runtime torch --device cuda --n-chunk-size 4096 --value-chunk-size 65536 --prime-square-chunk-size 256` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run --candidate-mode ladder-sweep --base-tail 332 --ladder-rounds 6 --perturb-offsets 0,-5,5` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-bundle` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-profile-bundle research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json` +- `python3 research/frontier-engine/src/frontier_engine/cli.py prototype-run` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-m8-bundle` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-m8-sat-bundle` + +## Build-first rule + +Do not wire this into the public CLI as a first-class engine until it has: + +1. one benchmark with a finite exact target +2. one measurable frontier-reduction story +3. one artifact schema that `erdos-problems` can ingest honestly diff --git a/research/frontier-engine/ROADMAP.md b/research/frontier-engine/ROADMAP.md new file mode 100644 index 0000000..6914490 --- /dev/null +++ b/research/frontier-engine/ROADMAP.md @@ -0,0 +1,98 @@ +# Roadmap + +## Phase 0: Archaeology + +- inventory legacy systems such as Motif Classifier, Pair Surrogate, and + Trifield Searcher +- identify which ideas are still live +- normalize naming and artifacts + +## Phase 1: Finite benchmark + +- choose one exact benchmark with a measurable target +- define the finite gap the engine is trying to shrink +- lock one verifier backend + +Examples: + +- SAT cube count +- exact `M(n,3)` lane reduction +- bounded witness search with exact rejection + +Current recommended benchmark: + +- exact `M(8,3)` reduction rail +- exact target: certify the target-46 instance route as cheaply as possible +- primary backend: SAT / cube-and-conquer style verifier +- primary hardware: Windows RTX 4090 CUDA box +- first finite gap: count of 3-sunflower triples in a size-46 family on `[8]` + +## Phase 2: Generator + +- build motif-aware candidate generation +- add canonicalization and symmetry reduction +- make GPU chunking hardware-adaptive +- support a giant random combination stream as the first practical search mode +- validate the first CUDA search rail on the 4090 before worrying about + multi-GPU scaling + +Current status: + +- benchmark-specific mutation rail scaffolded +- Windows RTX 4090 profile defined +- runtime probe plus `python` / `torch` backend split implemented +- artifact export contract defined +- SAT-seed bundle export implemented +- native frontier fleet provisioning/sync now supports `2x` / `8x H100` + independent-sweep workflows +- next step is a true CUDA or Triton hot-path implementation behind the same + rail shape + +Compute topology after the first single-GPU rail: + +- Tier A: single-GPU sweeps on `4090` / single `H100` +- Tier B: many independent sweeps in parallel across multiple boxes +- Tier C: multi-GPU shared-lane execution on `2x` or `8x H100` + +Recommendation: + +- For `p848`, Tier B is the next best step after the current `4090` lane. +- Use additional `H100` boxes for wider sweep fleets only when they improve + throughput per dollar over the 4090. +- Native workflow: + - `erdos frontier create-brev-fleet --type hyperstack_H100 --count 2 --attach --sync-lane p848_anchor_ladder --apply` + - `erdos frontier sync-fleet --lane p848_anchor_ladder --apply` +- Do not treat `8x H100` as the default until the lane supports real + distributed or multi-GPU batching rather than only single-device Torch. + +## Phase 3: Rarity and uniqueness + +- score candidates by stream-relative rarity +- define uniqueness ratings that survive exact scrutiny +- inventory the rarest, highest-signal structures instead of the whole stream + +## Phase 4: Surrogate + +- implement pairwise and higher-order scoring surfaces +- measure rank correlation against verifier outcomes +- reject surrogates that are smooth but verifier-misaligned + +## Phase 5: Frontier manager + +- enforce diversity and deduplication +- keep the engine from collapsing into one narrow basin +- record exact reasons candidates were kept or dropped + +## Phase 6: Exact loop + +- connect verifier requests to frontier items +- cache verifier outcomes +- teach the surrogate from exact success and exact failure + +## Phase 7: Earned integration + +Only after the engine shows benchmark value: + +- define `erdos-problems` artifact ingest shape +- add CLI adapter hooks +- expose search status without overstating mathematical claims diff --git a/research/frontier-engine/VISION.md b/research/frontier-engine/VISION.md new file mode 100644 index 0000000..7bff8ef --- /dev/null +++ b/research/frontier-engine/VISION.md @@ -0,0 +1,72 @@ +# Vision + +`frontier-engine` is meant to turn high-volume random exploration into a usable +exact-search funnel. + +The intended loop is: + +1. produce millions of combinations per second +2. classify them into uniqueness ratings +3. inventory the structures with the rarest and strongest signals +4. solve on top of those rather than on the raw stream + +That loop captures the spirit behind: + +- Motif Classifier +- Pair Surrogate +- Trifield Searcher + +## Working thesis + +Raw brute force is too wasteful. +Pure surrogate search is too easy to fool. +Pure SAT is too expensive to aim at the whole space. + +The right middle layer is: + +- massive generation +- rarity and motif compression +- disciplined inventory +- exact verification on the elite set + +## Why rarity matters + +The engine should care about structures that are not merely high-scoring, but +structurally rare relative to the stream that produced them. + +That means the prototype should explicitly track: + +- how often a motif signature appears +- how many unusual properties a candidate concentrates +- which combinations show high distinctness instead of only high local score + +The inventory should therefore answer: + +- what almost never shows up? +- what has the strongest unusual structure? +- what deserves exact solving time? + +## Near-SAT posture + +The goal is to get finitely as close as a SAT solver would while spending GPU +time to shrink the search space first. + +This is not "GPU instead of SAT." +It is "GPU before SAT." + +Success means the engine can reduce exact work by improving: + +- witness quality +- branch ordering +- cube prioritization +- contradiction likelihood +- finite gap on a benchmark with a known exact target + +For the first `M(8,3)` rail, that finite gap should be concrete: + +- family size fixed at `46` +- exact target is zero 3-sunflower triples +- prototype closeness metric is therefore the exact count of violating triples + +That gives the engine a real target before final SAT handoff: +find rare, high-signal families whose 3-sunflower triple count is unusually low. diff --git a/research/frontier-engine/experiments/README.md b/research/frontier-engine/experiments/README.md new file mode 100644 index 0000000..a1455a0 --- /dev/null +++ b/research/frontier-engine/experiments/README.md @@ -0,0 +1,17 @@ +# Experiments + +Future benchmark runs for `frontier-engine` should live here. + +Recommended shape: + +- `experiments//README.md` +- `experiments//config/` +- `experiments//runs/` +- `experiments//analysis/` + +Each benchmark should define one exact target and one measurable finite gap. + +Examples now in scope: + +- `m8-sat-rail` +- `p848-anchor-ladder` diff --git a/research/frontier-engine/experiments/m8-sat-rail/ARTIFACT_SCHEMA.md b/research/frontier-engine/experiments/m8-sat-rail/ARTIFACT_SCHEMA.md new file mode 100644 index 0000000..140f487 --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/ARTIFACT_SCHEMA.md @@ -0,0 +1,48 @@ +# M8 Artifact Schema + +The first `frontier-engine` benchmark artifacts should be written as portable +JSON bundles so a CPU scaffold and a later CUDA rail can emit the same shape. + +## Top-level fields + +- `artifact_version` + - current value: `1` +- `run_id` + - benchmark-stamped unique identifier +- `created_at_utc` + - UTC timestamp in compact sortable format +- `benchmark` + - benchmark metadata for the run +- `hardware_profile` + - execution target metadata, starting with the Windows RTX 4090 profile +- `summary` + - compact run summary for quick comparison +- `generator_metadata` + - search strategy details and generation trace +- `elite_inventory` + - promoted rare structures kept for exact follow-up +- `frontier_items` + - explicit promoted frontier objects +- `verification_requests` + - exact work requests emitted from the frontier +- `verification_results` + - placeholder or exact verifier responses + +## Purpose + +This artifact shape matters because it gives us: + +- one stable interchange format across CPU and CUDA rails +- a reviewable record of why candidates were promoted +- a direct future ingest packet for SAT-facing verification work +- a claim-safe summary surface for `erdos-problems` + +## First invariant + +The CUDA rail should be free to change throughput and batching, but it should +not silently change: + +- candidate payload semantics +- the finite-gap metric +- the meaning of promoted inventory records +- the artifact bundle fields used by downstream exact tooling diff --git a/research/frontier-engine/experiments/m8-sat-rail/CANDIDATE_SCHEMA.md b/research/frontier-engine/experiments/m8-sat-rail/CANDIDATE_SCHEMA.md new file mode 100644 index 0000000..76dbc7e --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/CANDIDATE_SCHEMA.md @@ -0,0 +1,52 @@ +# M8 Candidate Schema + +The first benchmark-specific candidate should represent a proposed size-46 family +for the `M(8,3)` exactness rail. + +## Candidate payload + +- `benchmark_id` + - fixed value: `m8_sat_rail` +- `n` + - fixed value: `8` +- `k` + - fixed value: `3` +- `target_family_size` + - fixed value: `46` +- `family_masks` + - sorted unique bitmasks for the proposed family +- `family_size_histogram` + - counts of set sizes `0..8` +- `coverage_count` + - number of ground elements touched by the family +- `pair_intersection_histogram` + - histogram of pairwise intersection sizes +- `distinct_pair_intersections` + - number of distinct pairwise intersections seen +- `sunflower_triple_count` + - exact count of 3-sunflower triples inside the family +- `motif_signature` + - coarse summary used for rarity bucketing +- `signal_score` + - prototype structural-signal measure + +## Interpretation + +This candidate schema is useful because it contains: + +- enough structure for rarity and motif inventory +- a real finite gap (`sunflower_triple_count`) +- a direct path to an exact verifier bundle + +## Promotion rule + +The first prototype promotion rule should prefer candidates that combine: + +- low `sunflower_triple_count` +- high structural rarity +- high distinctness across pair intersections and set-size profile + +## Runtime note + +The current CPU scaffold and the future CUDA rail should both emit this exact +candidate shape. Throughput should change. Semantics should not. diff --git a/research/frontier-engine/experiments/m8-sat-rail/README.md b/research/frontier-engine/experiments/m8-sat-rail/README.md new file mode 100644 index 0000000..4d44963 --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/README.md @@ -0,0 +1,103 @@ +# M8 SAT Rail + +This experiment is the first concrete proving ground for `frontier-engine`. + +Target: + +- weak-sunflower exactness lane around `M(8,3)` +- exact question: whether the target-46 instance is unsatisfiable + +Why this benchmark: + +- the target is finite and exact +- the verifier backend is natural +- progress can be measured as a reduced exact frontier rather than vague search + motion +- it connects cleanly back to the problem `857` compute lane + +## Engine role + +`frontier-engine` should not try to replace the exact backend here. + +Instead, it should: + +- generate large volumes of candidate structures on GPU +- classify them by uniqueness and rarity +- inventory the rare, high-signal motifs +- promote only the elite subset into exact verification work + +## Current rail shape + +The first runnable rail now uses: + +- random seed families +- warm-start augmentation from the known size-45 lower-bound family +- mutation around the current elite families +- exact counting of `sunflower_triple_count` +- rarity and structural signal scoring +- export of elite verifier-facing bundles as JSON +- runtime selection across baseline Python and Torch-backed device execution + +This is still a scaffold, but it is now shaped like a real benchmark rail rather +than a generic placeholder. + +## Candidate shape + +The first candidate shape should be a proposed family of `46` subset bitmasks on +`[8]`. + +That means the prototype can already measure a useful exact-style gap: + +- `sunflower_triple_count` + +For this benchmark: + +- `sunflower_triple_count = 0` means the candidate family is already feasible +- lower counts mean the candidate is a better near-SAT prospect +- rarity and uniqueness should be used to decide which low-violation structures + deserve exact follow-up first + +## Desired benchmark metrics + +- candidates generated per second +- unique motif signatures discovered per batch +- elite inventory size after rarity filtering +- best `sunflower_triple_count` in batch +- verifier promotion rate +- fraction of promoted candidates that produce useful exact work +- reduction in unresolved exact frontier relative to a naive baseline + +## Primary hardware target + +- Windows RTX 4090 + +Profile: + +- [windows_rtx4090_search_profile.json](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/m8-sat-rail/windows_rtx4090_search_profile.json) + +## Exact handoff + +The rail now exports SAT-seed bundles for elite candidates. + +These are intentionally seed bundles, not witness certificates: + +- they preserve candidate families in SAT-friendly JSON +- they record observed `sunflower_triple_count` +- they are meant for exact follow-up, not for claiming success by themselves + +## Reference seed + +The current warm-start reference family is stored locally in: + +- [reference_m8_lower_bound_45.json](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/m8-sat-rail/reference_m8_lower_bound_45.json) + +The current default rail expands that known size-45 family into ranked size-46 +augmentations and uses the best augmentations as initial frontier seeds. + +## Later ingest path + +Once this rail earns trust, its promoted artifacts can be summarized back into: + +- sunflower compute lane notes +- problem `857` evidence +- governed `erdos-problems` ingest packets diff --git a/research/frontier-engine/experiments/m8-sat-rail/SAT_BUNDLE_SCHEMA.md b/research/frontier-engine/experiments/m8-sat-rail/SAT_BUNDLE_SCHEMA.md new file mode 100644 index 0000000..a7cbcfd --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/SAT_BUNDLE_SCHEMA.md @@ -0,0 +1,62 @@ +# M8 SAT Seed Bundle Schema + +The SAT-facing handoff for the first rail should be a seed bundle, not a +certificate bundle. + +Why: + +- elite families can be valuable exact inputs even when they still contain + sunflower violations +- a near-miss should not be mislabeled as a witness +- the seed bundle should preserve exact-work provenance without overstating what + has been proved + +## Bundle layout + +- `manifest.json` + - benchmark metadata + - run summary + - generator metadata + - ranked list of seed files +- `rank-XX-.json` + - one elite family per file + +## Seed file fields + +- `schema` + - fixed value: `frontier_engine.m8_sat_seed/1` +- `problem_id` + - current value: `857` +- `benchmark_id` + - current value: `m8_sat_rail` +- `n` + - current value: `8` +- `k` + - current value: `3` +- `family_size` + - current value: `46` +- `family` + - the candidate bitmask family +- `candidate_id` + - frontier-engine candidate identifier +- `source` + - current value: `frontier-engine` +- `observed_sunflower_triple_count` + - finite-gap metric at export time +- `motif_signature` + - rarity bucket summary +- `signal_score` + - structural signal score +- `rarity_score` + - rarity score at promotion time +- `uniqueness_rating` + - coarse promotion label + +## Interpretation + +These files are suitable for: + +- SAT-facing seed ingestion +- branch-order experiments +- exact local repair attempts +- witness verification only after a candidate reaches zero observed violations diff --git a/research/frontier-engine/experiments/m8-sat-rail/benchmark.json b/research/frontier-engine/experiments/m8-sat-rail/benchmark.json new file mode 100644 index 0000000..a7b66c0 --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/benchmark.json @@ -0,0 +1,17 @@ +{ + "benchmark_id": "m8_sat_rail", + "problem_id": "857", + "family": "sunflower", + "exact_target": "M(8,3) exactness / target-46 UNSAT route", + "backend": "sat", + "primary_hardware_profile": "windows_rtx4090", + "primary_goal": "Reduce the finite exact frontier before exact solving.", + "measures": [ + "candidates_per_second", + "unique_signatures_per_batch", + "elite_inventory_size", + "verifier_promotion_rate", + "useful_exact_followups", + "frontier_reduction_against_baseline" + ] +} diff --git a/research/frontier-engine/experiments/m8-sat-rail/reference_m8_lower_bound_45.json b/research/frontier-engine/experiments/m8-sat-rail/reference_m8_lower_bound_45.json new file mode 100644 index 0000000..8a19869 --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/reference_m8_lower_bound_45.json @@ -0,0 +1,59 @@ +{ + "benchmark_id": "m8_sat_rail", + "problem_id": "857", + "n": 8, + "k": 3, + "family_size": 45, + "family": [ + 14, + 19, + 25, + 38, + 42, + 44, + 69, + 79, + 95, + 96, + 103, + 107, + 109, + 119, + 123, + 125, + 133, + 143, + 146, + 152, + 159, + 167, + 171, + 173, + 183, + 187, + 189, + 195, + 196, + 201, + 206, + 211, + 217, + 222, + 223, + 230, + 234, + 236, + 246, + 247, + 250, + 251, + 252, + 253, + 255 + ], + "provenance": { + "label": "known_m8_lb45", + "note": "Improved size-45 construction via H* witness analysis.", + "source_path": "/Users/codymitchell/documents/code/sunflower-coda/repo/data/result_m_8_3_improved.json" + } +} diff --git a/research/frontier-engine/experiments/m8-sat-rail/windows_rtx4090_search_profile.json b/research/frontier-engine/experiments/m8-sat-rail/windows_rtx4090_search_profile.json new file mode 100644 index 0000000..c696b68 --- /dev/null +++ b/research/frontier-engine/experiments/m8-sat-rail/windows_rtx4090_search_profile.json @@ -0,0 +1,21 @@ +{ + "profile_id": "m8_sat_rail_windows_rtx4090_v1", + "benchmark_id": "m8_sat_rail", + "hardware_profile": "windows_rtx4090", + "generator": "m8_adaptive_mutation_sampler", + "runtime_mode": "auto", + "device": "auto", + "seed": 857, + "initial_batch_size": 64, + "generations": 5, + "parent_limit": 8, + "children_per_parent": 12, + "mutation_count": 3, + "random_injections": 16, + "notes": [ + "This is the first proving profile for the Windows RTX 4090 rig.", + "The current rail can resolve to Python or Torch depending on local capabilities.", + "On the target 4090 box, auto mode should resolve to Torch on CUDA.", + "The first Triton port should preserve these knobs so baseline and GPU runs stay directly comparable." + ] +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/BUNDLE_SCHEMA.md b/research/frontier-engine/experiments/p848-anchor-ladder/BUNDLE_SCHEMA.md new file mode 100644 index 0000000..2c2be03 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/BUNDLE_SCHEMA.md @@ -0,0 +1,70 @@ +# P848 Anchor Tail Seed Bundle Schema + +This bundle records candidate continuation tails for the anchor ladder route. + +It is a search bundle, not a theorem certificate. + +## Bundle purpose + +- rank continuations against the known failure ladder +- preserve direct scan summaries on a chosen frontier window +- export promising tails for deeper compute or proof-facing follow-up + +## Manifest fields + +- `bundle_version` +- `bundle_kind` +- `lane` +- `summary` +- `candidate_generation` +- `backend_metadata` +- `search_profile` +- `known_failure_packets` +- `observed_continuations` +- `candidate_files` + +## Candidate file fields + +- `schema` + - fixed value: `frontier_engine.p848_anchor_tail_seed/1` +- `lane_id` + - fixed value: `p848_anchor_ladder` +- `problem_id` + - fixed value: `848` +- `prefix_anchors` +- `continuation` +- `all_anchors` +- `known_packet_repairs` +- `repaired_known_packets` +- `missed_known_packets` +- `direct_scan` + - threshold + - max + - first failure if present + - clean-through + - witness counts +- `observed_frontier` + - frozen status already earned in the live frontier + - known first failure or clean-through +- `frontier_evidence` + - effective clean-through after merging frozen evidence with the latest direct scan + - effective first failure if one is known + - whether the live window was contiguous with prior evidence + +## Backend metadata + +The manifest now also records the runtime used to produce the bundle: + +- resolved runtime +- resolved device +- chunk sizes for batched scans +- runtime probe snapshot + +## Interpretation + +These seed files are suitable for: + +- deeper direct frontier scans +- batched GPU continuation comparisons +- CRT-family clustering around new failures +- theorem-facing route selection diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json b/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json new file mode 100644 index 0000000..dd12369 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json @@ -0,0 +1,58 @@ +{ + "shared_prefix": [7, 32, 57, 82, 132, 182], + "current_ladder": [ + { + "continuation": 157, + "status": "fails", + "repairs_known_packets": 2, + "first_failure_n": 19094395 + }, + { + "continuation": 232, + "status": "fails", + "repairs_known_packets": 3, + "first_failure_n": 27949928 + }, + { + "continuation": 282, + "status": "fails", + "repairs_known_packets": 4, + "first_failure_n": 137720141 + }, + { + "continuation": 332, + "status": "clean_through", + "repairs_known_packets": 5, + "direct_clean_through": 250000000 + } + ], + "current_best_continuation": 332, + "current_best_clean_through": 250000000, + "latest_live_shared_prefix_failure": 136702637, + "latest_live_family_menu": { + "known_failure_matches": 25, + "next_unmatched": 137720141, + "source_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/latest/SIX_PREFIX_TWENTY_FOUR_FAMILY_MENU.json" + }, + "family_aware_search_leader": { + "continuation": 432, + "repaired_known_packets": 26, + "repaired_predicted_families": 242, + "tested_clean_through": 250050000, + "source_path": "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/artifacts/p848-anchor-ladder/p848_anchor_ladder-seeds-20260406T020706Z/manifest.json" + }, + "notes": [ + "This is a recurrence candidate, not yet a theorem.", + "The theorem-facing question is whether +50 repairs arise from a stable obstruction menu rather than a long transient.", + "332 remains the strongest completed structured tail, while 432 is the current family-aware search leader on the tested 250000001..250050000 window.", + "The next unmatched six-prefix family representative is 137720141, which is also the known first failure of the 282 continuation.", + "The new shared-prefix failures at 127682743 and 136702637 introduced witness moduli 17161 = 131^2 and 1849 = 43^2, so the previous repaired square pool was not yet closed." + ], + "source_paths": [ + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md", + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_332_TAIL_OVERTAKE_LEDGER.md", + "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FRONTIER_NOTE.md", + "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/VERIFICATION_REGIMES.md", + "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/observed_continuations.json" + ] +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/README.md b/research/frontier-engine/experiments/p848-anchor-ladder/README.md new file mode 100644 index 0000000..747777c --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/README.md @@ -0,0 +1,136 @@ +# P848 Anchor Ladder Lane + +This lane is the first non-sunflower search rail implemented in `frontier-engine`. + +It targets the structured `+50` repair ladder that has emerged in the current +Problem 848 frontier workspace. + +## Why this belongs in the engine + +This is a good fit for GPU-assisted structured search because the engine can: + +- score many candidate continuations in parallel +- scan many `n` values for each continuation in parallel +- classify first-failure packets by recurring CRT-locked residue shapes +- rank which continuations are real structural repairs rather than transient wins + +## Current frontier snapshot + +Shared prefix: + +- `{7, 32, 57, 82, 132, 182}` + +Current completed ladder: + +- `157` fails at `19094395` +- `232` fails at `27949928` +- `282` fails at `137720141` +- `332` is clean through `250000000` + +That is very suggestive, but it is not yet a theorem. + +The live six-prefix classifier has now advanced farther than that frozen ladder: + +- the shared prefix has `24` known failures through `136702637` +- the rebuilt twenty-four-family menu recovers those failures with `25` matched + family rows because `84036163` still appears twice +- the next unmatched family representative is now `137720141` +- that next unmatched representative is also the known first failure of the + `282` continuation +- the newest packets at `127682743` and `136702637` introduced new witness + moduli `17161 = 131^2` and `1849 = 43^2`, so the previous repaired square + pool was not yet closed + +So the live theorem-facing question is no longer just “does `332` keep going?” +It is whether the apparent `+50` repair ladder is driven by a stable finite +obstruction menu or whether a later obstruction family eventually breaks the +pattern. + +## Candidate shape + +The first candidate shape for this lane should be: + +- shared anchor prefix plus one continuation tail + +For example: + +- `{7, 32, 57, 82, 132, 182, t}` + +## Finite-gap metric + +This lane does not optimize a sunflower count. It should optimize: + +- `direct_clean_through` +- `first_failure_n` +- `repaired_packet_count` +- `crt_locked_obstruction_count` + +Higher clean-through ranges and more repaired packets are better. + +## Engine role + +The engine should not claim the recurrence. + +Its job is to: + +- search continuations +- cluster failure packets +- detect repeated obstruction types +- surface the continuations that look theorem-worthy + +## Current runnable prototype + +The lane now supports: + +- ranking candidate continuations against the frozen failure ladder +- ingesting the live six-prefix frontier packet from `/tmp/erdos-problems-848-frontier` +- scoring continuations against the richest live six-prefix family menu +- merging frozen frontier evidence with new direct-scan windows +- skipping redundant scans when a continuation already has an earlier known failure +- generated ladder sweeps around the current best tail with perturbation offsets +- a Torch batch backend for many tails across many `n` values at once +- counting repaired known packets +- falling back to repo-owned live-frontier sync artifacts when `/tmp` is absent +- direct first-failure scans on a configurable finite frontier window +- export of ranked anchor-tail seed bundles + +Current CLI surface: + +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-live-frontier` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run-profile research/frontier-engine/experiments/p848-anchor-ladder/batched_smoke_profile.json` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run-profile research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run --runtime torch --device cuda --n-chunk-size 4096 --value-chunk-size 65536 --prime-square-chunk-size 256` +- `python3 research/frontier-engine/src/frontier_engine/cli.py p848-run --candidate-mode ladder-sweep --base-tail 332 --ladder-rounds 6 --perturb-offsets 0,-5,5` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-bundle` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-profile-bundle research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json` +- `python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-theorem-bridge` + +## Source frontier + +The current frozen frontier state is copied into: + +- [FRONTIER_STATE.json](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json) +- [observed_continuations.json](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/observed_continuations.json) +- [batched_smoke_profile.json](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/batched_smoke_profile.json) +- [windows_rtx4090_search_profile.json](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json) +- [live-frontier-sync/latest/README.md](/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/live-frontier-sync/latest/README.md) +- canonical pack bridge: [SEARCH_THEOREM_BRIDGE.md](/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md) + +The live supporting notes currently sit in: + +- `/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md` +- `/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_332_TAIL_OVERTAKE_LEDGER.md` + +Latest family-aware search signal: + +- `332` remains the strongest completed structured tail with contiguous evidence + through `250000000` +- the updated twenty-four-family menu shifts the current family-aware leader to + `432`; the latest 4090 ladder sweep orders the top finishers as `432`, `782`, + `832`, `332`, and `382` +- `432`, `782`, and `832` tie on repaired known packets, repaired + predicted-family rows, and tested clean-through on that window +- `282` now repairs the most predicted-family rows among those tails, but still + loses overall because it misses its own known obstruction packet at + `137720141` diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/batched_smoke_profile.json b/research/frontier-engine/experiments/p848-anchor-ladder/batched_smoke_profile.json new file mode 100644 index 0000000..c6772fc --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/batched_smoke_profile.json @@ -0,0 +1,27 @@ +{ + "profile_id": "p848_anchor_ladder_batched_smoke_v1", + "lane_id": "p848_anchor_ladder", + "hardware_profile": "local_or_windows", + "prefix_anchors": [7, 32, 57, 82, 132, 182], + "candidate_mode": "ladder-sweep", + "candidates": [], + "base_tail": 332, + "ladder_step": 50, + "ladder_rounds": 3, + "perturb_offsets": [0, -5, 5], + "direct_threshold": 250000001, + "direct_max": 250000500, + "top_k": 6, + "runtime_mode": "torch", + "device": "auto", + "search_backend": "batched_anchor_tail_scan", + "n_chunk_size": 2048, + "value_chunk_size": 32768, + "prime_square_chunk_size": 128, + "output_dir": "research/frontier-engine/artifacts/p848-anchor-ladder", + "candidate_scan_kind": "many_tails_many_n", + "notes": [ + "This is the quick smoke-test profile for the p848 batched backend.", + "It keeps the same candidate contract as the 4090 profile but on a much smaller direct window." + ] +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/benchmark.json b/research/frontier-engine/experiments/p848-anchor-ladder/benchmark.json new file mode 100644 index 0000000..3c21793 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/benchmark.json @@ -0,0 +1,12 @@ +{ + "lane_id": "p848_anchor_ladder", + "problem_id": "848", + "family": "number_theory", + "route_posture": "finite_check_gap_closure", + "search_objective": "Extend the +50 repair ladder and convert recurring finite repair into a structural explanation.", + "candidate_shape": "structured tail continuation {7,32,57,82,132,182,t}", + "finite_gap": "maximize direct_clean_through and explained_packet_repairs while minimizing unexplained first-failure packets", + "primary_hardware_profile": "windows_rtx4090", + "primary_backend": "batched_anchor_tail_scan", + "artifact_kind": "anchor_tail_seed_bundle" +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/brev_h100_search_profile.json b/research/frontier-engine/experiments/p848-anchor-ladder/brev_h100_search_profile.json new file mode 100644 index 0000000..37edbc6 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/brev_h100_search_profile.json @@ -0,0 +1,34 @@ +{ + "profile_id": "p848_anchor_ladder_brev_h100_v1", + "lane_id": "p848_anchor_ladder", + "hardware_profile": "brev_h100", + "prefix_anchors": [7, 32, 57, 82, 132, 182], + "candidate_mode": "ladder-sweep", + "candidates": [], + "base_tail": 332, + "ladder_step": 50, + "ladder_rounds": 18, + "perturb_offsets": [0, -10, -5, 5, 10], + "direct_threshold": 250000001, + "direct_max": 250075000, + "top_k": 16, + "runtime_mode": "torch", + "device": "auto", + "search_backend": "batched_anchor_tail_scan", + "n_chunk_size": 8192, + "value_chunk_size": 131072, + "prime_square_chunk_size": 512, + "output_dir": "research/frontier-engine/artifacts/p848-anchor-ladder", + "candidate_scan_kind": "many_tails_many_n", + "signal_objectives": [ + "maximize direct clean-through range", + "rank continuations by repaired packet count", + "cluster first failures by CRT-locked residue class", + "identify whether +50 steps escape a stable obstruction menu" + ], + "notes": [ + "This profile is tuned for a single high-VRAM Linux H100 instance on Brev.", + "It pushes the p848 ladder sweep wider than the 4090 profile while keeping the same artifact contract.", + "The goal is still frontier compression and structural packet discovery, not theorem claiming." + ] +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/known_failure_packets.json b/research/frontier-engine/experiments/p848-anchor-ladder/known_failure_packets.json new file mode 100644 index 0000000..f3a00b0 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/known_failure_packets.json @@ -0,0 +1,39 @@ +{ + "shared_prefix": [7, 32, 57, 82, 132, 182], + "current_best_continuation": 332, + "current_best_clean_through": 250000000, + "known_failure_packets": [ + { + "packet_id": "shared_prefix_2678425", + "n": 2678425, + "kind": "shared_prefix_failure", + "note": "First known failure of the shared six-anchor prefix." + }, + { + "packet_id": "shared_prefix_16293829", + "n": 16293829, + "kind": "shared_prefix_failure", + "note": "Second known failure of the shared six-anchor prefix." + }, + { + "packet_id": "shared_prefix_19094395", + "n": 19094395, + "kind": "shared_prefix_failure", + "note": "Third known failure of the shared six-anchor prefix." + }, + { + "packet_id": "tail_232_27949928", + "n": 27949928, + "kind": "tail_failure", + "tail": 232, + "note": "First known failure of the 232 continuation." + }, + { + "packet_id": "tail_282_137720141", + "n": 137720141, + "kind": "tail_failure", + "tail": 282, + "note": "First known failure of the 282 continuation." + } + ] +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/observed_continuations.json b/research/frontier-engine/experiments/p848-anchor-ladder/observed_continuations.json new file mode 100644 index 0000000..fb46266 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/observed_continuations.json @@ -0,0 +1,50 @@ +{ + "observed_continuations": [ + { + "continuation": 157, + "status": "fails", + "repaired_known_packets": 2, + "first_failure_n": 19094395, + "note": "Smallest-repair seven-anchor continuation; no longer the strongest structured tail.", + "source_paths": [ + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md", + "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json" + ] + }, + { + "continuation": 232, + "status": "fails", + "repaired_known_packets": 3, + "first_failure_n": 27949928, + "note": "First clean structured +50 tail after the shared six-anchor prefix, but it fails at 27949928.", + "source_paths": [ + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md", + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_SINGLETON_CRT_27949928_232tail.json", + "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json" + ] + }, + { + "continuation": 282, + "status": "fails", + "repaired_known_packets": 4, + "first_failure_n": 137720141, + "note": "Previous best completed structured tail before the 332 overtake.", + "source_paths": [ + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md", + "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json" + ] + }, + { + "continuation": 332, + "status": "clean_through", + "repaired_known_packets": 5, + "clean_through": 250000000, + "note": "Current strongest completed structured tail in the repo.", + "source_paths": [ + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md", + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_332_TAIL_OVERTAKE_LEDGER.md", + "/Volumes/Code_2TB/code/erdos-problems/research/frontier-engine/experiments/p848-anchor-ladder/FRONTIER_STATE.json" + ] + } + ] +} diff --git a/research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json b/research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json new file mode 100644 index 0000000..1eb3866 --- /dev/null +++ b/research/frontier-engine/experiments/p848-anchor-ladder/windows_rtx4090_search_profile.json @@ -0,0 +1,34 @@ +{ + "profile_id": "p848_anchor_ladder_windows_rtx4090_v1", + "lane_id": "p848_anchor_ladder", + "hardware_profile": "windows_rtx4090", + "prefix_anchors": [7, 32, 57, 82, 132, 182], + "candidate_mode": "ladder-sweep", + "candidates": [], + "base_tail": 332, + "ladder_step": 50, + "ladder_rounds": 10, + "perturb_offsets": [0, -5, 5], + "direct_threshold": 250000001, + "direct_max": 250050000, + "top_k": 12, + "runtime_mode": "torch", + "device": "auto", + "search_backend": "batched_anchor_tail_scan", + "n_chunk_size": 4096, + "value_chunk_size": 65536, + "prime_square_chunk_size": 256, + "output_dir": "research/frontier-engine/artifacts/p848-anchor-ladder", + "candidate_scan_kind": "many_tails_many_n", + "signal_objectives": [ + "maximize direct clean-through range", + "rank continuations by repaired packet count", + "cluster first failures by CRT-locked residue class", + "identify whether +50 steps escape a stable obstruction menu" + ], + "notes": [ + "This lane is ideal for GPU batching because many tail continuations can be scanned across many n values in parallel.", + "The first implementation target is batched continuation scoring, not theorem claiming.", + "The exact objective is to turn the observed repair ladder into a stable structural menu of obstruction packets." + ] +} diff --git a/research/frontier-engine/hardware/legacy_multi_gpu_reference.json b/research/frontier-engine/hardware/legacy_multi_gpu_reference.json new file mode 100644 index 0000000..affc331 --- /dev/null +++ b/research/frontier-engine/hardware/legacy_multi_gpu_reference.json @@ -0,0 +1,10 @@ +{ + "profile_id": "legacy_multi_gpu_reference", + "os": "mixed", + "gpu": "multi_gpu_reference", + "role": "historical_scaling_reference", + "notes": [ + "Historical systems may have assumed larger aggregate GPU volume.", + "Keep those assumptions as scale-up notes rather than prototype requirements." + ] +} diff --git a/research/frontier-engine/hardware/windows_rtx4090.json b/research/frontier-engine/hardware/windows_rtx4090.json new file mode 100644 index 0000000..ca258cd --- /dev/null +++ b/research/frontier-engine/hardware/windows_rtx4090.json @@ -0,0 +1,11 @@ +{ + "profile_id": "windows_rtx4090", + "os": "windows", + "gpu": "RTX 4090", + "role": "primary_cuda_prototype", + "notes": [ + "Treat this as the first-class CUDA development box.", + "Prove the search rail here before adding heavier orchestration.", + "Use this profile to tune batch size, chunking, and search throughput." + ] +} diff --git a/research/frontier-engine/pyproject.toml b/research/frontier-engine/pyproject.toml new file mode 100644 index 0000000..bd39d06 --- /dev/null +++ b/research/frontier-engine/pyproject.toml @@ -0,0 +1,26 @@ +[build-system] +requires = ["setuptools>=68"] +build-backend = "setuptools.build_meta" + +[project] +name = "frontier-engine" +version = "0.1.0" +description = "Prototype scaffold for GPU-assisted frontier search with exact verification hooks." +readme = "README.md" +requires-python = ">=3.10" +authors = [ + { name = "Cody Mitchell" } +] +dependencies = [] + +[project.optional-dependencies] +torch = ["torch>=2.8"] + +[project.scripts] +frontier-engine = "frontier_engine.cli:main" + +[tool.setuptools] +package-dir = {"" = "src"} + +[tool.setuptools.packages.find] +where = ["src"] diff --git a/research/frontier-engine/src/frontier_engine/__init__.py b/research/frontier-engine/src/frontier_engine/__init__.py new file mode 100644 index 0000000..6f38ffd --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/__init__.py @@ -0,0 +1,21 @@ +"""Prototype package scaffold for frontier-engine.""" + +from .contracts import Candidate, FrontierItem, InventoryRecord, ScoreBundle, VerificationRequest, VerificationResult +from .lanes import LaneSpec, get_lane_spec, list_lane_specs +from .pipeline import FrontierPipeline +from .runtime import RuntimeProbe, probe_runtime + +__all__ = [ + "Candidate", + "FrontierItem", + "FrontierPipeline", + "InventoryRecord", + "LaneSpec", + "RuntimeProbe", + "ScoreBundle", + "VerificationRequest", + "VerificationResult", + "get_lane_spec", + "list_lane_specs", + "probe_runtime", +] diff --git a/research/frontier-engine/src/frontier_engine/artifacts.py b/research/frontier-engine/src/frontier_engine/artifacts.py new file mode 100644 index 0000000..1b408a8 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/artifacts.py @@ -0,0 +1,57 @@ +"""Artifact serialization for benchmark search runs.""" + +from __future__ import annotations + +from dataclasses import asdict, is_dataclass +from datetime import datetime, timezone +import json +from pathlib import Path +from typing import Any + + +def _serialize(value: Any) -> Any: + """Convert dataclasses and paths into JSON-safe structures.""" + + if is_dataclass(value): + return _serialize(asdict(value)) + if isinstance(value, dict): + return {str(key): _serialize(item) for key, item in value.items()} + if isinstance(value, list): + return [_serialize(item) for item in value] + if isinstance(value, tuple): + return [_serialize(item) for item in value] + if isinstance(value, Path): + return str(value) + return value + + +def write_run_artifact( + *, + report: dict[str, Any], + output_dir: Path, + benchmark: dict[str, Any], + hardware: dict[str, Any], +) -> Path: + """Write a portable JSON artifact for a benchmark search run.""" + + timestamp = datetime.now(timezone.utc).strftime("%Y%m%dT%H%M%SZ") + run_id = f"{benchmark['benchmark_id']}-{timestamp}" + output_dir.mkdir(parents=True, exist_ok=True) + artifact_path = output_dir / f"{run_id}.json" + + artifact = { + "artifact_version": 1, + "run_id": run_id, + "created_at_utc": timestamp, + "benchmark": benchmark, + "hardware_profile": hardware, + "summary": report["summary"], + "generator_metadata": report.get("generator_metadata", {}), + "elite_inventory": report.get("inventory_records", []), + "frontier_items": report.get("frontier_items", []), + "verification_requests": report.get("verification_requests", []), + "verification_results": report.get("verification_results", []), + } + + artifact_path.write_text(json.dumps(_serialize(artifact), indent=2) + "\n", encoding="utf-8") + return artifact_path diff --git a/research/frontier-engine/src/frontier_engine/benchmarks/__init__.py b/research/frontier-engine/src/frontier_engine/benchmarks/__init__.py new file mode 100644 index 0000000..84e1225 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/benchmarks/__init__.py @@ -0,0 +1 @@ +"""Benchmark-specific helpers for frontier-engine.""" diff --git a/research/frontier-engine/src/frontier_engine/benchmarks/m8_sat_rail.py b/research/frontier-engine/src/frontier_engine/benchmarks/m8_sat_rail.py new file mode 100644 index 0000000..2f90129 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/benchmarks/m8_sat_rail.py @@ -0,0 +1,178 @@ +"""Benchmark helpers for the M(8,3) SAT rail.""" + +from __future__ import annotations + +from collections import Counter +from itertools import combinations + +from frontier_engine.contracts import Candidate + + +N = 8 +K = 3 +TARGET_FAMILY_SIZE = 46 +ALL_MASKS = list(range(1 << N)) + + +def subset_size(mask: int) -> int: + """Return the number of set bits in a mask.""" + + return mask.bit_count() if hasattr(int, "bit_count") else bin(mask).count("1") + + +def is_3_sunflower(a: int, b: int, c: int) -> bool: + """Weak/non-uniform 3-sunflower test for bitmasks.""" + + ab = a & b + return (a & c) == ab and (b & c) == ab + + +def size_histogram(family_masks: list[int]) -> list[int]: + """Count family members by subset size.""" + + hist = [0] * (N + 1) + for mask in family_masks: + hist[subset_size(mask)] += 1 + return hist + + +def pair_intersection_histogram(family_masks: list[int]) -> list[int]: + """Count pairwise intersections by intersection size.""" + + hist = [0] * (N + 1) + for left, right in combinations(family_masks, 2): + hist[subset_size(left & right)] += 1 + return hist + + +def coverage_count(family_masks: list[int]) -> int: + """Count how many ground elements appear somewhere in the family.""" + + union_mask = 0 + for mask in family_masks: + union_mask |= mask + return subset_size(union_mask) + + +def sunflower_triple_count(family_masks: list[int]) -> int: + """Count exact 3-sunflower violations in the family.""" + + total = 0 + for a, b, c in combinations(family_masks, 3): + if is_3_sunflower(a, b, c): + total += 1 + return total + + +def motif_signature( + family_masks: list[int], + *, + size_hist: list[int], + pair_hist: list[int], + sunflower_violations: int, +) -> str: + """Create a coarse signature for rarity bucketing.""" + + size_key = ".".join(str(value) for value in size_hist) + pair_key = ".".join(str(value) for value in pair_hist[:5]) + violation_bucket = sunflower_violations // 25 + return f"size={size_key}|pair={pair_key}|viol={violation_bucket}" + + +def structural_signal_score( + family_masks: list[int], + *, + size_hist: list[int], + pair_hist: list[int], + sunflower_violations: int, +) -> float: + """Prototype structural-signal measure for the benchmark.""" + + size_support = sum(1 for value in size_hist if value > 0) + pair_support = sum(1 for value in pair_hist if value > 0) + distinct_intersections = len({left & right for left, right in combinations(family_masks, 2)}) + feasibility = 1.0 / (1.0 + sunflower_violations / 50.0) + diversity = (size_support + pair_support + distinct_intersections / 10.0) / 20.0 + return feasibility + diversity + + +def build_candidate_from_metrics( + candidate_id: str, + family_masks: list[int], + *, + size_hist: list[int], + pair_hist: list[int], + coverage: int, + distinct_pair_intersections: int, + sunflower_violations: int, +) -> Candidate: + """Build a candidate once exact metrics have already been computed.""" + + sorted_masks = sorted(set(family_masks)) + if len(sorted_masks) != len(family_masks): + raise ValueError("family_masks must be unique") + if len(sorted_masks) != TARGET_FAMILY_SIZE: + raise ValueError( + f"family_masks must contain exactly {TARGET_FAMILY_SIZE} masks; " + f"got {len(sorted_masks)}" + ) + + signal = structural_signal_score( + sorted_masks, + size_hist=size_hist, + pair_hist=pair_hist, + sunflower_violations=sunflower_violations, + ) + + signature = motif_signature( + sorted_masks, + size_hist=size_hist, + pair_hist=pair_hist, + sunflower_violations=sunflower_violations, + ) + + return Candidate( + candidate_id=candidate_id, + payload={ + "benchmark_id": "m8_sat_rail", + "n": N, + "k": K, + "target_family_size": TARGET_FAMILY_SIZE, + "family_masks": sorted_masks, + "family_size_histogram": size_hist, + "coverage_count": coverage, + "pair_intersection_histogram": pair_hist, + "distinct_pair_intersections": distinct_pair_intersections, + "sunflower_triple_count": sunflower_violations, + "motif_signature": signature, + "signal_score": signal, + }, + source="m8_sat_rail", + tags=["benchmark:m8_sat_rail", "family_candidate", "sunflower"], + ) + + +def build_candidate(candidate_id: str, family_masks: list[int]) -> Candidate: + """Build a benchmark-aligned candidate payload.""" + + sorted_masks = sorted(set(family_masks)) + if len(sorted_masks) != len(family_masks): + raise ValueError("family_masks must be unique") + if len(sorted_masks) != TARGET_FAMILY_SIZE: + raise ValueError( + f"family_masks must contain exactly {TARGET_FAMILY_SIZE} masks; " + f"got {len(sorted_masks)}" + ) + + size_hist = size_histogram(sorted_masks) + pair_hist = pair_intersection_histogram(sorted_masks) + violations = sunflower_triple_count(sorted_masks) + return build_candidate_from_metrics( + candidate_id, + sorted_masks, + size_hist=size_hist, + pair_hist=pair_hist, + coverage=coverage_count(sorted_masks), + distinct_pair_intersections=len({left & right for left, right in combinations(sorted_masks, 2)}), + sunflower_violations=violations, + ) diff --git a/research/frontier-engine/src/frontier_engine/cli.py b/research/frontier-engine/src/frontier_engine/cli.py new file mode 100644 index 0000000..ba40a68 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/cli.py @@ -0,0 +1,596 @@ +"""CLI entrypoint for the frontier-engine prototype.""" + +from __future__ import annotations + +import argparse +import json +from pathlib import Path +import sys + +if __package__ in {None, ""}: + sys.path.insert(0, str(Path(__file__).resolve().parents[1])) + from frontier_engine.artifacts import write_run_artifact + from frontier_engine.lanes import get_lane_spec, list_lane_specs + from frontier_engine.m8_search import M8SatRailAdaptiveSampler, M8SearchConfig + from frontier_engine.p848_anchor_search import ( + P848SearchConfig, + load_live_p848_frontier_snapshot, + load_p848_search_profile, + parse_candidate_csv, + parse_int_csv, + run_p848_anchor_search, + ) + from frontier_engine.p848_bundle import write_p848_anchor_seed_bundle + from frontier_engine.p848_theorem_bridge import write_p848_theorem_bridge + from frontier_engine.pipeline import FrontierPipeline + from frontier_engine.plans import PRIMARY_BENCHMARK, PRIMARY_HARDWARE, PRIMARY_SEARCH_PROFILE + from frontier_engine.runtime import probe_runtime + from frontier_engine.verifier_bundle import write_m8_sat_seed_bundle +else: + from .artifacts import write_run_artifact + from .lanes import get_lane_spec, list_lane_specs + from .m8_search import M8SatRailAdaptiveSampler, M8SearchConfig + from .p848_anchor_search import ( + P848SearchConfig, + load_live_p848_frontier_snapshot, + load_p848_search_profile, + parse_candidate_csv, + parse_int_csv, + run_p848_anchor_search, + ) + from .p848_bundle import write_p848_anchor_seed_bundle + from .p848_theorem_bridge import write_p848_theorem_bridge + from .pipeline import FrontierPipeline + from .plans import PRIMARY_BENCHMARK, PRIMARY_HARDWARE, PRIMARY_SEARCH_PROFILE + from .runtime import probe_runtime + from .verifier_bundle import write_m8_sat_seed_bundle + + +def build_parser() -> argparse.ArgumentParser: + parser = argparse.ArgumentParser(prog="frontier-engine") + subparsers = parser.add_subparsers(dest="command", required=True) + + for command in ("status", "vision", "benchmark-plan", "runtime-probe", "p848-live-frontier"): + subparsers.add_parser(command) + + list_lanes_parser = subparsers.add_parser("list-lanes") + list_lanes_parser.add_argument("--json", action="store_true", dest="as_json") + + show_lane_parser = subparsers.add_parser("show-lane") + show_lane_parser.add_argument("lane_id") + show_lane_parser.add_argument("--json", action="store_true", dest="as_json") + + p848_run_profile_parser = subparsers.add_parser("p848-run-profile") + p848_run_profile_parser.add_argument("profile_file") + + p848_export_profile_parser = subparsers.add_parser("export-p848-profile-bundle") + p848_export_profile_parser.add_argument("profile_file") + + p848_run_parser = subparsers.add_parser("p848-run") + p848_run_parser.add_argument( + "--prefix-anchors", + default="7,32,57,82,132,182", + help="Comma-separated shared prefix anchors.", + ) + p848_run_parser.add_argument( + "--candidates", + default="157,232,282,332,382,432", + help="Comma-separated continuation candidates.", + ) + p848_run_parser.add_argument( + "--candidate-mode", + choices=["explicit", "hybrid", "ladder-sweep"], + default="explicit", + help="Use explicit candidates, a generated ladder sweep, or both.", + ) + p848_run_parser.add_argument( + "--base-tail", + type=int, + help="Base continuation for generated ladder sweeps. Defaults to the current best observed tail.", + ) + p848_run_parser.add_argument( + "--ladder-step", + type=int, + default=50, + help="Step size for generated ladder continuations.", + ) + p848_run_parser.add_argument( + "--ladder-rounds", + type=int, + default=0, + help="Number of forward ladder steps to generate from the base tail.", + ) + p848_run_parser.add_argument( + "--perturb-offsets", + default="0", + help="Comma-separated offsets added around each generated ladder center.", + ) + p848_run_parser.add_argument( + "--runtime", + choices=["auto", "python", "torch"], + default="auto", + help="Backend runtime for the p848 lane.", + ) + p848_run_parser.add_argument( + "--device", + choices=["auto", "cpu", "cuda"], + default="auto", + help="Requested device for the selected p848 runtime.", + ) + p848_run_parser.add_argument( + "--n-chunk-size", + type=int, + default=2048, + help="How many n values to scan per batched backend chunk.", + ) + p848_run_parser.add_argument( + "--value-chunk-size", + type=int, + default=32768, + help="How many candidate values to squarefree-test per backend chunk.", + ) + p848_run_parser.add_argument( + "--prime-square-chunk-size", + type=int, + default=128, + help="How many prime squares to test per squarefree subchunk.", + ) + p848_run_parser.add_argument( + "--direct-threshold", + type=int, + default=250000001, + help="Direct scan threshold for candidate tails.", + ) + p848_run_parser.add_argument( + "--direct-max", + type=int, + default=250020000, + help="Direct scan maximum for candidate tails.", + ) + p848_run_parser.add_argument("--top-k", type=int, default=8) + + p848_export_parser = subparsers.add_parser("export-p848-bundle") + p848_export_parser.add_argument( + "--prefix-anchors", + default="7,32,57,82,132,182", + help="Comma-separated shared prefix anchors.", + ) + p848_export_parser.add_argument( + "--candidates", + default="157,232,282,332,382,432", + help="Comma-separated continuation candidates.", + ) + p848_export_parser.add_argument( + "--candidate-mode", + choices=["explicit", "hybrid", "ladder-sweep"], + default="explicit", + help="Use explicit candidates, a generated ladder sweep, or both.", + ) + p848_export_parser.add_argument( + "--base-tail", + type=int, + help="Base continuation for generated ladder sweeps. Defaults to the current best observed tail.", + ) + p848_export_parser.add_argument( + "--ladder-step", + type=int, + default=50, + help="Step size for generated ladder continuations.", + ) + p848_export_parser.add_argument( + "--ladder-rounds", + type=int, + default=0, + help="Number of forward ladder steps to generate from the base tail.", + ) + p848_export_parser.add_argument( + "--perturb-offsets", + default="0", + help="Comma-separated offsets added around each generated ladder center.", + ) + p848_export_parser.add_argument( + "--runtime", + choices=["auto", "python", "torch"], + default="auto", + help="Backend runtime for the p848 lane.", + ) + p848_export_parser.add_argument( + "--device", + choices=["auto", "cpu", "cuda"], + default="auto", + help="Requested device for the selected p848 runtime.", + ) + p848_export_parser.add_argument( + "--n-chunk-size", + type=int, + default=2048, + help="How many n values to scan per batched backend chunk.", + ) + p848_export_parser.add_argument( + "--value-chunk-size", + type=int, + default=32768, + help="How many candidate values to squarefree-test per backend chunk.", + ) + p848_export_parser.add_argument( + "--prime-square-chunk-size", + type=int, + default=128, + help="How many prime squares to test per squarefree subchunk.", + ) + p848_export_parser.add_argument( + "--direct-threshold", + type=int, + default=250000001, + help="Direct scan threshold for candidate tails.", + ) + p848_export_parser.add_argument( + "--direct-max", + type=int, + default=250020000, + help="Direct scan maximum for candidate tails.", + ) + p848_export_parser.add_argument("--top-k", type=int, default=8) + p848_export_parser.add_argument( + "--output-dir", + default="research/frontier-engine/artifacts/p848-anchor-ladder", + help="Directory for exported p848 seed bundles.", + ) + + p848_bridge_parser = subparsers.add_parser("export-p848-theorem-bridge") + p848_bridge_parser.add_argument( + "--prefix-anchors", + default="7,32,57,82,132,182", + help="Comma-separated shared prefix anchors.", + ) + p848_bridge_parser.add_argument( + "--candidates", + default="157,232,282,332,382,432,782,832", + help="Comma-separated continuation tails for the theorem bridge matrix.", + ) + p848_bridge_parser.add_argument( + "--runtime", + choices=["auto", "python", "torch"], + default="python", + help="Backend runtime used to build the tracked-tail matrix.", + ) + p848_bridge_parser.add_argument( + "--device", + choices=["auto", "cpu", "cuda"], + default="auto", + help="Requested device for the theorem-bridge tracked-tail run.", + ) + p848_bridge_parser.add_argument( + "--n-chunk-size", + type=int, + default=2048, + help="How many n values to scan per batched backend chunk.", + ) + p848_bridge_parser.add_argument( + "--value-chunk-size", + type=int, + default=32768, + help="How many candidate values to squarefree-test per backend chunk.", + ) + p848_bridge_parser.add_argument( + "--prime-square-chunk-size", + type=int, + default=128, + help="How many prime squares to test per squarefree subchunk.", + ) + p848_bridge_parser.add_argument( + "--direct-threshold", + type=int, + default=250000001, + help="Direct scan threshold for tracked tails.", + ) + p848_bridge_parser.add_argument( + "--direct-max", + type=int, + default=250050000, + help="Direct scan maximum for tracked tails.", + ) + p848_bridge_parser.add_argument("--top-k", type=int, default=8) + p848_bridge_parser.add_argument( + "--output-json", + default="packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.json", + help="Destination JSON file in the canonical 848 pack.", + ) + p848_bridge_parser.add_argument( + "--output-md", + default="packs/number-theory/problems/848/SEARCH_THEOREM_BRIDGE.md", + help="Destination Markdown file in the canonical 848 pack.", + ) + p848_bridge_parser.add_argument( + "--gpu-manifest", + help="Optional explicit p848 GPU bundle manifest to cite instead of the latest one.", + ) + + for command in ("prototype-run", "export-m8-bundle", "export-m8-sat-bundle"): + command_parser = subparsers.add_parser(command) + command_parser.add_argument( + "--runtime", + choices=["auto", "python", "torch"], + default=PRIMARY_SEARCH_PROFILE["runtime_mode"], + ) + command_parser.add_argument( + "--device", + choices=["auto", "cpu", "cuda"], + default=PRIMARY_SEARCH_PROFILE["device"], + ) + command_parser.add_argument( + "--warm-start", + choices=["none", "known_m8_lb45"], + default=PRIMARY_SEARCH_PROFILE["warm_start"], + ) + command_parser.add_argument( + "--warm-start-count", + type=int, + default=PRIMARY_SEARCH_PROFILE["warm_start_count"], + ) + command_parser.add_argument("--seed", type=int, default=PRIMARY_SEARCH_PROFILE["seed"]) + command_parser.add_argument( + "--initial-batch-size", + type=int, + default=PRIMARY_SEARCH_PROFILE["initial_batch_size"], + ) + command_parser.add_argument( + "--generations", + type=int, + default=PRIMARY_SEARCH_PROFILE["generations"], + ) + command_parser.add_argument( + "--parent-limit", + type=int, + default=PRIMARY_SEARCH_PROFILE["parent_limit"], + ) + command_parser.add_argument( + "--children-per-parent", + type=int, + default=PRIMARY_SEARCH_PROFILE["children_per_parent"], + ) + command_parser.add_argument( + "--mutation-count", + type=int, + default=PRIMARY_SEARCH_PROFILE["mutation_count"], + ) + command_parser.add_argument( + "--random-injections", + type=int, + default=PRIMARY_SEARCH_PROFILE["random_injections"], + ) + + export_parser = subparsers.choices["export-m8-bundle"] + export_parser.add_argument( + "--output-dir", + default="research/frontier-engine/artifacts/m8-sat-rail", + help="Directory for exported JSON run artifacts.", + ) + sat_export_parser = subparsers.choices["export-m8-sat-bundle"] + sat_export_parser.add_argument( + "--output-dir", + default="research/frontier-engine/artifacts/m8-sat-seeds", + help="Directory for exported SAT-seed bundles.", + ) + return parser + + +def build_pipeline(args: argparse.Namespace) -> FrontierPipeline: + config = M8SearchConfig( + seed=args.seed, + runtime=args.runtime, + device=args.device, + warm_start=args.warm_start, + warm_start_count=args.warm_start_count, + initial_batch_size=args.initial_batch_size, + generations=args.generations, + parent_limit=args.parent_limit, + children_per_parent=args.children_per_parent, + mutation_count=args.mutation_count, + random_injections=args.random_injections, + ) + return FrontierPipeline(generator=M8SatRailAdaptiveSampler(config=config)) + + +def build_p848_config(args: argparse.Namespace) -> P848SearchConfig: + return P848SearchConfig( + prefix_anchors=parse_candidate_csv(args.prefix_anchors), + candidates=parse_candidate_csv(args.candidates), + direct_threshold=args.direct_threshold, + direct_max=args.direct_max, + top_k=args.top_k, + candidate_mode=args.candidate_mode, + base_tail=args.base_tail, + ladder_step=args.ladder_step, + ladder_rounds=args.ladder_rounds, + perturb_offsets=parse_int_csv(args.perturb_offsets, allow_empty=True), + runtime=args.runtime, + device=args.device, + n_chunk_size=args.n_chunk_size, + value_chunk_size=args.value_chunk_size, + prime_square_chunk_size=args.prime_square_chunk_size, + ) + + +def load_profile_config(profile_file: str) -> tuple[P848SearchConfig, dict[str, object]]: + return load_p848_search_profile(Path(profile_file)) + + +def main() -> None: + parser = build_parser() + args = parser.parse_args() + + if args.command == "status": + print("frontier-engine: scaffolded") + print("mode: build-first, prove-first") + print("integration: not yet wired into erdos-problems") + return + + if args.command == "prototype-run": + report = build_pipeline(args).run_once_report() + print(json.dumps(report["summary"], indent=2)) + print(json.dumps(report["generator_metadata"], indent=2)) + return + + if args.command == "vision": + print("frontier-engine loop:") + print("random generation -> uniqueness scoring -> rare-structure inventory -> exact follow-up") + return + + if args.command == "benchmark-plan": + print("primary benchmark:", PRIMARY_BENCHMARK["benchmark_id"]) + print("exact target:", PRIMARY_BENCHMARK["exact_target"]) + print("backend:", PRIMARY_BENCHMARK["backend"]) + print("goal:", PRIMARY_BENCHMARK["primary_goal"]) + print("hardware profile:", PRIMARY_HARDWARE["profile_id"]) + print("hardware gpu:", PRIMARY_HARDWARE["gpu"]) + print("hardware os:", PRIMARY_HARDWARE["os"]) + print("search strategy:", PRIMARY_SEARCH_PROFILE["generator"]) + print("search mode:", PRIMARY_SEARCH_PROFILE["runtime_mode"]) + print("search device:", PRIMARY_SEARCH_PROFILE["device"]) + print("warm start:", PRIMARY_SEARCH_PROFILE["warm_start"]) + print("warm start count:", PRIMARY_SEARCH_PROFILE["warm_start_count"]) + print("batch size:", PRIMARY_SEARCH_PROFILE["initial_batch_size"]) + print("generations:", PRIMARY_SEARCH_PROFILE["generations"]) + return + + if args.command == "runtime-probe": + print(json.dumps(probe_runtime().to_dict(), indent=2)) + return + + if args.command == "p848-live-frontier": + snapshot = load_live_p848_frontier_snapshot() + print(json.dumps(snapshot, indent=2)) + return + + if args.command == "list-lanes": + if args.as_json: + print(json.dumps([lane.to_dict() for lane in list_lane_specs()], indent=2)) + return + for lane in list_lane_specs(): + print(f"{lane.lane_id}: problem {lane.problem_id} | {lane.status}") + return + + if args.command == "show-lane": + lane = get_lane_spec(args.lane_id) + if args.as_json: + print(json.dumps(lane.to_dict(), indent=2)) + return + print("lane:", lane.lane_id) + print("problem:", lane.problem_id) + print("family:", lane.family) + print("status:", lane.status) + print("route posture:", lane.route_posture) + print("objective:", lane.search_objective) + print("candidate shape:", lane.candidate_shape) + print("finite gap:", lane.finite_gap) + print("hardware:", lane.primary_hardware_profile) + print("artifact kind:", lane.artifact_kind) + print("experiment dir:", lane.experiment_dir) + print("frontier:", json.dumps(lane.frontier_summary, indent=2)) + return + + if args.command == "p848-run": + report = run_p848_anchor_search(build_p848_config(args)) + print(json.dumps(report["summary"], indent=2)) + print(json.dumps(report["top_candidates"], indent=2)) + return + + if args.command == "p848-run-profile": + config, profile = load_profile_config(args.profile_file) + report = run_p848_anchor_search(config) + print("profile_id:", profile.get("profile_id")) + print(json.dumps(report["summary"], indent=2)) + print(json.dumps(report["top_candidates"], indent=2)) + return + + if args.command == "export-p848-bundle": + report = run_p848_anchor_search(build_p848_config(args)) + bundle_dir = write_p848_anchor_seed_bundle( + report=report, + output_dir=Path(args.output_dir), + top_k=args.top_k, + ) + print("p848_seed_bundle:", bundle_dir) + print(json.dumps(report["summary"], indent=2)) + return + + if args.command == "export-p848-profile-bundle": + config, profile = load_profile_config(args.profile_file) + output_dir = Path( + str( + profile.get( + "output_dir", + "research/frontier-engine/artifacts/p848-anchor-ladder", + ) + ) + ) + report = run_p848_anchor_search(config) + bundle_dir = write_p848_anchor_seed_bundle( + report=report, + output_dir=output_dir, + top_k=config.top_k, + ) + print("profile_id:", profile.get("profile_id")) + print("p848_seed_bundle:", bundle_dir) + print(json.dumps(report["summary"], indent=2)) + return + + if args.command == "export-p848-theorem-bridge": + config = P848SearchConfig( + prefix_anchors=parse_candidate_csv(args.prefix_anchors), + candidates=parse_candidate_csv(args.candidates), + direct_threshold=args.direct_threshold, + direct_max=args.direct_max, + top_k=args.top_k, + candidate_mode="explicit", + base_tail=None, + ladder_step=50, + ladder_rounds=0, + perturb_offsets=[0], + runtime=args.runtime, + device=args.device, + n_chunk_size=args.n_chunk_size, + value_chunk_size=args.value_chunk_size, + prime_square_chunk_size=args.prime_square_chunk_size, + ) + report = run_p848_anchor_search(config) + output_paths = write_p848_theorem_bridge( + report=report, + output_json_path=Path(args.output_json), + output_md_path=Path(args.output_md), + gpu_manifest_path=(Path(args.gpu_manifest) if args.gpu_manifest else None), + ) + print("p848_theorem_bridge_json:", output_paths["json_path"]) + print("p848_theorem_bridge_md:", output_paths["md_path"]) + print(json.dumps(report["summary"], indent=2)) + return + + if args.command == "export-m8-bundle": + report = build_pipeline(args).run_once_report() + artifact_path = write_run_artifact( + report=report, + output_dir=Path(args.output_dir), + benchmark=PRIMARY_BENCHMARK, + hardware=PRIMARY_HARDWARE, + ) + print("artifact:", artifact_path) + print(json.dumps(report["summary"], indent=2)) + return + + if args.command == "export-m8-sat-bundle": + report = build_pipeline(args).run_once_report() + bundle_dir = write_m8_sat_seed_bundle( + report=report, + output_dir=Path(args.output_dir), + benchmark=PRIMARY_BENCHMARK, + ) + print("sat_seed_bundle:", bundle_dir) + print(json.dumps(report["summary"], indent=2)) + return + + parser.error(f"unknown command: {args.command}") + + +if __name__ == "__main__": + main() diff --git a/research/frontier-engine/src/frontier_engine/contracts.py b/research/frontier-engine/src/frontier_engine/contracts.py new file mode 100644 index 0000000..4cc0a94 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/contracts.py @@ -0,0 +1,70 @@ +"""Core logical contracts for the frontier-engine prototype.""" + +from __future__ import annotations + +from dataclasses import dataclass, field +from typing import Any + + +@dataclass +class Candidate: + """A search object emitted by a generator.""" + + candidate_id: str + payload: dict[str, Any] + source: str = "generator" + tags: list[str] = field(default_factory=list) + + +@dataclass +class ScoreBundle: + """Heuristic and surrogate scores attached to a candidate.""" + + candidate_id: str + promise: float + rarity: float | None = None + hardness: float | None = None + diversity: float | None = None + metadata: dict[str, Any] = field(default_factory=dict) + + +@dataclass +class InventoryRecord: + """A promoted rare-structure record retained for exact follow-up.""" + + candidate: Candidate + rarity_score: float + uniqueness_rating: str + signal_score: float + notes: dict[str, Any] = field(default_factory=dict) + + +@dataclass +class FrontierItem: + """A retained candidate plus bookkeeping metadata.""" + + candidate: Candidate + scores: ScoreBundle + retained_reason: str + generation: int = 0 + + +@dataclass +class VerificationRequest: + """An exact-work request emitted by the frontier manager.""" + + request_id: str + candidate_id: str + payload: dict[str, Any] + backend: str + + +@dataclass +class VerificationResult: + """The exact verifier's response.""" + + request_id: str + candidate_id: str + status: str + proof_artifact: str | None = None + metadata: dict[str, Any] = field(default_factory=dict) diff --git a/research/frontier-engine/src/frontier_engine/frontier.py b/research/frontier-engine/src/frontier_engine/frontier.py new file mode 100644 index 0000000..3958fa3 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/frontier.py @@ -0,0 +1,49 @@ +"""Frontier management for frontier-engine.""" + +from __future__ import annotations + +from .contracts import Candidate, FrontierItem, InventoryRecord, ScoreBundle + + +class FrontierManager: + """Retain a small, explicit frontier instead of a raw candidate heap.""" + + def retain(self, candidates: list[Candidate], scores: list[ScoreBundle]) -> list[FrontierItem]: + items: list[FrontierItem] = [] + score_lookup = {score.candidate_id: score for score in scores} + + for candidate in candidates: + score = score_lookup[candidate.candidate_id] + items.append( + FrontierItem( + candidate=candidate, + scores=score, + retained_reason="prototype_frontier", + ) + ) + + items.sort(key=lambda item: item.scores.promise, reverse=True) + return items + + def retain_inventory(self, records: list[InventoryRecord]) -> list[FrontierItem]: + """Promote elite inventory items into frontier items for exact follow-up.""" + + items = [ + FrontierItem( + candidate=record.candidate, + scores=ScoreBundle( + candidate_id=record.candidate.candidate_id, + promise=float(record.notes.get("promise", record.rarity_score)), + rarity=record.rarity_score, + metadata={ + "inventory": True, + "uniqueness_rating": record.uniqueness_rating, + "signal_score": record.signal_score, + }, + ), + retained_reason="rare_structure_inventory", + ) + for record in records + ] + items.sort(key=lambda item: item.scores.promise, reverse=True) + return items diff --git a/research/frontier-engine/src/frontier_engine/generator.py b/research/frontier-engine/src/frontier_engine/generator.py new file mode 100644 index 0000000..71ec98d --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/generator.py @@ -0,0 +1,21 @@ +"""Generator interfaces for frontier-engine.""" + +from __future__ import annotations + +from typing import Protocol + +from .contracts import Candidate + + +class CandidateGenerator(Protocol): + """Emit raw candidates for the search loop.""" + + def generate(self) -> list[Candidate]: + """Return a batch of candidates.""" + + +class NullGenerator: + """Placeholder generator until a real GPU-backed implementation lands.""" + + def generate(self) -> list[Candidate]: + return [] diff --git a/research/frontier-engine/src/frontier_engine/inventory.py b/research/frontier-engine/src/frontier_engine/inventory.py new file mode 100644 index 0000000..2f54862 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/inventory.py @@ -0,0 +1,44 @@ +"""Rare-structure inventory for prototype frontier-engine.""" + +from __future__ import annotations + +from .contracts import Candidate, InventoryRecord, ScoreBundle + + +class InventoryManager: + """Retain only the rarest and strongest structures from a stream.""" + + def __init__(self, limit: int = 8) -> None: + self.limit = limit + + def collect(self, candidates: list[Candidate], scores: list[ScoreBundle]) -> list[InventoryRecord]: + score_lookup = {score.candidate_id: score for score in scores} + records: list[InventoryRecord] = [] + + for candidate in candidates: + score = score_lookup[candidate.candidate_id] + records.append( + InventoryRecord( + candidate=candidate, + rarity_score=float(score.rarity or 0.0), + uniqueness_rating=str(score.metadata.get("uniqueness_rating", "unknown")), + signal_score=float(score.metadata.get("signal_score", 0.0)), + notes={ + "promise": score.promise, + "signature": score.metadata.get("signature"), + "signature_count": score.metadata.get("signature_count"), + "sunflower_triple_count": score.metadata.get("sunflower_triple_count"), + "feasibility_score": score.metadata.get("feasibility_score"), + }, + ) + ) + + records.sort( + key=lambda record: ( + float(record.notes.get("feasibility_score", 0.0)), + record.rarity_score, + record.signal_score, + ), + reverse=True, + ) + return records[: self.limit] diff --git a/research/frontier-engine/src/frontier_engine/lanes.py b/research/frontier-engine/src/frontier_engine/lanes.py new file mode 100644 index 0000000..63a006f --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/lanes.py @@ -0,0 +1,105 @@ +"""Lane registry for frontier-engine.""" + +from __future__ import annotations + +from dataclasses import asdict, dataclass, field +from pathlib import Path +from typing import Any + + +@dataclass +class LaneSpec: + """A named search lane that frontier-engine can support.""" + + lane_id: str + problem_id: str + family: str + route_posture: str + search_objective: str + candidate_shape: str + finite_gap: str + primary_hardware_profile: str + artifact_kind: str + status: str + experiment_dir: str + evidence_paths: list[str] = field(default_factory=list) + frontier_summary: dict[str, Any] = field(default_factory=dict) + + def to_dict(self) -> dict[str, Any]: + return asdict(self) + + +REPO_ROOT = Path(__file__).resolve().parents[2] + + +LANE_REGISTRY = { + "m8_sat_rail": LaneSpec( + lane_id="m8_sat_rail", + problem_id="857", + family="sunflower", + route_posture="exactness_reduction", + search_objective="Reduce the exact M(8,3) target-46 frontier before exact solving.", + candidate_shape="size-46 family on [8]", + finite_gap="sunflower_triple_count", + primary_hardware_profile="windows_rtx4090", + artifact_kind="m8_sat_seed_bundle", + status="active_proving_ground", + experiment_dir=str(REPO_ROOT / "experiments" / "m8-sat-rail"), + evidence_paths=[ + str(REPO_ROOT / "experiments" / "m8-sat-rail" / "README.md"), + str(REPO_ROOT / "experiments" / "m8-sat-rail" / "reference_m8_lower_bound_45.json"), + ], + frontier_summary={ + "current_best_observed_sunflower_triple_count": 3, + "default_warm_start": "known_m8_lb45", + }, + ), + "p848_anchor_ladder": LaneSpec( + lane_id="p848_anchor_ladder", + problem_id="848", + family="number_theory", + route_posture="finite_check_gap_closure", + search_objective=( + "Extend the +50 repair ladder and determine whether recurring repairs arise " + "from a stable structural obstruction menu." + ), + candidate_shape="structured tail continuation {7,32,57,82,132,182,t}", + finite_gap="maximize direct_clean_through and explained_packet_repairs", + primary_hardware_profile="windows_rtx4090", + artifact_kind="anchor_tail_seed_bundle", + status="runnable_cpu_prototype", + experiment_dir=str(REPO_ROOT / "experiments" / "p848-anchor-ladder"), + evidence_paths=[ + str(REPO_ROOT / "experiments" / "p848-anchor-ladder" / "README.md"), + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_TAIL_COMPARISON_157_232_282.md", + "/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848/ANCHOR_332_TAIL_OVERTAKE_LEDGER.md", + "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/FRONTIER_NOTE.md", + ], + frontier_summary={ + "shared_prefix": [7, 32, 57, 82, 132, 182], + "known_ladder": { + "157": {"status": "fails", "first_failure_n": 19094395}, + "232": {"status": "fails", "first_failure_n": 27949928}, + "282": {"status": "fails", "first_failure_n": 137720141}, + "332": {"status": "clean_through", "direct_clean_through": 250000000}, + }, + "current_best_continuation": 332, + "default_direct_window": [250000001, 250020000], + }, + ), +} + + +def list_lane_specs() -> list[LaneSpec]: + """Return all configured lane specifications.""" + + return [LANE_REGISTRY[key] for key in sorted(LANE_REGISTRY)] + + +def get_lane_spec(lane_id: str) -> LaneSpec: + """Return one lane specification by id.""" + + try: + return LANE_REGISTRY[lane_id] + except KeyError as exc: + raise KeyError(f"unknown lane: {lane_id}") from exc diff --git a/research/frontier-engine/src/frontier_engine/m8_backends.py b/research/frontier-engine/src/frontier_engine/m8_backends.py new file mode 100644 index 0000000..17af0cc --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/m8_backends.py @@ -0,0 +1,338 @@ +"""Backend implementations for the M(8,3) search rail.""" + +from __future__ import annotations + +from itertools import combinations +import random +from typing import Any, Protocol + +from .benchmarks.m8_sat_rail import ( + ALL_MASKS, + N, + TARGET_FAMILY_SIZE, + build_candidate, + build_candidate_from_metrics, +) +from .contracts import Candidate +from .runtime import RuntimeProbe, probe_runtime, resolve_device, resolve_runtime_mode + +try: + import torch + import torch.nn.functional as torch_functional +except ImportError: # pragma: no cover - optional dependency + torch = None + torch_functional = None + + +class M8SearchBackend(Protocol): + """Backend contract for runtime-specific family generation and evaluation.""" + + def initial_family_pool(self, count: int, *, seed_families: list[tuple[int, ...]] | None = None) -> Any: + """Return an initial family pool.""" + + def expand_from_parents( + self, + parents: list[Candidate], + *, + children_per_parent: int, + mutation_count: int, + random_injections: int, + ) -> Any: + """Return the next generation family pool.""" + + def evaluate_generation( + self, + *, + generation: int, + family_pool: Any, + seen_families: set[tuple[int, ...]], + ) -> list[Candidate]: + """Evaluate the current pool into concrete candidates.""" + + def metadata(self) -> dict[str, object]: + """Return runtime metadata for artifact logs.""" + + +class PythonM8SearchBackend: + """Pure-Python baseline backend.""" + + def __init__(self, *, seed: int, probe: RuntimeProbe) -> None: + self.random = random.Random(seed) + self.seed = seed + self.probe = probe + + def initial_family_pool( + self, + count: int, + *, + seed_families: list[tuple[int, ...]] | None = None, + ) -> list[tuple[int, ...]]: + seeds = list(seed_families or []) + remaining = max(0, count - len(seeds)) + return seeds + [self._random_family() for _ in range(remaining)] + + def expand_from_parents( + self, + parents: list[Candidate], + *, + children_per_parent: int, + mutation_count: int, + random_injections: int, + ) -> list[tuple[int, ...]]: + pool = [tuple(parent.payload["family_masks"]) for parent in parents] + for parent in parents: + family = tuple(parent.payload["family_masks"]) + for _ in range(children_per_parent): + pool.append(self._mutate_family(family, mutation_count)) + for _ in range(random_injections): + pool.append(self._random_family()) + return pool + + def evaluate_generation( + self, + *, + generation: int, + family_pool: list[tuple[int, ...]], + seen_families: set[tuple[int, ...]], + ) -> list[Candidate]: + candidates: list[Candidate] = [] + for index, family in enumerate(family_pool): + canonical_family = tuple(sorted(family)) + if canonical_family in seen_families: + continue + seen_families.add(canonical_family) + candidates.append( + build_candidate( + candidate_id=f"m8-g{generation}-c{index}", + family_masks=list(canonical_family), + ) + ) + return candidates + + def metadata(self) -> dict[str, object]: + return { + "resolved_runtime": "python", + "resolved_device": "cpu", + "probe": self.probe.to_dict(), + } + + def _random_family(self) -> tuple[int, ...]: + return tuple(sorted(self.random.sample(ALL_MASKS, TARGET_FAMILY_SIZE))) + + def _mutate_family(self, family: tuple[int, ...], mutation_count: int) -> tuple[int, ...]: + if mutation_count <= 0: + return family + + indices = self.random.sample(range(TARGET_FAMILY_SIZE), min(mutation_count, TARGET_FAMILY_SIZE)) + family_list = list(family) + existing_masks = set(family_list) + available_masks = [mask for mask in ALL_MASKS if mask not in existing_masks] + replacements = self.random.sample(available_masks, len(indices)) + + for index, replacement in zip(indices, replacements): + family_list[index] = replacement + + return tuple(sorted(family_list)) + + +class TorchM8SearchBackend: + """Torch-backed backend that can run on CPU or CUDA.""" + + def __init__(self, *, seed: int, device: str, probe: RuntimeProbe) -> None: + if torch is None or torch_functional is None: # pragma: no cover - guarded by runtime probe + raise RuntimeError("Torch backend requested, but torch is not installed") + + self.device = device + self.seed = seed + self.probe = probe + generator_device = "cuda" if device == "cuda" else "cpu" + self.generator = torch.Generator(device=generator_device) + self.generator.manual_seed(seed) + + self.size_lookup = torch.tensor( + [mask.bit_count() if hasattr(int, "bit_count") else bin(mask).count("1") for mask in ALL_MASKS], + dtype=torch.int64, + device=self.device, + ) + pair_indices = list(combinations(range(TARGET_FAMILY_SIZE), 2)) + triple_indices = list(combinations(range(TARGET_FAMILY_SIZE), 3)) + self.pair_left_idx = torch.tensor([left for left, _ in pair_indices], dtype=torch.int64, device=self.device) + self.pair_right_idx = torch.tensor([right for _, right in pair_indices], dtype=torch.int64, device=self.device) + self.triple_a_idx = torch.tensor([a for a, _, _ in triple_indices], dtype=torch.int64, device=self.device) + self.triple_b_idx = torch.tensor([b for _, b, _ in triple_indices], dtype=torch.int64, device=self.device) + self.triple_c_idx = torch.tensor([c for _, _, c in triple_indices], dtype=torch.int64, device=self.device) + + def initial_family_pool( + self, + count: int, + *, + seed_families: list[tuple[int, ...]] | None = None, + ) -> "torch.Tensor": + parts: list[torch.Tensor] = [] + seeds = list(seed_families or []) + if seeds: + parts.append(torch.tensor(seeds, dtype=torch.int64, device=self.device)) + remaining = max(0, count - len(seeds)) + if remaining > 0: + parts.append(self._sample_random_families(remaining)) + if not parts: + return torch.empty((0, TARGET_FAMILY_SIZE), dtype=torch.int64, device=self.device) + return torch.cat(parts, dim=0) + + def expand_from_parents( + self, + parents: list[Candidate], + *, + children_per_parent: int, + mutation_count: int, + random_injections: int, + ) -> "torch.Tensor": + parent_rows = [parent.payload["family_masks"] for parent in parents] + parts: list[torch.Tensor] = [] + + if parent_rows: + parts.append(torch.tensor(parent_rows, dtype=torch.int64, device=self.device)) + mutated_children: list[torch.Tensor] = [] + for row in parent_rows: + family = torch.tensor(row, dtype=torch.int64, device=self.device) + for _ in range(children_per_parent): + mutated_children.append(self._mutate_family(family, mutation_count)) + if mutated_children: + parts.append(torch.stack(mutated_children)) + + if random_injections > 0: + parts.append(self._sample_random_families(random_injections)) + + if not parts: + return torch.empty((0, TARGET_FAMILY_SIZE), dtype=torch.int64, device=self.device) + return torch.cat(parts, dim=0) + + def evaluate_generation( + self, + *, + generation: int, + family_pool: "torch.Tensor", + seen_families: set[tuple[int, ...]], + ) -> list[Candidate]: + family_rows = family_pool.detach().cpu().tolist() + unique_rows: list[list[int]] = [] + row_indices: list[int] = [] + + for index, row in enumerate(family_rows): + canonical_family = tuple(sorted(int(mask) for mask in row)) + if canonical_family in seen_families: + continue + seen_families.add(canonical_family) + unique_rows.append(list(canonical_family)) + row_indices.append(index) + + if not unique_rows: + return [] + + families = torch.tensor(unique_rows, dtype=torch.int64, device=self.device) + metrics = self._evaluate_metrics(families) + size_histories = metrics["size_histograms"].cpu().tolist() + pair_histories = metrics["pair_histograms"].cpu().tolist() + coverages = metrics["coverage_counts"].cpu().tolist() + distinct_counts = metrics["distinct_pair_intersections"].cpu().tolist() + violation_counts = metrics["sunflower_triple_counts"].cpu().tolist() + + candidates: list[Candidate] = [] + for local_index, family in enumerate(unique_rows): + candidates.append( + build_candidate_from_metrics( + candidate_id=f"m8-g{generation}-c{row_indices[local_index]}", + family_masks=family, + size_hist=[int(value) for value in size_histories[local_index]], + pair_hist=[int(value) for value in pair_histories[local_index]], + coverage=int(coverages[local_index]), + distinct_pair_intersections=int(distinct_counts[local_index]), + sunflower_violations=int(violation_counts[local_index]), + ) + ) + return candidates + + def metadata(self) -> dict[str, object]: + return { + "resolved_runtime": "torch", + "resolved_device": self.device, + "probe": self.probe.to_dict(), + } + + def _sample_random_families(self, count: int) -> "torch.Tensor": + if count <= 0: + return torch.empty((0, TARGET_FAMILY_SIZE), dtype=torch.int64, device=self.device) + scores = torch.rand((count, len(ALL_MASKS)), generator=self.generator, device=self.device) + families = torch.topk(scores, TARGET_FAMILY_SIZE, dim=1).indices.to(torch.int64) + return torch.sort(families, dim=1).values + + def _mutate_family(self, family: "torch.Tensor", mutation_count: int) -> "torch.Tensor": + if mutation_count <= 0: + return family.clone() + + child = family.clone() + actual_mutation_count = min(mutation_count, TARGET_FAMILY_SIZE) + positions = torch.randperm( + TARGET_FAMILY_SIZE, + generator=self.generator, + device=self.device, + )[:actual_mutation_count] + replacement_scores = torch.rand(len(ALL_MASKS), generator=self.generator, device=self.device) + replacement_scores[child] = -1.0 + replacements = torch.topk(replacement_scores, actual_mutation_count).indices.to(torch.int64) + child[positions] = replacements + return torch.sort(child).values + + def _evaluate_metrics(self, families: "torch.Tensor") -> dict[str, "torch.Tensor"]: + subset_sizes = self.size_lookup[families] + size_histograms = torch_functional.one_hot(subset_sizes, num_classes=N + 1).sum(dim=1) + + pair_left = families[:, self.pair_left_idx] + pair_right = families[:, self.pair_right_idx] + pair_intersections = pair_left.bitwise_and(pair_right) + pair_sizes = self.size_lookup[pair_intersections] + pair_histograms = torch_functional.one_hot(pair_sizes, num_classes=N + 1).sum(dim=1) + + sorted_intersections = torch.sort(pair_intersections, dim=1).values + distinct_pair_intersections = torch.ones( + (families.shape[0],), dtype=torch.int64, device=self.device + ) + if sorted_intersections.shape[1] > 1: + distinct_pair_intersections += ( + sorted_intersections[:, 1:] != sorted_intersections[:, :-1] + ).sum(dim=1) + + union_masks = families[:, 0].clone() + for column in range(1, TARGET_FAMILY_SIZE): + union_masks = union_masks.bitwise_or(families[:, column]) + coverage_counts = self.size_lookup[union_masks] + + triple_a = families[:, self.triple_a_idx] + triple_b = families[:, self.triple_b_idx] + triple_c = families[:, self.triple_c_idx] + ab = triple_a.bitwise_and(triple_b) + sunflower_triple_counts = ( + ((triple_a.bitwise_and(triple_c) == ab) & (triple_b.bitwise_and(triple_c) == ab)) + .sum(dim=1) + .to(torch.int64) + ) + + return { + "size_histograms": size_histograms.to(torch.int64), + "pair_histograms": pair_histograms.to(torch.int64), + "coverage_counts": coverage_counts.to(torch.int64), + "distinct_pair_intersections": distinct_pair_intersections.to(torch.int64), + "sunflower_triple_counts": sunflower_triple_counts, + } + + +def build_m8_search_backend(*, runtime_mode: str, device: str, seed: int) -> M8SearchBackend: + """Build the requested backend for the current runtime environment.""" + + probe = probe_runtime() + resolved_runtime = resolve_runtime_mode(runtime_mode, probe) + resolved_device = resolve_device(device, resolved_runtime, probe) + + if resolved_runtime == "torch": + return TorchM8SearchBackend(seed=seed, device=resolved_device, probe=probe) + return PythonM8SearchBackend(seed=seed, probe=probe) diff --git a/research/frontier-engine/src/frontier_engine/m8_search.py b/research/frontier-engine/src/frontier_engine/m8_search.py new file mode 100644 index 0000000..6671972 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/m8_search.py @@ -0,0 +1,139 @@ +"""Benchmark-specific rail search for the M(8,3) proving ground.""" + +from __future__ import annotations + +from dataclasses import dataclass, asdict + +from .contracts import Candidate +from .generator import CandidateGenerator +from .m8_backends import M8SearchBackend, build_m8_search_backend +from .m8_warm_start import build_warm_start_bundle + + +@dataclass +class M8SearchConfig: + """Tunable search knobs for the first local M(8,3) rail.""" + + seed: int = 857 + runtime: str = "auto" + device: str = "auto" + warm_start: str = "known_m8_lb45" + warm_start_count: int = 32 + initial_batch_size: int = 64 + generations: int = 5 + parent_limit: int = 8 + children_per_parent: int = 12 + mutation_count: int = 3 + random_injections: int = 16 + + def to_dict(self) -> dict[str, int]: + """Return a JSON-friendly config payload.""" + + return asdict(self) + + +class M8SatRailAdaptiveSampler(CandidateGenerator): + """Mutation-guided generator for the M(8,3) benchmark rail.""" + + def __init__(self, config: M8SearchConfig | None = None) -> None: + self.config = config or M8SearchConfig() + self.backend: M8SearchBackend = build_m8_search_backend( + runtime_mode=self.config.runtime, + device=self.config.device, + seed=self.config.seed, + ) + self.last_run_metadata: dict[str, object] = {} + + def generate(self) -> list[Candidate]: + seen_families: set[tuple[int, ...]] = set() + all_candidates: list[Candidate] = [] + global_elite: dict[tuple[int, ...], Candidate] = {} + warm_start_bundle = build_warm_start_bundle( + self.config.warm_start, + self.config.warm_start_count, + ) + current_pool = self.backend.initial_family_pool( + self.config.initial_batch_size, + seed_families=warm_start_bundle.families, + ) + best_trace: list[int] = [] + generation_summaries: list[dict[str, object]] = [] + + for generation in range(self.config.generations): + evaluated = self.backend.evaluate_generation( + generation=generation, + family_pool=current_pool, + seen_families=seen_families, + ) + if not evaluated: + break + + all_candidates.extend(evaluated) + ranked = sorted(evaluated, key=self._rank_key) + for candidate in ranked: + family_key = tuple(candidate.payload["family_masks"]) + incumbent = global_elite.get(family_key) + if incumbent is None or self._rank_key(candidate) < self._rank_key(incumbent): + global_elite[family_key] = candidate + + elite_ranked = sorted(global_elite.values(), key=self._rank_key) + parents = elite_ranked[: self.config.parent_limit] + generation_best_candidate = ranked[0] + best_candidate = parents[0] + best_trace.append(int(best_candidate.payload["sunflower_triple_count"])) + generation_summaries.append( + { + "generation": generation, + "evaluated_candidates": len(evaluated), + "generation_best_candidate_id": generation_best_candidate.candidate_id, + "generation_best_sunflower_triple_count": int( + generation_best_candidate.payload["sunflower_triple_count"] + ), + "generation_best_signal_score": float( + generation_best_candidate.payload["signal_score"] + ), + "best_candidate_id": best_candidate.candidate_id, + "best_sunflower_triple_count": int( + best_candidate.payload["sunflower_triple_count"] + ), + "best_signal_score": float(best_candidate.payload["signal_score"]), + } + ) + + if generation == self.config.generations - 1: + break + + current_pool = self.backend.expand_from_parents( + parents, + children_per_parent=self.config.children_per_parent, + mutation_count=self.config.mutation_count, + random_injections=self.config.random_injections, + ) + + best_candidate = min(all_candidates, key=self._rank_key) if all_candidates else None + self.last_run_metadata = { + "search_strategy": "m8_adaptive_mutation_sampler", + "benchmark_id": "m8_sat_rail", + "config": self.config.to_dict(), + "unique_candidates": len(all_candidates), + "generations_completed": len(generation_summaries), + "best_sunflower_trace": best_trace, + "best_candidate_id": best_candidate.candidate_id if best_candidate else None, + "best_sunflower_triple_count": ( + int(best_candidate.payload["sunflower_triple_count"]) if best_candidate else None + ), + "generation_summaries": generation_summaries, + "runtime": self.backend.metadata(), + "warm_start": warm_start_bundle.metadata, + } + return all_candidates + + @staticmethod + def _rank_key(candidate: Candidate) -> tuple[float, float, float, str]: + payload = candidate.payload + return ( + float(payload["sunflower_triple_count"]), + -float(payload["signal_score"]), + -float(payload["distinct_pair_intersections"]), + candidate.candidate_id, + ) diff --git a/research/frontier-engine/src/frontier_engine/m8_warm_start.py b/research/frontier-engine/src/frontier_engine/m8_warm_start.py new file mode 100644 index 0000000..d8da322 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/m8_warm_start.py @@ -0,0 +1,89 @@ +"""Warm-start helpers for the M(8,3) benchmark rail.""" + +from __future__ import annotations + +from dataclasses import asdict, dataclass +import json +from pathlib import Path +from typing import Any + +from .benchmarks.m8_sat_rail import ALL_MASKS, TARGET_FAMILY_SIZE, build_candidate + + +REPO_ROOT = Path(__file__).resolve().parents[2] +REFERENCE_FAMILY_PATH = ( + REPO_ROOT / "experiments" / "m8-sat-rail" / "reference_m8_lower_bound_45.json" +) + + +@dataclass +class WarmStartBundle: + """Warm-start families plus the metadata needed to explain them.""" + + families: list[tuple[int, ...]] + metadata: dict[str, Any] + + def to_dict(self) -> dict[str, Any]: + return { + "families": [list(family) for family in self.families], + "metadata": self.metadata, + } + + +def build_warm_start_bundle(mode: str, count: int) -> WarmStartBundle: + """Return warm-start families for the requested mode.""" + + if mode == "none" or count <= 0: + return WarmStartBundle( + families=[], + metadata={"mode": "none", "seed_count": 0}, + ) + if mode != "known_m8_lb45": + raise ValueError(f"unknown warm-start mode: {mode}") + + reference_doc = json.loads(REFERENCE_FAMILY_PATH.read_text(encoding="utf-8")) + base_family = tuple(sorted(int(mask) for mask in reference_doc["family"])) + if len(base_family) != 45: + raise ValueError("reference warm-start family must contain 45 masks") + + candidates: list[tuple[int, int, float, tuple[int, ...]]] = [] + base_set = set(base_family) + for add_mask in ALL_MASKS: + if add_mask in base_set: + continue + family = tuple(sorted(base_set | {add_mask})) + if len(family) != TARGET_FAMILY_SIZE: + raise ValueError("augmented warm-start family must contain 46 masks") + candidate = build_candidate(f"warm-start-{add_mask}", list(family)) + candidates.append( + ( + int(candidate.payload["sunflower_triple_count"]), + int(add_mask), + -float(candidate.payload["signal_score"]), + family, + ) + ) + + candidates.sort() + selected = candidates[:count] + families = [family for _, _, _, family in selected] + top_additions = [ + { + "added_mask": add_mask, + "sunflower_triple_count": violations, + } + for violations, add_mask, _, _ in selected[:10] + ] + + return WarmStartBundle( + families=families, + metadata={ + "mode": mode, + "reference_family_path": str(REFERENCE_FAMILY_PATH), + "reference_family_size": len(base_family), + "seed_count": len(families), + "best_observed_sunflower_triple_count": selected[0][0] if selected else None, + "top_additions": top_additions, + "provenance": reference_doc.get("provenance", {}), + }, + ) diff --git a/research/frontier-engine/src/frontier_engine/p848_anchor_search.py b/research/frontier-engine/src/frontier_engine/p848_anchor_search.py new file mode 100644 index 0000000..ce99818 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/p848_anchor_search.py @@ -0,0 +1,1084 @@ +"""Runnable search surface for the Problem 848 anchor ladder lane.""" + +from __future__ import annotations + +from dataclasses import asdict, dataclass, field +import json +import os +from pathlib import Path +from typing import Any + +from .p848_torch_backend import evaluate_p848_candidates_torch +from .runtime import probe_runtime, resolve_device, resolve_runtime_mode + + +REPO_ROOT = Path(__file__).resolve().parents[2] +KNOWN_FAILURE_PACKET_PATH = ( + REPO_ROOT / "experiments" / "p848-anchor-ladder" / "known_failure_packets.json" +) +OBSERVED_CONTINUATION_PATH = ( + REPO_ROOT / "experiments" / "p848-anchor-ladder" / "observed_continuations.json" +) +TMP_FRONTIER_ROOT = Path("/tmp/erdos-problems-848-frontier/packs/number-theory/problems/848") +SYNC_FRONTIER_ROOT = REPO_ROOT / "experiments" / "p848-anchor-ladder" / "live-frontier-sync" +EXPECTED_SHARED_PREFIX = (7, 32, 57, 82, 132, 182) + + +@dataclass +class P848KnownFailurePacket: + """A frozen frontier failure packet used to score repair power.""" + + packet_id: str + n: int + kind: str + tail: int | None = None + note: str | None = None + + +@dataclass +class P848ObservedContinuation: + """Observed frontier evidence for a concrete continuation tail.""" + + continuation: int + status: str + repaired_known_packets: int + first_failure_n: int | None = None + clean_through: int | None = None + note: str | None = None + source_paths: list[str] = field(default_factory=list) + + +@dataclass +class P848SearchConfig: + """Configuration for anchor-tail continuation ranking.""" + + prefix_anchors: list[int] + candidates: list[int] + direct_threshold: int + direct_max: int + top_k: int = 8 + candidate_mode: str = "explicit" + base_tail: int | None = None + ladder_step: int = 50 + ladder_rounds: int = 0 + perturb_offsets: list[int] = field(default_factory=list) + runtime: str = "auto" + device: str = "auto" + n_chunk_size: int = 2048 + value_chunk_size: int = 32768 + prime_square_chunk_size: int = 128 + profile_id: str | None = None + profile_path: str | None = None + + def to_dict(self) -> dict[str, Any]: + return asdict(self) + + +class SquarefreeOracle: + """Reusable squarefreeness and factorization helper.""" + + MAX_CACHE_SIZE = 200000 + + def __init__(self, max_value: int) -> None: + self.primes = self._build_prime_list(int(max_value**0.5) + 1) + self.squarefree_cache: dict[int, bool] = {} + + @staticmethod + def _build_prime_list(limit: int) -> list[int]: + sieve = bytearray(limit + 1) + primes: list[int] = [] + for n in range(2, limit + 1): + if sieve[n]: + continue + primes.append(n) + step = n + start = n * n + for value in range(start, limit + 1, step): + sieve[value] = 1 + return primes + + def is_squarefree(self, n: int) -> bool: + cached = self.squarefree_cache.get(n) + if cached is not None: + return cached + + x = n + for prime in self.primes: + if prime * prime > x: + break + if x % prime != 0: + continue + x //= prime + if x % prime == 0: + self._remember(n, False) + return False + while x % prime == 0: + x //= prime + self._remember(n, True) + return True + + def factor_exponents(self, n: int) -> list[dict[str, int]]: + x = n + factors: list[dict[str, int]] = [] + for prime in self.primes: + if prime * prime > x: + break + if x % prime != 0: + continue + exponent = 0 + while x % prime == 0: + x //= prime + exponent += 1 + factors.append({"prime": prime, "exponent": exponent}) + if x > 1: + factors.append({"prime": x, "exponent": 1}) + return factors + + def _remember(self, key: int, value: bool) -> None: + if len(self.squarefree_cache) >= self.MAX_CACHE_SIZE: + self.squarefree_cache.clear() + self.squarefree_cache[key] = value + + +def load_known_failure_packets() -> dict[str, Any]: + """Load the frozen frontier failure ladder for Problem 848.""" + + return json.loads(KNOWN_FAILURE_PACKET_PATH.read_text(encoding="utf-8")) + + +def _load_json_if_exists(path: Path) -> dict[str, Any] | None: + """Load a JSON document when the file exists and parses cleanly.""" + + if not path.exists(): + return None + try: + return json.loads(path.read_text(encoding="utf-8")) + except (OSError, json.JSONDecodeError): + return None + + +def _matches_expected_prefix(anchors: list[int] | tuple[int, ...]) -> bool: + """Check whether a packet targets the shared six-anchor prefix.""" + + return tuple(int(anchor) for anchor in anchors) == EXPECTED_SHARED_PREFIX + + +def _summarize_family_menu(menu_doc: dict[str, Any], *, path: Path) -> dict[str, Any]: + """Extract the live repair hierarchy from a six-prefix family menu.""" + + repair_anchor_counts: dict[str, dict[str, int]] = {} + for anchor in menu_doc.get("parameters", {}).get("repairAnchors", []): + repair_anchor_counts[str(int(anchor))] = {"repairs": 0, "fails": 0} + + next_unmatched = None + for family in menu_doc.get("families", []): + if next_unmatched is None and not bool(family.get("matchesKnownFailure")): + next_unmatched = int(family["representative"]) + for row in family.get("repairRows", []): + anchor_key = str(int(row["anchor"])) + bucket = "repairs" if bool(row.get("squarefree")) else "fails" + if anchor_key not in repair_anchor_counts: + repair_anchor_counts[anchor_key] = {"repairs": 0, "fails": 0} + repair_anchor_counts[anchor_key][bucket] += 1 + + known_failures = [int(value) for value in menu_doc.get("parameters", {}).get("knownFailures", [])] + return { + "source_path": str(path), + "family_count": int(menu_doc.get("summary", {}).get("familyCount", len(menu_doc.get("families", [])))), + "known_failure_matches": int(menu_doc.get("summary", {}).get("knownFailureMatches", 0)), + "known_failures": known_failures, + "last_known_matched": known_failures[-1] if known_failures else None, + "next_unmatched": next_unmatched, + "repair_anchor_counts": repair_anchor_counts, + } + + +def _load_live_p848_frontier_snapshot_from_root(root: Path) -> dict[str, Any] | None: + """Load one six-prefix frontier snapshot from a specific root.""" + + if not root.exists(): + return None + + live_chunks_root = root / "chunks" + shared_prefix_failures: set[int] = set() + if live_chunks_root.exists(): + for summary_path in sorted(live_chunks_root.glob("six_anchor_frontier_after*/SUMMARY_*.json")): + summary_doc = _load_json_if_exists(summary_path) + if summary_doc is None: + continue + anchors = summary_doc.get("parameters", {}).get("anchors", []) + if not _matches_expected_prefix(anchors): + continue + first_failure = summary_doc.get("summary", {}).get("firstFailure") + if isinstance(first_failure, int): + shared_prefix_failures.add(int(first_failure)) + + menu_summaries: list[dict[str, Any]] = [] + for menu_path in sorted(root.glob("SIX_PREFIX_*FAMILY_MENU.json")): + menu_doc = _load_json_if_exists(menu_path) + if menu_doc is None: + continue + anchors = menu_doc.get("parameters", {}).get("anchors", []) + if not _matches_expected_prefix(anchors): + continue + menu_summary = _summarize_family_menu(menu_doc, path=menu_path) + shared_prefix_failures.update(menu_summary["known_failures"]) + menu_summaries.append(menu_summary) + + if not shared_prefix_failures and not menu_summaries: + return None + + best_menu = None + if menu_summaries: + best_menu = max( + menu_summaries, + key=lambda row: ( + int(row["known_failure_matches"]), + len(row["known_failures"]), + int(row["family_count"]), + row["source_path"], + ), + ) + + ordered_failures = sorted(shared_prefix_failures) + latest_direct_failure = ordered_failures[-1] if ordered_failures else None + return { + "source_root": str(root), + "shared_prefix": list(EXPECTED_SHARED_PREFIX), + "shared_prefix_failure_count": len(ordered_failures), + "shared_prefix_failure_ns": ordered_failures, + "latest_direct_failure": latest_direct_failure, + "best_family_menu": best_menu, + } + + +def _candidate_live_frontier_roots() -> list[Path]: + """Return candidate live-frontier roots ordered by preference.""" + + override = os.environ.get("FRONTIER_ENGINE_P848_LIVE_ROOT") + if override: + return [Path(override)] + + roots: list[Path] = [] + if TMP_FRONTIER_ROOT.exists(): + roots.append(TMP_FRONTIER_ROOT) + + synced_latest = SYNC_FRONTIER_ROOT / "latest" + if synced_latest.exists(): + roots.append(synced_latest.resolve()) + return roots + + +def load_live_p848_frontier_snapshot() -> dict[str, Any] | None: + """Load the freshest live six-prefix frontier snapshot from temp or repo sync.""" + + snapshots = [ + snapshot + for root in _candidate_live_frontier_roots() + if (snapshot := _load_live_p848_frontier_snapshot_from_root(root)) is not None + ] + if not snapshots: + return None + + return max( + snapshots, + key=lambda snapshot: ( + int(snapshot["shared_prefix_failure_count"]), + int((snapshot.get("best_family_menu") or {}).get("known_failure_matches", 0)), + int((snapshot.get("best_family_menu") or {}).get("family_count", 0)), + snapshot["source_root"], + ), + ) + + +def load_best_family_menu_surface( + snapshot: dict[str, Any] | None = None, +) -> dict[str, Any] | None: + """Load the richest live six-prefix family menu into a scoring surface.""" + + resolved_snapshot = snapshot if snapshot is not None else load_live_p848_frontier_snapshot() + if resolved_snapshot is None: + return None + + best_menu = resolved_snapshot.get("best_family_menu") + if not isinstance(best_menu, dict): + return None + + source_path = Path(str(best_menu.get("source_path", ""))) + menu_doc = _load_json_if_exists(source_path) + if menu_doc is None: + return None + + families = [] + for family in menu_doc.get("families", []): + families.append( + { + "representative": int(family["representative"]), + "matches_known_failure": bool(family.get("matchesKnownFailure")), + "tuple_key": family.get("tupleKey"), + } + ) + + return { + "source_path": str(source_path), + "family_count": len(families), + "known_failure_matches": int(best_menu.get("known_failure_matches", 0)), + "next_unmatched": best_menu.get("next_unmatched"), + "families": families, + } + + +def load_observed_continuations() -> dict[int, P848ObservedContinuation]: + """Load frozen continuation evidence earned in the live 848 frontier.""" + + raw = json.loads(OBSERVED_CONTINUATION_PATH.read_text(encoding="utf-8")) + rows: dict[int, P848ObservedContinuation] = {} + for item in raw["observed_continuations"]: + continuation = int(item["continuation"]) + rows[continuation] = P848ObservedContinuation( + continuation=continuation, + status=str(item["status"]), + repaired_known_packets=int(item["repaired_known_packets"]), + first_failure_n=( + int(item["first_failure_n"]) if item.get("first_failure_n") is not None else None + ), + clean_through=( + int(item["clean_through"]) if item.get("clean_through") is not None else None + ), + note=item.get("note"), + source_paths=[str(path) for path in item.get("source_paths", [])], + ) + return rows + + +def load_p848_search_profile(profile_path: Path) -> tuple[P848SearchConfig, dict[str, Any]]: + """Load a p848 search profile file into a runnable search config.""" + + raw = json.loads(profile_path.read_text(encoding="utf-8")) + if raw.get("lane_id") != "p848_anchor_ladder": + raise ValueError(f"profile does not target p848_anchor_ladder: {profile_path}") + + config = P848SearchConfig( + prefix_anchors=[int(value) for value in raw.get("prefix_anchors", [])], + candidates=[int(value) for value in raw.get("candidates", [])], + direct_threshold=int(raw["direct_threshold"]), + direct_max=int(raw["direct_max"]), + top_k=int(raw.get("top_k", 8)), + candidate_mode=str(raw.get("candidate_mode", "explicit")), + base_tail=( + int(raw["base_tail"]) if raw.get("base_tail") is not None else None + ), + ladder_step=int(raw.get("ladder_step", 50)), + ladder_rounds=int(raw.get("ladder_rounds", 0)), + perturb_offsets=[int(value) for value in raw.get("perturb_offsets", [])], + runtime=str(raw.get("runtime_mode", raw.get("runtime", "auto"))), + device=str(raw.get("device", "auto")), + n_chunk_size=int(raw.get("n_chunk_size", 2048)), + value_chunk_size=int(raw.get("value_chunk_size", 32768)), + prime_square_chunk_size=int(raw.get("prime_square_chunk_size", 128)), + profile_id=str(raw.get("profile_id")) if raw.get("profile_id") is not None else None, + profile_path=str(profile_path), + ) + return config, raw + + +def parse_int_csv(value: str, *, allow_empty: bool = False) -> list[int]: + """Parse a comma-separated integer list.""" + + if not value.strip(): + if allow_empty: + return [] + raise ValueError("integer list must not be empty") + items = [int(token.strip()) for token in value.split(",") if token.strip()] + if not items: + raise ValueError("integer list must not be empty") + return items + + +def parse_candidate_csv(value: str) -> list[int]: + """Parse a comma-separated candidate list.""" + + return parse_int_csv(value) + + +def _sorted_unique(values: list[int]) -> list[int]: + return sorted(set(int(value) for value in values)) + + +def _resolve_p848_runtime(*, requested_runtime: str, requested_device: str) -> tuple[str, str, Any]: + """Resolve runtime selection for the p848 lane.""" + + probe = probe_runtime() + if requested_runtime == "auto": + runtime_mode = "torch" if probe.torch_installed and probe.cuda_available else "python" + else: + runtime_mode = resolve_runtime_mode(requested_runtime, probe) + device = resolve_device(requested_device, runtime_mode, probe) + return runtime_mode, device, probe + + +def generate_candidate_pool( + *, + config: P848SearchConfig, + observed: dict[int, P848ObservedContinuation], + default_base_tail: int, +) -> tuple[list[int], dict[str, Any]]: + """Assemble the continuation pool from explicit and ladder-sweep sources.""" + + pool: set[int] = set() + explicit_candidates = _sorted_unique(config.candidates) + if config.candidate_mode in {"explicit", "hybrid"}: + pool.update(explicit_candidates) + + resolved_base_tail = config.base_tail if config.base_tail is not None else default_base_tail + ladder_offsets = _sorted_unique(config.perturb_offsets or [0]) + generated_candidates: list[int] = [] + if config.candidate_mode in {"hybrid", "ladder-sweep"}: + lower_bound = max(config.prefix_anchors) + 1 + for step_index in range(config.ladder_rounds + 1): + center = resolved_base_tail + step_index * config.ladder_step + for offset in ladder_offsets: + candidate = center + offset + if candidate < lower_bound: + continue + generated_candidates.append(candidate) + pool.add(candidate) + + observed_hits = sorted(candidate for candidate in pool if candidate in observed) + return _sorted_unique(list(pool)), { + "mode": config.candidate_mode, + "explicit_candidates": explicit_candidates, + "generated_candidates": _sorted_unique(generated_candidates), + "resolved_base_tail": resolved_base_tail, + "ladder_step": config.ladder_step, + "ladder_rounds": config.ladder_rounds, + "perturb_offsets": ladder_offsets, + "observed_candidates_in_pool": observed_hits, + } + + +def search_first_failure( + *, + anchors: list[int], + threshold: int, + max_n: int, + oracle: SquarefreeOracle, +) -> dict[str, Any]: + """Direct first-failure search on a finite window.""" + + witness_counts = {anchor: 0 for anchor in anchors} + checked_count = 0 + scanned_until = threshold - 1 + sorted_anchors = _sorted_unique(anchors) + anchor_index = 0 + + for n in range(threshold, max_n + 1): + if n % 25 == 7: + continue + checked_count += 1 + scanned_until = n + + while anchor_index < len(sorted_anchors) and sorted_anchors[anchor_index] <= n: + anchor_index += 1 + usable_anchors = sorted_anchors[:anchor_index] + + witness_anchor = None + for anchor in usable_anchors: + if oracle.is_squarefree(anchor * n + 1): + witness_anchor = anchor + break + + if witness_anchor is not None: + witness_counts[witness_anchor] += 1 + continue + + obstruction_rows = [] + for anchor in usable_anchors: + value = anchor * n + 1 + factors = oracle.factor_exponents(value) + obstruction_rows.append( + { + "anchor": anchor, + "value": value, + "square_witnesses": [ + factor for factor in factors if int(factor["exponent"]) >= 2 + ], + } + ) + return { + "threshold": threshold, + "max_n": max_n, + "performed": True, + "skipped": False, + "skip_reason": None, + "first_failure": n, + "clean_through": n - 1, + "scanned_until": scanned_until, + "checked_count": checked_count, + "all_covered_on_window": False, + "witness_counts": witness_counts, + "obstruction_rows": obstruction_rows, + } + + return { + "threshold": threshold, + "max_n": max_n, + "performed": True, + "skipped": False, + "skip_reason": None, + "first_failure": None, + "clean_through": scanned_until, + "scanned_until": scanned_until, + "checked_count": checked_count, + "all_covered_on_window": True, + "witness_counts": witness_counts, + "obstruction_rows": [], + } + + +def _skipped_direct_scan( + *, + anchors: list[int], + threshold: int, + max_n: int, + reason: str, + first_failure: int, +) -> dict[str, Any]: + """Return a direct-scan stub when historical evidence already blocks the window.""" + + return { + "threshold": threshold, + "max_n": max_n, + "performed": False, + "skipped": True, + "skip_reason": reason, + "first_failure": first_failure, + "clean_through": first_failure - 1, + "scanned_until": first_failure - 1, + "checked_count": 0, + "all_covered_on_window": False, + "witness_counts": {anchor: 0 for anchor in anchors}, + "obstruction_rows": [], + } + + +def _observed_evidence_row( + observed: P848ObservedContinuation | None, +) -> dict[str, Any] | None: + """Serialize frozen continuation evidence for reporting.""" + + if observed is None: + return None + return { + "continuation": observed.continuation, + "status": observed.status, + "repaired_known_packets": observed.repaired_known_packets, + "first_failure_n": observed.first_failure_n, + "clean_through": observed.clean_through, + "note": observed.note, + "source_paths": observed.source_paths, + } + + +def _build_obstruction_rows( + *, + anchors: list[int], + failure_n: int, + oracle: SquarefreeOracle, +) -> list[dict[str, Any]]: + """Build the explicit obstruction packet for a known first failure.""" + + obstruction_rows: list[dict[str, Any]] = [] + for anchor in anchors: + if anchor > failure_n: + continue + value = anchor * failure_n + 1 + factors = oracle.factor_exponents(value) + obstruction_rows.append( + { + "anchor": anchor, + "value": value, + "square_witnesses": [ + factor for factor in factors if int(factor["exponent"]) >= 2 + ], + } + ) + return obstruction_rows + + +def _score_family_menu_surface( + *, + continuation: int, + family_menu_surface: dict[str, Any] | None, + oracle: SquarefreeOracle, + rescue_flags: list[bool] | None = None, +) -> dict[str, Any] | None: + """Summarize how well a continuation repairs the live family-menu surface.""" + + if family_menu_surface is None: + return None + + family_rows = list(family_menu_surface.get("families", [])) + if rescue_flags is not None and len(rescue_flags) != len(family_rows): + raise ValueError("family-menu rescue flag length mismatch") + + repaired_rows: list[dict[str, Any]] = [] + missed_rows: list[dict[str, Any]] = [] + repaired_predicted = 0 + repaired_known = 0 + missed_predicted = 0 + + for index, row in enumerate(family_rows): + representative = int(row["representative"]) + rescued = ( + bool(rescue_flags[index]) + if rescue_flags is not None + else continuation <= representative and oracle.is_squarefree(continuation * representative + 1) + ) + scored_row = { + "representative": representative, + "matches_known_failure": bool(row.get("matches_known_failure")), + "rescued": rescued, + "tuple_key": row.get("tuple_key"), + } + if rescued: + repaired_rows.append(scored_row) + if scored_row["matches_known_failure"]: + repaired_known += 1 + else: + repaired_predicted += 1 + else: + missed_rows.append(scored_row) + if not scored_row["matches_known_failure"]: + missed_predicted += 1 + + predicted_count = len(family_rows) - int(family_menu_surface.get("known_failure_matches", 0)) + return { + "source_path": family_menu_surface["source_path"], + "family_count": len(family_rows), + "known_failure_matches": int(family_menu_surface.get("known_failure_matches", 0)), + "predicted_family_count": predicted_count, + "next_unmatched": family_menu_surface.get("next_unmatched"), + "repaired_family_count": len(repaired_rows), + "repaired_known_family_count": repaired_known, + "repaired_predicted_family_count": repaired_predicted, + "missed_family_count": len(missed_rows), + "missed_predicted_family_count": missed_predicted, + "first_missed_representatives": [row["representative"] for row in missed_rows[:8]], + "first_missed_predicted_representatives": [ + row["representative"] for row in missed_rows if not row["matches_known_failure"] + ][:8], + } + + +def _merge_frontier_evidence( + *, + observed: P848ObservedContinuation | None, + direct_scan: dict[str, Any], +) -> dict[str, Any]: + """Combine historical frontier evidence with the latest finite direct scan.""" + + if observed is None: + return { + "observed_status": "unseen", + "observed_clean_through": None, + "observed_first_failure": None, + "effective_clean_through": int(direct_scan["clean_through"]), + "effective_first_failure": direct_scan["first_failure"], + "live_window_contiguous_with_observed": False, + "frontier_gain_vs_observed": None, + "extension_mode": "direct_window_only", + } + + if observed.first_failure_n is not None: + return { + "observed_status": observed.status, + "observed_clean_through": observed.first_failure_n - 1, + "observed_first_failure": observed.first_failure_n, + "effective_clean_through": observed.first_failure_n - 1, + "effective_first_failure": observed.first_failure_n, + "live_window_contiguous_with_observed": False, + "frontier_gain_vs_observed": 0, + "extension_mode": "historical_failure_locked", + } + + observed_clean_through = int(observed.clean_through or 0) + contiguous = bool(direct_scan["performed"]) and int(direct_scan["threshold"]) <= ( + observed_clean_through + 1 + ) + effective_clean_through = observed_clean_through + effective_first_failure = None + extension_mode = "historical_clean_preserved" + + if contiguous: + if direct_scan["first_failure"] is None: + effective_clean_through = max( + observed_clean_through, + int(direct_scan["clean_through"]), + ) + extension_mode = "contiguous_clean_extension" + else: + effective_first_failure = int(direct_scan["first_failure"]) + effective_clean_through = effective_first_failure - 1 + extension_mode = "contiguous_failure_found" + + return { + "observed_status": observed.status, + "observed_clean_through": observed_clean_through, + "observed_first_failure": observed.first_failure_n, + "effective_clean_through": effective_clean_through, + "effective_first_failure": effective_first_failure, + "live_window_contiguous_with_observed": contiguous, + "frontier_gain_vs_observed": effective_clean_through - observed_clean_through, + "extension_mode": extension_mode, + } + + +def evaluate_continuation( + *, + prefix_anchors: list[int], + continuation: int, + known_failure_packets: list[P848KnownFailurePacket], + family_menu_surface: dict[str, Any] | None, + observed: P848ObservedContinuation | None, + direct_threshold: int, + direct_max: int, + oracle: SquarefreeOracle, +) -> dict[str, Any]: + """Score one continuation against frozen packets plus a direct scan window.""" + + all_anchors = _sorted_unique(prefix_anchors + [continuation]) + repaired_known_packets: list[dict[str, Any]] = [] + missed_known_packets: list[dict[str, Any]] = [] + + for packet in known_failure_packets: + rescued = continuation <= packet.n and oracle.is_squarefree(continuation * packet.n + 1) + row = { + "packet_id": packet.packet_id, + "n": packet.n, + "kind": packet.kind, + "rescued": rescued, + "tail": packet.tail, + } + if rescued: + repaired_known_packets.append(row) + else: + missed_known_packets.append(row) + + if observed is not None and observed.first_failure_n is not None and direct_threshold > observed.first_failure_n: + direct_scan = _skipped_direct_scan( + anchors=all_anchors, + threshold=direct_threshold, + max_n=direct_max, + reason=f"known earlier failure at {observed.first_failure_n}", + first_failure=observed.first_failure_n, + ) + else: + direct_scan = search_first_failure( + anchors=all_anchors, + threshold=direct_threshold, + max_n=direct_max, + oracle=oracle, + ) + + frontier_evidence = _merge_frontier_evidence(observed=observed, direct_scan=direct_scan) + family_menu_repairs = _score_family_menu_surface( + continuation=continuation, + family_menu_surface=family_menu_surface, + oracle=oracle, + ) + + return { + "continuation": continuation, + "prefix_anchors": _sorted_unique(prefix_anchors), + "all_anchors": all_anchors, + "repaired_known_packets": len(repaired_known_packets), + "known_packet_repairs": repaired_known_packets, + "missed_known_packets": missed_known_packets, + "family_menu_repairs": family_menu_repairs, + "direct_scan": direct_scan, + "observed_frontier": _observed_evidence_row(observed), + "frontier_evidence": frontier_evidence, + "tail_step_from_182": continuation - 182 if 182 in prefix_anchors else None, + "plus50_alignment": ((continuation - 132) % 50 == 0) if continuation >= 132 else False, + } + + +def _build_repair_rows( + *, + continuation: int, + known_failure_packets: list[P848KnownFailurePacket], + rescue_flags: list[bool], +) -> tuple[list[dict[str, Any]], list[dict[str, Any]]]: + """Build repaired and missed packet rows from boolean repair flags.""" + + repaired_known_packets: list[dict[str, Any]] = [] + missed_known_packets: list[dict[str, Any]] = [] + for packet, rescued in zip(known_failure_packets, rescue_flags): + row = { + "packet_id": packet.packet_id, + "n": packet.n, + "kind": packet.kind, + "rescued": bool(rescued), + "tail": packet.tail, + } + if rescued: + repaired_known_packets.append(row) + else: + missed_known_packets.append(row) + return repaired_known_packets, missed_known_packets + + +def _build_candidate_row_from_backend( + *, + prefix_anchors: list[int], + continuation: int, + known_failure_packets: list[P848KnownFailurePacket], + family_menu_surface: dict[str, Any] | None, + observed: P848ObservedContinuation | None, + rescue_flags: list[bool], + family_menu_rescue_flags: list[bool] | None, + direct_scan: dict[str, Any], + oracle: SquarefreeOracle, +) -> dict[str, Any]: + """Assemble one candidate row from backend outputs.""" + + all_anchors = _sorted_unique(prefix_anchors + [continuation]) + repaired_known_packets, missed_known_packets = _build_repair_rows( + continuation=continuation, + known_failure_packets=known_failure_packets, + rescue_flags=rescue_flags, + ) + + if ( + direct_scan["performed"] + and direct_scan["first_failure"] is not None + and not direct_scan.get("obstruction_rows") + ): + direct_scan = dict(direct_scan) + direct_scan["obstruction_rows"] = _build_obstruction_rows( + anchors=all_anchors, + failure_n=int(direct_scan["first_failure"]), + oracle=oracle, + ) + elif "obstruction_rows" not in direct_scan: + direct_scan = dict(direct_scan) + direct_scan["obstruction_rows"] = [] + + frontier_evidence = _merge_frontier_evidence(observed=observed, direct_scan=direct_scan) + family_menu_repairs = _score_family_menu_surface( + continuation=continuation, + family_menu_surface=family_menu_surface, + oracle=oracle, + rescue_flags=family_menu_rescue_flags, + ) + return { + "continuation": continuation, + "prefix_anchors": _sorted_unique(prefix_anchors), + "all_anchors": all_anchors, + "repaired_known_packets": len(repaired_known_packets), + "known_packet_repairs": repaired_known_packets, + "missed_known_packets": missed_known_packets, + "family_menu_repairs": family_menu_repairs, + "direct_scan": direct_scan, + "observed_frontier": _observed_evidence_row(observed), + "frontier_evidence": frontier_evidence, + "tail_step_from_182": continuation - 182 if 182 in prefix_anchors else None, + "plus50_alignment": ((continuation - 132) % 50 == 0) if continuation >= 132 else False, + } + + +def run_p848_anchor_search(config: P848SearchConfig) -> dict[str, Any]: + """Run the 848 anchor-ladder continuation search.""" + + frozen = load_known_failure_packets() + live_frontier = load_live_p848_frontier_snapshot() + family_menu_surface = load_best_family_menu_surface(live_frontier) + observed = load_observed_continuations() + packets = [ + P848KnownFailurePacket( + packet_id=str(packet["packet_id"]), + n=int(packet["n"]), + kind=str(packet["kind"]), + tail=(int(packet["tail"]) if packet.get("tail") is not None else None), + note=packet.get("note"), + ) + for packet in frozen["known_failure_packets"] + ] + seen_packet_keys = {(packet.kind, packet.n, packet.tail) for packet in packets} + if live_frontier is not None: + for failure_n in live_frontier["shared_prefix_failure_ns"]: + packet_key = ("shared_prefix_failure", int(failure_n), None) + if packet_key in seen_packet_keys: + continue + packets.append( + P848KnownFailurePacket( + packet_id=f"shared_prefix_{failure_n}", + n=int(failure_n), + kind="shared_prefix_failure", + tail=None, + note="Recovered from the live six-prefix frontier snapshot.", + ) + ) + seen_packet_keys.add(packet_key) + packets.sort(key=lambda packet: (packet.n, packet.kind, packet.tail or -1)) + + candidates, candidate_generation = generate_candidate_pool( + config=config, + observed=observed, + default_base_tail=int(frozen["current_best_continuation"]), + ) + if not candidates: + raise ValueError("candidate pool is empty") + + max_anchor = max(_sorted_unique(config.prefix_anchors + candidates)) + family_menu_ns = ( + [int(row["representative"]) for row in family_menu_surface.get("families", [])] + if family_menu_surface is not None + else [] + ) + max_value = max( + max_anchor + * max( + config.direct_max, + max(packet.n for packet in packets), + max(family_menu_ns, default=0), + ) + + 1, + 2, + ) + oracle = SquarefreeOracle(max_value=max_value) + runtime_mode, resolved_device, probe = _resolve_p848_runtime( + requested_runtime=config.runtime, + requested_device=config.device, + ) + + if runtime_mode == "torch": + backend_result = evaluate_p848_candidates_torch( + prefix_anchors=config.prefix_anchors, + continuations=candidates, + known_packet_ns=[packet.n for packet in packets], + family_menu_ns=family_menu_ns, + observed_first_failures={ + continuation: int(observed_row.first_failure_n) + for continuation, observed_row in observed.items() + if observed_row.first_failure_n is not None + }, + direct_threshold=config.direct_threshold, + direct_max=config.direct_max, + device=resolved_device, + probe=probe, + n_chunk_size=config.n_chunk_size, + value_chunk_size=config.value_chunk_size, + prime_square_chunk_size=config.prime_square_chunk_size, + ) + candidate_rows = [ + _build_candidate_row_from_backend( + prefix_anchors=config.prefix_anchors, + continuation=continuation, + known_failure_packets=packets, + family_menu_surface=family_menu_surface, + observed=observed.get(continuation), + rescue_flags=backend_result["repair_flags_by_continuation"][continuation], + family_menu_rescue_flags=backend_result["family_menu_repair_flags_by_continuation"].get( + continuation + ), + direct_scan=backend_result["direct_scans"][continuation], + oracle=oracle, + ) + for continuation in candidates + ] + backend_metadata = backend_result["backend_metadata"] + else: + candidate_rows = [ + evaluate_continuation( + prefix_anchors=config.prefix_anchors, + continuation=continuation, + known_failure_packets=packets, + family_menu_surface=family_menu_surface, + observed=observed.get(continuation), + direct_threshold=config.direct_threshold, + direct_max=config.direct_max, + oracle=oracle, + ) + for continuation in candidates + ] + backend_metadata = { + "resolved_runtime": runtime_mode, + "resolved_device": resolved_device, + "probe": probe.to_dict(), + "candidate_scan_kind": "scalar_continuation_scan", + } + + candidate_rows.sort( + key=lambda row: ( + -int(row["repaired_known_packets"]), + -int((row.get("family_menu_repairs") or {}).get("repaired_predicted_family_count", 0)), + -int((row.get("family_menu_repairs") or {}).get("repaired_family_count", 0)), + -int(row["frontier_evidence"]["effective_clean_through"]), + -int(row["frontier_evidence"]["observed_clean_through"] or 0), + row["frontier_evidence"]["effective_first_failure"] is not None, + not bool(row["plus50_alignment"]), + int(row["continuation"]), + ) + ) + + top_rows = candidate_rows[: config.top_k] + best = top_rows[0] if top_rows else None + return { + "lane_id": "p848_anchor_ladder", + "problem_id": "848", + "config": config.to_dict(), + "search_profile": ( + { + "profile_id": config.profile_id, + "profile_path": config.profile_path, + } + if config.profile_id or config.profile_path + else None + ), + "candidate_generation": candidate_generation, + "backend_metadata": backend_metadata, + "known_failure_packet_count": len(packets), + "known_failure_packets": [asdict(packet) for packet in packets], + "live_frontier_snapshot": live_frontier, + "family_menu_surface": ( + { + "source_path": family_menu_surface["source_path"], + "family_count": family_menu_surface["family_count"], + "known_failure_matches": family_menu_surface["known_failure_matches"], + "next_unmatched": family_menu_surface["next_unmatched"], + } + if family_menu_surface is not None + else None + ), + "observed_continuations": [ + _observed_evidence_row(observed_row) + for observed_row in sorted(observed.values(), key=lambda row: row.continuation) + ], + "summary": { + "candidates_evaluated": len(candidate_rows), + "known_failure_packet_count": len(packets), + "family_menu_count": family_menu_surface["family_count"] if family_menu_surface else 0, + "best_continuation": best["continuation"] if best else None, + "best_repaired_known_packets": best["repaired_known_packets"] if best else None, + "best_repaired_predicted_families": ( + (best.get("family_menu_repairs") or {}).get("repaired_predicted_family_count") + if best + else None + ), + "best_effective_clean_through": ( + best["frontier_evidence"]["effective_clean_through"] if best else None + ), + "best_direct_clean_through": ( + best["direct_scan"]["clean_through"] if best else None + ), + }, + "candidate_rows": candidate_rows, + "top_candidates": top_rows, + "frozen_frontier": { + "shared_prefix": frozen["shared_prefix"], + "current_best_continuation": frozen["current_best_continuation"], + "current_best_clean_through": frozen["current_best_clean_through"], + }, + } diff --git a/research/frontier-engine/src/frontier_engine/p848_bundle.py b/research/frontier-engine/src/frontier_engine/p848_bundle.py new file mode 100644 index 0000000..21ca7ca --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/p848_bundle.py @@ -0,0 +1,85 @@ +"""Artifact export for the Problem 848 anchor ladder lane.""" + +from __future__ import annotations + +from datetime import datetime, timezone +import json +from pathlib import Path +from typing import Any + +from .artifacts import _serialize + + +def write_p848_anchor_seed_bundle( + *, + report: dict[str, Any], + output_dir: Path, + top_k: int, +) -> Path: + """Write the top continuation candidates as a portable bundle.""" + + timestamp = datetime.now(timezone.utc).strftime("%Y%m%dT%H%M%SZ") + bundle_dir = output_dir / f"p848_anchor_ladder-seeds-{timestamp}" + bundle_dir.mkdir(parents=True, exist_ok=True) + + rows = list(report.get("top_candidates", []))[:top_k] + candidate_files: list[dict[str, Any]] = [] + + for rank, row in enumerate(rows, start=1): + continuation = int(row["continuation"]) + filename = f"rank-{rank:02d}-tail-{continuation}.json" + path = bundle_dir / filename + doc = { + "schema": "frontier_engine.p848_anchor_tail_seed/1", + "lane_id": "p848_anchor_ladder", + "problem_id": "848", + "prefix_anchors": row["prefix_anchors"], + "continuation": continuation, + "all_anchors": row["all_anchors"], + "repaired_known_packets": row["repaired_known_packets"], + "known_packet_repairs": row["known_packet_repairs"], + "missed_known_packets": row["missed_known_packets"], + "family_menu_repairs": row.get("family_menu_repairs"), + "direct_scan": row["direct_scan"], + "observed_frontier": row.get("observed_frontier"), + "frontier_evidence": row.get("frontier_evidence"), + "plus50_alignment": row["plus50_alignment"], + "tail_step_from_182": row["tail_step_from_182"], + } + path.write_text(json.dumps(_serialize(doc), indent=2) + "\n", encoding="utf-8") + candidate_files.append( + { + "rank": rank, + "continuation": continuation, + "file": filename, + "repaired_known_packets": row["repaired_known_packets"], + "repaired_predicted_families": ( + (row.get("family_menu_repairs") or {}).get("repaired_predicted_family_count") + ), + "direct_clean_through": row["direct_scan"]["clean_through"], + "effective_clean_through": row["frontier_evidence"]["effective_clean_through"], + } + ) + + manifest = { + "bundle_version": 1, + "bundle_kind": "anchor_tail_seed_bundle", + "lane": { + "lane_id": "p848_anchor_ladder", + "problem_id": "848", + }, + "search_profile": report.get("search_profile"), + "summary": report["summary"], + "candidate_generation": report.get("candidate_generation", {}), + "backend_metadata": report.get("backend_metadata", {}), + "live_frontier_snapshot": report.get("live_frontier_snapshot"), + "family_menu_surface": report.get("family_menu_surface"), + "known_failure_packets": report["known_failure_packets"], + "observed_continuations": report.get("observed_continuations", []), + "candidate_files": candidate_files, + } + (bundle_dir / "manifest.json").write_text( + json.dumps(_serialize(manifest), indent=2) + "\n", + encoding="utf-8", + ) + return bundle_dir diff --git a/research/frontier-engine/src/frontier_engine/p848_theorem_bridge.py b/research/frontier-engine/src/frontier_engine/p848_theorem_bridge.py new file mode 100644 index 0000000..61ca515 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/p848_theorem_bridge.py @@ -0,0 +1,487 @@ +"""Canonical search-to-theorem bridge artifacts for Problem 848.""" + +from __future__ import annotations + +from datetime import datetime, timezone +import json +from pathlib import Path +from typing import Any + +from .artifacts import _serialize + + +ENGINE_ROOT = Path(__file__).resolve().parents[2] +PROJECT_ROOT = ENGINE_ROOT.parent.parent +PACK_ROOT = PROJECT_ROOT / "packs" / "number-theory" / "problems" / "848" +P848_ARTIFACT_ROOT = ENGINE_ROOT / "artifacts" / "p848-anchor-ladder" +EXPECTED_SHARED_PREFIX = (7, 32, 57, 82, 132, 182) + +DEFAULT_BRIDGE_JSON_PATH = PACK_ROOT / "SEARCH_THEOREM_BRIDGE.json" +DEFAULT_BRIDGE_MD_PATH = PACK_ROOT / "SEARCH_THEOREM_BRIDGE.md" + + +def _load_json(path: Path) -> dict[str, Any] | None: + """Load a JSON file when it exists and parses cleanly.""" + + if not path.exists(): + return None + try: + return json.loads(path.read_text(encoding="utf-8")) + except (OSError, json.JSONDecodeError): + return None + + +def _manifest_evidence_score(path: Path) -> tuple[int, int, int, int, int, int, int, int, str] | None: + """Score a p848 GPU manifest by theorem-relevant evidence strength.""" + + manifest = _load_json(path) + if manifest is None: + return None + summary = manifest.get("summary") or {} + return ( + int(summary.get("known_failure_packet_count") or 0), + int(summary.get("family_menu_count") or 0), + int(summary.get("best_repaired_known_packets") or 0), + int(summary.get("best_repaired_predicted_families") or 0), + int(summary.get("best_effective_clean_through") or 0), + int(summary.get("best_direct_clean_through") or 0), + int(summary.get("candidates_evaluated") or 0), + len(manifest.get("candidate_files") or []), + str(path), + ) + + +def _latest_gpu_manifest_path(explicit_path: Path | None = None) -> Path | None: + """Resolve the strongest available p848 GPU bundle manifest.""" + + if explicit_path is not None: + return explicit_path if explicit_path.exists() else None + + scored_manifests = [ + (score, manifest_path) + for manifest_path in P848_ARTIFACT_ROOT.glob("p848_anchor_ladder-seeds-*/manifest.json") + if (score := _manifest_evidence_score(manifest_path)) is not None + ] + return max(scored_manifests)[1] if scored_manifests else None + + +def _format_witness_token(prime: int, exponent: int) -> str: + """Format one witness factor in the same style as the frontier notes.""" + + if exponent == 2 and prime in {2, 3}: + return str(prime**2) + if exponent == 2: + return f"{prime}^2" + return f"{prime}^{exponent}" + + +def _packet_doc_for_failure(source_root: Path, failure_n: int) -> tuple[Path | None, dict[str, Any] | None]: + """Locate the frozen packet document for one shared-prefix failure.""" + + chunks_root = source_root / "chunks" + if not chunks_root.exists(): + return None, None + + for packet_path in sorted(chunks_root.glob("six_anchor_frontier_after*/ANCHOR_FIRST_FAILURE_*.json")): + doc = _load_json(packet_path) + if doc is None: + continue + anchors = tuple(int(anchor) for anchor in doc.get("parameters", {}).get("anchors", [])) + if anchors != EXPECTED_SHARED_PREFIX: + continue + first_failure = doc.get("summary", {}).get("firstFailure") + if isinstance(first_failure, int) and first_failure == failure_n: + return packet_path, doc + return None, None + + +def _packet_entry( + *, + source_root: Path, + failure_n: int, + seen_square_moduli: set[int], +) -> dict[str, Any]: + """Build one packet-ledger row from the frozen live frontier.""" + + packet_path, packet_doc = _packet_doc_for_failure(source_root, failure_n) + crt_path = source_root / f"ANCHOR_SINGLETON_CRT_{failure_n}.json" + crt_doc = _load_json(crt_path) + + obstruction_rows = list((packet_doc or {}).get("obstructionRows", [])) + tuple_tokens: list[str] = [] + square_moduli: list[int] = [] + + for row in obstruction_rows: + square_witnesses = list(row.get("squareWitnesses", [])) + if not square_witnesses: + tuple_tokens.append("none") + continue + factor = square_witnesses[0] + prime = int(factor["prime"]) + exponent = int(factor["exponent"]) + tuple_tokens.append(_format_witness_token(prime, exponent)) + for witness in square_witnesses: + witness_prime = int(witness["prime"]) + witness_exponent = int(witness["exponent"]) + if witness_exponent >= 2: + square_moduli.append(witness_prime * witness_prime) + + ordered_square_moduli: list[int] = [] + for modulus in square_moduli: + if modulus not in ordered_square_moduli: + ordered_square_moduli.append(modulus) + + new_square_moduli = [modulus for modulus in ordered_square_moduli if modulus not in seen_square_moduli] + seen_square_moduli.update(ordered_square_moduli) + + return { + "n": failure_n, + "tuple_key": ", ".join(tuple_tokens) if tuple_tokens else None, + "square_moduli": ordered_square_moduli, + "new_square_moduli": new_square_moduli, + "packet_path": str(packet_path) if packet_path is not None else None, + "singleton_crt_path": str(crt_path) if crt_doc is not None else None, + "singleton_crt_modulus": ( + int(crt_doc["modulus"]) + if crt_doc is not None and crt_doc.get("modulus") is not None + else None + ), + "singleton_crt_residue": ( + int(crt_doc["residue"]) + if crt_doc is not None and crt_doc.get("residue") is not None + else None + ), + } + + +def _build_packet_ledger(live_snapshot: dict[str, Any]) -> list[dict[str, Any]]: + """Build the shared-prefix packet ledger from the live frontier snapshot.""" + + source_root = Path(str(live_snapshot["source_root"])) + seen_square_moduli: set[int] = set() + ledger: list[dict[str, Any]] = [] + for failure_n in live_snapshot.get("shared_prefix_failure_ns", []): + entry = _packet_entry( + source_root=source_root, + failure_n=int(failure_n), + seen_square_moduli=seen_square_moduli, + ) + if entry["packet_path"] is not None: + ledger.append(entry) + return ledger + + +def _display_path(value: str | None) -> str: + """Render repo-local paths compactly in Markdown output.""" + + if not value: + return "-" + path = Path(value) + try: + return str(path.relative_to(PROJECT_ROOT)) + except ValueError: + return str(path) + + +def _tracked_tail_matrix(report: dict[str, Any]) -> list[dict[str, Any]]: + """Build a stable continuation matrix from one p848 report.""" + + rows: list[dict[str, Any]] = [] + for row in sorted(report.get("candidate_rows", []), key=lambda item: int(item["continuation"])): + family_repairs = row.get("family_menu_repairs") or {} + frontier_evidence = row.get("frontier_evidence") or {} + observed = row.get("observed_frontier") or {} + direct_scan = row.get("direct_scan") or {} + rows.append( + { + "continuation": int(row["continuation"]), + "observed_status": observed.get("status", "unseen"), + "observed_clean_through": observed.get("clean_through"), + "observed_first_failure": observed.get("first_failure_n"), + "repaired_known_packets": int(row["repaired_known_packets"]), + "missed_known_packets": len(row.get("missed_known_packets", [])), + "repaired_known_family_count": family_repairs.get("repaired_known_family_count"), + "repaired_predicted_family_count": family_repairs.get("repaired_predicted_family_count"), + "first_missed_predicted_representatives": family_repairs.get( + "first_missed_predicted_representatives", [] + ), + "effective_clean_through": frontier_evidence.get("effective_clean_through"), + "effective_first_failure": frontier_evidence.get("effective_first_failure"), + "extension_mode": frontier_evidence.get("extension_mode"), + "direct_scan_performed": bool(direct_scan.get("performed")), + "direct_scan_skipped": bool(direct_scan.get("skipped")), + "plus50_alignment": bool(row.get("plus50_alignment")), + } + ) + return rows + + +def _leader_tie_class(candidate_files: list[dict[str, Any]]) -> list[int]: + """Return the current tie class at the top of the GPU leaderboard.""" + + if not candidate_files: + return [] + best = candidate_files[0] + return [ + int(row["continuation"]) + for row in candidate_files + if int(row.get("repaired_known_packets", -1)) == int(best.get("repaired_known_packets", -2)) + and int(row.get("repaired_predicted_families", -1)) == int(best.get("repaired_predicted_families", -2)) + and int(row.get("effective_clean_through", -1)) == int(best.get("effective_clean_through", -2)) + and int(row.get("direct_clean_through", -1)) == int(best.get("direct_clean_through", -2)) + ] + + +def _find_known_tail_failure( + report: dict[str, Any], + *, + tail: int, +) -> int | None: + """Look up the known tail failure n for one continuation if present.""" + + for packet in report.get("known_failure_packets", []): + if packet.get("kind") == "tail_failure" and packet.get("tail") == tail: + return int(packet["n"]) + return None + + +def _gpu_leaderboard(manifest: dict[str, Any] | None) -> list[dict[str, Any]]: + """Normalize the latest GPU leaderboard summary.""" + + if manifest is None: + return [] + rows: list[dict[str, Any]] = [] + for row in manifest.get("candidate_files", []): + rows.append( + { + "rank": int(row["rank"]), + "continuation": int(row["continuation"]), + "repaired_known_packets": int(row["repaired_known_packets"]), + "repaired_predicted_families": int(row["repaired_predicted_families"]), + "direct_clean_through": int(row["direct_clean_through"]), + "effective_clean_through": int(row["effective_clean_through"]), + } + ) + return rows + + +def build_p848_theorem_bridge( + *, + report: dict[str, Any], + gpu_manifest_path: Path | None = None, +) -> dict[str, Any]: + """Build the canonical 848 search/theorem bridge artifact.""" + + live_snapshot = report.get("live_frontier_snapshot") or {} + family_menu_surface = report.get("family_menu_surface") or {} + packet_ledger = _build_packet_ledger(live_snapshot) if live_snapshot else [] + tracked_tail_matrix = _tracked_tail_matrix(report) + + manifest_path = _latest_gpu_manifest_path(gpu_manifest_path) + gpu_manifest = _load_json(manifest_path) if manifest_path is not None else None + gpu_leaderboard = _gpu_leaderboard(gpu_manifest) + tie_class = _leader_tie_class(gpu_leaderboard) + gpu_leader = gpu_leaderboard[0] if gpu_leaderboard else None + + strongest_completed_tail = report.get("frozen_frontier", {}) + next_unmatched = family_menu_surface.get("next_unmatched") + tail_282_failure = _find_known_tail_failure(report, tail=282) + newest_modulus_events = [ + row for row in packet_ledger if row.get("new_square_moduli") + ] + + bridge = { + "schema": "frontier_engine.p848_search_theorem_bridge/1", + "generated_at_utc": datetime.now(timezone.utc).strftime("%Y-%m-%dT%H:%M:%SZ"), + "problem_id": "848", + "shared_prefix": live_snapshot.get("shared_prefix", []), + "sources": { + "live_frontier_root": live_snapshot.get("source_root"), + "family_menu_source_path": family_menu_surface.get("source_path"), + "gpu_manifest_path": str(manifest_path) if manifest_path is not None else None, + }, + "current_bridge_state": { + "shared_prefix_failure_count": live_snapshot.get("shared_prefix_failure_count"), + "latest_shared_prefix_failure": live_snapshot.get("latest_direct_failure"), + "family_menu_count": family_menu_surface.get("family_count"), + "known_family_matches": family_menu_surface.get("known_failure_matches"), + "next_unmatched_representative": next_unmatched, + "next_unmatched_matches_282_failure": ( + next_unmatched is not None + and tail_282_failure is not None + and int(next_unmatched) == int(tail_282_failure) + ), + "strongest_completed_structured_tail": { + "continuation": strongest_completed_tail.get("current_best_continuation"), + "clean_through": strongest_completed_tail.get("current_best_clean_through"), + }, + "current_family_aware_leader": { + "continuation": ( + gpu_leader["continuation"] + if gpu_leader is not None + else report.get("summary", {}).get("best_continuation") + ), + "repaired_known_packets": ( + gpu_leader["repaired_known_packets"] + if gpu_leader is not None + else report.get("summary", {}).get("best_repaired_known_packets") + ), + "repaired_predicted_families": ( + gpu_leader["repaired_predicted_families"] + if gpu_leader is not None + else report.get("summary", {}).get("best_repaired_predicted_families") + ), + "effective_clean_through": ( + gpu_leader["effective_clean_through"] + if gpu_leader is not None + else report.get("summary", {}).get("best_effective_clean_through") + ), + }, + "top_gpu_tie_class": tie_class, + "recent_pool_expansion_moduli": [ + modulus + for row in newest_modulus_events[-4:] + for modulus in row.get("new_square_moduli", []) + ], + }, + "shared_prefix_packet_ledger": packet_ledger, + "tracked_tail_matrix": tracked_tail_matrix, + "gpu_leaderboard": gpu_leaderboard, + "candidate_theorem_hooks": [ + { + "hook_id": "next_unmatched_equals_282_failure", + "status": ( + "supported" + if ( + next_unmatched is not None + and tail_282_failure is not None + and int(next_unmatched) == int(tail_282_failure) + ) + else "not_yet_supported" + ), + "detail": "The next unmatched shared-prefix representative currently coincides with the known first failure of the 282 continuation.", + }, + { + "hook_id": "completed_tail_vs_search_leader_split", + "status": "supported", + "detail": "The strongest completed structured tail remains 332, while the current family-aware search leader can move on the finite tested window.", + }, + { + "hook_id": "repair_pool_not_closed", + "status": ("supported" if newest_modulus_events else "unclear"), + "detail": "Recent shared-prefix packets introduced new square moduli into the live family menu, so the repaired local square pool is not yet closed.", + }, + { + "hook_id": "top_repair_class_cluster", + "status": ("supported" if len(tie_class) >= 2 else "weak"), + "detail": "The current top continuation class shares the same repaired-known, repaired-predicted, and tested-clean-through profile on the live finite window.", + }, + ], + } + return bridge + + +def _bridge_markdown(doc: dict[str, Any]) -> str: + """Render the search/theorem bridge as a compact Markdown note.""" + + current = doc["current_bridge_state"] + strongest = current["strongest_completed_structured_tail"] + leader = current["current_family_aware_leader"] + packet_rows = doc["shared_prefix_packet_ledger"] + recent_packets = packet_rows[-6:] if len(packet_rows) > 6 else packet_rows + tracked_rows = doc["tracked_tail_matrix"] + gpu_rows = doc["gpu_leaderboard"][:5] + hooks = doc["candidate_theorem_hooks"] + + lines = [ + "# Problem 848 Search-Theorem Bridge", + "", + "This note is the canonical bridge between the live `frontier-engine` search lane and the theorem-facing `erdos-problems` pack.", + "", + "## Current state", + "", + f"- Shared-prefix failures frozen: `{current['shared_prefix_failure_count']}` through `{current['latest_shared_prefix_failure']}`.", + f"- Current family menu: `{_display_path(doc['sources']['family_menu_source_path'])}` with `{current['family_menu_count']}` rows and `{current['known_family_matches']}` matched known-family rows.", + f"- Strongest completed structured tail: `{strongest['continuation']}` clean through `{strongest['clean_through']}`.", + f"- Current family-aware leader on the tested window: `{leader['continuation']}` with `{leader['repaired_known_packets']}` repaired known packets and `{leader['repaired_predicted_families']}` repaired predicted-family rows.", + f"- Next unmatched representative: `{current['next_unmatched_representative']}`.", + f"- `282` tail alignment: `{'matches' if current['next_unmatched_matches_282_failure'] else 'does not match'}` the next unmatched representative.", + f"- Current top GPU tie class: `{', '.join(str(value) for value in current['top_gpu_tie_class']) if current['top_gpu_tie_class'] else 'none'}`.", + "", + "## Recent Packet Ledger", + "", + "| n | Tuple | New Square Moduli | CRT Modulus |", + "| --- | --- | --- | --- |", + ] + for row in recent_packets: + new_moduli = ", ".join(str(value) for value in row["new_square_moduli"]) or "-" + crt_modulus = str(row["singleton_crt_modulus"]) if row["singleton_crt_modulus"] is not None else "-" + lines.append(f"| `{row['n']}` | `{row['tuple_key']}` | `{new_moduli}` | `{crt_modulus}` |") + + lines.extend( + [ + "", + "## Tracked Tail Matrix", + "", + "| Tail | Known Packets | Predicted Families | Effective Clean Through | Observed Status |", + "| --- | --- | --- | --- | --- |", + ] + ) + for row in tracked_rows: + lines.append( + f"| `{row['continuation']}` | `{row['repaired_known_packets']}` | " + f"`{row['repaired_predicted_family_count']}` | `{row['effective_clean_through']}` | " + f"`{row['observed_status']}` |" + ) + + lines.extend( + [ + "", + "## GPU Leaderboard", + "", + "| Rank | Tail | Known Packets | Predicted Families | Effective Clean Through |", + "| --- | --- | --- | --- | --- |", + ] + ) + for row in gpu_rows: + lines.append( + f"| `{row['rank']}` | `{row['continuation']}` | `{row['repaired_known_packets']}` | " + f"`{row['repaired_predicted_families']}` | `{row['effective_clean_through']}` |" + ) + + lines.extend(["", "## Theorem Hooks", ""]) + for hook in hooks: + lines.append(f"- `{hook['hook_id']}`: {hook['status']} | {hook['detail']}") + + lines.extend( + [ + "", + "## Refresh", + "", + "```bash", + "python3 research/frontier-engine/src/frontier_engine/cli.py export-p848-theorem-bridge", + "```", + "", + ] + ) + return "\n".join(lines) + + +def write_p848_theorem_bridge( + *, + report: dict[str, Any], + output_json_path: Path, + output_md_path: Path, + gpu_manifest_path: Path | None = None, +) -> dict[str, Path]: + """Write the canonical search/theorem bridge artifacts for Problem 848.""" + + doc = build_p848_theorem_bridge(report=report, gpu_manifest_path=gpu_manifest_path) + output_json_path.parent.mkdir(parents=True, exist_ok=True) + output_md_path.parent.mkdir(parents=True, exist_ok=True) + output_json_path.write_text(json.dumps(_serialize(doc), indent=2) + "\n", encoding="utf-8") + output_md_path.write_text(_bridge_markdown(doc), encoding="utf-8") + return { + "json_path": output_json_path, + "md_path": output_md_path, + } diff --git a/research/frontier-engine/src/frontier_engine/p848_torch_backend.py b/research/frontier-engine/src/frontier_engine/p848_torch_backend.py new file mode 100644 index 0000000..bfb45cf --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/p848_torch_backend.py @@ -0,0 +1,334 @@ +"""Torch-backed batched evaluator for the Problem 848 anchor ladder lane.""" + +from __future__ import annotations + +from math import isqrt +from typing import Any + +from .runtime import RuntimeProbe + +try: + import torch +except ImportError: # pragma: no cover - optional dependency + torch = None + + +def _build_prime_squares(max_value: int) -> list[int]: + """Return all prime squares up to the square root of `max_value`.""" + + limit = max(2, isqrt(max_value) + 1) + sieve = bytearray(limit + 1) + prime_squares: list[int] = [] + for n in range(2, limit + 1): + if sieve[n]: + continue + prime_squares.append(n * n) + start = n * n + for value in range(start, limit + 1, n): + sieve[value] = 1 + return prime_squares + + +def _torch_squarefree_flags( + values: "torch.Tensor", + *, + prime_squares: "torch.Tensor", + value_chunk_size: int, + prime_square_chunk_size: int, +) -> "torch.Tensor": + """Return a boolean squarefree mask for the provided tensor values.""" + + flat = values.reshape(-1) + flags = torch.ones(flat.shape[0], dtype=torch.bool, device=flat.device) + if flat.numel() == 0 or prime_squares.numel() == 0: + return flags.reshape(values.shape) + + for value_start in range(0, flat.numel(), value_chunk_size): + value_stop = min(value_start + value_chunk_size, flat.numel()) + block = flat[value_start:value_stop] + block_flags = torch.ones(block.shape[0], dtype=torch.bool, device=flat.device) + if block.numel() == 0: + continue + + block_max = int(block.max().item()) + prime_limit = int(torch.searchsorted(prime_squares, block_max, right=True).item()) + relevant_prime_squares = prime_squares[:prime_limit] + for prime_start in range(0, relevant_prime_squares.numel(), prime_square_chunk_size): + prime_stop = min(prime_start + prime_square_chunk_size, relevant_prime_squares.numel()) + chunk = relevant_prime_squares[prime_start:prime_stop] + if chunk.numel() == 0: + continue + divisibility = block.unsqueeze(1).remainder(chunk.unsqueeze(0)) == 0 + block_flags &= ~divisibility.any(dim=1) + if not bool(block_flags.any().item()): + break + + flags[value_start:value_stop] = block_flags + + return flags.reshape(values.shape) + + +def _repair_flags_for_targets( + *, + continuation_tensor: "torch.Tensor", + target_ns: list[int], + prime_squares: "torch.Tensor", + value_chunk_size: int, + prime_square_chunk_size: int, +) -> list[list[bool]]: + """Return continuation-by-target repair flags for the provided target `n` values.""" + + if not target_ns: + return [[] for _ in range(int(continuation_tensor.shape[0]))] + + target_tensor = torch.tensor(target_ns, dtype=torch.int64, device=continuation_tensor.device) + repair_values = continuation_tensor.unsqueeze(1) * target_tensor.unsqueeze(0) + 1 + repair_squarefree = _torch_squarefree_flags( + repair_values, + prime_squares=prime_squares, + value_chunk_size=value_chunk_size, + prime_square_chunk_size=prime_square_chunk_size, + ) + repair_mask = (continuation_tensor.unsqueeze(1) <= target_tensor.unsqueeze(0)) & repair_squarefree + repair_rows = repair_mask.detach().cpu().tolist() + return [[bool(value) for value in row] for row in repair_rows] + + +def evaluate_p848_candidates_torch( + *, + prefix_anchors: list[int], + continuations: list[int], + known_packet_ns: list[int], + family_menu_ns: list[int], + observed_first_failures: dict[int, int], + direct_threshold: int, + direct_max: int, + device: str, + probe: RuntimeProbe, + n_chunk_size: int, + value_chunk_size: int, + prime_square_chunk_size: int, +) -> dict[str, Any]: + """Batch-evaluate candidate repairs and direct finite windows with torch.""" + + if torch is None: # pragma: no cover - guarded by runtime resolution + raise RuntimeError("Torch backend requested, but torch is not installed") + + sorted_prefix = sorted(set(int(anchor) for anchor in prefix_anchors)) + sorted_continuations = sorted(set(int(value) for value in continuations)) + anchor_rows = [sorted(set(sorted_prefix + [continuation])) for continuation in sorted_continuations] + anchor_rows_by_continuation = { + continuation: row for continuation, row in zip(sorted_continuations, anchor_rows) + } + max_anchor = max(max(row) for row in anchor_rows) if anchor_rows else max(sorted_prefix, default=0) + packet_max = max(known_packet_ns, default=0) + max_scan_n = max(direct_max, packet_max) + max_value = max(2, max_anchor * max_scan_n + 1) + + prime_square_values = _build_prime_squares(max_value) + prime_squares = torch.tensor(prime_square_values, dtype=torch.int64, device=device) + continuation_tensor = torch.tensor(sorted_continuations, dtype=torch.int64, device=device) + anchor_tensor = torch.tensor(anchor_rows, dtype=torch.int64, device=device) + + repair_flags_by_continuation: dict[int, list[bool]] = {} + known_packet_rows = _repair_flags_for_targets( + continuation_tensor=continuation_tensor, + target_ns=known_packet_ns, + prime_squares=prime_squares, + value_chunk_size=value_chunk_size, + prime_square_chunk_size=prime_square_chunk_size, + ) + for continuation, repair_row in zip(sorted_continuations, known_packet_rows): + repair_flags_by_continuation[continuation] = repair_row + + family_menu_repair_flags_by_continuation: dict[int, list[bool]] = {} + family_menu_rows = _repair_flags_for_targets( + continuation_tensor=continuation_tensor, + target_ns=family_menu_ns, + prime_squares=prime_squares, + value_chunk_size=value_chunk_size, + prime_square_chunk_size=prime_square_chunk_size, + ) + for continuation, repair_row in zip(sorted_continuations, family_menu_rows): + family_menu_repair_flags_by_continuation[continuation] = repair_row + + direct_scans: dict[int, dict[str, Any]] = {} + checked_count = {continuation: 0 for continuation in sorted_continuations} + witness_counts = { + continuation: {anchor: 0 for anchor in row} + for continuation, row in zip(sorted_continuations, anchor_rows) + } + + active_indices = [ + index + for index, continuation in enumerate(sorted_continuations) + if not ( + continuation in observed_first_failures + and direct_threshold > int(observed_first_failures[continuation]) + ) + ] + + for continuation in sorted_continuations: + known_failure = observed_first_failures.get(continuation) + if known_failure is None or direct_threshold <= int(known_failure): + continue + row = anchor_rows_by_continuation[continuation] + direct_scans[continuation] = { + "threshold": direct_threshold, + "max_n": direct_max, + "performed": False, + "skipped": True, + "skip_reason": f"known earlier failure at {known_failure}", + "first_failure": int(known_failure), + "clean_through": int(known_failure) - 1, + "scanned_until": int(known_failure) - 1, + "checked_count": 0, + "all_covered_on_window": False, + "witness_counts": {anchor: 0 for anchor in row}, + } + + if direct_threshold <= direct_max and active_indices: + unresolved = torch.tensor(active_indices, dtype=torch.int64, device=device) + positions_cache: dict[int, torch.Tensor] = {} + + for chunk_start in range(direct_threshold, direct_max + 1, n_chunk_size): + if unresolved.numel() == 0: + break + + chunk_stop = min(chunk_start + n_chunk_size - 1, direct_max) + n_values = torch.arange(chunk_start, chunk_stop + 1, dtype=torch.int64, device=device) + n_values = n_values[n_values.remainder(25) != 7] + if n_values.numel() == 0: + continue + + current_anchors = anchor_tensor.index_select(0, unresolved) + values = current_anchors.unsqueeze(2) * n_values.view(1, 1, -1) + 1 + squarefree = _torch_squarefree_flags( + values, + prime_squares=prime_squares, + value_chunk_size=value_chunk_size, + prime_square_chunk_size=prime_square_chunk_size, + ) + available = current_anchors.unsqueeze(2) <= n_values.view(1, 1, -1) + witness_mask = available & squarefree + has_witness = witness_mask.any(dim=1) + failure_mask = ~has_witness + failure_any = failure_mask.any(dim=1) + first_failure_idx = torch.argmax(failure_mask.to(torch.int64), dim=1) + cutoff = torch.where( + failure_any, + first_failure_idx, + torch.full_like(first_failure_idx, n_values.numel()), + ) + + position_tensor = positions_cache.get(int(n_values.numel())) + if position_tensor is None: + position_tensor = torch.arange(n_values.numel(), dtype=torch.int64, device=device) + positions_cache[int(n_values.numel())] = position_tensor + + valid_prefix = position_tensor.unsqueeze(0) < cutoff.unsqueeze(1) + first_witness = witness_mask & (witness_mask.cumsum(dim=1) == 1) + counted_witness = first_witness & valid_prefix.unsqueeze(1) + witness_increment = counted_witness.sum(dim=2).to(torch.int64).detach().cpu().tolist() + + unresolved_list = unresolved.detach().cpu().tolist() + failure_any_list = failure_any.detach().cpu().tolist() + failure_idx_list = first_failure_idx.detach().cpu().tolist() + cutoff_list = cutoff.detach().cpu().tolist() + n_value_list = n_values.detach().cpu().tolist() + last_n = int(n_value_list[-1]) + + next_unresolved: list[int] = [] + for local_index, candidate_index in enumerate(unresolved_list): + continuation = sorted_continuations[int(candidate_index)] + row_anchors = anchor_rows[int(candidate_index)] + checked_count[continuation] += int(cutoff_list[local_index]) + ( + 1 if bool(failure_any_list[local_index]) else 0 + ) + for anchor_offset, anchor in enumerate(row_anchors): + witness_counts[continuation][anchor] += int(witness_increment[local_index][anchor_offset]) + + if bool(failure_any_list[local_index]): + failure_n = int(n_value_list[int(failure_idx_list[local_index])]) + direct_scans[continuation] = { + "threshold": direct_threshold, + "max_n": direct_max, + "performed": True, + "skipped": False, + "skip_reason": None, + "first_failure": failure_n, + "clean_through": failure_n - 1, + "scanned_until": failure_n, + "checked_count": checked_count[continuation], + "all_covered_on_window": False, + "witness_counts": dict(witness_counts[continuation]), + } + continue + + direct_scans[continuation] = { + "threshold": direct_threshold, + "max_n": direct_max, + "performed": True, + "skipped": False, + "skip_reason": None, + "first_failure": None, + "clean_through": last_n, + "scanned_until": last_n, + "checked_count": checked_count[continuation], + "all_covered_on_window": True, + "witness_counts": dict(witness_counts[continuation]), + } + next_unresolved.append(int(candidate_index)) + + unresolved = torch.tensor(next_unresolved, dtype=torch.int64, device=device) + + if direct_threshold > direct_max: + for continuation, row_anchors in zip(sorted_continuations, anchor_rows): + if continuation in direct_scans: + continue + direct_scans[continuation] = { + "threshold": direct_threshold, + "max_n": direct_max, + "performed": True, + "skipped": False, + "skip_reason": None, + "first_failure": None, + "clean_through": direct_threshold - 1, + "scanned_until": direct_threshold - 1, + "checked_count": 0, + "all_covered_on_window": True, + "witness_counts": {anchor: 0 for anchor in row_anchors}, + } + + for continuation, row_anchors in zip(sorted_continuations, anchor_rows): + if continuation in direct_scans: + continue + direct_scans[continuation] = { + "threshold": direct_threshold, + "max_n": direct_max, + "performed": True, + "skipped": False, + "skip_reason": None, + "first_failure": None, + "clean_through": direct_max, + "scanned_until": direct_max, + "checked_count": checked_count[continuation], + "all_covered_on_window": True, + "witness_counts": dict(witness_counts[continuation]), + } + + return { + "repair_flags_by_continuation": repair_flags_by_continuation, + "family_menu_repair_flags_by_continuation": family_menu_repair_flags_by_continuation, + "direct_scans": direct_scans, + "backend_metadata": { + "resolved_runtime": "torch", + "resolved_device": device, + "probe": probe.to_dict(), + "n_chunk_size": n_chunk_size, + "value_chunk_size": value_chunk_size, + "prime_square_chunk_size": prime_square_chunk_size, + "prime_square_count": len(prime_square_values), + "candidate_scan_kind": "many_tails_many_n", + }, + } diff --git a/research/frontier-engine/src/frontier_engine/pipeline.py b/research/frontier-engine/src/frontier_engine/pipeline.py new file mode 100644 index 0000000..95b67da --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/pipeline.py @@ -0,0 +1,65 @@ +"""Prototype search pipeline for frontier-engine.""" + +from __future__ import annotations + +from dataclasses import dataclass, field + +from .frontier import FrontierManager +from .generator import CandidateGenerator +from .inventory import InventoryManager +from .m8_search import M8SatRailAdaptiveSampler +from .rarity import RarityScorer +from .surrogate import SurrogateModel +from .verifier import SatSeedBundleVerifier + + +@dataclass +class FrontierPipeline: + """Prototype orchestrator for sample -> classify -> inventory -> verify.""" + + generator: CandidateGenerator = field(default_factory=M8SatRailAdaptiveSampler) + surrogate: SurrogateModel = field(default_factory=RarityScorer) + inventory: InventoryManager = field(default_factory=InventoryManager) + frontier: FrontierManager = field(default_factory=FrontierManager) + verifier: SatSeedBundleVerifier = field(default_factory=SatSeedBundleVerifier) + + def run_once_report(self) -> dict[str, object]: + candidates = self.generator.generate() + scores = self.surrogate.score(candidates) + inventory_records = self.inventory.collect(candidates, scores) + items = self.frontier.retain_inventory(inventory_records) + requests = self.verifier.build_requests(items) + results = self.verifier.verify(requests) + + top_signatures = [record.notes.get("signature") for record in inventory_records[:3]] + top_ratings = [record.uniqueness_rating for record in inventory_records[:3]] + best_violation_count = None + if inventory_records: + best_violation_count = min( + int(record.notes.get("sunflower_triple_count", 0)) for record in inventory_records + ) + + summary = { + "candidates": len(candidates), + "inventory_records": len(inventory_records), + "frontier_items": len(items), + "verification_requests": len(requests), + "verification_results": len(results), + "best_sunflower_triple_count": best_violation_count, + "top_signatures": top_signatures, + "top_ratings": top_ratings, + } + + return { + "summary": summary, + "candidates": candidates, + "scores": scores, + "inventory_records": inventory_records, + "frontier_items": items, + "verification_requests": requests, + "verification_results": results, + "generator_metadata": getattr(self.generator, "last_run_metadata", {}), + } + + def run_once(self) -> dict[str, object]: + return dict(self.run_once_report()["summary"]) diff --git a/research/frontier-engine/src/frontier_engine/plans.py b/research/frontier-engine/src/frontier_engine/plans.py new file mode 100644 index 0000000..b02f6db --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/plans.py @@ -0,0 +1,47 @@ +"""Named plans for benchmarks and hardware targets.""" + +from __future__ import annotations + + +PRIMARY_BENCHMARK = { + "benchmark_id": "m8_sat_rail", + "problem_id": "857", + "family": "sunflower", + "exact_target": "M(8,3) exactness / target-46 UNSAT route", + "backend": "sat", + "primary_hardware_profile": "windows_rtx4090", + "primary_goal": "Reduce the finite exact frontier before exact solving.", + "measures": [ + "candidates_per_second", + "unique_signatures_per_batch", + "elite_inventory_size", + "verifier_promotion_rate", + "useful_exact_followups", + "frontier_reduction_against_baseline", + ], +} + + +PRIMARY_HARDWARE = { + "profile_id": "windows_rtx4090", + "os": "windows", + "gpu": "RTX 4090", + "role": "primary_cuda_prototype", +} + + +PRIMARY_SEARCH_PROFILE = { + "profile_id": "m8_sat_rail_windows_rtx4090_v1", + "generator": "m8_adaptive_mutation_sampler", + "runtime_mode": "auto", + "device": "auto", + "warm_start": "known_m8_lb45", + "warm_start_count": 32, + "seed": 857, + "initial_batch_size": 64, + "generations": 5, + "parent_limit": 8, + "children_per_parent": 12, + "mutation_count": 3, + "random_injections": 16, +} diff --git a/research/frontier-engine/src/frontier_engine/rarity.py b/research/frontier-engine/src/frontier_engine/rarity.py new file mode 100644 index 0000000..d9c231b --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/rarity.py @@ -0,0 +1,57 @@ +"""Rarity and uniqueness scoring for prototype frontier-engine.""" + +from __future__ import annotations + +from collections import Counter +import math + +from .contracts import Candidate, ScoreBundle +from .surrogate import SurrogateModel + + +def uniqueness_label(rarity_score: float) -> str: + """Map a rarity score to a simple prototype label.""" + + if rarity_score >= 1.5: + return "ultra_rare" + if rarity_score >= 1.0: + return "rare" + if rarity_score >= 0.6: + return "uncommon" + return "common" + + +class RarityScorer(SurrogateModel): + """Score candidates by stream-relative rarity and signal.""" + + def score(self, candidates: list[Candidate]) -> list[ScoreBundle]: + signatures = [candidate.payload["motif_signature"] for candidate in candidates] + counts = Counter(signatures) + + bundles: list[ScoreBundle] = [] + for candidate in candidates: + signature = candidate.payload["motif_signature"] + count = counts[signature] + rarity = 1.0 / float(count) + signal_score = float(candidate.payload.get("signal_score", 0.0)) + sunflower_violations = int(candidate.payload.get("sunflower_triple_count", 0)) + feasibility = math.exp(-sunflower_violations / 250.0) + promise = (1.4 * rarity) + (1.6 * feasibility) + signal_score + + bundles.append( + ScoreBundle( + candidate_id=candidate.candidate_id, + promise=promise, + rarity=rarity, + metadata={ + "signature": signature, + "signature_count": count, + "signal_score": signal_score, + "sunflower_triple_count": sunflower_violations, + "feasibility_score": feasibility, + "uniqueness_rating": uniqueness_label(rarity), + }, + ) + ) + + return bundles diff --git a/research/frontier-engine/src/frontier_engine/runtime.py b/research/frontier-engine/src/frontier_engine/runtime.py new file mode 100644 index 0000000..e7ba486 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/runtime.py @@ -0,0 +1,78 @@ +"""Runtime probing and selection for frontier-engine search backends.""" + +from __future__ import annotations + +from dataclasses import asdict, dataclass +import importlib.util +from typing import Any + + +@dataclass +class RuntimeProbe: + """Local capability snapshot for optional acceleration backends.""" + + torch_installed: bool + torch_version: str | None + cuda_available: bool + cuda_device_count: int + cuda_device_name: str | None + triton_installed: bool + + def to_dict(self) -> dict[str, Any]: + return asdict(self) + + +def probe_runtime() -> RuntimeProbe: + """Return the available optional runtime capabilities.""" + + triton_installed = importlib.util.find_spec("triton") is not None + torch_spec = importlib.util.find_spec("torch") + if torch_spec is None: + return RuntimeProbe( + torch_installed=False, + torch_version=None, + cuda_available=False, + cuda_device_count=0, + cuda_device_name=None, + triton_installed=triton_installed, + ) + + import torch + + cuda_available = bool(torch.cuda.is_available()) + cuda_device_count = int(torch.cuda.device_count()) if cuda_available else 0 + cuda_device_name = torch.cuda.get_device_name(0) if cuda_device_count else None + return RuntimeProbe( + torch_installed=True, + torch_version=str(getattr(torch, "__version__", "")) or None, + cuda_available=cuda_available, + cuda_device_count=cuda_device_count, + cuda_device_name=cuda_device_name, + triton_installed=triton_installed, + ) + + +def resolve_runtime_mode(requested_runtime: str, probe: RuntimeProbe) -> str: + """Resolve `auto` into a concrete backend name.""" + + if requested_runtime == "auto": + return "torch" if probe.torch_installed else "python" + if requested_runtime == "torch" and not probe.torch_installed: + raise RuntimeError("runtime='torch' requested, but torch is not installed") + if requested_runtime not in {"python", "torch"}: + raise ValueError(f"unknown runtime mode: {requested_runtime}") + return requested_runtime + + +def resolve_device(requested_device: str, runtime_mode: str, probe: RuntimeProbe) -> str: + """Resolve device selection for the chosen runtime.""" + + if runtime_mode == "python": + return "cpu" + if requested_device == "auto": + return "cuda" if probe.cuda_available else "cpu" + if requested_device == "cuda" and not probe.cuda_available: + raise RuntimeError("device='cuda' requested, but no CUDA device is available") + if requested_device not in {"cpu", "cuda"}: + raise ValueError(f"unknown device selection: {requested_device}") + return requested_device diff --git a/research/frontier-engine/src/frontier_engine/sampler.py b/research/frontier-engine/src/frontier_engine/sampler.py new file mode 100644 index 0000000..3c7e635 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/sampler.py @@ -0,0 +1,26 @@ +"""Prototype random sampling for rare-structure search.""" + +from __future__ import annotations + +import random + +from .benchmarks.m8_sat_rail import ALL_MASKS, TARGET_FAMILY_SIZE, build_candidate +from .contracts import Candidate +from .generator import CandidateGenerator + + +class PrototypeRandomSampler(CandidateGenerator): + """Emit benchmark-shaped family candidates for the M(8,3) rail.""" + + def __init__(self, batch_size: int = 64, seed: int = 857) -> None: + self.batch_size = batch_size + self.random = random.Random(seed) + + def generate(self) -> list[Candidate]: + candidates: list[Candidate] = [] + + for index in range(self.batch_size): + family_masks = self.random.sample(ALL_MASKS, TARGET_FAMILY_SIZE) + candidates.append(build_candidate(candidate_id=f"m8-seed-{index}", family_masks=family_masks)) + + return candidates diff --git a/research/frontier-engine/src/frontier_engine/surrogate.py b/research/frontier-engine/src/frontier_engine/surrogate.py new file mode 100644 index 0000000..bd5ded8 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/surrogate.py @@ -0,0 +1,24 @@ +"""Surrogate interfaces for frontier-engine.""" + +from __future__ import annotations + +from typing import Protocol + +from .contracts import Candidate, ScoreBundle + + +class SurrogateModel(Protocol): + """Score candidates for promise and verifier alignment.""" + + def score(self, candidates: list[Candidate]) -> list[ScoreBundle]: + """Return score bundles for each candidate.""" + + +class NullSurrogate: + """Placeholder surrogate that scores nothing yet.""" + + def score(self, candidates: list[Candidate]) -> list[ScoreBundle]: + return [ + ScoreBundle(candidate_id=c.candidate_id, promise=0.0, metadata={"placeholder": True}) + for c in candidates + ] diff --git a/research/frontier-engine/src/frontier_engine/verifier.py b/research/frontier-engine/src/frontier_engine/verifier.py new file mode 100644 index 0000000..c0b9d55 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/verifier.py @@ -0,0 +1,81 @@ +"""Exact verifier interfaces for frontier-engine.""" + +from __future__ import annotations + +from typing import Protocol + +from .contracts import FrontierItem, VerificationRequest, VerificationResult + + +class ExactVerifier(Protocol): + """Run exact work on promoted frontier items.""" + + def verify(self, requests: list[VerificationRequest]) -> list[VerificationResult]: + """Return exact verification results.""" + + +class NullVerifier: + """Placeholder verifier until a SAT or exact backend is attached.""" + + def build_requests(self, items: list[FrontierItem]) -> list[VerificationRequest]: + return [ + VerificationRequest( + request_id=f"verify:{item.candidate.candidate_id}", + candidate_id=item.candidate.candidate_id, + payload=item.candidate.payload, + backend="null", + ) + for item in items + ] + + def verify(self, requests: list[VerificationRequest]) -> list[VerificationResult]: + return [ + VerificationResult( + request_id=request.request_id, + candidate_id=request.candidate_id, + status="unverified_placeholder", + metadata={"backend": request.backend}, + ) + for request in requests + ] + + +class SatSeedBundleVerifier: + """Prepare promoted candidates as SAT-facing seed work packets.""" + + def build_requests(self, items: list[FrontierItem]) -> list[VerificationRequest]: + return [ + VerificationRequest( + request_id=f"seed:{item.candidate.candidate_id}", + candidate_id=item.candidate.candidate_id, + payload={ + "benchmark_id": item.candidate.payload["benchmark_id"], + "n": item.candidate.payload["n"], + "k": item.candidate.payload["k"], + "family_size": item.candidate.payload["target_family_size"], + "family": item.candidate.payload["family_masks"], + "observed_sunflower_triple_count": item.candidate.payload[ + "sunflower_triple_count" + ], + }, + backend="sat_seed_bundle", + ) + for item in items + ] + + def verify(self, requests: list[VerificationRequest]) -> list[VerificationResult]: + return [ + VerificationResult( + request_id=request.request_id, + candidate_id=request.candidate_id, + status="seed_bundle_ready", + metadata={ + "backend": request.backend, + "family_size": request.payload["family_size"], + "observed_sunflower_triple_count": request.payload[ + "observed_sunflower_triple_count" + ], + }, + ) + for request in requests + ] diff --git a/research/frontier-engine/src/frontier_engine/verifier_bundle.py b/research/frontier-engine/src/frontier_engine/verifier_bundle.py new file mode 100644 index 0000000..858dd71 --- /dev/null +++ b/research/frontier-engine/src/frontier_engine/verifier_bundle.py @@ -0,0 +1,72 @@ +"""Bundle exporters for SAT-facing seed families.""" + +from __future__ import annotations + +from datetime import datetime, timezone +import json +from pathlib import Path +from typing import Any + +from .artifacts import _serialize + + +def write_m8_sat_seed_bundle( + *, + report: dict[str, Any], + output_dir: Path, + benchmark: dict[str, Any], + top_k: int = 8, +) -> Path: + """Write a seed bundle for SAT-facing follow-up on elite families.""" + + timestamp = datetime.now(timezone.utc).strftime("%Y%m%dT%H%M%SZ") + bundle_dir = output_dir / f"{benchmark['benchmark_id']}-sat-seeds-{timestamp}" + bundle_dir.mkdir(parents=True, exist_ok=True) + + records = list(report.get("inventory_records", []))[:top_k] + seed_files: list[dict[str, Any]] = [] + + for rank, record in enumerate(records, start=1): + candidate = record.candidate + payload = candidate.payload + filename = f"rank-{rank:02d}-{candidate.candidate_id}.json" + path = bundle_dir / filename + doc = { + "schema": "frontier_engine.m8_sat_seed/1", + "problem_id": benchmark.get("problem_id"), + "benchmark_id": benchmark["benchmark_id"], + "n": payload["n"], + "k": payload["k"], + "family_size": payload["target_family_size"], + "family": payload["family_masks"], + "candidate_id": candidate.candidate_id, + "source": "frontier-engine", + "observed_sunflower_triple_count": payload["sunflower_triple_count"], + "motif_signature": payload["motif_signature"], + "signal_score": payload["signal_score"], + "rarity_score": record.rarity_score, + "uniqueness_rating": record.uniqueness_rating, + } + path.write_text(json.dumps(_serialize(doc), indent=2) + "\n", encoding="utf-8") + seed_files.append( + { + "rank": rank, + "candidate_id": candidate.candidate_id, + "file": filename, + "observed_sunflower_triple_count": payload["sunflower_triple_count"], + } + ) + + manifest = { + "bundle_version": 1, + "bundle_kind": "m8_sat_seed_bundle", + "benchmark": benchmark, + "summary": report["summary"], + "generator_metadata": report.get("generator_metadata", {}), + "seed_files": seed_files, + } + (bundle_dir / "manifest.json").write_text( + json.dumps(_serialize(manifest), indent=2) + "\n", + encoding="utf-8", + ) + return bundle_dir diff --git a/src/commands/frontier.js b/src/commands/frontier.js new file mode 100644 index 0000000..9b9b558 --- /dev/null +++ b/src/commands/frontier.js @@ -0,0 +1,1717 @@ +import { + applyFrontierBrevProvision, + applyFrontierBrevFleetProvision, + applyFrontierFleetSync, + setFrontierPaidFleetAccess, + setFrontierPaidRemoteAccess, + applyFrontierRemoteAttach, + applyFrontierRemoteSetup, + applyFrontierRemoteSync, + applyFrontierSetup, + applyFrontierUseRemote, + getFrontierBrevProvisionSnapshot, + getFrontierBrevFleetProvisionSnapshot, + getFrontierFleetSnapshot, + getFrontierFleetsSnapshot, + getFrontierFleetSyncSnapshot, + getFrontierLanesSnapshot, + getFrontierRemoteAttachSnapshot, + getFrontierRemoteSetupSnapshot, + getFrontierRemotesSnapshot, + getFrontierRemoteSyncSnapshot, + getFrontierDoctorSnapshot, + getFrontierSetupSnapshot, + syncFrontierDoctorSnapshot, +} from '../runtime/frontier.js'; +import { + getFrontierSessionSnapshot, + listFrontierSessionSnapshots, + stopFrontierSession, +} from '../runtime/frontier-sessions.js'; +import { getWorkspaceRoot } from '../runtime/paths.js'; + +function parseDoctorArgs(args) { + const parsed = { asJson: false }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + return { error: `Unknown frontier doctor option: ${token}` }; + } + return parsed; +} + +function parseLanesArgs(args) { + const parsed = { asJson: false }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + return { error: `Unknown frontier lanes option: ${token}` }; + } + return parsed; +} + +function parseRemotesArgs(args) { + const parsed = { asJson: false }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + return { error: `Unknown frontier remotes option: ${token}` }; + } + return parsed; +} + +function parseFleetsArgs(args) { + const parsed = { asJson: false, fleetId: null }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (!parsed.fleetId) { + parsed.fleetId = token; + continue; + } + return { error: `Unknown frontier fleet option: ${token}` }; + } + return parsed; +} + +function parseSessionsArgs(args) { + const parsed = { asJson: false }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + return { error: `Unknown frontier sessions option: ${token}` }; + } + return parsed; +} + +function parseSessionArgs(args) { + const parsed = { + asJson: false, + sessionId: null, + }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (!parsed.sessionId) { + parsed.sessionId = token; + continue; + } + return { error: `Unknown frontier session option: ${token}` }; + } + if (!parsed.sessionId) { + return { error: 'Missing frontier session id.' }; + } + return parsed; +} + +function parseUseRemoteArgs(args) { + const parsed = { + asJson: false, + remoteId: null, + }; + for (const token of args) { + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (!parsed.remoteId) { + parsed.remoteId = token; + continue; + } + return { error: `Unknown frontier use-remote option: ${token}` }; + } + if (!parsed.remoteId) { + return { error: 'Missing frontier remote id.' }; + } + return parsed; +} + +function parseAttachArgs(args) { + const parsed = { + asJson: false, + apply: false, + provider: 'ssh', + remoteId: null, + instanceName: null, + sshHost: null, + engineRoot: null, + pythonCommand: null, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--ssh-host') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing host after --ssh-host.' }; + } + parsed.sshHost = nextValue; + index += 1; + continue; + } + if (token === '--remote-id') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing remote id after --remote-id.' }; + } + parsed.remoteId = nextValue; + index += 1; + continue; + } + if (token === '--engine-root') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing path after --engine-root.' }; + } + parsed.engineRoot = nextValue; + index += 1; + continue; + } + if (token === '--python-command') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing command after --python-command.' }; + } + parsed.pythonCommand = nextValue; + index += 1; + continue; + } + return { error: `Unknown frontier attach-ssh option: ${token}` }; + } + + return parsed; +} + +function parseAttachBrevArgs(args) { + const parsed = { + asJson: false, + apply: false, + provider: 'brev', + remoteId: null, + instanceName: null, + sshHost: null, + engineRoot: null, + pythonCommand: null, + enablePaidRung: false, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--enable-paid-rung') { + parsed.enablePaidRung = true; + continue; + } + if (token === '--instance') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing instance name after --instance.' }; + } + parsed.instanceName = nextValue; + index += 1; + continue; + } + if (token === '--remote-id') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing remote id after --remote-id.' }; + } + parsed.remoteId = nextValue; + index += 1; + continue; + } + if (token === '--ssh-host') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing SSH host after --ssh-host.' }; + } + parsed.sshHost = nextValue; + index += 1; + continue; + } + if (token === '--engine-root') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing path after --engine-root.' }; + } + parsed.engineRoot = nextValue; + index += 1; + continue; + } + if (token === '--python-command') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing command after --python-command.' }; + } + parsed.pythonCommand = nextValue; + index += 1; + continue; + } + return { error: `Unknown frontier attach-brev option: ${token}` }; + } + + if (!parsed.instanceName && !parsed.sshHost) { + return { error: 'Brev attach requires --instance or --ssh-host.' }; + } + + return parsed; +} + +function parseSyncArgs(args) { + const parsed = { + asJson: false, + apply: false, + remoteId: null, + sshHost: null, + engineRoot: null, + pythonCommand: null, + laneId: null, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--ssh-host') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing host after --ssh-host.' }; + } + parsed.sshHost = nextValue; + index += 1; + continue; + } + if (token === '--remote-id') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing remote id after --remote-id.' }; + } + parsed.remoteId = nextValue; + index += 1; + continue; + } + if (token === '--engine-root') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing path after --engine-root.' }; + } + parsed.engineRoot = nextValue; + index += 1; + continue; + } + if (token === '--python-command') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing command after --python-command.' }; + } + parsed.pythonCommand = nextValue; + index += 1; + continue; + } + if (token === '--lane') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing lane id after --lane.' }; + } + parsed.laneId = nextValue; + index += 1; + continue; + } + return { error: `Unknown frontier sync-ssh option: ${token}` }; + } + + return parsed; +} + +function parseFleetSyncArgs(args) { + const parsed = { + asJson: false, + apply: false, + fleetId: null, + laneId: null, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--lane') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing lane id after --lane.' }; + } + parsed.laneId = nextValue; + index += 1; + continue; + } + if (!parsed.fleetId) { + parsed.fleetId = token; + continue; + } + return { error: `Unknown frontier sync-fleet option: ${token}` }; + } + + if (!parsed.fleetId) { + return { error: 'Missing frontier fleet id.' }; + } + + return parsed; +} + +function parseCreateBrevArgs(args) { + const parsed = { + asJson: false, + apply: false, + dryRun: false, + attach: false, + instanceName: null, + type: null, + gpuName: null, + provider: null, + count: null, + parallel: null, + minVram: null, + minTotalVram: null, + maxBootTime: null, + minDisk: null, + minCapability: null, + sort: null, + startupScript: null, + detached: false, + syncLane: null, + sshHost: null, + engineRoot: null, + pythonCommand: null, + enablePaidRung: false, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--dry-run') { + parsed.dryRun = true; + continue; + } + if (token === '--attach') { + parsed.attach = true; + continue; + } + if (token === '--enable-paid-rung') { + parsed.enablePaidRung = true; + continue; + } + if (token === '--detached') { + parsed.detached = true; + continue; + } + if (!token.startsWith('--') && !parsed.instanceName) { + parsed.instanceName = token; + continue; + } + const nextValue = args[index + 1]; + if (token === '--name') { + if (!nextValue) { + return { error: 'Missing instance name after --name.' }; + } + parsed.instanceName = nextValue; + index += 1; + continue; + } + if (token === '--type') { + if (!nextValue) { + return { error: 'Missing type after --type.' }; + } + parsed.type = nextValue; + index += 1; + continue; + } + if (token === '--gpu-name') { + if (!nextValue) { + return { error: 'Missing gpu name after --gpu-name.' }; + } + parsed.gpuName = nextValue; + index += 1; + continue; + } + if (token === '--provider') { + if (!nextValue) { + return { error: 'Missing provider after --provider.' }; + } + parsed.provider = nextValue; + index += 1; + continue; + } + if (token === '--count') { + if (!nextValue) { + return { error: 'Missing count after --count.' }; + } + parsed.count = nextValue; + index += 1; + continue; + } + if (token === '--parallel') { + if (!nextValue) { + return { error: 'Missing parallel value after --parallel.' }; + } + parsed.parallel = nextValue; + index += 1; + continue; + } + if (token === '--min-vram') { + if (!nextValue) { + return { error: 'Missing value after --min-vram.' }; + } + parsed.minVram = nextValue; + index += 1; + continue; + } + if (token === '--min-total-vram') { + if (!nextValue) { + return { error: 'Missing value after --min-total-vram.' }; + } + parsed.minTotalVram = nextValue; + index += 1; + continue; + } + if (token === '--max-boot-time') { + if (!nextValue) { + return { error: 'Missing value after --max-boot-time.' }; + } + parsed.maxBootTime = nextValue; + index += 1; + continue; + } + if (token === '--min-disk') { + if (!nextValue) { + return { error: 'Missing value after --min-disk.' }; + } + parsed.minDisk = nextValue; + index += 1; + continue; + } + if (token === '--min-capability') { + if (!nextValue) { + return { error: 'Missing value after --min-capability.' }; + } + parsed.minCapability = nextValue; + index += 1; + continue; + } + if (token === '--sort') { + if (!nextValue) { + return { error: 'Missing value after --sort.' }; + } + parsed.sort = nextValue; + index += 1; + continue; + } + if (token === '--startup-script') { + if (!nextValue) { + return { error: 'Missing value after --startup-script.' }; + } + parsed.startupScript = nextValue; + index += 1; + continue; + } + if (token === '--sync-lane') { + if (!nextValue) { + return { error: 'Missing lane id after --sync-lane.' }; + } + parsed.syncLane = nextValue; + index += 1; + continue; + } + if (token === '--ssh-host') { + if (!nextValue) { + return { error: 'Missing SSH host after --ssh-host.' }; + } + parsed.sshHost = nextValue; + index += 1; + continue; + } + if (token === '--engine-root') { + if (!nextValue) { + return { error: 'Missing path after --engine-root.' }; + } + parsed.engineRoot = nextValue; + index += 1; + continue; + } + if (token === '--python-command') { + if (!nextValue) { + return { error: 'Missing command after --python-command.' }; + } + parsed.pythonCommand = nextValue; + index += 1; + continue; + } + return { error: `Unknown frontier create-brev option: ${token}` }; + } + + if (!parsed.instanceName) { + return { error: 'Missing Brev instance name.' }; + } + + return parsed; +} + +function parseCreateBrevFleetArgs(args) { + const parsed = parseCreateBrevArgs(args); + if (parsed.error) { + return parsed; + } + if (parsed.count === null) { + parsed.count = '2'; + } + return parsed; +} + +function parseSetupArgs(args) { + const parsed = { + asJson: false, + apply: false, + mode: 'base', + torchIndexUrl: null, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--base') { + parsed.mode = 'base'; + continue; + } + if (token === '--cpu') { + parsed.mode = 'cpu'; + continue; + } + if (token === '--cuda') { + parsed.mode = 'cuda'; + continue; + } + if (token === '--torch-index-url') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing URL after --torch-index-url.' }; + } + parsed.torchIndexUrl = nextValue; + index += 1; + continue; + } + return { error: `Unknown frontier setup option: ${token}` }; + } + + return parsed; +} + +function parseRemoteSetupArgs(args) { + const parsed = { + asJson: false, + apply: false, + mode: 'base', + remoteId: null, + torchIndexUrl: null, + }; + + for (let index = 0; index < args.length; index += 1) { + const token = args[index]; + if (token === '--json') { + parsed.asJson = true; + continue; + } + if (token === '--apply') { + parsed.apply = true; + continue; + } + if (token === '--base') { + parsed.mode = 'base'; + continue; + } + if (token === '--cpu') { + parsed.mode = 'cpu'; + continue; + } + if (token === '--cuda') { + parsed.mode = 'cuda'; + continue; + } + if (token === '--remote-id') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing remote id after --remote-id.' }; + } + parsed.remoteId = nextValue; + index += 1; + continue; + } + if (token === '--torch-index-url') { + const nextValue = args[index + 1]; + if (!nextValue) { + return { error: 'Missing URL after --torch-index-url.' }; + } + parsed.torchIndexUrl = nextValue; + index += 1; + continue; + } + return { error: `Unknown frontier setup-remote option: ${token}` }; + } + + return parsed; +} + +function formatRuntime(runtime, label) { + if (!runtime.available) { + return `${label}: unavailable${runtime.error ? ` (${runtime.error})` : ''}`; + } + const torch = runtime.torchInstalled + ? `torch ${runtime.torchVersion ?? '(unknown version)'}` + : 'torch missing'; + const cuda = runtime.cudaAvailable + ? `cuda yes (${runtime.cudaDeviceCount} device${runtime.cudaDeviceCount === 1 ? '' : 's'}${runtime.cudaDeviceNames.length > 0 ? `: ${runtime.cudaDeviceNames.join(', ')}` : ''})` + : 'cuda no'; + return `${label}: ${runtime.pythonVersion} at ${runtime.pythonExecutable} | ${torch} | ${cuda}`; +} + +function printDoctor(snapshot) { + console.log('Frontier runtime doctor'); + console.log(`Workspace root: ${snapshot.workspaceRoot}`); + console.log(`Frontier workspace dir: ${snapshot.frontierWorkspaceDir}`); + console.log(`Managed venv dir: ${snapshot.managedVenvDir}`); + console.log(`Bundled engine: ${snapshot.bundledEnginePresent ? 'yes' : 'no'}`); + console.log(`Bundled engine root: ${snapshot.bundledEngineRoot}`); + console.log(`Bundled pyproject: ${snapshot.bundledEnginePyprojectPresent ? snapshot.bundledEnginePyprojectPath : '(missing)'}`); + console.log(`Bundled engine CLI: ${snapshot.bundledEngineCliPresent ? snapshot.bundledEngineCliPath : '(missing)'}`); + console.log(formatRuntime(snapshot.systemPython, 'System python')); + console.log(formatRuntime(snapshot.managedPython, 'Managed python')); + console.log(`Frontier loop opt-in: ${snapshot.frontierLoopOptIn ? 'yes' : 'no'}`); + console.log(`Frontier loop mode: ${snapshot.frontierLoopMode ?? 'inactive'}`); + console.log(`Bridge refresh ready: ${snapshot.bridgeRefreshReady ? 'yes' : 'no'}`); + console.log(`Managed frontier ready: ${snapshot.managedFrontierReady ? 'yes' : 'no'}`); + console.log(`GPU search ready: ${snapshot.gpuSearchReady ? 'yes' : 'no'}`); + if (snapshot.registeredRemotes?.length) { + console.log(`Registered remotes: ${snapshot.registeredRemotes.length}`); + console.log(`Active remote id: ${snapshot.activeRemoteId ?? '(none)'}`); + } + if (snapshot.registeredFleets?.length) { + console.log(`Registered fleets: ${snapshot.registeredFleets.length}`); + } + if (snapshot.remote?.sshHost) { + console.log(`Remote provider: ${snapshot.remote.provider ?? 'ssh'}`); + if (snapshot.remote.instanceName) { + console.log(`Remote instance: ${snapshot.remote.instanceName}`); + } + console.log(`Remote paid rung: ${snapshot.remote.paidRung ? 'yes' : 'no'}`); + if (snapshot.remote.paidRung) { + console.log(`Remote paid enabled: ${snapshot.remote.paidEnabled ? 'yes' : 'no'}`); + } + console.log(`Remote SSH host: ${snapshot.remote.sshHost}`); + console.log(`Remote engine root: ${snapshot.remote.engineRoot}`); + console.log(`Remote last sync: ${snapshot.remote.lastSyncAt ?? '(never)'}`); + console.log(`Remote sync scope: ${snapshot.remote.lastSyncScope ?? '(none)'}`); + console.log(formatRuntime(snapshot.remote, 'Remote runtime')); + } + if (snapshot.researchModes) { + console.log(`Bridge refresh mode: ${snapshot.researchModes.bridgeRefresh?.mode ?? 'unavailable'}`); + console.log(`Family search mode: ${snapshot.researchModes.familySearch?.mode ?? 'unavailable'}`); + console.log(`Heavy search mode: ${snapshot.researchModes.heavySearch?.mode ?? 'unavailable'}`); + } + console.log('Suggested commands:'); + console.log(`- ${snapshot.commands.lanes}`); + console.log(`- ${snapshot.commands.remotes}`); + console.log(`- ${snapshot.commands.fleets}`); + console.log(`- ${snapshot.commands.useRemote}`); + console.log(`- ${snapshot.commands.setupBase}`); + console.log(`- ${snapshot.commands.setupCpu}`); + console.log(`- ${snapshot.commands.setupCuda}`); + console.log(`- ${snapshot.commands.createBrev}`); + console.log(`- ${snapshot.commands.createBrevFleet}`); + console.log(`- ${snapshot.commands.attachSsh}`); + console.log(`- ${snapshot.commands.attachBrev}`); + console.log(`- ${snapshot.commands.enablePaidRemote}`); + console.log(`- ${snapshot.commands.enablePaidFleet}`); + console.log(`- ${snapshot.commands.syncSsh}`); + console.log(`- ${snapshot.commands.syncFleet}`); + console.log(`- ${snapshot.commands.bridgeRefresh848}`); +} + +function printLanes(snapshot) { + if (!snapshot.available) { + console.log('Frontier lanes: unavailable'); + console.log(`Error: ${snapshot.error ?? '(unknown)'}`); + return; + } + console.log('Frontier lanes'); + console.log(`Runner mode: ${snapshot.runnerMode ?? '(unknown)'}`); + for (const lane of snapshot.lanes) { + console.log(`- ${lane.lane_id} [problem ${lane.problem_id}]`); + console.log(` status: ${lane.status}`); + console.log(` family: ${lane.family}`); + console.log(` route posture: ${lane.route_posture}`); + console.log(` objective: ${lane.search_objective}`); + console.log(` experiment dir: ${lane.experiment_dir}`); + } + if (snapshot.errors?.length) { + console.log('Lane load errors:'); + for (const error of snapshot.errors) { + console.log(`- ${error.laneId}: ${error.error}`); + } + } +} + +function printRemotes(snapshot) { + console.log('Frontier remotes'); + console.log(`Workspace root: ${snapshot.workspaceRoot}`); + console.log(`Remote count: ${snapshot.remoteCount}`); + console.log(`Active remote id: ${snapshot.activeRemoteId ?? '(none)'}`); + for (const remote of snapshot.remotes) { + console.log(`- ${remote.remoteId}${remote.active ? ' [active]' : ''}`); + console.log(` provider: ${remote.provider ?? 'ssh'}`); + console.log(` paid rung: ${remote.paidRung ? 'yes' : 'no'}`); + if (remote.paidRung) { + console.log(` paid enabled: ${remote.paidEnabled ? 'yes' : 'no'}`); + } + console.log(` instance: ${remote.instanceName ?? '(none)'}`); + console.log(` ssh host: ${remote.sshHost ?? '(none)'}`); + console.log(` engine root: ${remote.engineRoot ?? '(none)'}`); + console.log(` python command: ${remote.pythonCommand ?? '(none)'}`); + } +} + +function printFleets(snapshot) { + console.log('Frontier fleets'); + console.log(`Workspace root: ${snapshot.workspaceRoot}`); + console.log(`Fleet count: ${snapshot.fleetCount}`); + for (const fleet of snapshot.fleets) { + console.log(`- ${fleet.fleetId}`); + console.log(` provider: ${fleet.provider ?? 'brev'}`); + console.log(` paid rung: ${fleet.paidRung ? 'yes' : 'no'}`); + if (fleet.paidRung) { + console.log(` paid enabled: ${fleet.paidEnabled ? 'yes' : 'no'}`); + } + console.log(` count: ${fleet.count}`); + console.log(` lane: ${fleet.laneId ?? '(none)'}`); + console.log(` topology: ${fleet.intendedTopology ?? '(none)'}`); + console.log(` attached/ready: ${fleet.attachedCount}/${fleet.readyGpuCount}`); + console.log(` remotes: ${fleet.remoteIds.join(', ') || '(none)'}`); + } +} + +function printFleet(snapshot) { + if (!snapshot) { + console.log('Frontier fleet: unavailable'); + return; + } + console.log('Frontier fleet'); + console.log(`Fleet id: ${snapshot.fleetId}`); + console.log(`Provider: ${snapshot.provider ?? 'brev'}`); + console.log(`Paid rung: ${snapshot.paidRung ? 'yes' : 'no'}`); + if (snapshot.paidRung) { + console.log(`Paid enabled: ${snapshot.paidEnabled ? 'yes' : 'no'}`); + } + console.log(`Count: ${snapshot.count}`); + console.log(`Lane: ${snapshot.laneId ?? '(none)'}`); + console.log(`Topology: ${snapshot.intendedTopology ?? '(none)'}`); + console.log(`Created at: ${snapshot.createdAt ?? '(unknown)'}`); + console.log(`Last provisioned at: ${snapshot.lastProvisionedAt ?? '(unknown)'}`); + console.log(`Attached members: ${snapshot.attachedCount}`); + console.log(`GPU-ready members: ${snapshot.readyGpuCount}`); + console.log('Members:'); + for (const member of snapshot.members ?? []) { + console.log(`- ${member.remoteId}${member.active ? ' [active]' : ''}`); + console.log(` provider: ${member.provider ?? '(unknown)'}`); + console.log(` instance: ${member.instanceName ?? '(none)'}`); + console.log(` ssh host: ${member.sshHost ?? '(none)'}`); + console.log(` attached: ${member.attached ? 'yes' : 'no'}`); + console.log(` gpu ready: ${member.gpuSearchReady ? 'yes' : 'no'}`); + console.log(` last sync: ${member.lastSyncAt ?? '(never)'}`); + } +} + +function printUseRemoteResult(result) { + if (!result.ok) { + console.log('Frontier use-remote: failed'); + console.log(`Error: ${result.error ?? '(unknown)'}`); + return; + } + console.log('Frontier use-remote: complete'); + console.log(`Applied at: ${result.appliedAt}`); + console.log(`Active remote id: ${result.snapshot.activeRemoteId ?? '(none)'}`); +} + +function printPaidRungResult(result, targetLabel) { + if (!result.ok) { + console.log(`Frontier ${targetLabel}: failed`); + console.log(`Error: ${result.error ?? '(unknown)'}`); + return; + } + console.log(`Frontier ${targetLabel}: complete`); + console.log(`Applied at: ${result.appliedAt}`); + console.log(`Enabled: ${result.enabled ? 'yes' : 'no'}`); + if (result.remoteId) { + console.log(`Remote id: ${result.remoteId}`); + } + if (result.fleetId) { + console.log(`Fleet id: ${result.fleetId}`); + } +} + +function printSessions(snapshot) { + console.log('Frontier sessions'); + console.log(`Workspace root: ${snapshot.workspaceRoot}`); + console.log(`Sessions dir: ${snapshot.sessionsDir}`); + console.log(`Session count: ${snapshot.sessionCount}`); + for (const session of snapshot.sessions) { + console.log(`- ${session.sessionId} [${session.status}]`); + console.log(` label: ${session.label}`); + console.log(` problem/action: ${session.problemId ?? '(none)'} / ${session.actionId ?? '(none)'}`); + console.log(` mode/source: ${session.mode ?? '(none)'} / ${session.source ?? '(none)'}`); + console.log(` launched: ${session.launchedAt}`); + if (session.reviewDueAt) { + console.log(` review due: ${session.reviewDueAt} [${session.reviewState}]`); + } + if (session.runDir) { + console.log(` run dir: ${session.runDir}`); + } + } +} + +function printSession(snapshot) { + if (!snapshot) { + console.log('Frontier session: unavailable'); + return; + } + console.log('Frontier session'); + console.log(`Session id: ${snapshot.sessionId}`); + console.log(`Status: ${snapshot.status}`); + console.log(`Label: ${snapshot.label}`); + console.log(`Problem id: ${snapshot.problemId ?? '(none)'}`); + console.log(`Action id: ${snapshot.actionId ?? '(none)'}`); + console.log(`Mode: ${snapshot.mode ?? '(none)'}`); + console.log(`Source: ${snapshot.source ?? '(none)'}`); + console.log(`Launched at: ${snapshot.launchedAt}`); + console.log(`PID: ${snapshot.pid ?? '(none)'}`); + console.log(`Running: ${snapshot.running ? 'yes' : 'no'}`); + console.log(`Command: ${snapshot.commandLine}`); + console.log(`Stdout log: ${snapshot.stdoutPath}`); + console.log(`Stderr log: ${snapshot.stderrPath}`); + if (snapshot.reviewDueAt) { + console.log(`Review due: ${snapshot.reviewDueAt}`); + console.log(`Review state: ${snapshot.reviewState}`); + } + if (snapshot.runDir) { + console.log(`Run dir: ${snapshot.runDir}`); + } + if (snapshot.stdoutTail?.length) { + console.log('Stdout tail:'); + for (const line of snapshot.stdoutTail) { + console.log(`- ${line}`); + } + } + if (snapshot.stderrTail?.length) { + console.log('Stderr tail:'); + for (const line of snapshot.stderrTail) { + console.log(`- ${line}`); + } + } +} + +function printStopSessionResult(result) { + if (!result.ok) { + console.log('Frontier stop-session: failed'); + console.log(`Error: ${result.error ?? '(unknown)'}`); + return; + } + console.log('Frontier stop-session: complete'); + console.log(`Requested stop: ${result.requested ? 'yes' : 'no'}`); + console.log(`Already exited: ${result.alreadyExited ? 'yes' : 'no'}`); + if (result.session) { + console.log(`Session id: ${result.session.sessionId}`); + console.log(`Status: ${result.session.status}`); + } +} + +function printSetup(snapshot) { + console.log('Frontier setup plan'); + console.log(`Workspace root: ${snapshot.plan.workspaceRoot}`); + console.log(`Mode: ${snapshot.plan.mode}`); + console.log(`Frontier workspace dir: ${snapshot.plan.frontierWorkspaceDir}`); + console.log(`Managed venv dir: ${snapshot.plan.managedVenvDir}`); + console.log(`Bundled engine root: ${snapshot.plan.bundledEngineRoot}`); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log('Planned commands:'); + for (const [index, step] of snapshot.plan.steps.entries()) { + console.log(`${index + 1}. ${step.commandLine}${step.optional ? ' [optional]' : ''}`); + if (step.note) { + console.log(` note: ${step.note}`); + } + } + console.log('Notes:'); + for (const note of snapshot.plan.notes) { + console.log(`- ${note}`); + } + console.log('Current readiness:'); + console.log(`- bridge refresh ready: ${snapshot.doctor.bridgeRefreshReady ? 'yes' : 'no'}`); + console.log(`- managed frontier ready: ${snapshot.doctor.managedFrontierReady ? 'yes' : 'no'}`); + console.log(`- GPU search ready: ${snapshot.doctor.gpuSearchReady ? 'yes' : 'no'}`); +} + +function printSetupResult(result) { + if (!result.ok) { + console.log('Frontier setup: failed'); + if (result.error) { + console.log(`Error: ${result.error}`); + } + printSetup({ + apply: true, + plan: result.plan, + doctor: result.doctor, + }); + return; + } + + console.log('Frontier setup: complete'); + console.log(`Applied at: ${result.appliedAt}`); + console.log('Executed steps:'); + for (const step of result.stepResults) { + console.log(`- ${step.label}: ${step.ok ? 'ok' : 'failed'} (${step.commandLine})`); + } + printDoctor(result.doctor); +} + +function printRemoteSetup(snapshot) { + console.log('Frontier remote setup plan'); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log(`Mode: ${snapshot.plan.mode}`); + console.log(`Remote id: ${snapshot.plan.remoteId ?? '(none)'}`); + console.log(`Remote provider: ${snapshot.plan.remote?.provider ?? 'ssh'}`); + if (snapshot.plan.remote?.instanceName) { + console.log(`Remote instance: ${snapshot.plan.remote.instanceName}`); + } + console.log(`Remote host: ${snapshot.plan.remote?.sshHost ?? '(none)'}`); + console.log(`Remote python command: ${snapshot.plan.remote?.pythonCommand ?? '(none)'}`); + console.log('Planned commands:'); + for (const [index, step] of snapshot.plan.steps.entries()) { + console.log(`${index + 1}. ${step.remoteCommand}`); + if (step.note) { + console.log(` note: ${step.note}`); + } + } + console.log('Notes:'); + for (const note of snapshot.plan.notes ?? []) { + console.log(`- ${note}`); + } +} + +function printRemoteSetupResult(result) { + if (!result.ok) { + console.log('Frontier remote setup: failed'); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printRemoteSetup(result.snapshot); + } + return; + } + + console.log('Frontier remote setup: complete'); + console.log(`Applied at: ${result.appliedAt}`); + for (const step of result.stepResults) { + console.log(`- ${step.label}: ${step.ok ? 'ok' : 'failed'} (${step.commandLine})`); + } + printDoctor(result.doctor); +} + +function printAttachSnapshot(snapshot) { + console.log(`Frontier ${snapshot.remote.provider === 'brev' ? 'Brev' : 'SSH'} attach plan`); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log(`Remote id: ${snapshot.remote.remoteId ?? '(none)'}`); + if (snapshot.remote.instanceName) { + console.log(`Instance: ${snapshot.remote.instanceName}`); + } + console.log(`SSH host: ${snapshot.remote.sshHost ?? '(missing)'}`); + console.log(`Remote engine root: ${snapshot.remote.engineRoot}`); + console.log(`Remote python command: ${snapshot.remote.pythonCommand}`); + console.log(`Paid rung: ${snapshot.paidRung ? 'yes' : 'no'}`); + if (snapshot.paidRung) { + console.log(`Paid enabled: ${snapshot.paidEnabled ? 'yes' : 'no'}`); + } + if (snapshot.doctor) { + console.log(formatRuntime(snapshot.doctor, 'Remote runtime')); + console.log(`Remote frontier ready: ${snapshot.doctor.frontierEngineReady ? 'yes' : 'no'}`); + console.log(`Remote GPU ready: ${snapshot.doctor.frontierEngineReady && snapshot.doctor.cudaAvailable ? 'yes' : 'no'}`); + } +} + +function printAttachResult(result) { + if (!result.ok) { + console.log(`Frontier ${result.snapshot?.remote?.provider === 'brev' ? 'Brev' : 'SSH'} attach: failed`); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printAttachSnapshot(result.snapshot); + } + return; + } + + console.log(`Frontier ${result.snapshot.remote.provider === 'brev' ? 'Brev' : 'SSH'} attach: complete`); + console.log(`Applied at: ${result.appliedAt}`); + printAttachSnapshot(result.snapshot); +} + +function printSyncSnapshot(snapshot) { + console.log('Frontier SSH sync plan'); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log(`Remote id: ${snapshot.remote.remoteId ?? '(none)'}`); + console.log(`Provider: ${snapshot.remote.provider ?? 'ssh'}`); + console.log(`SSH host: ${snapshot.remote.sshHost ?? '(missing)'}`); + console.log(`Remote engine root: ${snapshot.remote.engineRoot}`); + console.log(`Remote python command: ${snapshot.remote.pythonCommand}`); + console.log(`Sync scope: ${snapshot.scope?.mode === 'lane' ? snapshot.scope.laneId : 'all lanes'}`); + console.log(`Local engine root: ${snapshot.local.engineRoot}`); + console.log(`Local experiments root: ${snapshot.local.experimentsRoot}`); + if (snapshot.doctor) { + console.log(formatRuntime(snapshot.doctor, 'Remote runtime')); + } +} + +function printSyncResult(result) { + if (!result.ok) { + console.log('Frontier SSH sync: failed'); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printSyncSnapshot(result.snapshot); + } + return; + } + + console.log('Frontier SSH sync: complete'); + console.log(`Applied at: ${result.appliedAt}`); + console.log(`Synced scope: ${result.snapshot.scope?.mode === 'lane' ? result.snapshot.scope.laneId : 'all lanes'}`); + for (const step of result.stepResults) { + console.log(`- ${step.label}: ${step.ok ? 'ok' : 'failed'} (${step.commandLine})`); + } + if (result.remoteVerification && result.snapshot.scope?.mode === 'lane' && result.snapshot.scope?.laneId) { + console.log(`Remote lane verified: ${result.snapshot.scope.laneId}`); + } + if (result.remoteLiveFrontier?.shared_prefix_failure_count !== undefined) { + console.log( + `Remote shared-prefix failures: ${result.remoteLiveFrontier.shared_prefix_failure_count} through ${result.remoteLiveFrontier.latest_direct_failure}`, + ); + } +} + +function printCreateBrevSnapshot(snapshot) { + console.log('Frontier Brev provision plan'); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log(`Instance: ${snapshot.instanceName}`); + console.log(`Count: ${snapshot.count}`); + console.log(`Enable paid rung: ${snapshot.enablePaidRung ? 'yes' : 'no'}`); + console.log(`Attach after create: ${snapshot.attach ? 'yes' : 'no'}`); + if (snapshot.syncLane) { + console.log(`Sync lane after attach: ${snapshot.syncLane}`); + } + console.log(`Create command: ${snapshot.plan.createCommandLine}`); + if (snapshot.plan.attachCommand) { + console.log(`Attach command: ${snapshot.plan.attachCommand}`); + } + if (snapshot.plan.syncCommand) { + console.log(`Sync command: ${snapshot.plan.syncCommand}`); + } + console.log('Notes:'); + for (const note of snapshot.notes ?? []) { + console.log(`- ${note}`); + } + if (snapshot.warnings?.length) { + console.log('Warnings:'); + for (const warning of snapshot.warnings) { + console.log(`- ${warning}`); + } + } +} + +function printCreateBrevResult(result) { + if (!result.ok) { + console.log('Frontier Brev provision: failed'); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printCreateBrevSnapshot(result.snapshot); + } + return; + } + console.log('Frontier Brev provision: complete'); + console.log(`Applied at: ${result.appliedAt}`); + console.log(`Instance: ${result.snapshot.instanceName}`); + console.log(`Create command: ${result.snapshot.plan.createCommandLine}`); + if (result.snapshot.dryRun) { + console.log('Dry run output:'); + } else { + console.log('Create output:'); + } + for (const line of String(result.createResult?.stdout ?? '').split(/\r?\n/).filter(Boolean)) { + console.log(`- ${line}`); + } + if (result.attachResult) { + console.log(`Attach result: ${result.attachResult.ok ? 'ok' : 'failed'}`); + } + if (result.syncResult) { + console.log(`Sync result: ${result.syncResult.ok ? 'ok' : 'failed'}`); + } +} + +function printCreateBrevFleetSnapshot(snapshot) { + console.log('Frontier Brev fleet provision plan'); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log(`Fleet: ${snapshot.fleetId}`); + console.log(`Count: ${snapshot.count}`); + console.log(`Enable paid rung: ${snapshot.enablePaidRung ? 'yes' : 'no'}`); + console.log(`Topology: ${snapshot.intendedTopology}`); + console.log(`Attach after create: ${snapshot.attach ? 'yes' : 'no'}`); + if (snapshot.syncLane) { + console.log(`Sync lane after attach: ${snapshot.syncLane}`); + } + console.log('Members:'); + for (const member of snapshot.members) { + console.log(`- ${member.instanceName}`); + console.log(` create: ${member.createCommandLine}`); + if (member.attachCommand) { + console.log(` attach: ${member.attachCommand}`); + } + if (member.syncCommand) { + console.log(` sync: ${member.syncCommand}`); + } + } + console.log('Notes:'); + for (const note of snapshot.notes ?? []) { + console.log(`- ${note}`); + } + if (snapshot.warnings?.length) { + console.log('Warnings:'); + for (const warning of snapshot.warnings) { + console.log(`- ${warning}`); + } + } +} + +function printCreateBrevFleetResult(result) { + if (!result.ok) { + console.log('Frontier Brev fleet provision: failed'); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printCreateBrevFleetSnapshot(result.snapshot); + } + return; + } + console.log('Frontier Brev fleet provision: complete'); + console.log(`Applied at: ${result.appliedAt}`); + console.log(`Fleet: ${result.snapshot.fleetId}`); + console.log(`Members provisioned: ${result.memberResults.length}`); + for (const member of result.memberResults) { + console.log(`- ${member.instanceName}: ${member.ok ? 'ok' : 'failed'}`); + } +} + +function printFleetSyncSnapshot(snapshot) { + console.log('Frontier fleet sync plan'); + console.log(`Apply now: ${snapshot.apply ? 'yes' : 'no'}`); + console.log(`Fleet: ${snapshot.fleetId ?? '(none)'}`); + console.log(`Lane: ${snapshot.laneId ?? 'all lanes'}`); + console.log(`Topology: ${snapshot.intendedTopology ?? '(none)'}`); + console.log('Members:'); + for (const member of snapshot.members ?? []) { + console.log(`- ${member.remoteId}`); + console.log(` sync: ${member.syncCommand}`); + } +} + +function printFleetSyncResult(result) { + if (!result.ok) { + console.log('Frontier fleet sync: failed'); + if (result.error) { + console.log(`Error: ${result.error}`); + } + if (result.snapshot) { + printFleetSyncSnapshot(result.snapshot); + } + return; + } + console.log('Frontier fleet sync: complete'); + console.log(`Applied at: ${result.appliedAt}`); + console.log(`Fleet: ${result.snapshot.fleetId}`); + for (const member of result.memberResults) { + console.log(`- ${member.remoteId}: ${member.ok ? 'ok' : 'failed'}`); + } +} + +export function runFrontierCommand(args) { + const [subcommand, ...rest] = args; + const workspaceRoot = getWorkspaceRoot(); + + if (!subcommand || subcommand === 'help' || subcommand === '--help') { + console.log('Usage:'); + console.log(' erdos frontier doctor [--json]'); + console.log(' erdos frontier lanes [--json]'); + console.log(' erdos frontier remotes [--json]'); + console.log(' erdos frontier fleets [--json]'); + console.log(' erdos frontier fleet [--json]'); + console.log(' erdos frontier use-remote [--json]'); + console.log(' erdos frontier sessions [--json]'); + console.log(' erdos frontier session [--json]'); + console.log(' erdos frontier stop-session [--json]'); + console.log(' erdos frontier setup [--base|--cpu|--cuda] [--torch-index-url ] [--apply] [--json]'); + console.log(' erdos frontier setup-remote [--remote-id ] [--base|--cpu|--cuda] [--torch-index-url ] [--apply] [--json]'); + console.log(' erdos frontier create-brev [--gpu-name ] [--type ] [--provider ] [--count ] [--attach] [--enable-paid-rung] [--sync-lane ] [--dry-run] [--apply] [--json]'); + console.log(' erdos frontier create-brev-fleet [--gpu-name ] [--type ] [--provider ] [--count ] [--attach] [--enable-paid-rung] [--sync-lane ] [--dry-run] [--apply] [--json]'); + console.log(' erdos frontier attach-ssh --ssh-host [--remote-id ] [--engine-root ] [--python-command ] [--apply] [--json]'); + console.log(' erdos frontier attach-brev --instance [--remote-id ] [--ssh-host ] [--engine-root ] [--python-command ] [--enable-paid-rung] [--apply] [--json]'); + console.log(' erdos frontier enable-paid-remote [--json]'); + console.log(' erdos frontier disable-paid-remote [--json]'); + console.log(' erdos frontier enable-paid-fleet [--json]'); + console.log(' erdos frontier disable-paid-fleet [--json]'); + console.log(' erdos frontier sync-ssh [--remote-id ] [--ssh-host ] [--engine-root ] [--python-command ] [--lane ] [--apply] [--json]'); + console.log(' erdos frontier sync-fleet [--lane ] [--apply] [--json]'); + return 0; + } + + if (subcommand === 'doctor') { + const parsed = parseDoctorArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const snapshot = syncFrontierDoctorSnapshot(workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printDoctor(snapshot); + return 0; + } + + if (subcommand === 'lanes') { + const parsed = parseLanesArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const snapshot = getFrontierLanesSnapshot(workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return snapshot.available ? 0 : 1; + } + printLanes(snapshot); + return snapshot.available ? 0 : 1; + } + + if (subcommand === 'remotes') { + const parsed = parseRemotesArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const snapshot = getFrontierRemotesSnapshot(workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printRemotes(snapshot); + return 0; + } + + if (subcommand === 'fleets') { + const parsed = parseFleetsArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const snapshot = getFrontierFleetsSnapshot(workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printFleets(snapshot); + return 0; + } + + if (subcommand === 'fleet') { + const parsed = parseFleetsArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (!parsed.fleetId) { + console.error('Missing frontier fleet id.'); + return 1; + } + const snapshot = getFrontierFleetSnapshot(parsed.fleetId, workspaceRoot); + if (!snapshot) { + console.error(`Unknown frontier fleet: ${parsed.fleetId}`); + return 1; + } + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printFleet(snapshot); + return 0; + } + + if (subcommand === 'use-remote') { + const parsed = parseUseRemoteArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const result = applyFrontierUseRemote(parsed.remoteId, workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printUseRemoteResult(result); + return result.ok ? 0 : 1; + } + + if (subcommand === 'enable-paid-remote' || subcommand === 'disable-paid-remote') { + const parsed = parseUseRemoteArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const result = setFrontierPaidRemoteAccess(parsed.remoteId, subcommand === 'enable-paid-remote', workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printPaidRungResult(result, subcommand); + return result.ok ? 0 : 1; + } + + if (subcommand === 'enable-paid-fleet' || subcommand === 'disable-paid-fleet') { + const parsed = parseFleetsArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (!parsed.fleetId) { + console.error('Missing frontier fleet id.'); + return 1; + } + const result = setFrontierPaidFleetAccess(parsed.fleetId, subcommand === 'enable-paid-fleet', workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printPaidRungResult(result, subcommand); + return result.ok ? 0 : 1; + } + + if (subcommand === 'sessions') { + const parsed = parseSessionsArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const snapshot = listFrontierSessionSnapshots(workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printSessions(snapshot); + return 0; + } + + if (subcommand === 'session') { + const parsed = parseSessionArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const snapshot = getFrontierSessionSnapshot(parsed.sessionId, workspaceRoot); + if (!snapshot) { + console.error(`Unknown frontier session: ${parsed.sessionId}`); + return 1; + } + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printSession(snapshot); + return 0; + } + + if (subcommand === 'stop-session') { + const parsed = parseSessionArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + const result = stopFrontierSession(parsed.sessionId, workspaceRoot); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printStopSessionResult(result); + return result.ok ? 0 : 1; + } + + if (subcommand === 'setup') { + const parsed = parseSetupArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierSetup(parsed.mode, workspaceRoot, { + torchIndexUrl: parsed.torchIndexUrl, + }); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printSetupResult(result); + return result.ok ? 0 : 1; + } + + const snapshot = getFrontierSetupSnapshot(parsed.mode, workspaceRoot, { + apply: false, + torchIndexUrl: parsed.torchIndexUrl, + }); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printSetup(snapshot); + return 0; + } + + if (subcommand === 'setup-remote') { + const parsed = parseRemoteSetupArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierRemoteSetup(parsed.mode, workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printRemoteSetupResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierRemoteSetupSnapshot(parsed.mode, workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printRemoteSetup(snapshot); + return 0; + } + + if (subcommand === 'create-brev') { + const parsed = parseCreateBrevArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierBrevProvision(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printCreateBrevResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierBrevProvisionSnapshot(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printCreateBrevSnapshot(snapshot); + return 0; + } + + if (subcommand === 'create-brev-fleet') { + const parsed = parseCreateBrevFleetArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierBrevFleetProvision(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printCreateBrevFleetResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierBrevFleetProvisionSnapshot(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printCreateBrevFleetSnapshot(snapshot); + return 0; + } + + if (subcommand === 'attach-ssh') { + const parsed = parseAttachArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierRemoteAttach(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printAttachResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierRemoteAttachSnapshot(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printAttachSnapshot(snapshot); + return 0; + } + + if (subcommand === 'attach-brev') { + const parsed = parseAttachBrevArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierRemoteAttach(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printAttachResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierRemoteAttachSnapshot(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printAttachSnapshot(snapshot); + return 0; + } + + if (subcommand === 'sync-ssh') { + const parsed = parseSyncArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierRemoteSync(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printSyncResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierRemoteSyncSnapshot(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return 0; + } + printSyncSnapshot(snapshot); + return 0; + } + + if (subcommand === 'sync-fleet') { + const parsed = parseFleetSyncArgs(rest); + if (parsed.error) { + console.error(parsed.error); + return 1; + } + if (parsed.apply) { + const result = applyFrontierFleetSync(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(result, null, 2)); + return result.ok ? 0 : 1; + } + printFleetSyncResult(result); + return result.ok ? 0 : 1; + } + const snapshot = getFrontierFleetSyncSnapshot(workspaceRoot, parsed); + if (parsed.asJson) { + console.log(JSON.stringify(snapshot, null, 2)); + return snapshot.available ? 0 : 1; + } + printFleetSyncSnapshot(snapshot); + return snapshot.available ? 0 : 1; + } + + console.error(`Unknown frontier subcommand: ${subcommand}`); + return 1; +} diff --git a/src/runtime/frontier-remote.js b/src/runtime/frontier-remote.js new file mode 100644 index 0000000..8d487f8 --- /dev/null +++ b/src/runtime/frontier-remote.js @@ -0,0 +1,267 @@ +import { execFileSync } from 'node:child_process'; + +import { repoRoot } from './paths.js'; + +function runCommandCapture(command, options = {}) { + try { + const stdout = execFileSync(command.executable, command.args ?? [], { + cwd: options.cwd ?? repoRoot, + encoding: 'utf8', + stdio: ['ignore', 'pipe', 'pipe'], + }); + return { + ok: true, + stdout: stdout.trim(), + stderr: null, + }; + } catch (error) { + return { + ok: false, + stdout: error?.stdout?.toString().trim() || null, + stderr: error?.stderr?.toString().trim() || error?.message || null, + }; + } +} + +export function isBrevRemote(remote = {}) { + return String(remote?.provider ?? '').trim().toLowerCase() === 'brev'; +} + +export function getDefaultRemotePythonCommand(provider = 'ssh') { + return provider === 'brev' ? 'python3' : 'py -3'; +} + +export function getDefaultRemoteEngineRoot(provider = 'ssh', homeDir = null) { + if (provider === 'brev') { + const normalizedHomeDir = String(homeDir ?? '').trim(); + return normalizedHomeDir + ? `${normalizedHomeDir.replace(/[\\/]+$/, '')}/frontier-engine` + : '~/frontier-engine'; + } + return '%USERPROFILE%\\frontier-engine'; +} + +export function quoteRemoteWindowsPath(value) { + return `"${String(value).replace(/"/g, '\\"')}"`; +} + +export function quotePosixShellArg(value) { + return `'${String(value ?? '').replaceAll("'", "'\\''")}'`; +} + +function normalizeRemoteExecutionTarget(target) { + if (typeof target === 'string') { + return { + provider: 'ssh', + sshHost: target, + }; + } + if (!target || typeof target !== 'object') { + return { + provider: 'ssh', + sshHost: null, + instanceName: null, + }; + } + return { + provider: target.provider ?? 'ssh', + sshHost: target.sshHost ?? null, + instanceName: target.instanceName ?? null, + engineRoot: target.engineRoot ?? null, + pythonCommand: target.pythonCommand ?? null, + remoteId: target.remoteId ?? null, + }; +} + +function escapeRegex(value) { + return String(value).replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); +} + +function buildBrevWrappedShellCommand(remoteCommand) { + const markerId = `${Date.now()}_${Math.random().toString(36).slice(2, 10)}`; + const startMarker = `__ERDOS_REMOTE_START_${markerId}__`; + const endMarker = `__ERDOS_REMOTE_END_${markerId}__`; + const wrappedScript = [ + 'set +e', + `printf '%s\\n' ${quotePosixShellArg(startMarker)}`, + String(remoteCommand ?? ''), + 'status=$?', + `printf '\\n%s:%s\\n' ${quotePosixShellArg(endMarker)} "$status"`, + 'exit "$status"', + ].join('\n'); + return { + startMarker, + endMarker, + command: `bash -lc ${quotePosixShellArg(wrappedScript)}`, + }; +} + +function parseBrevWrappedOutput(text, startMarker, endMarker) { + const pattern = new RegExp( + `${escapeRegex(startMarker)}\\r?\\n?([\\s\\S]*?)\\r?\\n${escapeRegex(endMarker)}:(\\d+)`, + ); + const match = String(text ?? '').match(pattern); + if (!match) { + return { + stdout: String(text ?? '').trim(), + remoteExitCode: null, + }; + } + return { + stdout: String(match[1] ?? '').trim(), + remoteExitCode: Number(match[2] ?? 0), + }; +} + +export function toRemoteCopyPath(remote, remotePath) { + if (!remotePath) { + return null; + } + const target = normalizeRemoteExecutionTarget(remote); + if (isBrevRemote(target)) { + return String(remotePath).replaceAll('\\', '/'); + } + const normalized = String(remotePath).replaceAll('\\', '/'); + if (normalized.startsWith('%USERPROFILE%/')) { + return normalized.slice('%USERPROFILE%/'.length); + } + if (/^[A-Za-z]:\//.test(normalized)) { + return `/${normalized}`; + } + return normalized.replace(/^\.\/+/, ''); +} + +export function joinRemotePath(remote, ...parts) { + const target = normalizeRemoteExecutionTarget(remote); + const separator = isBrevRemote(target) ? '/' : '\\'; + return parts + .filter((part) => part !== null && part !== undefined && String(part) !== '') + .map((part, index) => { + const text = String(part); + if (index === 0) { + return text.replace(new RegExp(`${separator === '\\' ? '\\\\' : '/'}+$`), ''); + } + return text.replace(/^[\\/]+|[\\/]+$/g, ''); + }) + .join(separator); +} + +export function runRemoteCommandCapture(target, remoteCommand, options = {}) { + const remote = normalizeRemoteExecutionTarget(target); + if (!remoteCommand) { + return { + ok: false, + stdout: null, + stderr: 'remote command missing', + }; + } + + if (isBrevRemote(remote)) { + const instanceName = remote.instanceName ?? remote.sshHost ?? null; + if (!instanceName) { + return { + ok: false, + stdout: null, + stderr: 'brev instance missing', + }; + } + const wrapped = buildBrevWrappedShellCommand(remoteCommand); + const result = runCommandCapture({ + executable: 'brev', + args: ['exec', instanceName, wrapped.command], + }, options); + const parsed = parseBrevWrappedOutput(result.stdout, wrapped.startMarker, wrapped.endMarker); + return { + ok: result.ok, + stdout: parsed.stdout, + stderr: result.stderr, + remoteExitCode: parsed.remoteExitCode, + }; + } + + const sshHost = remote.sshHost ?? null; + if (!sshHost) { + return { + ok: false, + stdout: null, + stderr: 'remote ssh host missing', + }; + } + return runCommandCapture({ + executable: 'ssh', + args: [sshHost, remoteCommand], + }, options); +} + +export function runRemoteCopyToCapture(target, localPath, remotePath, options = {}) { + const remote = normalizeRemoteExecutionTarget(target); + if (!localPath || !remotePath) { + return { + ok: false, + stdout: null, + stderr: 'local path or remote path missing', + }; + } + + if (isBrevRemote(remote)) { + const instanceName = remote.instanceName ?? remote.sshHost ?? null; + return runCommandCapture({ + executable: 'brev', + args: ['copy', localPath, `${instanceName}:${toRemoteCopyPath(remote, remotePath)}`], + }, options); + } + + const args = []; + if (options.recursive) { + args.push('-r'); + } + args.push(localPath, `${remote.sshHost}:${toRemoteCopyPath(remote, remotePath)}`); + return runCommandCapture({ + executable: 'scp', + args, + }, options); +} + +export function runRemoteCopyFromCapture(target, remotePath, localPath, options = {}) { + const remote = normalizeRemoteExecutionTarget(target); + if (!localPath || !remotePath) { + return { + ok: false, + stdout: null, + stderr: 'remote path or local path missing', + }; + } + + if (isBrevRemote(remote)) { + const instanceName = remote.instanceName ?? remote.sshHost ?? null; + return runCommandCapture({ + executable: 'brev', + args: ['copy', `${instanceName}:${toRemoteCopyPath(remote, remotePath)}`, localPath], + }, options); + } + + const args = []; + if (options.recursive) { + args.push('-r'); + } + args.push(`${remote.sshHost}:${toRemoteCopyPath(remote, remotePath)}`, localPath); + return runCommandCapture({ + executable: 'scp', + args, + }, options); +} + +export function probeBrevRemoteHome(instanceName, options = {}) { + if (!instanceName) { + return null; + } + const result = runRemoteCommandCapture({ + provider: 'brev', + instanceName, + }, 'printf \'%s\\n\' "$HOME"', options); + if (!result.ok || !result.stdout) { + return null; + } + const homeDir = String(result.stdout).split(/\r?\n/).map((line) => line.trim()).find(Boolean) ?? null; + return homeDir || null; +} diff --git a/src/runtime/frontier-sessions.js b/src/runtime/frontier-sessions.js new file mode 100644 index 0000000..ae80096 --- /dev/null +++ b/src/runtime/frontier-sessions.js @@ -0,0 +1,1345 @@ +import fs from 'node:fs'; +import path from 'node:path'; +import { execFileSync, spawn } from 'node:child_process'; +import { ensureDir, readJson, writeJson, writeText } from './files.js'; +import { + joinRemotePath, + quotePosixShellArg, + runRemoteCommandCapture, + runRemoteCopyFromCapture, + runRemoteCopyToCapture, +} from './frontier-remote.js'; +import { getWorkspaceDir, getWorkspaceRoot, repoRoot } from './paths.js'; + +function getFrontierSessionsDir(workspaceRoot = getWorkspaceRoot()) { + return path.join(getWorkspaceDir(workspaceRoot), 'frontier', 'sessions'); +} + +function getFrontierSessionDir(sessionId, workspaceRoot = getWorkspaceRoot()) { + return path.join(getFrontierSessionsDir(workspaceRoot), String(sessionId)); +} + +function getFrontierSessionRecordPath(sessionId, workspaceRoot = getWorkspaceRoot()) { + return path.join(getFrontierSessionDir(sessionId, workspaceRoot), 'SESSION.json'); +} + +function getFrontierSessionStdoutPath(sessionId, workspaceRoot = getWorkspaceRoot()) { + return path.join(getFrontierSessionDir(sessionId, workspaceRoot), 'stdout.log'); +} + +function getFrontierSessionStderrPath(sessionId, workspaceRoot = getWorkspaceRoot()) { + return path.join(getFrontierSessionDir(sessionId, workspaceRoot), 'stderr.log'); +} + +function formatShellArg(value) { + if (value === null || value === undefined) { + return ''; + } + const text = String(value); + if (/^[A-Za-z0-9_./:=+-]+$/.test(text)) { + return text; + } + return JSON.stringify(text); +} + +function formatCommandLine(executable, args = []) { + return [executable, ...args].map(formatShellArg).join(' '); +} + +function parseJsonDocument(text) { + if (!text) { + return null; + } + try { + return JSON.parse(String(text).trim()); + } catch { + return null; + } +} + +function stableSortValue(value) { + if (Array.isArray(value)) { + return value.map((item) => stableSortValue(item)); + } + if (value && typeof value === 'object') { + return Object.keys(value) + .sort() + .reduce((accumulator, key) => { + accumulator[key] = stableSortValue(value[key]); + return accumulator; + }, {}); + } + return value; +} + +function buildSessionReuseFingerprint(spec = {}) { + const backend = spec.backend ?? 'local'; + const base = { + backend, + kind: spec.kind ?? 'frontier_dispatch', + problemId: spec.problemId ?? null, + actionId: spec.actionId ?? null, + mode: spec.mode ?? null, + source: spec.source ?? null, + }; + + if (backend === 'remote_ssh' || backend === 'remote_brev') { + const remoteProvider = spec.remoteProvider ?? (backend === 'remote_brev' ? 'brev' : 'ssh'); + const remoteInstanceName = spec.remoteInstanceName ?? null; + const remoteHost = spec.remoteHost ?? (remoteProvider === 'brev' ? remoteInstanceName : null); + return JSON.stringify(stableSortValue({ + ...base, + remoteProvider, + remoteInstanceName, + remoteHost, + remoteEngineRoot: spec.remoteEngineRoot ?? null, + remotePythonCommand: spec.remotePythonCommand ?? null, + remoteCommandLine: String(spec.remoteCommandLine ?? '').trim(), + })); + } + + return JSON.stringify(stableSortValue({ + ...base, + cwd: spec.cwd ?? null, + executable: spec.executable ?? 'node', + args: Array.isArray(spec.args) ? spec.args : [], + })); +} + +function buildRecordReuseFingerprint(record = {}) { + if (!record) { + return null; + } + return buildSessionReuseFingerprint({ + backend: record.backend ?? 'local', + kind: record.kind ?? 'frontier_dispatch', + problemId: record.problemId ?? null, + actionId: record.actionId ?? null, + mode: record.mode ?? null, + source: record.source ?? null, + cwd: record.cwd ?? null, + executable: record.executable ?? 'node', + args: Array.isArray(record.args) ? record.args : [], + remoteProvider: record.metadata?.remoteProvider ?? (record.backend === 'remote_brev' ? 'brev' : 'ssh'), + remoteInstanceName: record.metadata?.remoteInstanceName ?? null, + remoteHost: record.metadata?.remoteHost ?? null, + remoteEngineRoot: record.metadata?.remoteEngineRoot ?? null, + remotePythonCommand: record.metadata?.remotePythonCommand ?? null, + remoteCommandLine: record.metadata?.remoteCommandLine ?? null, + }); +} + +function parseP848RemoteBundleDir(text) { + const match = String(text ?? '').match(/p848_seed_bundle:\s*(.+)$/m); + return match ? match[1].trim() : null; +} + +function normalizeRemoteBundleDir(record, remoteBundleDir) { + if (!remoteBundleDir) { + return null; + } + const provider = record?.metadata?.remoteProvider ?? (record?.backend === 'remote_brev' ? 'brev' : 'ssh'); + if (provider === 'brev') { + const normalized = String(remoteBundleDir).replaceAll('\\', '/'); + if (normalized.startsWith('/')) { + return normalized; + } + const engineRoot = String(record?.metadata?.remoteEngineRoot ?? '~/frontier-engine').replaceAll('\\', '/'); + const homeDir = engineRoot.includes('/') + ? engineRoot.replace(/\/frontier-engine$/, '').replace(/\/+$/, '') + : '$HOME'; + return `${homeDir}/${normalized.replace(/^\.\/+/, '')}`; + } + const normalized = String(remoteBundleDir).replaceAll('/', '\\'); + if (/^[A-Za-z]:\\/.test(normalized) || normalized.startsWith('%USERPROFILE%\\')) { + return normalized; + } + return `%USERPROFILE%\\${normalized}`; +} + +function getP848LocalBundleDir(remoteBundleDir) { + if (!remoteBundleDir) { + return null; + } + const bundleName = remoteBundleDir.includes('\\') + ? path.win32.basename(remoteBundleDir) + : path.posix.basename(remoteBundleDir); + return path.join(repoRoot, 'research', 'frontier-engine', 'artifacts', 'p848-anchor-ladder', bundleName); +} + +function readP848Manifest(localBundleDir) { + if (!localBundleDir) { + return null; + } + const manifestPath = path.join(localBundleDir, 'manifest.json'); + if (!fs.existsSync(manifestPath)) { + return null; + } + try { + return readJson(manifestPath); + } catch { + return null; + } +} + +function maybeHarvestRemoteP848Bundle(record, snapshot, workspaceRoot = getWorkspaceRoot()) { + const isP848GpuSweep = String(record?.problemId ?? '') === '848' + && String(record?.actionId ?? '') === 'gpu_profile_sweep' + && (record?.backend === 'remote_brev' || record?.backend === 'remote_ssh'); + if (!isP848GpuSweep || snapshot?.running || snapshot?.status !== 'completed') { + return null; + } + + const existingHarvest = record?.metadata?.harvestedBundle ?? null; + if (existingHarvest?.ok && existingHarvest?.localBundleDir && fs.existsSync(existingHarvest.localBundleDir)) { + return existingHarvest; + } + + const remoteBundleDir = normalizeRemoteBundleDir( + record, + parseP848RemoteBundleDir((snapshot?.stdoutTail ?? []).join('\n')), + ); + if (!remoteBundleDir) { + return null; + } + + const localBundleDir = getP848LocalBundleDir(remoteBundleDir); + ensureDir(path.dirname(localBundleDir)); + + const existingManifest = readP848Manifest(localBundleDir); + if (existingManifest) { + return { + ok: true, + remoteBundleDir, + localBundleDir, + manifestPath: path.join(localBundleDir, 'manifest.json'), + candidateFiles: existingManifest.candidate_files?.map((row) => row?.file).filter(Boolean) ?? [], + harvestedAt: new Date().toISOString(), + harvestedBy: 'session_snapshot', + alreadyPresent: true, + }; + } + + const remoteTarget = { + provider: record?.metadata?.remoteProvider ?? (record?.backend === 'remote_brev' ? 'brev' : 'ssh'), + instanceName: record?.metadata?.remoteInstanceName ?? null, + sshHost: record?.metadata?.remoteHost ?? null, + }; + const copyResult = runRemoteCopyFromCapture(remoteTarget, remoteBundleDir, path.dirname(localBundleDir), { + cwd: workspaceRoot, + recursive: true, + }); + if (!copyResult.ok) { + return { + ok: false, + remoteBundleDir, + localBundleDir, + error: copyResult.stderr ?? 'failed to harvest remote bundle', + harvestedAt: new Date().toISOString(), + harvestedBy: 'session_snapshot', + }; + } + + const manifest = readP848Manifest(localBundleDir); + if (!manifest) { + return { + ok: false, + remoteBundleDir, + localBundleDir, + error: 'remote bundle copied but manifest.json is missing locally', + harvestedAt: new Date().toISOString(), + harvestedBy: 'session_snapshot', + }; + } + + return { + ok: true, + remoteBundleDir, + localBundleDir, + manifestPath: path.join(localBundleDir, 'manifest.json'), + candidateFiles: manifest.candidate_files?.map((row) => row?.file).filter(Boolean) ?? [], + harvestedAt: new Date().toISOString(), + harvestedBy: 'session_snapshot', + alreadyPresent: false, + }; +} + +function runCommandCapture(command, options = {}) { + try { + const stdout = execFileSync(command.executable, command.args ?? [], { + cwd: options.cwd ?? repoRoot, + encoding: 'utf8', + stdio: ['ignore', 'pipe', 'pipe'], + }); + return { + ok: true, + stdout: stdout.trim(), + stderr: null, + }; + } catch (error) { + return { + ok: false, + stdout: error?.stdout?.toString().trim() || null, + stderr: error?.stderr?.toString().trim() || error?.message || null, + }; + } +} + +function toPowerShellEncodedCommand(script) { + return Buffer.from(String(script), 'utf16le').toString('base64'); +} + +function quotePowerShellString(value) { + return `'${String(value ?? '').replaceAll("'", "''")}'`; +} + +function runRemotePowerShellCapture(sshHost, script, options = {}) { + if (!sshHost) { + return { + ok: false, + stdout: null, + stderr: 'remote ssh host missing', + }; + } + return runCommandCapture({ + executable: 'ssh', + args: [ + sshHost, + 'powershell', + '-NoProfile', + '-NonInteractive', + '-EncodedCommand', + toPowerShellEncodedCommand(script), + ], + }, options); +} + +function generateSessionId({ problemId = 'unknown', actionId = 'session' } = {}) { + const timestamp = new Date().toISOString().replaceAll(':', '-'); + return `${timestamp}__frontier__p${problemId}__${actionId}`; +} + +function readTail(filePath, maxLines = 12) { + if (!fs.existsSync(filePath)) { + return []; + } + const text = fs.readFileSync(filePath, 'utf8').trimEnd(); + if (!text) { + return []; + } + const lines = text.split(/\r?\n/); + return lines.slice(Math.max(0, lines.length - maxLines)); +} + +function parseRunDirFromTail(lines) { + for (let index = lines.length - 1; index >= 0; index -= 1) { + const match = String(lines[index]).match(/^Run dir:\s*(.+)$/); + if (match) { + return match[1].trim(); + } + } + return null; +} + +function probeLocalProcess(pid) { + if (!Number.isInteger(pid) || pid <= 0) { + return { running: false, error: 'missing pid' }; + } + try { + process.kill(pid, 0); + return { running: true, error: null }; + } catch (error) { + if (error?.code === 'EPERM') { + return { running: true, error: null }; + } + if (error?.code === 'ESRCH') { + return { running: false, error: null }; + } + return { running: false, error: error?.message ?? 'process probe failed' }; + } +} + +function computeReviewState(record, running) { + if (!record.reviewAfterHours) { + return { + dueAt: null, + state: 'not_scheduled', + }; + } + const launchedAtMs = Date.parse(record.launchedAt); + if (Number.isNaN(launchedAtMs)) { + return { + dueAt: null, + state: 'not_scheduled', + }; + } + const dueAt = new Date(launchedAtMs + (Number(record.reviewAfterHours) * 60 * 60 * 1000)).toISOString(); + const due = Date.now() >= Date.parse(dueAt); + return { + dueAt, + state: running ? (due ? 'due' : 'scheduled') : 'completed', + }; +} + +function buildRemoteSessionDir(remoteRoot, sessionId) { + return `${String(remoteRoot).replace(/[\\\/]+$/, '')}\\sessions\\${sessionId}`; +} + +function buildRemoteLinuxSessionDir(remoteRoot, sessionId) { + return joinRemotePath({ provider: 'brev' }, remoteRoot, 'sessions', sessionId); +} + +function toRemoteScpPath(remoteWindowsPath) { + if (!remoteWindowsPath) { + return null; + } + const normalized = String(remoteWindowsPath).replaceAll('\\', '/'); + if (normalized.startsWith('%USERPROFILE%/')) { + return normalized.slice('%USERPROFILE%/'.length); + } + if (/^[A-Za-z]:\//.test(normalized)) { + return `/${normalized}`; + } + return normalized.replace(/^\.\/+/, ''); +} + +function buildRemoteLinuxWorkerScript({ + sessionId, + remoteSessionDir, + remoteCommandLine, +}) { + return `#!/usr/bin/env python3 +import json +import os +import subprocess +from datetime import datetime, timezone + +def now(): + return datetime.now(timezone.utc).isoformat().replace("+00:00", "Z") + +def write_record(payload): + with open(record_path, "w", encoding="utf-8") as handle: + json.dump(payload, handle, indent=2) + +session_dir = ${JSON.stringify(String(remoteSessionDir))} +record_path = os.path.join(session_dir, "SESSION.json") +stdout_path = os.path.join(session_dir, "stdout.log") +stderr_path = os.path.join(session_dir, "stderr.log") +command_line = ${JSON.stringify(String(remoteCommandLine))} + +os.makedirs(session_dir, exist_ok=True) +record = { + "schema": "erdos.remote_frontier_session/3", + "remoteSessionId": ${JSON.stringify(String(sessionId))}, + "launchedAt": now(), + "status": "running", + "workerPid": os.getpid(), + "childPid": None, + "sessionDir": session_dir, + "stdoutPath": stdout_path, + "stderrPath": stderr_path, + "remoteCommandLine": command_line, + "exitCode": None, + "error": None, +} +write_record(record) + +try: + with open(stdout_path, "ab") as stdout_handle, open(stderr_path, "ab") as stderr_handle: + child = subprocess.Popen( + command_line, + shell=True, + executable="/bin/bash", + stdout=stdout_handle, + stderr=stderr_handle, + start_new_session=True, + ) + record["childPid"] = child.pid + record["startedCommandAt"] = now() + write_record(record) + exit_code = child.wait() + record["completedAt"] = now() + record["exitCode"] = int(exit_code) + if record.get("status") == "stop_requested": + record["status"] = "stopped" + elif exit_code == 0: + record["status"] = "completed" + else: + record["status"] = "failed" +except Exception as exc: + record["completedAt"] = now() + if record.get("status") == "stop_requested": + record["status"] = "stopped" + else: + record["status"] = "failed" + record["error"] = str(exc) +finally: + record["workerCompletedAt"] = now() + write_record(record) +`; +} + +function buildRemoteWorkerScript({ + sessionId, + remoteSessionDir, + remoteCommandLine, +}) { + return [ + `$ErrorActionPreference = 'Stop'`, + `$sessionDir = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(remoteSessionDir)})`, + `$sessionRecordPath = Join-Path $sessionDir 'SESSION.json'`, + `$stdoutPath = Join-Path $sessionDir 'stdout.log'`, + `$stderrPath = Join-Path $sessionDir 'stderr.log'`, + `$commandLine = ${quotePowerShellString(remoteCommandLine)}`, + `New-Item -ItemType Directory -Force -Path $sessionDir | Out-Null`, + `$record = [ordered]@{`, + ` schema = 'erdos.remote_frontier_session/2'`, + ` remoteSessionId = ${quotePowerShellString(sessionId)}`, + ` launchedAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` status = 'running'`, + ` workerPid = $PID`, + ` childPid = $null`, + ` sessionDir = $sessionDir`, + ` stdoutPath = $stdoutPath`, + ` stderrPath = $stderrPath`, + ` remoteCommandLine = $commandLine`, + ` exitCode = $null`, + ` error = $null`, + `}`, + `$record | ConvertTo-Json -Depth 10 | Set-Content -Path $sessionRecordPath`, + `try {`, + ` $child = Start-Process -FilePath 'cmd.exe' -ArgumentList @('/d','/c',$commandLine) -RedirectStandardOutput $stdoutPath -RedirectStandardError $stderrPath -PassThru -WindowStyle Hidden`, + ` $record.childPid = $child.Id`, + ` $record.startedCommandAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` $record | ConvertTo-Json -Depth 10 | Set-Content -Path $sessionRecordPath`, + ` $child.WaitForExit()`, + ` $record.completedAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` $record.exitCode = $child.ExitCode`, + ` if ($record.status -eq 'stop_requested') {`, + ` $record.status = 'stopped'`, + ` } elseif ($child.ExitCode -eq 0) {`, + ` $record.status = 'completed'`, + ` } else {`, + ` $record.status = 'failed'`, + ` }`, + `} catch {`, + ` $record.completedAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` if ($record.status -eq 'stop_requested') {`, + ` $record.status = 'stopped'`, + ` } else {`, + ` $record.status = 'failed'`, + ` }`, + ` $record.error = $_.Exception.Message`, + `} finally {`, + ` $record.workerCompletedAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` $record | ConvertTo-Json -Depth 10 | Set-Content -Path $sessionRecordPath`, + `}`, + ].join('\n'); +} + +function resolveRemoteSnapshotStatus(record, running, remoteState) { + if (remoteState?.remoteRecord) { + const remoteStatus = String(remoteState.remoteRecord.status ?? '').trim().toLowerCase(); + if (running) { + if (record.stopRequestedAt || remoteStatus === 'stop_requested') { + return 'stop_requested'; + } + return remoteStatus || 'running'; + } + if (record.stopRequestedAt || remoteStatus === 'stop_requested' || remoteStatus === 'stopped') { + return 'stopped'; + } + if (remoteStatus === 'failed') { + return 'failed'; + } + if (remoteStatus === 'launching') { + return 'launching'; + } + if (remoteStatus) { + return remoteStatus; + } + } + + if (running) { + return record.stopRequestedAt ? 'stop_requested' : 'running'; + } + return record.stopRequestedAt ? 'stopped' : 'completed'; +} + +function launchRemoteSshSession(spec, workspaceRoot = getWorkspaceRoot()) { + const sessionId = spec.sessionId ?? generateSessionId(spec); + const sessionDir = getFrontierSessionDir(sessionId, workspaceRoot); + ensureDir(sessionDir); + + const remoteSessionDir = buildRemoteSessionDir(spec.remoteEngineRoot, sessionId); + const remoteRecordPath = `${remoteSessionDir}\\SESSION.json`; + const remoteStdoutPath = `${remoteSessionDir}\\stdout.log`; + const remoteStderrPath = `${remoteSessionDir}\\stderr.log`; + const remoteWorkerPath = `${remoteSessionDir}\\run-session.ps1`; + const remoteScpSessionDir = toRemoteScpPath(remoteSessionDir); + const remoteCommandLine = String(spec.remoteCommandLine ?? '').trim(); + const localWorkerPath = path.join(sessionDir, 'remote-worker.ps1'); + + if (!remoteScpSessionDir) { + return { + ok: false, + error: 'Failed to resolve remote SCP session directory.', + session: null, + }; + } + if (!remoteCommandLine) { + return { + ok: false, + error: 'Remote command line is missing.', + session: null, + }; + } + + const workerScript = buildRemoteWorkerScript({ + sessionId, + remoteSessionDir, + remoteCommandLine, + }); + writeText(localWorkerPath, workerScript); + + const ensureRemoteSessionDirScript = [ + `$engineRoot = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(spec.remoteEngineRoot)})`, + `$sessionsRoot = Join-Path $engineRoot 'sessions'`, + `$sessionDir = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(remoteSessionDir)})`, + `New-Item -ItemType Directory -Force -Path $engineRoot | Out-Null`, + `New-Item -ItemType Directory -Force -Path $sessionsRoot | Out-Null`, + `New-Item -ItemType Directory -Force -Path $sessionDir | Out-Null`, + `[pscustomobject]@{ sessionDir = $sessionDir } | ConvertTo-Json -Compress`, + ].join('\n'); + const ensureRemoteSessionDirResult = runRemotePowerShellCapture( + spec.remoteHost, + ensureRemoteSessionDirScript, + { cwd: workspaceRoot }, + ); + if (!ensureRemoteSessionDirResult.ok) { + return { + ok: false, + error: ensureRemoteSessionDirResult.stderr ?? 'Failed to prepare the remote frontier session directory.', + session: null, + }; + } + + const copyWorkerResult = runCommandCapture({ + executable: 'scp', + args: [localWorkerPath, `${spec.remoteHost}:${remoteScpSessionDir}/run-session.ps1`], + }, { cwd: workspaceRoot }); + if (!copyWorkerResult.ok) { + return { + ok: false, + error: copyWorkerResult.stderr ?? 'Failed to copy the remote frontier worker script.', + session: null, + }; + } + + const launchScript = [ + `$sessionDir = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(remoteSessionDir)})`, + `$workerPath = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(remoteWorkerPath)})`, + `$sessionRecordPath = Join-Path $sessionDir 'SESSION.json'`, + `$stdoutPath = Join-Path $sessionDir 'stdout.log'`, + `$stderrPath = Join-Path $sessionDir 'stderr.log'`, + `New-Item -ItemType Directory -Force -Path $sessionDir | Out-Null`, + `$proc = Start-Process -FilePath 'powershell.exe' -ArgumentList @('-NoProfile','-ExecutionPolicy','Bypass','-File',$workerPath) -PassThru -WindowStyle Hidden`, + `if (-not (Test-Path $sessionRecordPath)) {`, + ` [pscustomobject]@{`, + ` schema = 'erdos.remote_frontier_session/2'`, + ` remoteSessionId = ${quotePowerShellString(sessionId)}`, + ` launchedAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` status = 'launching'`, + ` workerPid = $proc.Id`, + ` childPid = $null`, + ` sessionDir = $sessionDir`, + ` stdoutPath = $stdoutPath`, + ` stderrPath = $stderrPath`, + ` remoteCommandLine = ${quotePowerShellString(remoteCommandLine)}`, + ` exitCode = $null`, + ` error = $null`, + ` } | ConvertTo-Json -Depth 10 | Set-Content -Path $sessionRecordPath`, + `}`, + `$deadline = (Get-Date).AddSeconds(2)`, + `do {`, + ` Start-Sleep -Milliseconds 100`, + ` $current = if (Test-Path $sessionRecordPath) { Get-Content -Raw $sessionRecordPath | ConvertFrom-Json } else { $null }`, + ` $ready = ($null -ne $current) -and (($current.status -ne 'launching') -or ($null -ne $current.childPid) -or (($null -ne $current.workerPid) -and ($current.workerPid -ne $proc.Id)))`, + `} while ((Get-Date) -lt $deadline -and -not $ready)`, + `[pscustomobject]@{`, + ` schema = 'erdos.remote_frontier_session_launch/2'`, + ` remoteSessionId = ${quotePowerShellString(sessionId)}`, + ` launchedAt = (Get-Date).ToUniversalTime().ToString('o')`, + ` pid = $proc.Id`, + ` workerPath = $workerPath`, + ` sessionDir = $sessionDir`, + ` stdoutPath = $stdoutPath`, + ` stderrPath = $stderrPath`, + ` remoteCommandLine = ${quotePowerShellString(remoteCommandLine)}`, + `} | ConvertTo-Json -Depth 10 -Compress`, + ].join('\n'); + + const launchResult = runRemotePowerShellCapture(spec.remoteHost, launchScript, { cwd: workspaceRoot }); + const remoteRecord = parseJsonDocument(launchResult.stdout); + if (!launchResult.ok || !remoteRecord) { + return { + ok: false, + error: launchResult.stderr ?? 'Failed to launch remote frontier session.', + session: null, + }; + } + + const record = { + schema: 'erdos.frontier_session/1', + backend: 'remote_ssh', + sessionId, + launchedAt: new Date().toISOString(), + kind: spec.kind ?? 'frontier_dispatch', + label: spec.label ?? spec.actionId ?? sessionId, + problemId: spec.problemId ?? null, + actionId: spec.actionId ?? null, + mode: spec.mode ?? null, + source: spec.source ?? null, + reviewAfterHours: spec.reviewAfterHours ?? null, + cwd: workspaceRoot, + pid: null, + executable: 'ssh', + args: [spec.remoteHost, remoteCommandLine], + commandLine: formatCommandLine('ssh', [spec.remoteHost, remoteCommandLine]), + stdoutPath: getFrontierSessionStdoutPath(sessionId, workspaceRoot), + stderrPath: getFrontierSessionStderrPath(sessionId, workspaceRoot), + stopRequestedAt: null, + detachedBy: spec.detachedBy ?? 'erdos', + metadata: { + ...(spec.metadata ?? {}), + reuseFingerprint: buildSessionReuseFingerprint(spec), + remoteHost: spec.remoteHost, + remoteEngineRoot: spec.remoteEngineRoot, + remoteCommandLine, + remoteSessionDir, + remoteRecordPath, + remoteStdoutPath, + remoteStderrPath, + remoteWorkerPath, + remoteScpSessionDir, + remotePid: remoteRecord.pid ?? null, + }, + }; + + writeSessionRecord(sessionId, record, workspaceRoot); + return { + ok: true, + session: buildSessionSnapshot(record, workspaceRoot), + }; +} + +function launchRemoteBrevSession(spec, workspaceRoot = getWorkspaceRoot()) { + const sessionId = spec.sessionId ?? generateSessionId(spec); + const sessionDir = getFrontierSessionDir(sessionId, workspaceRoot); + ensureDir(sessionDir); + + const remoteSessionDir = buildRemoteLinuxSessionDir(spec.remoteEngineRoot, sessionId); + const remoteRecordPath = joinRemotePath({ provider: 'brev' }, remoteSessionDir, 'SESSION.json'); + const remoteStdoutPath = joinRemotePath({ provider: 'brev' }, remoteSessionDir, 'stdout.log'); + const remoteStderrPath = joinRemotePath({ provider: 'brev' }, remoteSessionDir, 'stderr.log'); + const remoteWorkerPath = joinRemotePath({ provider: 'brev' }, remoteSessionDir, 'run-session.py'); + const remoteCommandLine = String(spec.remoteCommandLine ?? '').trim(); + const localWorkerPath = path.join(sessionDir, 'remote-worker.py'); + const remoteTarget = { + provider: 'brev', + instanceName: spec.remoteInstanceName ?? spec.remoteHost, + sshHost: spec.remoteHost, + }; + + if (!remoteTarget.instanceName) { + return { + ok: false, + error: 'Remote Brev instance is missing.', + session: null, + }; + } + if (!remoteCommandLine) { + return { + ok: false, + error: 'Remote command line is missing.', + session: null, + }; + } + + const workerScript = buildRemoteLinuxWorkerScript({ + sessionId, + remoteSessionDir, + remoteCommandLine, + }); + writeText(localWorkerPath, workerScript); + + const ensureRemoteSessionDirResult = runRemoteCommandCapture( + remoteTarget, + `mkdir -p ${quotePosixShellArg(remoteSessionDir)}`, + { cwd: workspaceRoot }, + ); + if (!ensureRemoteSessionDirResult.ok) { + return { + ok: false, + error: ensureRemoteSessionDirResult.stderr ?? 'Failed to prepare the remote Brev frontier session directory.', + session: null, + }; + } + + const copyWorkerResult = runRemoteCopyToCapture( + remoteTarget, + localWorkerPath, + remoteWorkerPath, + { cwd: workspaceRoot }, + ); + if (!copyWorkerResult.ok) { + return { + ok: false, + error: copyWorkerResult.stderr ?? 'Failed to copy the remote Brev frontier worker script.', + session: null, + }; + } + + const launchResult = runRemoteCommandCapture( + remoteTarget, + [ + `mkdir -p ${quotePosixShellArg(remoteSessionDir)}`, + `nohup ${quotePosixShellArg(spec.remotePythonCommand ?? 'python3')} ${quotePosixShellArg(remoteWorkerPath)} >/dev/null 2>&1 &`, + 'worker_pid=$!', + 'for _ in $(seq 1 20); do', + ` [ -f ${quotePosixShellArg(remoteRecordPath)} ] && break`, + ' sleep 0.1', + 'done', + 'printf \'{"pid":%s,"remoteSessionId":"%s","sessionDir":"%s","workerPath":"%s","stdoutPath":"%s","stderrPath":"%s"}\\n\' "$worker_pid" ' + + `${quotePosixShellArg(sessionId)} ${quotePosixShellArg(remoteSessionDir)} ${quotePosixShellArg(remoteWorkerPath)} ${quotePosixShellArg(remoteStdoutPath)} ${quotePosixShellArg(remoteStderrPath)}`, + ].join('\n'), + { cwd: workspaceRoot }, + ); + const remoteRecord = parseJsonDocument(launchResult.stdout); + if (!launchResult.ok || !remoteRecord) { + return { + ok: false, + error: launchResult.stderr ?? 'Failed to launch remote Brev frontier session.', + session: null, + }; + } + + const record = { + schema: 'erdos.frontier_session/1', + backend: 'remote_brev', + sessionId, + launchedAt: new Date().toISOString(), + kind: spec.kind ?? 'frontier_dispatch', + label: spec.label ?? spec.actionId ?? sessionId, + problemId: spec.problemId ?? null, + actionId: spec.actionId ?? null, + mode: spec.mode ?? null, + source: spec.source ?? null, + reviewAfterHours: spec.reviewAfterHours ?? null, + cwd: workspaceRoot, + pid: null, + executable: 'brev', + args: ['exec', remoteTarget.instanceName, remoteCommandLine], + commandLine: formatCommandLine('brev', ['exec', remoteTarget.instanceName, remoteCommandLine]), + stdoutPath: getFrontierSessionStdoutPath(sessionId, workspaceRoot), + stderrPath: getFrontierSessionStderrPath(sessionId, workspaceRoot), + stopRequestedAt: null, + detachedBy: spec.detachedBy ?? 'erdos', + metadata: { + ...(spec.metadata ?? {}), + reuseFingerprint: buildSessionReuseFingerprint(spec), + remoteProvider: 'brev', + remoteInstanceName: remoteTarget.instanceName, + remoteHost: spec.remoteHost ?? remoteTarget.instanceName, + remoteEngineRoot: spec.remoteEngineRoot, + remotePythonCommand: spec.remotePythonCommand ?? 'python3', + remoteCommandLine, + remoteSessionDir, + remoteRecordPath, + remoteStdoutPath, + remoteStderrPath, + remoteWorkerPath, + remotePid: remoteRecord.pid ?? null, + }, + }; + + writeSessionRecord(sessionId, record, workspaceRoot); + return { + ok: true, + session: buildSessionSnapshot(record, workspaceRoot), + }; +} + +function getRemoteSessionLiveSnapshot(record, workspaceRoot = getWorkspaceRoot()) { + const remoteHost = record?.metadata?.remoteHost ?? null; + const remoteRecordPath = record?.metadata?.remoteRecordPath ?? null; + if (!remoteHost || !remoteRecordPath) { + return { + running: false, + error: 'remote session metadata missing', + stdoutTail: [], + stderrTail: [], + runDir: null, + remoteRecord: null, + }; + } + + const statusScript = [ + `$recordPath = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(remoteRecordPath)})`, + `if (-not (Test-Path $recordPath)) { throw 'remote session record missing' }`, + `$record = Get-Content -Raw $recordPath | ConvertFrom-Json`, + `$worker = if ($record.workerPid) { Get-Process -Id $record.workerPid -ErrorAction SilentlyContinue } else { $null }`, + `$child = if ($record.childPid) { Get-Process -Id $record.childPid -ErrorAction SilentlyContinue } else { $null }`, + `$stdoutTail = if (Test-Path $record.stdoutPath) { @(Get-Content -Tail 12 $record.stdoutPath) } else { @() }`, + `$stderrTail = if (Test-Path $record.stderrPath) { @(Get-Content -Tail 12 $record.stderrPath) } else { @() }`, + `[pscustomobject]@{`, + ` running = (($record.status -eq 'running') -or (($record.status -eq 'launching') -and ($null -ne $worker)) -or (($record.status -eq 'stop_requested') -and (($null -ne $worker) -or ($null -ne $child))) -or ($null -ne $child))`, + ` remoteRecord = $record`, + ` stdoutTail = $stdoutTail`, + ` stderrTail = $stderrTail`, + `} | ConvertTo-Json -Depth 10 -Compress`, + ].join('\n'); + + const result = runRemotePowerShellCapture(remoteHost, statusScript, { cwd: workspaceRoot }); + const payload = parseJsonDocument(result.stdout); + if (!result.ok || !payload) { + return { + running: false, + error: result.stderr ?? 'failed to query remote session', + stdoutTail: [], + stderrTail: [], + runDir: null, + remoteRecord: null, + }; + } + + const stdoutTail = Array.isArray(payload.stdoutTail) ? payload.stdoutTail.map(String) : []; + const stderrTail = Array.isArray(payload.stderrTail) ? payload.stderrTail.map(String) : []; + return { + running: Boolean(payload.running), + error: null, + stdoutTail, + stderrTail, + runDir: parseRunDirFromTail(stdoutTail), + remoteRecord: payload.remoteRecord ?? null, + }; +} + +function getRemoteBrevSessionLiveSnapshot(record, workspaceRoot = getWorkspaceRoot()) { + const remoteInstanceName = record?.metadata?.remoteInstanceName ?? null; + const remoteRecordPath = record?.metadata?.remoteRecordPath ?? null; + if (!remoteInstanceName || !remoteRecordPath) { + return { + running: false, + error: 'remote brev session metadata missing', + stdoutTail: [], + stderrTail: [], + runDir: null, + remoteRecord: null, + }; + } + + const statusCommand = `${record.metadata?.remotePythonCommand ?? 'python3'} - <<'PY' +import json +import os +import signal + +record_path = ${JSON.stringify(String(remoteRecordPath))} +if not os.path.exists(record_path): + raise SystemExit("remote session record missing") +with open(record_path, "r", encoding="utf-8") as handle: + record = json.load(handle) + +def pid_alive(pid): + if not pid: + return False + try: + os.kill(int(pid), 0) + return True + except OSError: + return False + +def tail_lines(file_path, count=12): + if not file_path or not os.path.exists(file_path): + return [] + with open(file_path, "r", encoding="utf-8", errors="replace") as handle: + return handle.read().splitlines()[-count:] + +payload = { + "running": ( + record.get("status") in {"running", "launching"} + and (pid_alive(record.get("workerPid")) or pid_alive(record.get("childPid"))) + ) or ( + record.get("status") == "stop_requested" + and (pid_alive(record.get("workerPid")) or pid_alive(record.get("childPid"))) + ), + "remoteRecord": record, + "stdoutTail": tail_lines(record.get("stdoutPath")), + "stderrTail": tail_lines(record.get("stderrPath")), +} +print(json.dumps(payload)) +PY`; + + const result = runRemoteCommandCapture({ + provider: 'brev', + instanceName: remoteInstanceName, + }, statusCommand, { cwd: workspaceRoot }); + const payload = parseJsonDocument(result.stdout); + if (!result.ok || !payload) { + return { + running: false, + error: result.stderr ?? 'failed to query remote brev session', + stdoutTail: [], + stderrTail: [], + runDir: null, + remoteRecord: null, + }; + } + + const stdoutTail = Array.isArray(payload.stdoutTail) ? payload.stdoutTail.map(String) : []; + const stderrTail = Array.isArray(payload.stderrTail) ? payload.stderrTail.map(String) : []; + return { + running: Boolean(payload.running), + error: null, + stdoutTail, + stderrTail, + runDir: parseRunDirFromTail(stdoutTail), + remoteRecord: payload.remoteRecord ?? null, + }; +} + +function loadSessionRecord(sessionId, workspaceRoot = getWorkspaceRoot()) { + const recordPath = getFrontierSessionRecordPath(sessionId, workspaceRoot); + if (!fs.existsSync(recordPath)) { + return null; + } + return readJson(recordPath); +} + +function writeSessionRecord(sessionId, payload, workspaceRoot = getWorkspaceRoot()) { + writeJson(getFrontierSessionRecordPath(sessionId, workspaceRoot), payload); + return payload; +} + +function buildSessionSnapshot(record, workspaceRoot = getWorkspaceRoot()) { + if (!record) { + return null; + } + + const remoteState = record.backend === 'remote_ssh' + ? getRemoteSessionLiveSnapshot(record, workspaceRoot) + : record.backend === 'remote_brev' + ? getRemoteBrevSessionLiveSnapshot(record, workspaceRoot) + : null; + const stdoutTail = remoteState ? remoteState.stdoutTail : readTail(record.stdoutPath, 12); + const stderrTail = remoteState ? remoteState.stderrTail : readTail(record.stderrPath, 12); + const processState = remoteState ?? probeLocalProcess(record.pid); + const running = processState.running; + const review = computeReviewState(record, running); + const runDir = remoteState ? remoteState.runDir : parseRunDirFromTail(stdoutTail); + const status = resolveRemoteSnapshotStatus(record, running, remoteState); + + return { + ...record, + workspaceRoot, + status, + running, + processError: processState.error, + reviewDueAt: review.dueAt, + reviewState: review.state, + runDir, + stdoutTail, + stderrTail, + remotePid: remoteState?.remoteRecord?.pid ?? record.metadata?.remotePid ?? null, + remoteSessionDir: record.metadata?.remoteSessionDir ?? null, + remoteExitCode: remoteState?.remoteRecord?.exitCode ?? null, + remoteStatus: remoteState?.remoteRecord?.status ?? null, + remoteWorkerPid: remoteState?.remoteRecord?.workerPid ?? null, + remoteChildPid: remoteState?.remoteRecord?.childPid ?? null, + remoteError: remoteState?.remoteRecord?.error ?? null, + harvestedBundle: record?.metadata?.harvestedBundle ?? null, + }; +} + +export function launchFrontierDetachedSession(spec, workspaceRoot = getWorkspaceRoot()) { + if (spec.backend === 'remote_ssh') { + return launchRemoteSshSession(spec, workspaceRoot); + } + if (spec.backend === 'remote_brev') { + return launchRemoteBrevSession(spec, workspaceRoot); + } + const sessionId = spec.sessionId ?? generateSessionId(spec); + const sessionDir = getFrontierSessionDir(sessionId, workspaceRoot); + ensureDir(sessionDir); + + const stdoutPath = getFrontierSessionStdoutPath(sessionId, workspaceRoot); + const stderrPath = getFrontierSessionStderrPath(sessionId, workspaceRoot); + const stdoutFd = fs.openSync(stdoutPath, 'a'); + const stderrFd = fs.openSync(stderrPath, 'a'); + const executable = spec.executable ?? 'node'; + const args = Array.isArray(spec.args) ? spec.args : []; + const commandLine = formatCommandLine(executable, args); + + const child = spawn(executable, args, { + cwd: spec.cwd ?? workspaceRoot, + detached: true, + stdio: ['ignore', stdoutFd, stderrFd], + }); + fs.closeSync(stdoutFd); + fs.closeSync(stderrFd); + child.unref(); + + const record = { + schema: 'erdos.frontier_session/1', + sessionId, + launchedAt: new Date().toISOString(), + kind: spec.kind ?? 'frontier_dispatch', + label: spec.label ?? spec.actionId ?? sessionId, + problemId: spec.problemId ?? null, + actionId: spec.actionId ?? null, + mode: spec.mode ?? null, + source: spec.source ?? null, + reviewAfterHours: spec.reviewAfterHours ?? null, + cwd: spec.cwd ?? workspaceRoot, + pid: child.pid, + executable, + args, + commandLine, + stdoutPath, + stderrPath, + stopRequestedAt: null, + detachedBy: spec.detachedBy ?? 'erdos', + metadata: { + ...(spec.metadata ?? {}), + reuseFingerprint: buildSessionReuseFingerprint(spec), + }, + }; + + writeSessionRecord(sessionId, record, workspaceRoot); + return buildSessionSnapshot(record, workspaceRoot); +} + +export function findReusableFrontierDetachedSession(spec, workspaceRoot = getWorkspaceRoot()) { + const sessionsDir = getFrontierSessionsDir(workspaceRoot); + ensureDir(sessionsDir); + const targetFingerprint = buildSessionReuseFingerprint(spec); + const sessionIds = fs.readdirSync(sessionsDir, { withFileTypes: true }) + .filter((entry) => entry.isDirectory()) + .map((entry) => entry.name) + .sort() + .reverse(); + + for (const sessionId of sessionIds) { + const record = loadSessionRecord(sessionId, workspaceRoot); + if (!record || record.stopRequestedAt) { + continue; + } + if ((record.problemId ?? null) !== (spec.problemId ?? null) || (record.actionId ?? null) !== (spec.actionId ?? null)) { + continue; + } + const recordFingerprint = record.metadata?.reuseFingerprint ?? buildRecordReuseFingerprint(record); + if (recordFingerprint !== targetFingerprint) { + continue; + } + const snapshot = getFrontierSessionSnapshot(sessionId, workspaceRoot); + if (snapshot?.running && snapshot.status !== 'stop_requested') { + return snapshot; + } + } + + return null; +} + +export function getFrontierSessionSnapshot(sessionId, workspaceRoot = getWorkspaceRoot()) { + const record = loadSessionRecord(sessionId, workspaceRoot); + if (!record) { + return null; + } + + let effectiveRecord = record; + let snapshot = buildSessionSnapshot(record, workspaceRoot); + const harvestedBundle = maybeHarvestRemoteP848Bundle(record, snapshot, workspaceRoot); + if (harvestedBundle) { + effectiveRecord = { + ...record, + metadata: { + ...(record.metadata ?? {}), + harvestedBundle, + }, + }; + snapshot = buildSessionSnapshot(effectiveRecord, workspaceRoot); + } + const nextRecord = { + ...effectiveRecord, + lastObservedAt: new Date().toISOString(), + lastObservedStatus: snapshot.status, + lastObservedRunDir: snapshot.runDir ?? null, + }; + writeSessionRecord(sessionId, nextRecord, workspaceRoot); + return { + ...snapshot, + lastObservedAt: nextRecord.lastObservedAt, + lastObservedStatus: nextRecord.lastObservedStatus, + }; +} + +export function listFrontierSessionSnapshots(workspaceRoot = getWorkspaceRoot()) { + const sessionsDir = getFrontierSessionsDir(workspaceRoot); + ensureDir(sessionsDir); + const sessionIds = fs.readdirSync(sessionsDir, { withFileTypes: true }) + .filter((entry) => entry.isDirectory()) + .map((entry) => entry.name) + .sort() + .reverse(); + + const sessions = sessionIds + .map((sessionId) => getFrontierSessionSnapshot(sessionId, workspaceRoot)) + .filter(Boolean); + + return { + generatedAt: new Date().toISOString(), + workspaceRoot, + sessionsDir, + sessionCount: sessions.length, + sessions, + }; +} + +export function stopFrontierSession(sessionId, workspaceRoot = getWorkspaceRoot()) { + const record = loadSessionRecord(sessionId, workspaceRoot); + if (!record) { + return { + ok: false, + error: `Unknown frontier session: ${sessionId}`, + session: null, + }; + } + + const processState = probeLocalProcess(record.pid); + const stopRequestedAt = new Date().toISOString(); + const nextRecord = { + ...record, + stopRequestedAt, + }; + writeSessionRecord(sessionId, nextRecord, workspaceRoot); + + if (record.backend === 'remote_ssh') { + const remoteHost = record.metadata?.remoteHost ?? null; + const remoteRecordPath = record.metadata?.remoteRecordPath ?? null; + const stopScript = [ + `$recordPath = [Environment]::ExpandEnvironmentVariables(${quotePowerShellString(remoteRecordPath)})`, + `if (-not (Test-Path $recordPath)) { throw 'remote session record missing' }`, + `$record = Get-Content -Raw $recordPath | ConvertFrom-Json`, + `$child = if ($record.childPid) { Get-Process -Id $record.childPid -ErrorAction SilentlyContinue } else { $null }`, + `$worker = if ($record.workerPid) { Get-Process -Id $record.workerPid -ErrorAction SilentlyContinue } else { $null }`, + `$requested = $false`, + `if ($null -ne $child) { Stop-Process -Id $record.childPid -ErrorAction SilentlyContinue; $requested = $true }`, + `if ($null -ne $worker) { Stop-Process -Id $record.workerPid -ErrorAction SilentlyContinue; $requested = $true }`, + `$record | Add-Member -NotePropertyName stopRequestedAt -NotePropertyValue (Get-Date).ToUniversalTime().ToString('o') -Force`, + `$record | Add-Member -NotePropertyName stopCompletedAt -NotePropertyValue (Get-Date).ToUniversalTime().ToString('o') -Force`, + `$record | Add-Member -NotePropertyName previousChildPid -NotePropertyValue $record.childPid -Force`, + `$record | Add-Member -NotePropertyName previousWorkerPid -NotePropertyValue $record.workerPid -Force`, + `$record.childPid = $null`, + `$record.workerPid = $null`, + `$record | Add-Member -NotePropertyName status -NotePropertyValue 'stopped' -Force`, + `$record | ConvertTo-Json -Depth 10 | Set-Content -Path $recordPath`, + `[pscustomobject]@{ requested = $requested } | ConvertTo-Json -Compress`, + ].join('\n'); + const stopResult = runRemotePowerShellCapture(remoteHost, stopScript, { cwd: workspaceRoot }); + const payload = parseJsonDocument(stopResult.stdout); + return { + ok: stopResult.ok, + requested: Boolean(payload?.requested), + alreadyExited: !Boolean(payload?.requested), + error: stopResult.ok ? null : (stopResult.stderr ?? 'Failed to stop remote frontier session.'), + session: buildSessionSnapshot(nextRecord, workspaceRoot), + }; + } + + if (record.backend === 'remote_brev') { + const remoteInstanceName = record.metadata?.remoteInstanceName ?? null; + const remoteRecordPath = record.metadata?.remoteRecordPath ?? null; + const stopCommand = `${record.metadata?.remotePythonCommand ?? 'python3'} - <<'PY' +import json +import os +import signal + +record_path = ${JSON.stringify(String(remoteRecordPath ?? ''))} +if not os.path.exists(record_path): + raise SystemExit("remote session record missing") +with open(record_path, "r", encoding="utf-8") as handle: + record = json.load(handle) + +requested = False +for key in ("childPid", "workerPid"): + pid = record.get(key) + if pid: + try: + os.kill(int(pid), signal.SIGTERM) + requested = True + except OSError: + pass + +record["stopRequestedAt"] = ${JSON.stringify(stopRequestedAt)} +record["stopCompletedAt"] = ${JSON.stringify(stopRequestedAt)} +record["previousChildPid"] = record.get("childPid") +record["previousWorkerPid"] = record.get("workerPid") +record["childPid"] = None +record["workerPid"] = None +record["status"] = "stopped" + +with open(record_path, "w", encoding="utf-8") as handle: + json.dump(record, handle, indent=2) + +print(json.dumps({"requested": requested})) +PY`; + const stopResult = runRemoteCommandCapture({ + provider: 'brev', + instanceName: remoteInstanceName, + }, stopCommand, { cwd: workspaceRoot }); + const payload = parseJsonDocument(stopResult.stdout); + return { + ok: stopResult.ok, + requested: Boolean(payload?.requested), + alreadyExited: !Boolean(payload?.requested), + error: stopResult.ok ? null : (stopResult.stderr ?? 'Failed to stop remote Brev frontier session.'), + session: buildSessionSnapshot(nextRecord, workspaceRoot), + }; + } + + if (!processState.running) { + return { + ok: true, + requested: false, + alreadyExited: true, + session: buildSessionSnapshot(nextRecord, workspaceRoot), + }; + } + + try { + process.kill(record.pid, 'SIGTERM'); + return { + ok: true, + requested: true, + alreadyExited: false, + session: buildSessionSnapshot(nextRecord, workspaceRoot), + }; + } catch (error) { + return { + ok: false, + requested: false, + alreadyExited: false, + error: error?.message ?? 'Failed to stop frontier session.', + session: buildSessionSnapshot(nextRecord, workspaceRoot), + }; + } +} + +export function getFrontierSessionCommandSpec(commandArgs = [], workspaceRoot = getWorkspaceRoot()) { + return { + executable: 'node', + args: [path.join(repoRoot, 'src', 'cli', 'index.js'), ...commandArgs], + cwd: workspaceRoot, + commandLine: formatCommandLine('node', [path.join(repoRoot, 'src', 'cli', 'index.js'), ...commandArgs]), + }; +} diff --git a/src/runtime/frontier.js b/src/runtime/frontier.js new file mode 100644 index 0000000..8d89aa0 --- /dev/null +++ b/src/runtime/frontier.js @@ -0,0 +1,2875 @@ +import { execFileSync } from 'node:child_process'; +import fs from 'node:fs'; +import path from 'node:path'; +import { ensureDir } from './files.js'; +import { loadConfig, saveConfig } from './config.js'; +import { + getDefaultRemoteEngineRoot, + getDefaultRemotePythonCommand, + isBrevRemote, + joinRemotePath, + probeBrevRemoteHome, + quotePosixShellArg, + quoteRemoteWindowsPath, + runRemoteCommandCapture, + runRemoteCopyToCapture, + toRemoteCopyPath, +} from './frontier-remote.js'; +import { getWorkspaceDir, getWorkspaceRoot, repoRoot } from './paths.js'; + +const PYTHON_PROBE_SCRIPT = [ + 'import importlib.util, json, platform, sys', + 'payload = {', + ' "python_executable": sys.executable,', + ' "python_version": platform.python_version(),', + ' "frontier_engine_installed": False,', + ' "torch_installed": False,', + ' "torch_version": None,', + ' "cuda_available": False,', + ' "cuda_device_count": 0,', + ' "cuda_device_names": [],', + ' "cuda_error": None,', + '}', + 'payload["frontier_engine_installed"] = importlib.util.find_spec("frontier_engine") is not None', + 'torch_spec = importlib.util.find_spec("torch")', + 'payload["torch_installed"] = torch_spec is not None', + 'if torch_spec is not None:', + ' import torch', + ' payload["torch_version"] = getattr(torch, "__version__", None)', + ' try:', + ' payload["cuda_available"] = bool(torch.cuda.is_available())', + ' if payload["cuda_available"]:', + ' payload["cuda_device_count"] = int(torch.cuda.device_count())', + ' payload["cuda_device_names"] = [torch.cuda.get_device_name(index) for index in range(torch.cuda.device_count())]', + ' except Exception as exc:', + ' payload["cuda_error"] = str(exc)', + 'print(json.dumps(payload))', +].join('\n'); + +const PYTHON_EXECUTABLE_PROBE_SCRIPT = [ + 'import platform, sys', + 'print(sys.executable)', + 'print(platform.python_version())', +].join('\n'); + +function formatShellArg(value) { + if (value === null || value === undefined) { + return ''; + } + const text = String(value); + if (/^[A-Za-z0-9_./:=+-]+$/.test(text)) { + return text; + } + return JSON.stringify(text); +} + +function formatCommand(command) { + return [command.executable, ...(command.args ?? [])].map(formatShellArg).join(' '); +} + +function runCommandCapture(command, options = {}) { + try { + const stdout = execFileSync(command.executable, command.args ?? [], { + cwd: options.cwd ?? repoRoot, + encoding: 'utf8', + stdio: ['ignore', 'pipe', 'pipe'], + }); + return { + ok: true, + stdout: stdout.trim(), + stderr: null, + }; + } catch (error) { + return { + ok: false, + stdout: error?.stdout?.toString().trim() || null, + stderr: error?.stderr?.toString().trim() || error?.message || null, + }; + } +} + +function runBrevRefreshCapture(workspaceRoot = getWorkspaceRoot()) { + return runCommandCapture({ + executable: 'brev', + args: ['refresh'], + }, { cwd: workspaceRoot }); +} + +function getRemoteProviderLabel(remote = {}) { + if (remote.provider === 'brev') { + return remote.instanceName + ? `Brev instance ${remote.instanceName}` + : 'Brev remote'; + } + return remote.sshHost + ? `SSH host ${remote.sshHost}` + : 'remote SSH host'; +} + +function formatBrevNumeric(value) { + if (value === null || value === undefined || value === '') { + return null; + } + const parsed = Number(value); + return Number.isFinite(parsed) ? parsed : null; +} + +function buildBrevCreateArgs(options = {}) { + const args = ['create']; + const name = options.instanceName ?? options.name ?? null; + if (name) { + args.push(name); + } + if (options.type) { + args.push('--type', String(options.type)); + } + if (options.gpuName) { + args.push('--gpu-name', String(options.gpuName)); + } + if (options.provider) { + args.push('--provider', String(options.provider)); + } + if (formatBrevNumeric(options.count) !== null) { + args.push('--count', String(formatBrevNumeric(options.count))); + } + if (formatBrevNumeric(options.parallel) !== null) { + args.push('--parallel', String(formatBrevNumeric(options.parallel))); + } + if (formatBrevNumeric(options.minVram) !== null) { + args.push('--min-vram', String(formatBrevNumeric(options.minVram))); + } + if (formatBrevNumeric(options.minTotalVram) !== null) { + args.push('--min-total-vram', String(formatBrevNumeric(options.minTotalVram))); + } + if (formatBrevNumeric(options.maxBootTime) !== null) { + args.push('--max-boot-time', String(formatBrevNumeric(options.maxBootTime))); + } + if (formatBrevNumeric(options.minDisk) !== null) { + args.push('--min-disk', String(formatBrevNumeric(options.minDisk))); + } + if (formatBrevNumeric(options.minCapability) !== null) { + args.push('--min-capability', String(formatBrevNumeric(options.minCapability))); + } + if (options.sort) { + args.push('--sort', String(options.sort)); + } + if (options.startupScript) { + args.push('--startup-script', String(options.startupScript)); + } + if (options.detached) { + args.push('--detached'); + } + if (options.dryRun) { + args.push('--dry-run'); + } + return args; +} + +function classifyBrevProvision(options = {}) { + const count = formatBrevNumeric(options.count) ?? 1; + const gpuName = String(options.gpuName ?? options.type ?? '').toUpperCase(); + const warnings = []; + if (gpuName.includes('H100')) { + warnings.push('H100-class hardware can be expensive; review provider, hourly price, and expected sweep value before applying.'); + } + if (count > 1) { + warnings.push('Multi-instance provisioning is intended for parallel independent sweeps and should be launched intentionally.'); + } + if (options.attach && count !== 1) { + warnings.push('Auto-attach is only meaningful for a single Brev instance; clusters should be attached or orchestrated explicitly.'); + } + return warnings; +} + +function normalizeRemoteId(remote = {}, preferredId = null) { + const normalizedRemote = remote && typeof remote === 'object' ? remote : {}; + return String( + preferredId + ?? normalizedRemote.remoteId + ?? normalizedRemote.instanceName + ?? normalizedRemote.sshHost + ?? '', + ).trim() || null; +} + +function getFrontierRemoteRegistry(config = {}) { + const remotes = { + ...((config.frontier?.remotes && typeof config.frontier.remotes === 'object') + ? config.frontier.remotes + : {}), + }; + const legacyRemote = config.frontier?.remote ?? null; + const legacyRemoteId = normalizeRemoteId(legacyRemote, config.frontier?.activeRemoteId ?? null); + if (legacyRemote && legacyRemoteId && !remotes[legacyRemoteId]) { + remotes[legacyRemoteId] = { + ...legacyRemote, + remoteId: legacyRemoteId, + }; + } + const activeRemoteId = normalizeRemoteId( + remotes[config.frontier?.activeRemoteId ?? ''] ?? null, + config.frontier?.activeRemoteId ?? legacyRemoteId, + ); + const activeRemote = activeRemoteId ? (remotes[activeRemoteId] ?? null) : null; + return { + remotes, + activeRemoteId, + activeRemote, + }; +} + +function normalizeStringIdList(values = []) { + return Array.from(new Set( + (Array.isArray(values) ? values : []) + .map((value) => String(value ?? '').trim()) + .filter(Boolean), + )).sort(); +} + +function getFrontierPaidRungs(config = {}) { + return { + enabledRemoteIds: normalizeStringIdList(config.frontier?.paidRungs?.enabledRemoteIds), + enabledFleetIds: normalizeStringIdList(config.frontier?.paidRungs?.enabledFleetIds), + lastUpdatedAt: config.frontier?.paidRungs?.lastUpdatedAt ?? null, + }; +} + +function isPaidRemote(remote = {}) { + return remote?.provider === 'brev'; +} + +function isPaidFleet(fleet = {}) { + return fleet?.provider === 'brev'; +} + +function isRemotePaidEnabled(config = {}, remote = {}, remoteId = null) { + if (!isPaidRemote(remote)) { + return true; + } + const normalizedRemoteId = normalizeRemoteId(remote, remoteId ?? null); + if (!normalizedRemoteId) { + return false; + } + return getFrontierPaidRungs(config).enabledRemoteIds.includes(normalizedRemoteId); +} + +function isFleetPaidEnabled(config = {}, fleet = {}, fleetId = null) { + if (!isPaidFleet(fleet)) { + return true; + } + const normalizedFleetId = normalizeFleetId(fleet, fleetId ?? null); + if (!normalizedFleetId) { + return false; + } + return getFrontierPaidRungs(config).enabledFleetIds.includes(normalizedFleetId); +} + +function setFrontierPaidRemoteEnabled(config, remoteId, enabled) { + const paidRungs = getFrontierPaidRungs(config); + const nextRemoteIds = enabled + ? normalizeStringIdList([...paidRungs.enabledRemoteIds, remoteId]) + : paidRungs.enabledRemoteIds.filter((candidate) => candidate !== remoteId); + return { + ...config, + frontier: { + ...config.frontier, + paidRungs: { + ...paidRungs, + enabledRemoteIds: nextRemoteIds, + lastUpdatedAt: new Date().toISOString(), + }, + }, + }; +} + +function setFrontierPaidFleetEnabled(config, fleetId, remoteIds = [], enabled) { + const paidRungs = getFrontierPaidRungs(config); + const nextFleetIds = enabled + ? normalizeStringIdList([...paidRungs.enabledFleetIds, fleetId]) + : paidRungs.enabledFleetIds.filter((candidate) => candidate !== fleetId); + const nextRemoteIds = enabled + ? normalizeStringIdList([...paidRungs.enabledRemoteIds, ...remoteIds]) + : paidRungs.enabledRemoteIds.filter((candidate) => !remoteIds.includes(candidate)); + return { + ...config, + frontier: { + ...config.frontier, + paidRungs: { + ...paidRungs, + enabledRemoteIds: nextRemoteIds, + enabledFleetIds: nextFleetIds, + lastUpdatedAt: new Date().toISOString(), + }, + }, + }; +} + +function buildRegisteredRemotesSummary(config = {}) { + const registry = getFrontierRemoteRegistry(config); + return Object.entries(registry.remotes).map(([remoteId, remote]) => { + const resolvedRemote = resolveRemoteConfigDefaults(remote); + return { + remoteId, + provider: resolvedRemote.provider ?? 'ssh', + instanceName: resolvedRemote.instanceName ?? null, + sshHost: resolvedRemote.sshHost ?? null, + engineRoot: resolvedRemote.engineRoot ?? null, + pythonCommand: resolvedRemote.pythonCommand ?? null, + paidRung: isPaidRemote(resolvedRemote), + paidEnabled: isRemotePaidEnabled(config, resolvedRemote, remoteId), + active: remoteId === registry.activeRemoteId, + }; + }); +} + +function normalizeFleetId(fleet = {}, preferredId = null) { + const normalizedFleet = fleet && typeof fleet === 'object' ? fleet : {}; + return String( + preferredId + ?? normalizedFleet.fleetId + ?? normalizedFleet.instanceName + ?? '', + ).trim() || null; +} + +function normalizeRemoteIdList(remoteIds = []) { + return Array.from(new Set( + (Array.isArray(remoteIds) ? remoteIds : []) + .map((remoteId) => String(remoteId ?? '').trim()) + .filter(Boolean), + )).sort(); +} + +function getFrontierFleetRegistry(config = {}) { + return { + fleets: { + ...((config.frontier?.fleets && typeof config.frontier.fleets === 'object') + ? config.frontier.fleets + : {}), + }, + }; +} + +function buildFrontierFleetMemberIds(fleetId, count) { + const normalizedCount = Number(count); + if (!Number.isInteger(normalizedCount) || normalizedCount <= 0) { + return []; + } + const width = Math.max(2, String(normalizedCount).length); + return Array.from({ length: normalizedCount }, (_, index) => ( + `${fleetId}-${String(index + 1).padStart(width, '0')}` + )); +} + +function persistFrontierFleet(config, fleetConfig, options = {}) { + const registry = getFrontierFleetRegistry(config); + const fleetId = normalizeFleetId(fleetConfig, options.fleetId ?? null); + if (!fleetId) { + return { + frontier: { ...(config.frontier ?? {}) }, + fleetId: null, + fleet: null, + }; + } + + const fleets = { + ...registry.fleets, + [fleetId]: { + ...(registry.fleets[fleetId] ?? {}), + ...(fleetConfig ?? {}), + fleetId, + remoteIds: normalizeRemoteIdList(fleetConfig?.remoteIds ?? []), + }, + }; + + return { + frontier: { + ...(config.frontier ?? {}), + fleets, + }, + fleetId, + fleet: fleets[fleetId], + }; +} + +function persistFrontierRemote(config, remoteConfig, options = {}) { + const registry = getFrontierRemoteRegistry(config); + const remoteId = normalizeRemoteId(remoteConfig, options.remoteId ?? null); + if (!remoteId) { + return { + frontier: { + ...config.frontier, + }, + remoteId: null, + }; + } + const remotes = { + ...registry.remotes, + [remoteId]: { + ...(registry.remotes[remoteId] ?? {}), + ...remoteConfig, + remoteId, + }, + }; + const activeRemoteId = options.setActive === false + ? (registry.activeRemoteId ?? remoteId) + : remoteId; + const nextConfig = { + ...config, + frontier: { + ...config.frontier, + activeRemoteId, + remotes, + }, + }; + const activeRemote = remotes[activeRemoteId] ?? remotes[remoteId] ?? null; + return { + frontier: { + ...nextConfig.frontier, + remote: activeRemote + ? { + ...activeRemote, + paidEnabled: isRemotePaidEnabled(nextConfig, activeRemote, activeRemoteId), + } + : null, + }, + remoteId, + }; +} + +function resolveRemoteConfigDefaults(remoteConfig = {}, workspaceRoot = getWorkspaceRoot()) { + const provider = remoteConfig.provider === 'brev' ? 'brev' : 'ssh'; + const instanceName = remoteConfig.instanceName ?? null; + const sshHost = remoteConfig.sshHost ?? (provider === 'brev' ? instanceName : null); + const legacyBrevEngineRoot = provider === 'brev' + && String(remoteConfig.engineRoot ?? '').includes('%USERPROFILE%'); + const legacyBrevPythonCommand = provider === 'brev' + && String(remoteConfig.pythonCommand ?? '').trim().startsWith('py '); + const brevHomeDir = provider === 'brev' && (!remoteConfig.engineRoot || legacyBrevEngineRoot) + ? probeBrevRemoteHome(instanceName ?? sshHost ?? null, { cwd: workspaceRoot }) + : null; + const engineRoot = remoteConfig.engineRoot && !legacyBrevEngineRoot + ? remoteConfig.engineRoot + : getDefaultRemoteEngineRoot(provider, brevHomeDir); + const pythonCommand = remoteConfig.pythonCommand && !legacyBrevPythonCommand + ? remoteConfig.pythonCommand + : getDefaultRemotePythonCommand(provider); + return { + ...remoteConfig, + provider, + instanceName, + sshHost, + engineRoot, + pythonCommand, + }; +} + +function parseJsonDocument(text) { + if (!text) { + return null; + } + try { + return JSON.parse(String(text).trim()); + } catch { + return null; + } +} + +function probePythonCommand(spec, workspaceRoot = getWorkspaceRoot()) { + if (!spec) { + return { + available: false, + pythonExecutable: null, + pythonVersion: null, + error: 'python unavailable', + }; + } + + const result = runCommandCapture({ + executable: spec.executable, + args: [...(spec.argsPrefix ?? []), '-c', PYTHON_EXECUTABLE_PROBE_SCRIPT], + }, { cwd: workspaceRoot }); + + if (!result.ok || !result.stdout) { + return { + available: false, + pythonExecutable: spec.executable, + pythonVersion: null, + error: result.stderr ?? 'python executable probe failed', + }; + } + + const lines = String(result.stdout) + .split(/\r?\n/) + .map((line) => line.trim()) + .filter(Boolean); + + return { + available: true, + pythonExecutable: lines[0] ?? spec.executable, + pythonVersion: lines[1] ?? null, + error: null, + }; +} + +function resolveBundledFrontierCliRunner(workspaceRoot = getWorkspaceRoot()) { + const bundledEngineCliPath = getBundledFrontierEngineSourcePath(); + if (!fs.existsSync(bundledEngineCliPath)) { + return { + runner: null, + error: 'No runnable bundled frontier-engine CLI is currently available.', + }; + } + + const managedProbe = probePythonCommand(getManagedPythonSpec(workspaceRoot), workspaceRoot); + if (managedProbe.available) { + return { + runner: { + mode: 'managed', + executable: managedProbe.pythonExecutable, + argsPrefix: [bundledEngineCliPath], + pythonVersion: managedProbe.pythonVersion, + }, + error: null, + }; + } + + const systemProbe = probePythonCommand(detectSystemPythonSpec(), workspaceRoot); + if (systemProbe.available) { + return { + runner: { + mode: 'system', + executable: systemProbe.pythonExecutable, + argsPrefix: [bundledEngineCliPath], + pythonVersion: systemProbe.pythonVersion, + }, + error: null, + }; + } + + return { + runner: null, + error: managedProbe.error ?? systemProbe.error ?? 'No runnable bundled frontier-engine CLI is currently available.', + }; +} + +function runBundledFrontierCli(commandArgs = [], workspaceRoot = getWorkspaceRoot(), runnerOverride = null) { + const resolvedRunner = runnerOverride + ? { runner: runnerOverride, error: null } + : resolveBundledFrontierCliRunner(workspaceRoot); + + if (resolvedRunner.runner) { + return { + runner: resolvedRunner.runner, + result: runCommandCapture({ + executable: resolvedRunner.runner.executable, + args: [...(resolvedRunner.runner.argsPrefix ?? []), ...commandArgs], + }, { cwd: workspaceRoot }), + }; + } + + return { + runner: null, + result: { + ok: false, + stdout: null, + stderr: resolvedRunner.error ?? 'No runnable bundled frontier-engine CLI is currently available.', + }, + }; +} + +function probeRemoteFrontierRuntime(remoteConfig = {}, workspaceRoot = getWorkspaceRoot()) { + const provider = remoteConfig.provider ?? 'ssh'; + const sshHost = remoteConfig.sshHost ?? null; + const instanceName = remoteConfig.instanceName ?? null; + const remoteTarget = { + ...remoteConfig, + provider, + sshHost, + instanceName, + }; + const remoteIdentity = isBrevRemote(remoteTarget) + ? (instanceName ?? sshHost) + : sshHost; + if (!remoteIdentity) { + return null; + } + + const pythonCommand = remoteConfig.pythonCommand ?? getDefaultRemotePythonCommand(provider); + const engineRoot = remoteConfig.engineRoot ?? getDefaultRemoteEngineRoot(provider); + const cliPath = joinRemotePath(remoteTarget, engineRoot, 'src', 'frontier_engine', 'cli.py'); + const pyprojectPath = joinRemotePath(remoteTarget, engineRoot, 'pyproject.toml'); + const pythonProbeCommand = isBrevRemote(remoteTarget) + ? `${pythonCommand} - <<'PY' +import importlib.util, platform, sys +print(platform.python_version()) +print(sys.executable) +print(importlib.util.find_spec("torch") is not None) +PY` + : `${pythonCommand} -c "import platform, sys; import importlib.util; print(platform.python_version()); print(sys.executable); print(importlib.util.find_spec('torch') is not None)"`; + const torchProbeCommand = isBrevRemote(remoteTarget) + ? `${pythonCommand} - <<'PY' +import torch +print(torch.__version__) +print(torch.cuda.is_available()) +print(torch.cuda.device_count()) +print(torch.cuda.get_device_name(0) if torch.cuda.is_available() and torch.cuda.device_count() else "") +PY` + : `${pythonCommand} -c "import torch; print(torch.__version__); print(torch.cuda.is_available()); print(torch.cuda.device_count()); print(torch.cuda.get_device_name(0) if torch.cuda.is_available() and torch.cuda.device_count() else '')"`; + const engineProbeCommand = isBrevRemote(remoteTarget) + ? `test -f ${quotePosixShellArg(cliPath)} && printf 'true\\n' || printf 'false\\n'` + : `cmd /c if exist ${quoteRemoteWindowsPath(cliPath)} (echo true) else (echo false)`; + const pyprojectProbeCommand = isBrevRemote(remoteTarget) + ? `test -f ${quotePosixShellArg(pyprojectPath)} && printf 'true\\n' || printf 'false\\n'` + : `cmd /c if exist ${quoteRemoteWindowsPath(pyprojectPath)} (echo true) else (echo false)`; + + const pythonProbe = runRemoteCommandCapture(remoteTarget, pythonProbeCommand, { cwd: workspaceRoot }); + const torchProbe = runRemoteCommandCapture(remoteTarget, torchProbeCommand, { cwd: workspaceRoot }); + const engineProbe = runRemoteCommandCapture(remoteTarget, engineProbeCommand, { cwd: workspaceRoot }); + const pyprojectProbe = runRemoteCommandCapture(remoteTarget, pyprojectProbeCommand, { cwd: workspaceRoot }); + + const pythonLines = (pythonProbe.stdout ?? '').split(/\r?\n/).map((line) => line.trim()).filter(Boolean); + const torchLines = (torchProbe.stdout ?? '').split(/\r?\n/).map((line) => line.trim()).filter(Boolean); + + return { + attached: Boolean(remoteConfig.attached), + provider, + instanceName, + sshHost, + pythonCommand, + engineRoot, + available: pythonProbe.ok, + pythonVersion: pythonLines[0] ?? null, + pythonExecutable: pythonLines[1] ?? null, + torchInstalled: pythonLines[2] === 'True', + torchVersion: torchProbe.ok ? (torchLines[0] ?? null) : null, + cudaAvailable: torchProbe.ok ? torchLines[1] === 'True' : false, + cudaDeviceCount: torchProbe.ok ? Number(torchLines[2] ?? 0) : 0, + cudaDeviceNames: torchProbe.ok && torchLines[3] ? [torchLines[3]] : [], + frontierEngineReady: engineProbe.ok && engineProbe.stdout === 'true', + engineCliPresent: engineProbe.ok && engineProbe.stdout === 'true', + enginePyprojectPresent: pyprojectProbe.ok && pyprojectProbe.stdout === 'true', + error: pythonProbe.ok + ? (torchProbe.ok ? null : (torchProbe.stderr ?? null)) + : (pythonProbe.stderr ?? null), + }; +} + +function getBundledFrontierEngineRoot() { + return path.join(repoRoot, 'research', 'frontier-engine'); +} + +function getBundledFrontierEnginePyprojectPath() { + return path.join(getBundledFrontierEngineRoot(), 'pyproject.toml'); +} + +function getBundledFrontierEngineSourcePath() { + return path.join(getBundledFrontierEngineRoot(), 'src', 'frontier_engine', 'cli.py'); +} + +function getBundledFrontierExperimentPath(...parts) { + return path.join(getBundledFrontierEngineRoot(), 'experiments', ...parts); +} + +function getBundledFrontierExperimentsRoot() { + return getBundledFrontierExperimentPath(); +} + +function getBundledFrontierSourcePackagePath() { + return path.join(getBundledFrontierEngineRoot(), 'src', 'frontier_engine'); +} + +function getFrontierLaneExperimentDirName(laneId) { + return String(laneId ?? '').trim().replaceAll('_', '-'); +} + +function sanitizeSyncLabelSegment(value) { + return String(value ?? '') + .trim() + .replace(/[^A-Za-z0-9]+/g, '_') + .replace(/^_+|_+$/g, '') + || 'entry'; +} + +function buildLaneSyncEntries(laneId, experimentDir, experimentsReadmePath) { + const experimentDirName = path.basename(experimentDir); + const entries = []; + + if (experimentsReadmePath && fs.existsSync(experimentsReadmePath)) { + entries.push({ + label: 'sync_frontier_experiments_readme', + localPath: experimentsReadmePath, + remoteRelativePath: path.join('experiments', 'README.md'), + recursive: false, + }); + } + + if (laneId === 'p848_anchor_ladder') { + const topLevelEntries = fs.readdirSync(experimentDir, { withFileTypes: true }) + .filter((entry) => entry.isFile()) + .sort((left, right) => left.name.localeCompare(right.name)); + for (const entry of topLevelEntries) { + entries.push({ + label: `sync_frontier_lane_${laneId}_${sanitizeSyncLabelSegment(entry.name)}`, + localPath: path.join(experimentDir, entry.name), + remoteRelativePath: path.join('experiments', experimentDirName, entry.name), + recursive: false, + }); + } + + const latestRoot = path.join(experimentDir, 'live-frontier-sync', 'latest'); + if (fs.existsSync(latestRoot)) { + const latestChildren = fs.readdirSync(latestRoot, { withFileTypes: true }) + .sort((left, right) => left.name.localeCompare(right.name)); + for (const entry of latestChildren) { + entries.push({ + label: `sync_frontier_lane_${laneId}_live_latest_${sanitizeSyncLabelSegment(entry.name)}`, + localPath: path.join(latestRoot, entry.name), + remoteRelativePath: entry.isDirectory() + ? path.join('experiments', experimentDirName, 'live-frontier-sync', 'latest') + : path.join('experiments', experimentDirName, 'live-frontier-sync', 'latest', entry.name), + recursive: entry.isDirectory(), + }); + } + } + + return entries; + } + + entries.push({ + label: `sync_frontier_lane_${laneId}`, + localPath: experimentDir, + remoteRelativePath: path.join('experiments'), + recursive: true, + }); + return entries; +} + +function resolveFrontierSyncScope(laneId = null) { + const experimentsRoot = getBundledFrontierExperimentsRoot(); + const experimentsReadmePath = path.join(experimentsRoot, 'README.md'); + const normalizedLaneId = laneId ? String(laneId).trim() : null; + + if (!normalizedLaneId || normalizedLaneId === 'all') { + const experimentDirs = fs.existsSync(experimentsRoot) + ? fs.readdirSync(experimentsRoot, { withFileTypes: true }) + .filter((entry) => entry.isDirectory()) + .map((entry) => path.join(experimentsRoot, entry.name)) + .sort() + : []; + return { + mode: 'all', + laneId: null, + label: 'all frontier-engine lanes', + experimentsRoot, + experimentsReadmePath, + experimentDirs, + syncPaths: [experimentsRoot], + error: null, + }; + } + + const experimentDirName = getFrontierLaneExperimentDirName(normalizedLaneId); + const experimentDir = path.join(experimentsRoot, experimentDirName); + if (!fs.existsSync(experimentDir)) { + return { + mode: 'lane', + laneId: normalizedLaneId, + label: normalizedLaneId, + experimentsRoot, + experimentsReadmePath, + experimentDirName, + experimentDir, + syncPaths: [], + error: `No bundled frontier-engine experiment directory was found for lane ${normalizedLaneId}.`, + }; + } + + const syncEntries = buildLaneSyncEntries(normalizedLaneId, experimentDir, experimentsReadmePath); + + return { + mode: 'lane', + laneId: normalizedLaneId, + label: normalizedLaneId, + experimentsRoot, + experimentsReadmePath, + experimentDirName, + experimentDir, + syncEntries, + syncPaths: syncEntries.map((entry) => entry.localPath), + error: null, + }; +} + +function detectSystemPythonSpec() { + const candidates = process.platform === 'win32' + ? [ + { executable: 'py', argsPrefix: ['-3'] }, + { executable: 'python', argsPrefix: [] }, + { executable: 'python3', argsPrefix: [] }, + ] + : [ + { executable: 'python3.13', argsPrefix: [] }, + { executable: 'python3.12', argsPrefix: [] }, + { executable: 'python3.11', argsPrefix: [] }, + { executable: 'python3.10', argsPrefix: [] }, + { executable: 'python3', argsPrefix: [] }, + { executable: 'python', argsPrefix: [] }, + ]; + + for (const candidate of candidates) { + const probe = runCommandCapture({ + executable: candidate.executable, + args: [...candidate.argsPrefix, '-c', 'import sys; print(sys.executable)'], + }); + if (probe.ok) { + return candidate; + } + } + + return null; +} + +function getWorkspaceFrontierDir(workspaceRoot = getWorkspaceRoot()) { + return path.join(getWorkspaceDir(workspaceRoot), 'frontier'); +} + +function getWorkspaceFrontierVenvDir(workspaceRoot = getWorkspaceRoot()) { + return path.join(getWorkspaceFrontierDir(workspaceRoot), 'venv'); +} + +function getVenvPythonExecutable(venvDir) { + const candidates = process.platform === 'win32' + ? [path.join(venvDir, 'Scripts', 'python.exe')] + : [path.join(venvDir, 'bin', 'python3'), path.join(venvDir, 'bin', 'python')]; + return candidates.find((candidate) => fs.existsSync(candidate)) ?? candidates[0]; +} + +function probePythonRuntime(spec, workspaceRoot = getWorkspaceRoot()) { + if (!spec) { + return { + available: false, + pythonExecutable: null, + pythonVersion: null, + frontierEngineInstalled: false, + torchInstalled: false, + torchVersion: null, + cudaAvailable: false, + cudaDeviceCount: 0, + cudaDeviceNames: [], + error: 'python unavailable', + }; + } + + const result = runCommandCapture({ + executable: spec.executable, + args: [...(spec.argsPrefix ?? []), '-c', PYTHON_PROBE_SCRIPT], + }, { cwd: workspaceRoot }); + + if (!result.ok || !result.stdout) { + return { + available: false, + pythonExecutable: spec.executable, + pythonVersion: null, + frontierEngineInstalled: false, + torchInstalled: false, + torchVersion: null, + cudaAvailable: false, + cudaDeviceCount: 0, + cudaDeviceNames: [], + error: result.stderr ?? 'python probe failed', + }; + } + + try { + const payload = JSON.parse(result.stdout); + return { + available: true, + pythonExecutable: payload.python_executable ?? spec.executable, + pythonVersion: payload.python_version ?? null, + frontierEngineInstalled: Boolean(payload.frontier_engine_installed), + torchInstalled: Boolean(payload.torch_installed), + torchVersion: payload.torch_version ?? null, + cudaAvailable: Boolean(payload.cuda_available), + cudaDeviceCount: Number(payload.cuda_device_count ?? 0), + cudaDeviceNames: Array.isArray(payload.cuda_device_names) ? payload.cuda_device_names : [], + error: payload.cuda_error ?? null, + }; + } catch (error) { + return { + available: false, + pythonExecutable: spec.executable, + pythonVersion: null, + frontierEngineInstalled: false, + torchInstalled: false, + torchVersion: null, + cudaAvailable: false, + cudaDeviceCount: 0, + cudaDeviceNames: [], + error: error.message, + }; + } +} + +function parsePythonVersionTuple(version) { + const match = String(version ?? '').match(/^(\d+)\.(\d+)(?:\.(\d+))?/); + if (!match) { + return null; + } + return [Number(match[1]), Number(match[2]), Number(match[3] ?? 0)]; +} + +function isPythonVersionAtLeast(version, minimumMajor, minimumMinor) { + const parsed = parsePythonVersionTuple(version); + if (!parsed) { + return false; + } + const [major, minor] = parsed; + if (major !== minimumMajor) { + return major > minimumMajor; + } + return minor >= minimumMinor; +} + +function getManagedPythonSpec(workspaceRoot = getWorkspaceRoot()) { + const executable = getVenvPythonExecutable(getWorkspaceFrontierVenvDir(workspaceRoot)); + if (!fs.existsSync(executable)) { + return null; + } + return { executable, argsPrefix: [] }; +} + +function getFrontierSetupCommand(mode = 'base') { + return `erdos frontier setup --${mode}`; +} + +function resolveFrontierActiveMode(frontierConfig) { + const activeRemoteId = normalizeRemoteId(frontierConfig?.remote ?? {}, frontierConfig?.activeRemoteId ?? null); + const remotePaidEnabled = frontierConfig?.remote?.provider !== 'brev' + || getFrontierPaidRungs({ frontier: frontierConfig }).enabledRemoteIds.includes(activeRemoteId ?? ''); + const remoteGpuReady = Boolean(frontierConfig?.remote?.attached && frontierConfig?.remote?.gpuSearchReady && remotePaidEnabled); + if (!frontierConfig?.loopOptIn && !remoteGpuReady) { + return null; + } + if (remoteGpuReady) { + return 'gpu'; + } + if (frontierConfig.gpuSearchReady) { + return 'gpu'; + } + if (frontierConfig.managedFrontierReady) { + return 'cpu'; + } + return null; +} + +function buildFrontierResearchModes(snapshot) { + const remotePaidBlocked = Boolean(snapshot.remote?.attached && snapshot.remote?.paidRung && !snapshot.remote?.paidEnabled); + const remoteGpuMode = snapshot.remote?.attached && snapshot.remote?.gpuSearchReady && !remotePaidBlocked + ? { + available: true, + mode: 'gpu', + source: 'ssh_remote', + reason: `${getRemoteProviderLabel(snapshot.remote)} is attached and ready for heavy search`, + } + : null; + const explicitRemoteSelection = Boolean(snapshot.selectedRemoteId); + const managedMode = snapshot.frontierLoopOptIn + ? (snapshot.gpuSearchReady ? 'gpu' : (snapshot.managedFrontierReady ? 'cpu' : null)) + : null; + const managedHeavySearch = snapshot.frontierLoopOptIn && snapshot.gpuSearchReady + ? { + available: true, + mode: 'gpu', + source: 'managed_runtime', + reason: 'heavy search space clearing is GPU-eligible on the managed CUDA runtime', + } + : null; + + const bridgeRefresh = managedMode + ? { + available: true, + mode: managedMode, + source: 'managed_runtime', + reason: `managed frontier runtime is opted in and ready in ${managedMode} mode`, + } + : snapshot.bridgeRefreshReady + ? { + available: true, + mode: 'system', + source: 'system_python', + reason: snapshot.frontierLoopOptIn + ? 'managed frontier runtime is not ready yet, so bridge refresh falls back to the bundled CLI via system python' + : 'frontier loop is not opted in, so bridge refresh uses the bundled CLI via system python', + } + : { + available: false, + mode: null, + source: 'unavailable', + reason: 'no runnable python path is currently available for bridge refresh', + }; + + const familySearch = managedMode + ? { + available: true, + mode: managedMode, + source: 'managed_runtime', + reason: `family-aware frontier search can run on the opted-in managed ${managedMode} runtime`, + } + : { + available: false, + mode: null, + source: 'unavailable', + reason: snapshot.frontierLoopOptIn + ? 'managed frontier runtime is not ready yet for family-aware search' + : 'frontier loop is not opted in, so family-aware search stays out of the active loop', + }; + + let heavySearch = null; + if (explicitRemoteSelection) { + heavySearch = remoteGpuMode + ?? (remotePaidBlocked + ? { + available: false, + mode: null, + source: 'unavailable', + reason: `${getRemoteProviderLabel(snapshot.remote)} is attached and GPU-ready, but this paid rung is not enabled for the workspace`, + } + : { + available: false, + mode: null, + source: 'unavailable', + reason: snapshot.remote?.attached + ? `${getRemoteProviderLabel(snapshot.remote)} is selected, but its heavy-search runtime is not ready` + : 'the selected remote is not attached, so heavy GPU search is not available there yet', + }); + } else { + heavySearch = managedHeavySearch + ?? remoteGpuMode + ?? (remotePaidBlocked + ? { + available: false, + mode: null, + source: 'unavailable', + reason: `${getRemoteProviderLabel(snapshot.remote)} is attached and GPU-ready, but this paid rung is not enabled for the workspace`, + } + : { + available: false, + mode: null, + source: 'unavailable', + reason: snapshot.frontierLoopOptIn + ? 'CUDA is not ready yet, so heavy search stays unavailable' + : 'frontier loop is not opted in, so heavy GPU search stays out of the active loop', + }); + } + + return { + bridgeRefresh, + familySearch, + heavySearch, + }; +} + +export function getFrontierResearchModesForSnapshot(snapshot) { + return buildFrontierResearchModes(snapshot); +} + +function getFrontierSetupPlan(mode = 'base', workspaceRoot = getWorkspaceRoot(), options = {}) { + const normalizedMode = mode ?? 'base'; + const systemPython = detectSystemPythonSpec(); + const frontierDir = getWorkspaceFrontierDir(workspaceRoot); + const venvDir = getWorkspaceFrontierVenvDir(workspaceRoot); + const bundledRoot = getBundledFrontierEngineRoot(); + const pythonCommand = systemPython + ? { executable: systemPython.executable, args: [...systemPython.argsPrefix, '-m', 'venv', venvDir] } + : null; + const venvPython = getVenvPythonExecutable(venvDir); + const steps = []; + + if (pythonCommand) { + steps.push({ + label: 'create_managed_venv', + command: pythonCommand, + }); + steps.push({ + label: 'upgrade_pip', + command: { + executable: venvPython, + args: ['-m', 'pip', 'install', '--upgrade', 'pip'], + }, + }); + steps.push({ + label: 'install_bundled_frontier_engine', + command: { + executable: venvPython, + args: ['-m', 'pip', 'install', bundledRoot], + }, + }); + } + + if (normalizedMode === 'cpu') { + steps.push({ + label: 'install_torch_cpu', + command: { + executable: venvPython, + args: ['-m', 'pip', 'install', 'torch'], + }, + optional: false, + }); + } + + if (normalizedMode === 'cuda') { + if (options.torchIndexUrl) { + steps.push({ + label: 'install_torch_cuda', + command: { + executable: venvPython, + args: ['-m', 'pip', 'install', 'torch', '--index-url', options.torchIndexUrl], + }, + optional: false, + }); + } else { + steps.push({ + label: 'install_torch_cuda', + command: { + executable: venvPython, + args: ['-m', 'pip', 'install', 'torch', '--index-url', ''], + }, + optional: true, + note: 'Supply --torch-index-url to make the CUDA torch install concrete.', + }); + } + } + + return { + mode: normalizedMode, + workspaceRoot, + frontierWorkspaceDir: frontierDir, + managedVenvDir: venvDir, + bundledEngineRoot: bundledRoot, + bundledEnginePyprojectPath: getBundledFrontierEnginePyprojectPath(), + systemPythonCommand: systemPython + ? formatCommand({ + executable: systemPython.executable, + args: [...systemPython.argsPrefix, '-m', 'venv', venvDir], + }) + : null, + steps: steps.map((step) => ({ + ...step, + commandLine: formatCommand(step.command), + })), + notes: [ + 'npm install stays lightweight because frontier runtime setup only happens when you run this command.', + normalizedMode === 'cuda' + ? 'CUDA torch installation is intentionally explicit so users can choose the wheel/index URL that matches their GPU driver stack.' + : 'The bundled frontier-engine source is installed into a managed Python virtualenv under .erdos/frontier.', + 'Run `erdos frontier doctor` after setup to verify the runtime.', + ], + }; +} + +function executePlanStep(step, workspaceRoot = getWorkspaceRoot()) { + const result = runCommandCapture(step.command, { cwd: workspaceRoot }); + return { + label: step.label, + commandLine: formatCommand(step.command), + ok: result.ok, + stdout: result.stdout, + stderr: result.stderr, + }; +} + +function buildFrontierDoctorSnapshot(workspaceRoot = getWorkspaceRoot(), options = {}) { + const bundledRoot = getBundledFrontierEngineRoot(); + const bundledPyproject = getBundledFrontierEnginePyprojectPath(); + const bundledCli = getBundledFrontierEngineSourcePath(); + const systemPythonSpec = detectSystemPythonSpec(); + const managedPythonSpec = getManagedPythonSpec(workspaceRoot); + const systemRuntime = probePythonRuntime(systemPythonSpec, workspaceRoot); + const managedRuntime = probePythonRuntime(managedPythonSpec, workspaceRoot); + const config = loadConfig(workspaceRoot); + const remoteRegistry = getFrontierRemoteRegistry(config); + const selectedRemoteConfig = options.remoteId + ? (remoteRegistry.remotes[options.remoteId] ?? null) + : null; + const selectedRemoteId = options.remoteId + ? (selectedRemoteConfig ? normalizeRemoteId(selectedRemoteConfig, options.remoteId) : null) + : remoteRegistry.activeRemoteId; + const activeRemoteConfig = resolveRemoteConfigDefaults( + selectedRemoteConfig ?? remoteRegistry.activeRemote ?? (config.frontier?.remote ?? {}), + workspaceRoot, + ); + const remoteRuntime = probeRemoteFrontierRuntime(activeRemoteConfig, workspaceRoot); + const resolvedRemote = remoteRuntime + ? { + ...activeRemoteConfig, + ...remoteRuntime, + paidRung: isPaidRemote(activeRemoteConfig), + paidEnabled: isRemotePaidEnabled(config, activeRemoteConfig, selectedRemoteId ?? remoteRegistry.activeRemoteId), + gpuSearchReady: Boolean(remoteRuntime.frontierEngineReady && remoteRuntime.cudaAvailable), + } + : null; + const derivedFrontier = { + ...config.frontier, + managedFrontierReady: managedRuntime.available && managedRuntime.frontierEngineInstalled, + gpuSearchReady: managedRuntime.available && managedRuntime.frontierEngineInstalled && managedRuntime.torchInstalled && managedRuntime.cudaAvailable, + remote: { + ...(config.frontier?.remote ?? {}), + frontierEngineReady: Boolean(resolvedRemote?.frontierEngineReady), + gpuSearchReady: Boolean(resolvedRemote?.gpuSearchReady), + paidRung: Boolean(resolvedRemote?.paidRung), + paidEnabled: Boolean(resolvedRemote?.paidEnabled), + }, + }; + const frontierLoopMode = resolveFrontierActiveMode(derivedFrontier); + + const snapshot = { + generatedAt: new Date().toISOString(), + workspaceRoot, + frontierWorkspaceDir: getWorkspaceFrontierDir(workspaceRoot), + managedVenvDir: getWorkspaceFrontierVenvDir(workspaceRoot), + bundledEnginePresent: fs.existsSync(bundledRoot), + bundledEngineRoot: bundledRoot, + bundledEnginePyprojectPresent: fs.existsSync(bundledPyproject), + bundledEnginePyprojectPath: bundledPyproject, + bundledEngineCliPresent: fs.existsSync(bundledCli), + bundledEngineCliPath: bundledCli, + systemPython: systemRuntime, + managedPython: managedRuntime, + remote: resolvedRemote, + bridgeRefreshReady: systemRuntime.available && fs.existsSync(bundledCli), + managedFrontierReady: derivedFrontier.managedFrontierReady, + gpuSearchReady: derivedFrontier.gpuSearchReady, + frontierLoopOptIn: Boolean(config.frontier?.loopOptIn), + frontierLoopMode, + activeRemoteId: selectedRemoteId ?? remoteRegistry.activeRemoteId, + selectedRemoteId: options.remoteId ? selectedRemoteId : null, + selectedRemoteFound: options.remoteId ? Boolean(selectedRemoteConfig) : true, + registeredRemotes: buildRegisteredRemotesSummary(config), + registeredFleets: getFrontierFleetsSnapshot(workspaceRoot).fleets, + paidRungs: getFrontierPaidRungs(config), + commands: { + doctor: 'erdos frontier doctor', + lanes: 'erdos frontier lanes', + remotes: 'erdos frontier remotes', + fleets: 'erdos frontier fleets', + useRemote: 'erdos frontier use-remote ', + setupBase: getFrontierSetupCommand('base'), + setupCpu: getFrontierSetupCommand('cpu'), + setupCuda: `${getFrontierSetupCommand('cuda')} --torch-index-url `, + setupRemote: 'erdos frontier setup-remote --remote-id --cuda --torch-index-url ', + createBrev: 'erdos frontier create-brev --gpu-name H100 --dry-run', + createBrevFleet: 'erdos frontier create-brev-fleet --type hyperstack_H100 --count 2 --dry-run', + attachBrev: 'erdos frontier attach-brev --instance --apply', + enablePaidRemote: 'erdos frontier enable-paid-remote ', + enablePaidFleet: 'erdos frontier enable-paid-fleet ', + attachSsh: 'erdos frontier attach-ssh --ssh-host --apply', + syncSsh: 'erdos frontier sync-ssh --apply', + syncFleet: 'erdos frontier sync-fleet --lane p848_anchor_ladder --apply', + bridgeRefresh848: 'erdos number-theory bridge-refresh 848', + }, + }; + snapshot.researchModes = buildFrontierResearchModes(snapshot); + return snapshot; +} + +export function getFrontierDoctorSnapshot(workspaceRoot = getWorkspaceRoot()) { + return buildFrontierDoctorSnapshot(workspaceRoot); +} + +export function getFrontierDoctorSnapshotForRemote(remoteId, workspaceRoot = getWorkspaceRoot()) { + return buildFrontierDoctorSnapshot(workspaceRoot, { remoteId }); +} + +export function syncFrontierDoctorSnapshot(workspaceRoot = getWorkspaceRoot()) { + const snapshot = getFrontierDoctorSnapshot(workspaceRoot); + const config = loadConfig(workspaceRoot); + const persistedRemote = snapshot.remote + ? persistFrontierRemote(config, { + ...(config.frontier?.remote ?? {}), + ...(snapshot.remote ?? {}), + }, { + remoteId: snapshot.activeRemoteId ?? normalizeRemoteId(snapshot.remote), + setActive: true, + }) + : { frontier: { ...config.frontier }, remoteId: snapshot.activeRemoteId ?? null }; + saveConfig({ + ...config, + frontier: { + ...persistedRemote.frontier, + managedFrontierReady: snapshot.managedFrontierReady, + gpuSearchReady: snapshot.gpuSearchReady, + activeMode: snapshot.frontierLoopMode, + lastDoctorAt: snapshot.generatedAt, + activeRemoteId: snapshot.activeRemoteId ?? persistedRemote.remoteId ?? config.frontier?.activeRemoteId ?? null, + }, + }, workspaceRoot); + return snapshot; +} + +export function applyFrontierSetup(mode = 'base', workspaceRoot = getWorkspaceRoot(), options = {}) { + const plan = getFrontierSetupPlan(mode, workspaceRoot, options); + if (!plan.systemPythonCommand) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'python is not available on PATH. Install Python 3.10+ and rerun setup.', + plan, + stepResults: [], + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; + } + + if (mode === 'cuda' && !options.torchIndexUrl) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'CUDA setup requires --torch-index-url so the PyTorch wheel source stays explicit.', + plan, + stepResults: [], + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; + } + + const currentManagedRuntime = probePythonRuntime(getManagedPythonSpec(workspaceRoot), workspaceRoot); + const currentSystemRuntime = probePythonRuntime(detectSystemPythonSpec(), workspaceRoot); + ensureDir(plan.frontierWorkspaceDir); + const stepResults = []; + + const shouldResetManagedVenv = fs.existsSync(plan.managedVenvDir) && ( + !currentManagedRuntime.available + || !isPythonVersionAtLeast(currentManagedRuntime.pythonVersion, 3, 10) + || ( + currentManagedRuntime.pythonExecutable + && currentSystemRuntime.pythonExecutable + && currentManagedRuntime.pythonExecutable !== currentSystemRuntime.pythonExecutable + ) + ); + + if (shouldResetManagedVenv) { + fs.rmSync(plan.managedVenvDir, { recursive: true, force: true }); + stepResults.push({ + label: 'reset_managed_venv', + commandLine: `remove ${plan.managedVenvDir}`, + ok: true, + stdout: 'Removed stale managed frontier virtualenv before recreation.', + stderr: null, + }); + } + + for (const step of plan.steps) { + if (step.optional) { + continue; + } + const result = executePlanStep(step, workspaceRoot); + stepResults.push(result); + if (!result.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Setup failed on step ${step.label}.`, + plan, + stepResults, + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; + } + } + + const doctor = getFrontierDoctorSnapshot(workspaceRoot); + const config = loadConfig(workspaceRoot); + const frontierConfig = { + ...config.frontier, + loopOptIn: doctor.managedFrontierReady, + runtimeMode: mode, + activeMode: resolveFrontierActiveMode({ + ...config.frontier, + loopOptIn: doctor.managedFrontierReady, + managedFrontierReady: doctor.managedFrontierReady, + gpuSearchReady: doctor.gpuSearchReady, + }), + managedFrontierReady: doctor.managedFrontierReady, + gpuSearchReady: doctor.gpuSearchReady, + lastSetupAt: new Date().toISOString(), + lastDoctorAt: doctor.generatedAt, + }; + saveConfig({ + ...config, + frontier: frontierConfig, + }, workspaceRoot); + + return { + ok: true, + appliedAt: new Date().toISOString(), + plan, + stepResults, + doctor, + }; +} + +export function getFrontierSetupSnapshot(mode = 'base', workspaceRoot = getWorkspaceRoot(), options = {}) { + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + plan: getFrontierSetupPlan(mode, workspaceRoot, options), + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; +} + +function getFrontierRemoteSetupPlan(mode = 'base', workspaceRoot = getWorkspaceRoot(), options = {}) { + const config = loadConfig(workspaceRoot); + const registry = getFrontierRemoteRegistry(config); + const remoteConfig = resolveRemoteConfigDefaults( + options.remoteId + ? (registry.remotes[options.remoteId] ?? {}) + : (registry.activeRemote ?? config.frontier?.remote ?? {}), + workspaceRoot, + ); + const remoteId = normalizeRemoteId(remoteConfig, options.remoteId ?? registry.activeRemoteId ?? null); + const remoteTarget = { + provider: remoteConfig.provider, + instanceName: remoteConfig.instanceName, + sshHost: remoteConfig.sshHost, + }; + const pythonCommand = remoteConfig.pythonCommand ?? getDefaultRemotePythonCommand(remoteConfig.provider); + const steps = [ + { + label: 'upgrade_remote_pip', + remoteCommand: `${pythonCommand} -m pip install --user --upgrade pip`, + }, + ]; + + if (mode === 'cpu') { + steps.push({ + label: 'install_remote_torch_cpu', + remoteCommand: `${pythonCommand} -m pip install --user torch`, + }); + } + + if (mode === 'cuda') { + steps.push({ + label: 'install_remote_torch_cuda', + remoteCommand: options.torchIndexUrl + ? `${pythonCommand} -m pip install --user --upgrade --force-reinstall torch --index-url ${options.torchIndexUrl}` + : `${pythonCommand} -m pip install --user --upgrade torch`, + note: options.torchIndexUrl + ? 'CUDA wheel selection is pinned to the supplied torch index URL and forced to reinstall so the remote matches the chosen driver lane.' + : 'No explicit torch index URL was supplied, so the remote setup will use the default torch package source.', + }); + } + + return { + mode, + remoteId, + remote: remoteConfig, + remoteTarget, + steps, + notes: [ + 'Remote setup installs runtime dependencies on the active frontier remote; the engine source itself is synced separately via `erdos frontier sync-ssh`.', + 'Use CUDA mode on GPU remotes like Umbra or a Brev H100 when you want heavy search eligibility.', + ], + }; +} + +export function getFrontierRemoteSetupSnapshot(mode = 'base', workspaceRoot = getWorkspaceRoot(), options = {}) { + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + plan: getFrontierRemoteSetupPlan(mode, workspaceRoot, options), + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; +} + +export function applyFrontierRemoteSetup(mode = 'base', workspaceRoot = getWorkspaceRoot(), options = {}) { + const snapshot = getFrontierRemoteSetupSnapshot(mode, workspaceRoot, { + ...options, + apply: true, + }); + + if (!snapshot.plan.remote?.sshHost && !snapshot.plan.remote?.instanceName) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Remote frontier setup requires an attached remote.', + snapshot, + stepResults: [], + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; + } + + const stepResults = []; + for (const step of snapshot.plan.steps) { + const result = runRemoteCommandCapture(snapshot.plan.remoteTarget, step.remoteCommand, { cwd: workspaceRoot }); + const stepResult = { + label: step.label, + commandLine: step.remoteCommand, + ok: result.ok, + stdout: result.stdout, + stderr: result.stderr, + }; + stepResults.push(stepResult); + if (!result.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Remote frontier setup failed on step ${step.label}.`, + snapshot, + stepResults, + doctor: getFrontierDoctorSnapshot(workspaceRoot), + }; + } + } + + const doctor = syncFrontierDoctorSnapshot(workspaceRoot); + return { + ok: true, + appliedAt: new Date().toISOString(), + snapshot, + stepResults, + doctor, + }; +} + +export function getFrontierRemoteAttachSnapshot(workspaceRoot = getWorkspaceRoot(), options = {}) { + const config = loadConfig(workspaceRoot); + const provider = options.provider === 'brev' ? 'brev' : 'ssh'; + const instanceName = options.instanceName ?? null; + const brevHomeDir = provider === 'brev' && instanceName && !options.engineRoot + ? probeBrevRemoteHome(instanceName, { cwd: workspaceRoot }) + : null; + const remoteId = normalizeRemoteId({ + instanceName, + sshHost: options.sshHost ?? (provider === 'brev' ? instanceName : null), + }, options.remoteId ?? null); + const remote = resolveRemoteConfigDefaults({ + attached: Boolean(options.apply), + remoteId, + provider, + instanceName, + engineRoot: options.engineRoot ?? getDefaultRemoteEngineRoot(provider, brevHomeDir), + pythonCommand: options.pythonCommand ?? getDefaultRemotePythonCommand(provider), + sshHost: options.sshHost ?? (provider === 'brev' ? instanceName : null), + }, workspaceRoot); + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + remote, + enablePaidRung: Boolean(options.enablePaidRung), + paidRung: isPaidRemote(remote), + paidEnabled: Boolean(options.enablePaidRung) || isRemotePaidEnabled(config, remote, remoteId), + doctor: remote.sshHost ? probeRemoteFrontierRuntime(remote, workspaceRoot) : null, + }; +} + +export function applyFrontierRemoteAttach(workspaceRoot = getWorkspaceRoot(), options = {}) { + const provider = options.provider === 'brev' ? 'brev' : 'ssh'; + const instanceName = options.instanceName ?? null; + const sshHost = options.sshHost ?? (provider === 'brev' ? instanceName : null); + if (!sshHost) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: provider === 'brev' + ? 'Brev attach requires --instance or --ssh-host.' + : 'Remote SSH attach requires --ssh-host.', + snapshot: getFrontierRemoteAttachSnapshot(workspaceRoot, options), + }; + } + + const brevRefresh = provider === 'brev' + ? runBrevRefreshCapture(workspaceRoot) + : null; + if (provider === 'brev' && !brevRefresh?.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: brevRefresh.stderr ?? 'Failed to refresh Brev SSH configuration.', + brevRefresh, + snapshot: getFrontierRemoteAttachSnapshot(workspaceRoot, { + ...options, + sshHost, + }), + }; + } + + const snapshot = getFrontierRemoteAttachSnapshot(workspaceRoot, { + ...options, + provider, + instanceName, + sshHost, + apply: true, + }); + const config = loadConfig(workspaceRoot); + const persistedRemote = persistFrontierRemote(config, { + ...(config.frontier?.remote ?? {}), + ...snapshot.remote, + frontierEngineReady: Boolean(snapshot.doctor?.frontierEngineReady), + gpuSearchReady: Boolean(snapshot.doctor?.frontierEngineReady && snapshot.doctor?.cudaAvailable), + lastSyncAt: config.frontier?.remote?.lastSyncAt ?? null, + lastSyncScope: config.frontier?.remote?.lastSyncScope ?? null, + lastDoctorAt: snapshot.generatedAt, + }, { + remoteId: snapshot.remote.remoteId ?? options.remoteId ?? null, + setActive: true, + }); + let nextConfig = { + ...config, + frontier: { + ...persistedRemote.frontier, + activeMode: snapshot.doctor?.frontierEngineReady && snapshot.doctor?.cudaAvailable + ? 'gpu' + : config.frontier?.activeMode ?? null, + lastDoctorAt: snapshot.generatedAt, + }, + }; + if (snapshot.remote.provider === 'brev') { + nextConfig = setFrontierPaidRemoteEnabled(nextConfig, snapshot.remote.remoteId, Boolean(options.enablePaidRung)); + nextConfig = { + ...nextConfig, + frontier: { + ...nextConfig.frontier, + remote: { + ...nextConfig.frontier.remote, + paidEnabled: isRemotePaidEnabled(nextConfig, snapshot.remote, snapshot.remote.remoteId), + }, + }, + }; + } + saveConfig(nextConfig, workspaceRoot); + + return { + ok: true, + appliedAt: new Date().toISOString(), + brevRefresh, + snapshot, + }; +} + +export function getFrontierBrevProvisionSnapshot(workspaceRoot = getWorkspaceRoot(), options = {}) { + const config = loadConfig(workspaceRoot); + const instanceName = options.instanceName ?? options.name ?? null; + const count = formatBrevNumeric(options.count) ?? 1; + const attach = Boolean(options.attach); + const syncLane = options.syncLane ?? null; + const brevHomeDir = instanceName && count === 1 && !options.engineRoot + ? probeBrevRemoteHome(instanceName, { cwd: workspaceRoot }) + : null; + const createArgs = buildBrevCreateArgs({ + ...options, + instanceName, + count, + }); + const createCommand = { + executable: 'brev', + args: createArgs, + }; + const attachCommand = attach && count === 1 + ? `erdos frontier attach-brev --instance ${instanceName ?? ''} --apply` + : null; + const syncCommand = syncLane && attach && count === 1 + ? `erdos frontier sync-ssh --lane ${syncLane} --apply` + : null; + + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + dryRun: Boolean(options.dryRun), + instanceName, + count, + attach, + syncLane, + provider: 'brev', + enablePaidRung: Boolean(options.enablePaidRung), + paidEnabled: Boolean(options.enablePaidRung) || isRemotePaidEnabled(config, { provider: 'brev', instanceName }, instanceName), + plan: { + createCommandLine: formatCommand(createCommand), + attachCommand, + syncCommand, + engineRoot: options.engineRoot ?? getDefaultRemoteEngineRoot('brev', brevHomeDir), + pythonCommand: options.pythonCommand ?? getDefaultRemotePythonCommand('brev'), + sshHost: options.sshHost ?? instanceName ?? null, + }, + filters: { + type: options.type ?? null, + gpuName: options.gpuName ?? null, + provider: options.provider ?? null, + minVram: formatBrevNumeric(options.minVram), + minTotalVram: formatBrevNumeric(options.minTotalVram), + maxBootTime: formatBrevNumeric(options.maxBootTime), + minDisk: formatBrevNumeric(options.minDisk), + minCapability: formatBrevNumeric(options.minCapability), + sort: options.sort ?? null, + parallel: formatBrevNumeric(options.parallel), + startupScript: options.startupScript ?? null, + detached: Boolean(options.detached), + }, + warnings: classifyBrevProvision({ + ...options, + instanceName, + count, + attach, + }), + notes: [ + 'Use --dry-run to let Brev preview matching hardware types without creating anything.', + 'Single-instance H100 is the best near-term upgrade tier for p848; multi-instance runs are best used for parallel independent sweeps.', + 'Auto-attach reuses the existing frontier SSH sync/session stack after the instance is ready.', + 'Paid Brev/H100 rungs stay out of the active loop until the workspace explicitly enables them.', + ], + }; +} + +export function applyFrontierBrevProvision(workspaceRoot = getWorkspaceRoot(), options = {}) { + const snapshot = getFrontierBrevProvisionSnapshot(workspaceRoot, { + ...options, + apply: true, + }); + + if (!snapshot.instanceName) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Brev provisioning requires an instance name.', + snapshot, + createResult: null, + attachResult: null, + syncResult: null, + }; + } + + if (snapshot.attach && snapshot.count !== 1) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Auto-attach currently supports only a single Brev instance. Provision clusters without --attach and orchestrate them explicitly.', + snapshot, + createResult: null, + attachResult: null, + syncResult: null, + }; + } + + const createResult = runCommandCapture({ + executable: 'brev', + args: buildBrevCreateArgs({ + ...options, + instanceName: snapshot.instanceName, + count: snapshot.count, + }), + }, { cwd: workspaceRoot }); + + if (!createResult.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: createResult.stderr ?? 'Brev provisioning failed.', + snapshot, + createResult, + attachResult: null, + syncResult: null, + }; + } + + if (snapshot.dryRun) { + return { + ok: true, + appliedAt: new Date().toISOString(), + snapshot, + createResult, + attachResult: null, + syncResult: null, + }; + } + + let attachResult = null; + if (snapshot.attach) { + attachResult = applyFrontierRemoteAttach(workspaceRoot, { + provider: 'brev', + instanceName: snapshot.instanceName, + sshHost: snapshot.plan.sshHost, + engineRoot: snapshot.plan.engineRoot, + pythonCommand: snapshot.plan.pythonCommand, + enablePaidRung: Boolean(options.enablePaidRung), + apply: true, + }); + if (!attachResult.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: attachResult.error ?? 'Brev instance was created, but frontier attach failed.', + snapshot, + createResult, + attachResult, + syncResult: null, + }; + } + } + + let syncResult = null; + if (snapshot.syncLane && snapshot.attach) { + syncResult = applyFrontierRemoteSync(workspaceRoot, { + remoteId: snapshot.instanceName, + provider: 'brev', + instanceName: snapshot.instanceName, + sshHost: snapshot.plan.sshHost, + engineRoot: snapshot.plan.engineRoot, + pythonCommand: snapshot.plan.pythonCommand, + laneId: snapshot.syncLane, + apply: true, + }); + if (!syncResult.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: syncResult.error ?? 'Brev instance was created and attached, but frontier sync failed.', + snapshot, + createResult, + attachResult, + syncResult, + }; + } + } + + return { + ok: true, + appliedAt: new Date().toISOString(), + snapshot, + createResult, + attachResult, + syncResult, + }; +} + +export function getFrontierFleetsSnapshot(workspaceRoot = getWorkspaceRoot()) { + const config = loadConfig(workspaceRoot); + const registry = getFrontierFleetRegistry(config); + const remoteRegistry = getFrontierRemoteRegistry(config); + return { + generatedAt: new Date().toISOString(), + workspaceRoot, + fleetCount: Object.keys(registry.fleets).length, + fleets: Object.entries(registry.fleets).map(([fleetId, fleet]) => { + const remoteIds = normalizeRemoteIdList(fleet.remoteIds ?? []); + const memberRemotes = remoteIds.map((remoteId) => { + const remote = remoteRegistry.remotes[remoteId] ?? null; + return { + remoteId, + attached: Boolean(remote?.attached), + provider: remote?.provider ?? null, + instanceName: remote?.instanceName ?? null, + sshHost: remote?.sshHost ?? null, + gpuSearchReady: Boolean(remote?.gpuSearchReady), + frontierEngineReady: Boolean(remote?.frontierEngineReady), + paidRung: isPaidRemote(remote ?? {}), + paidEnabled: isRemotePaidEnabled(config, remote ?? {}, remoteId), + lastSyncAt: remote?.lastSyncAt ?? null, + active: remoteId === remoteRegistry.activeRemoteId, + }; + }); + return { + fleetId, + provider: fleet.provider ?? 'brev', + paidRung: isPaidFleet(fleet), + paidEnabled: isFleetPaidEnabled(config, fleet, fleetId), + laneId: fleet.laneId ?? null, + count: Number(fleet.count ?? remoteIds.length ?? 0), + remoteIds, + intendedTopology: fleet.intendedTopology ?? 'parallel_independent_sweeps', + createdAt: fleet.createdAt ?? null, + lastProvisionedAt: fleet.lastProvisionedAt ?? null, + attachedCount: memberRemotes.filter((member) => member.attached).length, + readyGpuCount: memberRemotes.filter((member) => member.gpuSearchReady).length, + activeRemoteIds: memberRemotes.filter((member) => member.active).map((member) => member.remoteId), + members: memberRemotes, + }; + }).sort((left, right) => left.fleetId.localeCompare(right.fleetId)), + }; +} + +export function getFrontierFleetSnapshot(fleetId, workspaceRoot = getWorkspaceRoot()) { + const snapshot = getFrontierFleetsSnapshot(workspaceRoot); + return snapshot.fleets.find((fleet) => fleet.fleetId === fleetId) ?? null; +} + +export function getFrontierBrevFleetProvisionSnapshot(workspaceRoot = getWorkspaceRoot(), options = {}) { + const config = loadConfig(workspaceRoot); + const fleetId = normalizeFleetId({ fleetId: options.fleetId ?? options.instanceName ?? options.name ?? null }); + const count = formatBrevNumeric(options.count) ?? 0; + const memberIds = fleetId ? buildFrontierFleetMemberIds(fleetId, count) : []; + const attach = Boolean(options.attach); + const syncLane = options.syncLane ?? null; + + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + dryRun: Boolean(options.dryRun), + fleetId, + count, + attach, + syncLane, + provider: 'brev', + enablePaidRung: Boolean(options.enablePaidRung), + paidEnabled: Boolean(options.enablePaidRung) || isFleetPaidEnabled(config, { provider: 'brev', fleetId }, fleetId), + intendedTopology: 'parallel_independent_sweeps', + notes: [ + 'This provisions separate Brev instances so the current p848 lane can run many independent sweeps in parallel.', + 'Use 2x or 8x H100 fleets to widen the sweep frontier before investing in true shared-lane distributed batching.', + 'Shared-lane multi-GPU execution is still a future engine phase; fleet members currently run separate single-GPU jobs.', + ], + warnings: [ + ...classifyBrevProvision({ + ...options, + instanceName: fleetId, + count, + attach: false, + }), + ...(attach + ? ['Fleet auto-attach will attach and optionally sync each member one by one.'] + : []), + ], + members: memberIds.map((memberId) => { + const memberSnapshot = getFrontierBrevProvisionSnapshot(workspaceRoot, { + ...options, + instanceName: memberId, + count: 1, + attach, + syncLane, + }); + return { + remoteId: memberId, + instanceName: memberId, + paidEnabled: memberSnapshot.paidEnabled, + createCommandLine: memberSnapshot.plan.createCommandLine, + attachCommand: memberSnapshot.plan.attachCommand, + syncCommand: memberSnapshot.plan.syncCommand, + engineRoot: memberSnapshot.plan.engineRoot, + pythonCommand: memberSnapshot.plan.pythonCommand, + }; + }), + }; +} + +export function applyFrontierBrevFleetProvision(workspaceRoot = getWorkspaceRoot(), options = {}) { + const snapshot = getFrontierBrevFleetProvisionSnapshot(workspaceRoot, { + ...options, + apply: true, + }); + + if (!snapshot.fleetId) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Brev fleet provisioning requires a fleet id.', + snapshot, + memberResults: [], + }; + } + + if (!Number.isInteger(snapshot.count) || snapshot.count < 2) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Brev fleet provisioning requires --count >= 2. Use `erdos frontier create-brev` for a single instance.', + snapshot, + memberResults: [], + }; + } + + const memberResults = []; + for (const member of snapshot.members) { + const memberResult = applyFrontierBrevProvision(workspaceRoot, { + ...options, + instanceName: member.instanceName, + count: 1, + attach: snapshot.attach, + syncLane: snapshot.syncLane, + apply: true, + dryRun: snapshot.dryRun, + }); + memberResults.push({ + remoteId: member.remoteId, + instanceName: member.instanceName, + ...memberResult, + }); + if (!memberResult.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Fleet member ${member.instanceName} failed to provision.`, + snapshot, + memberResults, + }; + } + } + + if (!snapshot.dryRun) { + const config = loadConfig(workspaceRoot); + const persistedFleet = persistFrontierFleet(config, { + fleetId: snapshot.fleetId, + provider: snapshot.provider, + count: snapshot.count, + laneId: snapshot.syncLane ?? null, + intendedTopology: snapshot.intendedTopology, + remoteIds: snapshot.members.map((member) => member.remoteId), + createdAt: config.frontier?.fleets?.[snapshot.fleetId]?.createdAt ?? new Date().toISOString(), + lastProvisionedAt: new Date().toISOString(), + }, { + fleetId: snapshot.fleetId, + }); + let nextConfig = { + ...config, + frontier: persistedFleet.frontier, + }; + if (snapshot.provider === 'brev') { + nextConfig = setFrontierPaidFleetEnabled( + nextConfig, + snapshot.fleetId, + snapshot.members.map((member) => member.remoteId), + Boolean(options.enablePaidRung), + ); + } + saveConfig(nextConfig, workspaceRoot); + } + + return { + ok: true, + appliedAt: new Date().toISOString(), + snapshot, + memberResults, + }; +} + +export function getFrontierFleetSyncSnapshot(workspaceRoot = getWorkspaceRoot(), options = {}) { + const fleet = getFrontierFleetSnapshot(options.fleetId ?? null, workspaceRoot); + const laneId = options.laneId ?? fleet?.laneId ?? null; + const config = loadConfig(workspaceRoot); + const remoteRegistry = getFrontierRemoteRegistry(config); + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + fleetId: fleet?.fleetId ?? options.fleetId ?? null, + available: Boolean(fleet), + laneId, + intendedTopology: fleet?.intendedTopology ?? null, + members: (fleet?.remoteIds ?? []).map((remoteId) => ({ + remoteId, + provider: remoteRegistry.remotes[remoteId]?.provider ?? null, + instanceName: remoteRegistry.remotes[remoteId]?.instanceName ?? null, + sshHost: remoteRegistry.remotes[remoteId]?.sshHost ?? null, + syncCommand: laneId + ? `erdos frontier sync-ssh --remote-id ${remoteId} --lane ${laneId} --apply` + : `erdos frontier sync-ssh --remote-id ${remoteId} --apply`, + })), + }; +} + +export function applyFrontierFleetSync(workspaceRoot = getWorkspaceRoot(), options = {}) { + const snapshot = getFrontierFleetSyncSnapshot(workspaceRoot, { + ...options, + apply: true, + }); + + if (!snapshot.available) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Unknown frontier fleet: ${options.fleetId}`, + snapshot, + memberResults: [], + }; + } + + const memberResults = []; + for (const member of snapshot.members) { + const result = applyFrontierRemoteSync(workspaceRoot, { + remoteId: member.remoteId, + laneId: snapshot.laneId, + apply: true, + }); + memberResults.push({ + remoteId: member.remoteId, + ...result, + }); + if (!result.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Fleet sync failed on member ${member.remoteId}.`, + snapshot, + memberResults, + }; + } + } + + return { + ok: true, + appliedAt: new Date().toISOString(), + snapshot, + memberResults, + }; +} + +export function getFrontierRemoteSyncSnapshot(workspaceRoot = getWorkspaceRoot(), options = {}) { + const config = loadConfig(workspaceRoot); + const remoteRegistry = getFrontierRemoteRegistry(config); + const remoteConfig = resolveRemoteConfigDefaults(options.remoteId + ? (remoteRegistry.remotes[options.remoteId] ?? {}) + : (remoteRegistry.activeRemote ?? config.frontier?.remote ?? {}), workspaceRoot); + const provider = remoteConfig.provider ?? (options.provider === 'brev' ? 'brev' : 'ssh'); + const instanceName = remoteConfig.instanceName ?? options.instanceName ?? null; + const sshHost = options.sshHost ?? remoteConfig.sshHost ?? null; + const engineRoot = options.engineRoot ?? remoteConfig.engineRoot ?? getDefaultRemoteEngineRoot(provider); + const pythonCommand = options.pythonCommand ?? remoteConfig.pythonCommand ?? getDefaultRemotePythonCommand(provider); + const remoteCopyRoot = toRemoteCopyPath({ provider, instanceName, sshHost }, engineRoot); + const scope = resolveFrontierSyncScope(options.laneId ?? null); + const localEngineRoot = getBundledFrontierEngineRoot(); + + return { + generatedAt: new Date().toISOString(), + apply: Boolean(options.apply), + scope, + remote: { + attached: Boolean(remoteConfig.attached), + remoteId: normalizeRemoteId(remoteConfig, options.remoteId ?? remoteRegistry.activeRemoteId ?? null), + provider, + instanceName, + sshHost, + engineRoot, + pythonCommand, + copyRoot: remoteCopyRoot, + }, + local: { + engineRoot: localEngineRoot, + pyprojectPath: getBundledFrontierEnginePyprojectPath(), + sourcePackagePath: getBundledFrontierSourcePackagePath(), + experimentsRoot: getBundledFrontierExperimentsRoot(), + experimentDirs: scope.mode === 'all' + ? scope.experimentDirs + : (scope.experimentDir ? [scope.experimentDir] : []), + experimentReadmePath: scope.experimentsReadmePath ?? null, + }, + doctor: sshHost + ? probeRemoteFrontierRuntime({ + attached: Boolean(remoteConfig.attached), + provider, + instanceName, + sshHost, + engineRoot, + pythonCommand, + }, workspaceRoot) + : null, + }; +} + +export function applyFrontierRemoteSync(workspaceRoot = getWorkspaceRoot(), options = {}) { + const snapshot = getFrontierRemoteSyncSnapshot(workspaceRoot, { + ...options, + apply: true, + }); + + if (!snapshot.remote.sshHost) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Remote frontier sync requires an attached SSH host or --ssh-host.', + snapshot, + stepResults: [], + remoteLiveFrontier: null, + }; + } + + if (!snapshot.remote.copyRoot) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: 'Remote frontier sync could not resolve a remote copy target path for the remote engine root.', + snapshot, + stepResults: [], + remoteLiveFrontier: null, + }; + } + + if (snapshot.scope?.error) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: snapshot.scope.error, + snapshot, + stepResults: [], + remoteVerification: null, + remoteLiveFrontier: null, + }; + } + + const remoteEngineRoot = snapshot.remote.engineRoot; + const remoteTarget = { + provider: snapshot.remote.provider, + instanceName: snapshot.remote.instanceName, + sshHost: snapshot.remote.sshHost, + }; + const remoteHost = snapshot.remote.sshHost; + const remoteCliPath = joinRemotePath(snapshot.remote, remoteEngineRoot, 'src', 'frontier_engine', 'cli.py'); + const remoteDirSet = new Set([ + remoteEngineRoot, + joinRemotePath(snapshot.remote, remoteEngineRoot, 'src'), + joinRemotePath(snapshot.remote, remoteEngineRoot, 'experiments'), + ]); + if (snapshot.scope.mode === 'lane' && snapshot.scope.experimentDirName) { + remoteDirSet.add(joinRemotePath(snapshot.remote, remoteEngineRoot, 'experiments', snapshot.scope.experimentDirName)); + } + for (const entry of snapshot.scope.syncEntries ?? []) { + const remoteRelativePath = String(entry.remoteRelativePath ?? '').trim(); + if (!remoteRelativePath) { + continue; + } + const destination = joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, remoteRelativePath); + const ensureDirPath = entry.recursive + ? destination + : ( + isBrevRemote(snapshot.remote) + ? path.posix.dirname(destination) + : path.win32.dirname(destination) + ); + if (ensureDirPath) { + remoteDirSet.add(ensureDirPath); + } + } + const ensureRemoteDirsCommand = isBrevRemote(snapshot.remote) + ? `mkdir -p ${Array.from(remoteDirSet).sort().map((value) => quotePosixShellArg(value)).join(' ')}` + : [ + 'cmd /c', + Array.from(remoteDirSet).sort().map((dir) => + `if not exist ${quoteRemoteWindowsPath(dir)} mkdir ${quoteRemoteWindowsPath(dir)}` + ).join(' & '), + ].join(' '); + const stepResults = []; + + const steps = [ + { + label: 'ensure_remote_frontier_dirs', + run: () => runRemoteCommandCapture(remoteTarget, ensureRemoteDirsCommand, { cwd: workspaceRoot }), + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ + executable: 'brev', + args: ['exec', snapshot.remote.instanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(ensureRemoteDirsCommand)}`], + }) + : formatCommand({ + executable: 'ssh', + args: [remoteHost, ensureRemoteDirsCommand], + }), + }, + { + label: 'sync_frontier_pyproject', + run: () => runRemoteCopyToCapture( + remoteTarget, + snapshot.local.pyprojectPath, + joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'pyproject.toml'), + { cwd: workspaceRoot }, + ), + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ + executable: 'brev', + args: ['copy', snapshot.local.pyprojectPath, `${snapshot.remote.instanceName}:${joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'pyproject.toml')}`], + }) + : formatCommand({ + executable: 'scp', + args: [snapshot.local.pyprojectPath, `${remoteHost}:${joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'pyproject.toml')}`], + }), + }, + { + label: 'sync_frontier_source_package', + run: () => runRemoteCopyToCapture( + remoteTarget, + snapshot.local.sourcePackagePath, + joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'src'), + { cwd: workspaceRoot, recursive: true }, + ), + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ + executable: 'brev', + args: ['copy', snapshot.local.sourcePackagePath, `${snapshot.remote.instanceName}:${joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'src')}`], + }) + : formatCommand({ + executable: 'scp', + args: ['-r', snapshot.local.sourcePackagePath, `${remoteHost}:${joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'src')}`], + }), + }, + ]; + + if (snapshot.scope.mode === 'all') { + steps.push({ + label: 'sync_frontier_experiments_root', + run: () => runRemoteCopyToCapture( + remoteTarget, + snapshot.local.experimentsRoot, + snapshot.remote.copyRoot, + { cwd: workspaceRoot, recursive: true }, + ), + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ + executable: 'brev', + args: ['copy', snapshot.local.experimentsRoot, `${snapshot.remote.instanceName}:${snapshot.remote.copyRoot}`], + }) + : formatCommand({ + executable: 'scp', + args: ['-r', snapshot.local.experimentsRoot, `${remoteHost}:${snapshot.remote.copyRoot}`], + }), + }); + } else { + if (Array.isArray(snapshot.scope.syncEntries) && snapshot.scope.syncEntries.length > 0) { + for (const entry of snapshot.scope.syncEntries) { + const remotePath = joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, entry.remoteRelativePath); + steps.push({ + label: entry.label, + run: () => runRemoteCopyToCapture( + remoteTarget, + entry.localPath, + remotePath, + { cwd: workspaceRoot, recursive: Boolean(entry.recursive) }, + ), + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ + executable: 'brev', + args: ['copy', entry.localPath, `${snapshot.remote.instanceName}:${remotePath}`], + }) + : formatCommand({ + executable: 'scp', + args: [ + ...(entry.recursive ? ['-r'] : []), + entry.localPath, + `${remoteHost}:${remotePath}`, + ], + }), + }); + } + } else if (snapshot.scope.experimentDir) { + steps.push({ + label: `sync_frontier_lane_${snapshot.scope.laneId}`, + run: () => runRemoteCopyToCapture( + remoteTarget, + snapshot.scope.experimentDir, + joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'experiments'), + { cwd: workspaceRoot, recursive: true }, + ), + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ + executable: 'brev', + args: ['copy', snapshot.scope.experimentDir, `${snapshot.remote.instanceName}:${joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'experiments')}`], + }) + : formatCommand({ + executable: 'scp', + args: ['-r', snapshot.scope.experimentDir, `${remoteHost}:${joinRemotePath(snapshot.remote, snapshot.remote.copyRoot, 'experiments')}`], + }), + }); + } + } + + for (const step of steps) { + const result = step.run(); + const stepResult = { + label: step.label, + commandLine: step.commandLine, + ok: result.ok, + stdout: result.stdout, + stderr: result.stderr, + }; + stepResults.push(stepResult); + if (!result.ok) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Remote frontier sync failed on step ${step.label}.`, + snapshot, + stepResults, + remoteLiveFrontier: null, + }; + } + } + + const verificationCommand = snapshot.scope.mode === 'lane' && snapshot.scope.laneId + ? isBrevRemote(snapshot.remote) + ? `${snapshot.remote.pythonCommand} ${quotePosixShellArg(remoteCliPath)} show-lane ${snapshot.scope.laneId} --json` + : `${snapshot.remote.pythonCommand} ${quoteRemoteWindowsPath(remoteCliPath)} show-lane ${snapshot.scope.laneId} --json` + : isBrevRemote(snapshot.remote) + ? `${snapshot.remote.pythonCommand} ${quotePosixShellArg(remoteCliPath)} list-lanes` + : `${snapshot.remote.pythonCommand} ${quoteRemoteWindowsPath(remoteCliPath)} list-lanes`; + const verificationLabel = snapshot.scope.mode === 'lane' && snapshot.scope.laneId + ? 'verify_remote_lane' + : 'verify_remote_lanes'; + const verificationResult = runRemoteCommandCapture(remoteTarget, verificationCommand, { cwd: workspaceRoot }); + const remoteVerification = snapshot.scope.mode === 'lane' && snapshot.scope.laneId + ? parseJsonDocument(verificationResult.stdout) + : verificationResult.stdout; + + const liveFrontierCommand = snapshot.scope.laneId === 'p848_anchor_ladder' + ? isBrevRemote(snapshot.remote) + ? `${snapshot.remote.pythonCommand} ${quotePosixShellArg(remoteCliPath)} p848-live-frontier` + : `${snapshot.remote.pythonCommand} ${quoteRemoteWindowsPath(remoteCliPath)} p848-live-frontier` + : null; + const liveFrontierResult = liveFrontierCommand + ? runRemoteCommandCapture(remoteTarget, liveFrontierCommand, { cwd: workspaceRoot }) + : null; + const remoteLiveFrontier = liveFrontierResult?.ok ? parseJsonDocument(liveFrontierResult.stdout) : null; + + if (!verificationResult.ok || (snapshot.scope.mode === 'lane' && snapshot.scope.laneId && !remoteVerification)) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: verificationResult.stderr ?? 'Remote frontier sync completed, but the remote verification probe did not return the expected result.', + snapshot, + stepResults: [ + ...stepResults, + { + label: verificationLabel, + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ executable: 'brev', args: ['exec', snapshot.remote.instanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(verificationCommand)}`] }) + : formatCommand({ executable: 'ssh', args: [remoteHost, verificationCommand] }), + ok: verificationResult.ok, + stdout: verificationResult.stdout, + stderr: verificationResult.stderr, + }, + ], + remoteVerification, + remoteLiveFrontier, + }; + } + + if (liveFrontierCommand && (!liveFrontierResult?.ok || !remoteLiveFrontier)) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: liveFrontierResult?.stderr ?? 'Remote frontier sync completed, but the p848 live-frontier probe did not return JSON.', + snapshot, + stepResults: [ + ...stepResults, + { + label: verificationLabel, + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ executable: 'brev', args: ['exec', snapshot.remote.instanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(verificationCommand)}`] }) + : formatCommand({ executable: 'ssh', args: [remoteHost, verificationCommand] }), + ok: verificationResult.ok, + stdout: verificationResult.stdout, + stderr: verificationResult.stderr, + }, + { + label: 'verify_remote_live_frontier', + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ executable: 'brev', args: ['exec', snapshot.remote.instanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(liveFrontierCommand)}`] }) + : formatCommand({ executable: 'ssh', args: [remoteHost, liveFrontierCommand] }), + ok: Boolean(liveFrontierResult?.ok), + stdout: liveFrontierResult?.stdout ?? null, + stderr: liveFrontierResult?.stderr ?? null, + }, + ], + remoteVerification, + remoteLiveFrontier, + }; + } + + const appliedAt = new Date().toISOString(); + const config = loadConfig(workspaceRoot); + const postSyncDoctor = probeRemoteFrontierRuntime({ + attached: true, + provider: snapshot.remote.provider, + instanceName: snapshot.remote.instanceName, + sshHost: snapshot.remote.sshHost, + engineRoot: snapshot.remote.engineRoot, + pythonCommand: snapshot.remote.pythonCommand, + }, workspaceRoot); + const persistedRemote = persistFrontierRemote(config, { + ...(snapshot.remote ?? {}), + attached: true, + frontierEngineReady: Boolean(postSyncDoctor?.frontierEngineReady), + gpuSearchReady: Boolean(postSyncDoctor?.frontierEngineReady && postSyncDoctor?.cudaAvailable), + lastSyncAt: appliedAt, + lastSyncScope: snapshot.scope.mode === 'lane' ? snapshot.scope.laneId : 'all', + lastDoctorAt: snapshot.generatedAt, + }, { + remoteId: snapshot.remote.remoteId ?? null, + setActive: true, + }); + saveConfig({ + ...config, + frontier: { + ...persistedRemote.frontier, + activeMode: config.frontier?.activeMode ?? resolveFrontierActiveMode({ + ...(config.frontier ?? {}), + remote: { + ...(persistedRemote.frontier.remote ?? {}), + attached: true, + gpuSearchReady: Boolean(postSyncDoctor?.frontierEngineReady && postSyncDoctor?.cudaAvailable), + }, + }), + lastDoctorAt: snapshot.generatedAt, + }, + }, workspaceRoot); + + return { + ok: true, + appliedAt, + snapshot, + stepResults: [ + ...stepResults, + { + label: verificationLabel, + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ executable: 'brev', args: ['exec', snapshot.remote.instanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(verificationCommand)}`] }) + : formatCommand({ executable: 'ssh', args: [remoteHost, verificationCommand] }), + ok: true, + stdout: verificationResult.stdout, + stderr: verificationResult.stderr, + }, + ...(liveFrontierCommand + ? [{ + label: 'verify_remote_live_frontier', + commandLine: isBrevRemote(snapshot.remote) + ? formatCommand({ executable: 'brev', args: ['exec', snapshot.remote.instanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(liveFrontierCommand)}`] }) + : formatCommand({ executable: 'ssh', args: [remoteHost, liveFrontierCommand] }), + ok: true, + stdout: liveFrontierResult.stdout, + stderr: liveFrontierResult.stderr, + }] + : []), + ], + remoteVerification, + remoteLiveFrontier, + postSyncDoctor, + }; +} + +export function getFrontierLanesSnapshot(workspaceRoot = getWorkspaceRoot()) { + const resolvedRunner = resolveBundledFrontierCliRunner(workspaceRoot); + if (!resolvedRunner.runner) { + return { + available: false, + generatedAt: new Date().toISOString(), + workspaceRoot, + error: resolvedRunner.error ?? 'Unable to run bundled frontier-engine lane discovery.', + lanes: [], + runnerMode: null, + }; + } + + const cliList = runBundledFrontierCli(['list-lanes', '--json'], workspaceRoot, resolvedRunner.runner); + if (!cliList.result.ok) { + return { + available: false, + generatedAt: new Date().toISOString(), + workspaceRoot, + error: cliList.result.stderr ?? 'Unable to run bundled frontier-engine lane discovery.', + lanes: [], + runnerMode: cliList.runner?.mode ?? null, + }; + } + + const payload = parseJsonDocument(cliList.result.stdout); + if (Array.isArray(payload)) { + return { + available: true, + generatedAt: new Date().toISOString(), + workspaceRoot, + runnerMode: cliList.runner?.mode ?? null, + lanes: payload, + errors: [], + }; + } + + return { + available: false, + generatedAt: new Date().toISOString(), + workspaceRoot, + runnerMode: cliList.runner?.mode ?? null, + lanes: [], + errors: [{ + error: 'failed to parse bundled frontier-engine lane list json', + }], + error: 'Unable to parse bundled frontier-engine lane metadata.', + }; +} + +export function getFrontierRemotesSnapshot(workspaceRoot = getWorkspaceRoot()) { + const config = loadConfig(workspaceRoot); + const registry = getFrontierRemoteRegistry(config); + return { + generatedAt: new Date().toISOString(), + workspaceRoot, + activeRemoteId: registry.activeRemoteId, + remoteCount: Object.keys(registry.remotes).length, + remotes: buildRegisteredRemotesSummary(config), + }; +} + +export function setFrontierPaidRemoteAccess(remoteId, enabled, workspaceRoot = getWorkspaceRoot()) { + const config = loadConfig(workspaceRoot); + const registry = getFrontierRemoteRegistry(config); + const selected = registry.remotes[remoteId] ?? null; + if (!selected) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Unknown frontier remote: ${remoteId}`, + snapshot: getFrontierRemotesSnapshot(workspaceRoot), + }; + } + if (!isPaidRemote(selected)) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Remote ${remoteId} is not a paid rung.`, + snapshot: getFrontierRemotesSnapshot(workspaceRoot), + }; + } + let nextConfig = setFrontierPaidRemoteEnabled(config, remoteId, enabled); + if (normalizeRemoteId(nextConfig.frontier?.remote ?? {}, nextConfig.frontier?.activeRemoteId ?? null) === remoteId) { + nextConfig = { + ...nextConfig, + frontier: { + ...nextConfig.frontier, + remote: { + ...nextConfig.frontier.remote, + paidEnabled: isRemotePaidEnabled(nextConfig, selected, remoteId), + }, + }, + }; + } + saveConfig(nextConfig, workspaceRoot); + return { + ok: true, + appliedAt: new Date().toISOString(), + enabled, + remoteId, + snapshot: getFrontierRemotesSnapshot(workspaceRoot), + }; +} + +export function setFrontierPaidFleetAccess(fleetId, enabled, workspaceRoot = getWorkspaceRoot()) { + const config = loadConfig(workspaceRoot); + const fleet = getFrontierFleetSnapshot(fleetId, workspaceRoot); + if (!fleet) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Unknown frontier fleet: ${fleetId}`, + snapshot: getFrontierFleetsSnapshot(workspaceRoot), + }; + } + if (!isPaidFleet(fleet)) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Fleet ${fleetId} is not a paid rung.`, + snapshot: getFrontierFleetsSnapshot(workspaceRoot), + }; + } + const nextConfig = setFrontierPaidFleetEnabled(config, fleetId, fleet.remoteIds ?? [], enabled); + saveConfig(nextConfig, workspaceRoot); + return { + ok: true, + appliedAt: new Date().toISOString(), + enabled, + fleetId, + snapshot: getFrontierFleetsSnapshot(workspaceRoot), + }; +} + +export function applyFrontierUseRemote(remoteId, workspaceRoot = getWorkspaceRoot()) { + const config = loadConfig(workspaceRoot); + const registry = getFrontierRemoteRegistry(config); + const selected = registry.remotes[remoteId] ?? null; + if (!selected) { + return { + ok: false, + appliedAt: new Date().toISOString(), + error: `Unknown frontier remote: ${remoteId}`, + snapshot: getFrontierRemotesSnapshot(workspaceRoot), + }; + } + saveConfig({ + ...config, + frontier: { + ...config.frontier, + activeRemoteId: remoteId, + remote: { + ...selected, + remoteId, + paidEnabled: isRemotePaidEnabled(config, selected, remoteId), + }, + }, + }, workspaceRoot); + return { + ok: true, + appliedAt: new Date().toISOString(), + snapshot: getFrontierRemotesSnapshot(workspaceRoot), + }; +} + +export function resolveFrontierExecutionPlan(intent, workspaceRoot = getWorkspaceRoot(), snapshotOverride = null) { + const snapshot = snapshotOverride ?? getFrontierDoctorSnapshot(workspaceRoot); + + if (intent === 'bridgeRefresh848') { + const researchMode = snapshot.researchModes?.bridgeRefresh; + if (!researchMode?.available) { + return { + available: false, + intent, + mode: null, + source: 'unavailable', + reason: researchMode?.reason ?? 'bridge refresh is not currently runnable', + snapshot, + }; + } + + if (researchMode.source === 'managed_runtime') { + const command = { + executable: snapshot.managedPython.pythonExecutable, + args: [snapshot.bundledEngineCliPath, 'export-p848-theorem-bridge'], + }; + return { + available: true, + intent, + mode: researchMode.mode, + source: researchMode.source, + reason: researchMode.reason, + executable: command.executable, + args: command.args, + commandLine: formatCommand(command), + snapshot, + }; + } + + const command = { + executable: snapshot.systemPython.pythonExecutable || 'python3', + args: [snapshot.bundledEngineCliPath, 'export-p848-theorem-bridge'], + }; + return { + available: true, + intent, + mode: researchMode.mode, + source: researchMode.source, + reason: researchMode.reason, + executable: command.executable, + args: command.args, + commandLine: formatCommand(command), + snapshot, + }; + } + + if (intent === 'p848FamilySearchProfile') { + const researchMode = snapshot.researchModes?.familySearch; + if (!researchMode?.available) { + return { + available: false, + intent, + mode: null, + source: 'unavailable', + reason: researchMode?.reason ?? 'family-aware search is not currently runnable', + snapshot, + }; + } + + const profilePath = getBundledFrontierExperimentPath('p848-anchor-ladder', 'batched_smoke_profile.json'); + const command = { + executable: snapshot.managedPython.pythonExecutable, + args: [snapshot.bundledEngineCliPath, 'p848-run-profile', profilePath], + }; + return { + available: true, + intent, + mode: researchMode.mode, + source: researchMode.source, + reason: researchMode.reason, + profilePath, + executable: command.executable, + args: command.args, + commandLine: formatCommand(command), + snapshot, + }; + } + + if (intent === 'p848HeavySearchProfile') { + const researchMode = snapshot.researchModes?.heavySearch; + if (!researchMode?.available) { + return { + available: false, + intent, + mode: null, + source: 'unavailable', + reason: researchMode?.reason ?? 'heavy GPU search is not currently runnable', + snapshot, + }; + } + + if (researchMode.source === 'ssh_remote') { + const remoteProvider = snapshot.remote?.provider ?? 'ssh'; + const remoteHost = snapshot.remote?.sshHost; + const remoteInstanceName = snapshot.remote?.instanceName ?? null; + const remoteEngineRoot = snapshot.remote?.engineRoot ?? getDefaultRemoteEngineRoot(remoteProvider); + const remotePythonCommand = snapshot.remote?.pythonCommand ?? getDefaultRemotePythonCommand(remoteProvider); + const profileFilename = remoteProvider === 'brev' + ? 'brev_h100_search_profile.json' + : 'windows_rtx4090_search_profile.json'; + const remoteProfilePath = joinRemotePath(snapshot.remote, remoteEngineRoot, 'experiments', 'p848-anchor-ladder', profileFilename); + const remoteCliPath = joinRemotePath(snapshot.remote, remoteEngineRoot, 'src', 'frontier_engine', 'cli.py'); + const remoteCommand = isBrevRemote(snapshot.remote) + ? `${remotePythonCommand} ${quotePosixShellArg(remoteCliPath)} export-p848-profile-bundle ${quotePosixShellArg(remoteProfilePath)}` + : `${remotePythonCommand} ${quoteRemoteWindowsPath(remoteCliPath)} export-p848-profile-bundle ${quoteRemoteWindowsPath(remoteProfilePath)}`; + return { + available: true, + intent, + mode: researchMode.mode, + source: researchMode.source, + reason: researchMode.reason, + profilePath: remoteProfilePath, + laneId: 'p848_anchor_ladder', + executable: isBrevRemote(snapshot.remote) ? 'brev' : 'ssh', + args: isBrevRemote(snapshot.remote) + ? ['exec', remoteInstanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(remoteCommand)}`] + : [remoteHost, remoteCommand], + commandLine: formatCommand( + isBrevRemote(snapshot.remote) + ? { + executable: 'brev', + args: ['exec', remoteInstanceName ?? remoteHost, `bash -lc ${quotePosixShellArg(remoteCommand)}`], + } + : { + executable: 'ssh', + args: [remoteHost, remoteCommand], + }, + ), + remoteHost, + remoteProvider, + remoteInstanceName, + remoteCommand, + remoteEngineRoot, + remotePythonCommand, + snapshot, + }; + } + + const profilePath = getBundledFrontierExperimentPath('p848-anchor-ladder', 'windows_rtx4090_search_profile.json'); + const command = { + executable: snapshot.managedPython.pythonExecutable, + args: [snapshot.bundledEngineCliPath, 'export-p848-profile-bundle', profilePath], + }; + return { + available: true, + intent, + mode: researchMode.mode, + source: researchMode.source, + reason: researchMode.reason, + profilePath, + laneId: 'p848_anchor_ladder', + executable: command.executable, + args: command.args, + commandLine: formatCommand(command), + snapshot, + }; + } + + return { + available: false, + intent, + mode: null, + source: 'unavailable', + reason: `Unknown frontier execution intent: ${intent}`, + snapshot, + }; +} diff --git a/src/runtime/research-stack.js b/src/runtime/research-stack.js new file mode 100644 index 0000000..a3eac15 --- /dev/null +++ b/src/runtime/research-stack.js @@ -0,0 +1,129 @@ +import { + getProblemClaimLoopSnapshot, + getProblemClaimPassSnapshot, + getProblemFormalizationSnapshot, + getProblemFormalizationWorkSnapshot, + getProblemTaskListSnapshot, + getProblemTheoremLoopSnapshot, +} from './theorem-loop.js'; + +function buildComputeSurface(problem, clusterSnapshot) { + if (problem.cluster === 'number-theory') { + const frontierLoop = clusterSnapshot?.frontierLoop ?? null; + return { + available: Boolean(frontierLoop), + kind: 'frontier_engine', + mode: frontierLoop?.mode ?? null, + summary: frontierLoop?.summary ?? null, + entryCommand: frontierLoop?.primaryCommand ?? `erdos number-theory dispatch ${problem.problemId}`, + refreshCommand: frontierLoop?.refreshCommand ?? null, + setupCommands: [ + frontierLoop?.activationCommand, + frontierLoop?.upgradeCommand, + ].filter(Boolean), + hardwareDoctorCommand: 'erdos frontier doctor', + }; + } + + if (problem.cluster === 'sunflower' && clusterSnapshot?.computeLanePresent) { + return { + available: true, + kind: 'packaged_compute_lane', + mode: 'cpu_or_paid_lane', + summary: clusterSnapshot.computeSummary ?? null, + entryCommand: `erdos sunflower compute run ${problem.problemId}`, + refreshCommand: null, + setupCommands: [], + hardwareDoctorCommand: null, + }; + } + + return { + available: false, + kind: 'none', + mode: null, + summary: null, + entryCommand: null, + refreshCommand: null, + setupCommands: [], + hardwareDoctorCommand: null, + }; +} + +export function buildResearchStackSummary(problem, inventory, orp, clusterSnapshot) { + const theoremLoop = getProblemTheoremLoopSnapshot(problem); + const claimLoop = getProblemClaimLoopSnapshot(problem); + const claimPass = getProblemClaimPassSnapshot(problem); + const formalization = getProblemFormalizationSnapshot(problem); + const formalizationWork = getProblemFormalizationWorkSnapshot(problem); + const taskList = getProblemTaskListSnapshot(problem); + const compute = buildComputeSurface(problem, clusterSnapshot); + + return { + problemId: problem.problemId, + displayName: problem.displayName, + canonicalSource: { + repo: 'SproutSeeds/erdos-problems', + sourceUrl: problem.sourceUrl, + importSnapshotKind: inventory?.upstreamSnapshot?.kind ?? null, + importSnapshotCommit: inventory?.upstreamSnapshot?.upstreamCommit ?? null, + commands: { + importShow: 'erdos import show', + importSync: 'erdos import sync', + importSyncMaintainer: 'erdos import sync --write-package-snapshot', + }, + }, + localProtocol: { + orpProtocolPresent: Boolean(orp?.workspace?.protocolPresent), + orpIntegrationPresent: Boolean(orp?.workspace?.integrationPresent), + checkpointShelfPresent: Boolean(clusterSnapshot), + commands: { + orpSync: 'erdos orp sync', + checkpointsSync: 'erdos checkpoints sync', + preflight: 'erdos preflight', + }, + }, + theorem: { + mode: theoremLoop.theoremLoopMode, + claimSurface: theoremLoop.currentState?.currentClaimSurface ?? null, + theoremLoopPath: theoremLoop.theoremLoopMarkdownPath, + claimLoopMode: claimLoop.claimLoopMode, + claimLoopPath: claimLoop.claimLoopMarkdownPath, + claimPassMode: claimPass.claimPassMode, + claimPassPath: claimPass.claimPassMarkdownPath, + formalizationMode: formalization.formalizationMode, + formalizationPath: formalization.formalizationMarkdownPath, + formalizationWorkMode: formalizationWork.formalizationWorkMode, + formalizationWorkPath: formalizationWork.formalizationWorkMarkdownPath, + taskListMode: taskList.taskListMode, + taskListPath: taskList.taskListMarkdownPath, + commands: { + show: theoremLoop.commands?.theoremLoop ?? null, + refresh: theoremLoop.commands?.theoremLoopRefresh ?? null, + claimShow: claimLoop.commands?.claimLoop ?? null, + claimRefresh: claimLoop.commands?.claimLoopRefresh ?? null, + claimPassShow: claimPass.commands?.claimPass ?? null, + claimPassRefresh: claimPass.commands?.claimPassRefresh ?? null, + formalizationShow: formalization.commands?.formalization ?? null, + formalizationRefresh: formalization.commands?.formalizationRefresh ?? null, + formalizationWorkShow: formalizationWork.commands?.formalizationWork ?? null, + formalizationWorkRefresh: formalizationWork.commands?.formalizationWorkRefresh ?? null, + taskListShow: taskList.commands?.taskList ?? null, + taskListRefresh: taskList.commands?.taskListRefresh ?? null, + sourceRefresh: theoremLoop.commands?.sourceRefresh ?? null, + }, + }, + compute, + writeback: { + problemArtifactsCommand: `erdos problem artifacts ${problem.problemId}`, + packagedRefreshCommand: theoremLoop.commands?.theoremLoopRefresh ?? null, + claimRefreshCommand: claimLoop.commands?.claimLoopRefresh ?? null, + claimPassRefreshCommand: claimPass.commands?.claimPassRefresh ?? null, + formalizationRefreshCommand: formalization.commands?.formalizationRefresh ?? null, + formalizationWorkRefreshCommand: formalizationWork.commands?.formalizationWorkRefresh ?? null, + taskListRefreshCommand: taskList.commands?.taskListRefresh ?? null, + sourceRefreshCommand: theoremLoop.commands?.sourceRefresh ?? null, + maintainerSeedTemplate: `erdos maintainer seed problem ${problem.problemId} --from-pull .erdos/pulls/${problem.problemId} --cluster ${problem.cluster}`, + }, + }; +} diff --git a/src/runtime/theorem-loop.js b/src/runtime/theorem-loop.js new file mode 100644 index 0000000..e9bf343 --- /dev/null +++ b/src/runtime/theorem-loop.js @@ -0,0 +1,21668 @@ +import fs from 'node:fs'; +import { execFileSync } from 'node:child_process'; +import path from 'node:path'; +import { parse } from 'yaml'; +import { ensureDir, writeJson, writeText } from './files.js'; +import { getPackProblemDir, repoRoot } from './paths.js'; + +function readYamlIfPresent(filePath) { + if (!fs.existsSync(filePath)) { + return null; + } + return parse(fs.readFileSync(filePath, 'utf8')); +} + +function readJsonIfPresent(filePath) { + if (!fs.existsSync(filePath)) { + return null; + } + try { + return JSON.parse(fs.readFileSync(filePath, 'utf8')); + } catch { + return null; + } +} + +function getProblemPackDir(problem) { + if (!problem?.cluster) { + return null; + } + return getPackProblemDir(problem.cluster, problem.problemId); +} + +export function getProblemTheoremLoopPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + theoremLoopJsonPath: null, + theoremLoopMarkdownPath: null, + legacyBridgeJsonPath: null, + legacyBridgeMarkdownPath: null, + }; + } + + return { + packProblemDir, + theoremLoopJsonPath: path.join(packProblemDir, 'THEOREM_LOOP.json'), + theoremLoopMarkdownPath: path.join(packProblemDir, 'THEOREM_LOOP.md'), + legacyBridgeJsonPath: path.join(packProblemDir, 'SEARCH_THEOREM_BRIDGE.json'), + legacyBridgeMarkdownPath: path.join(packProblemDir, 'SEARCH_THEOREM_BRIDGE.md'), + }; +} + +export function getProblemClaimLoopPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + claimLoopJsonPath: null, + claimLoopMarkdownPath: null, + }; + } + + return { + packProblemDir, + claimLoopJsonPath: path.join(packProblemDir, 'CLAIM_LOOP.json'), + claimLoopMarkdownPath: path.join(packProblemDir, 'CLAIM_LOOP.md'), + }; +} + +export function getProblemClaimPassPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + claimPassJsonPath: null, + claimPassMarkdownPath: null, + }; + } + + return { + packProblemDir, + claimPassJsonPath: path.join(packProblemDir, 'CLAIM_PASS.json'), + claimPassMarkdownPath: path.join(packProblemDir, 'CLAIM_PASS.md'), + }; +} + +export function getProblemFormalizationPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + formalizationJsonPath: null, + formalizationMarkdownPath: null, + }; + } + + return { + packProblemDir, + formalizationJsonPath: path.join(packProblemDir, 'FORMALIZATION.json'), + formalizationMarkdownPath: path.join(packProblemDir, 'FORMALIZATION.md'), + }; +} + +export function getProblemFormalizationWorkPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + formalizationWorkJsonPath: null, + formalizationWorkMarkdownPath: null, + formalizationWorkSvgPath: null, + }; + } + + return { + packProblemDir, + formalizationWorkJsonPath: path.join(packProblemDir, 'FORMALIZATION_WORK.json'), + formalizationWorkMarkdownPath: path.join(packProblemDir, 'FORMALIZATION_WORK.md'), + formalizationWorkSvgPath: path.join(packProblemDir, 'FORMALIZATION_WORK.svg'), + }; +} + +export function getProblemTaskListPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + taskListJsonPath: null, + taskListMarkdownPath: null, + }; + } + + return { + packProblemDir, + taskListJsonPath: path.join(packProblemDir, 'TASK_LIST.json'), + taskListMarkdownPath: path.join(packProblemDir, 'TASK_LIST.md'), + }; +} + +export function getProblemTaskLoopRunPaths(problem) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return { + packProblemDir: null, + taskLoopRunJsonPath: null, + taskLoopRunMarkdownPath: null, + }; + } + + return { + packProblemDir, + taskLoopRunJsonPath: path.join(packProblemDir, 'TASK_LOOP_RUN.json'), + taskLoopRunMarkdownPath: path.join(packProblemDir, 'TASK_LOOP_RUN.md'), + }; +} + +function getClusterStatusCommand(problem) { + switch (String(problem?.cluster ?? '')) { + case 'number-theory': + return `erdos number-theory status ${problem.problemId}`; + case 'sunflower': + return `erdos sunflower status ${problem.problemId}`; + case 'graph-theory': + return `erdos graph-theory status ${problem.problemId}`; + default: + return `erdos problem show ${problem.problemId}`; + } +} + +function getClusterFrontierCommand(problem) { + switch (String(problem?.cluster ?? '')) { + case 'number-theory': + return `erdos number-theory frontier ${problem.problemId}`; + case 'sunflower': + return `erdos sunflower frontier ${problem.problemId}`; + case 'graph-theory': + return `erdos graph-theory frontier ${problem.problemId}`; + default: + return null; + } +} + +function getSourceRefreshCommand(problem) { + if (String(problem?.cluster ?? '') === 'number-theory' && String(problem?.problemId ?? '') === '848') { + return { + command: `erdos number-theory bridge-refresh ${problem.problemId}`, + args: ['number-theory', 'bridge-refresh', String(problem.problemId), '--json'], + kind: 'frontier_bridge', + }; + } + return null; +} + +function getCurrentClaimSurface(problem, { bridge, theoremModule, routeBreakthrough }) { + if (bridge?.current_bridge_state) { + return 'bridge_backed_frontier_support'; + } + if (problem?.researchState?.problem_solved) { + return 'solved_result'; + } + if (routeBreakthrough) { + return 'frontier_supported_route'; + } + if (theoremModule) { + return 'theorem_module_registered'; + } + return 'route_scaffolding'; +} + +function buildBaselineHooks({ activeRoute, theoremModule, firstReadyAtom, frontierNotePresent }) { + const hooks = []; + + if (activeRoute) { + hooks.push({ + hook_id: 'active_route_recorded', + status: 'supported', + note: `The pack records an active route, currently \`${activeRoute}\`.`, + }); + } + + if (theoremModule) { + hooks.push({ + hook_id: 'theorem_module_registered', + status: 'supported', + note: `A theorem module is already registered for the active route: \`${theoremModule}\`.`, + }); + } + + if (firstReadyAtom?.atom_id) { + hooks.push({ + hook_id: 'ready_atom_present', + status: 'supported', + note: `The live route already has a ready atom, \`${firstReadyAtom.atom_id}\`, which can feed the theorem lane.`, + }); + } + + if (frontierNotePresent) { + hooks.push({ + hook_id: 'frontier_note_present', + status: 'supported', + note: 'The pack already carries a frontier note that can anchor theorem-facing updates.', + }); + } + + if (hooks.length === 0) { + hooks.push({ + hook_id: 'theorem_loop_seeded', + status: 'supported', + note: 'The theorem loop is available as a baseline scaffold even though no deeper bridge-specific hook has been recorded yet.', + }); + } + + return hooks; +} + +function buildBaselineAgenda({ + activeRoute, + theoremModule, + firstReadyAtom, + nextHonestMove, + currentClaimSurface, +}) { + const items = []; + + if (firstReadyAtom?.atom_id) { + items.push({ + item_id: 'promote_ready_atom', + status: 'ready', + task: `Turn ready atom \`${firstReadyAtom.atom_id}\` into the next theorem-facing checkpoint.`, + why: firstReadyAtom.next_move ?? nextHonestMove, + }); + } + + if (theoremModule) { + items.push({ + item_id: 'stabilize_theorem_module_boundary', + status: 'ready', + task: `Align the active route with theorem module \`${theoremModule}\` and freeze its public claim boundary.`, + why: `The current claim surface is \`${currentClaimSurface}\`, so the next theorem move should sharpen what that module actually certifies.`, + }); + } + + if (activeRoute) { + items.push({ + item_id: 'tighten_active_route_claim', + status: 'ready', + task: `Compress the active route \`${activeRoute}\` into the next honest theorem-facing claim unit.`, + why: nextHonestMove, + }); + } + + if (items.length === 0) { + items.push({ + item_id: 'seed_theorem_lane', + status: 'ready', + task: 'Seed the theorem lane with the smallest honest route-facing claim.', + why: nextHonestMove, + }); + } + + return items; +} + +function buildBridgeBackedAgenda({ theoremHooks, bridgeState, nextHonestMove }) { + const items = [ + { + item_id: 'choose_next_finite_gap_move', + status: 'ready', + task: 'Choose the next finite-gap closure move and keep the theorem-facing claim surface honest.', + why: nextHonestMove, + }, + ]; + + const hookIds = new Set((theoremHooks ?? []).map((hook) => hook.hook_id)); + + if (hookIds.has('next_unmatched_equals_282_failure') && bridgeState?.next_unmatched_representative !== undefined) { + items.push({ + item_id: 'explain_next_unmatched_alignment', + status: 'ready', + task: `Explain structurally why shared-prefix representative \`${bridgeState.next_unmatched_representative}\` aligns with the first failure of tail \`282\`.`, + why: 'If that alignment is structural rather than accidental, it turns a search coincidence into a theorem-facing obstruction class.', + }); + } + + if (hookIds.has('completed_tail_vs_search_leader_split') + && bridgeState?.strongest_completed_structured_tail?.continuation !== undefined + && bridgeState?.current_family_aware_leader?.continuation !== undefined) { + items.push({ + item_id: 'explain_completed_vs_search_leader_split', + status: 'ready', + task: `Explain why completed structured tail \`${bridgeState.strongest_completed_structured_tail.continuation}\` differs from current family-aware leader \`${bridgeState.current_family_aware_leader.continuation}\`.`, + why: 'That split tells us whether the live frontier is a finite-window artifact or a genuinely better structural continuation class.', + }); + } + + if (hookIds.has('repair_pool_not_closed')) { + items.push({ + item_id: 'model_repair_pool_growth', + status: 'ready', + task: 'Model the repaired square-modulus pool as a growing family rather than treating it as already closed.', + why: 'Recent packets introduced new square moduli, so the theorem lane should aim for controlled growth, not premature closure.', + }); + } + + if (hookIds.has('top_repair_class_cluster') && Array.isArray(bridgeState?.top_gpu_tie_class) && bridgeState.top_gpu_tie_class.length > 0) { + items.push({ + item_id: 'characterize_top_repair_cluster', + status: 'ready', + task: `Characterize what the top repair cluster \`${bridgeState.top_gpu_tie_class.join(', ')}\` shares structurally.`, + why: 'If the tied tails share a common repair mechanism, that mechanism is a strong candidate for the next lemma-level abstraction.', + }); + } + + return items; +} + +function buildGenericFeatureExtractors(problem, theoremLoop) { + const extractors = [ + { + extractor_id: 'pack_route_state', + kind: 'pack_context', + scope: 'all_problems', + status: 'ready', + note: 'Reads pack route, ticket, and atom state as the baseline theorem-search context.', + }, + { + extractor_id: 'theorem_loop_snapshot', + kind: 'theorem_loop', + scope: 'all_problems', + status: 'ready', + note: 'Uses the canonical theorem-loop as the current claim-surface ledger.', + }, + ]; + + if (theoremLoop.currentBridgeState) { + extractors.push({ + extractor_id: 'search_theorem_bridge_state', + kind: 'search_bridge', + scope: 'bridge_backed_problems', + status: 'ready', + note: 'Imports structured bridge state, packet ledgers, and search-side claim hooks.', + }); + } + + if (problem.cluster === 'number-theory') { + extractors.push({ + extractor_id: 'cluster_number_theory_features', + kind: 'cluster_adapter', + scope: 'number_theory', + status: 'ready', + note: 'Exposes number-theory specific finite-gap and verifier-facing metadata.', + }); + } else if (problem.cluster === 'sunflower') { + extractors.push({ + extractor_id: 'cluster_sunflower_features', + kind: 'cluster_adapter', + scope: 'sunflower', + status: 'ready', + note: 'Exposes sunflower-family route state, witness status, and compute packet context.', + }); + } else if (problem.cluster === 'graph-theory') { + extractors.push({ + extractor_id: 'cluster_graph_theory_features', + kind: 'cluster_adapter', + scope: 'graph_theory', + status: 'ready', + note: 'Exposes graph-theory archive or theorem-state context to the claim loop.', + }); + } + + return extractors; +} + +function buildGenericClaimGenerators(problem, theoremLoop) { + const generators = [ + { + generator_id: 'baseline_route_claims', + kind: 'route_state', + scope: 'all_problems', + status: 'ready', + note: 'Promotes active routes, ready atoms, and next-honest-move records into candidate claims.', + }, + { + generator_id: 'theorem_agenda_claims', + kind: 'agenda_projection', + scope: 'all_problems', + status: 'ready', + note: 'Turns theorem agenda items into explicit candidate claim tickets.', + }, + ]; + + if (theoremLoop.currentBridgeState) { + generators.push({ + generator_id: 'search_bridge_claims', + kind: 'bridge_pattern_projection', + scope: 'bridge_backed_problems', + status: 'ready', + note: 'Projects bridge-backed structural hooks into concrete claim candidates.', + }); + } + + if (problem.problemId === '848' && theoremLoop.currentBridgeState) { + generators.push({ + generator_id: 'p848_repair_obstruction_claims', + kind: 'problem_adapter', + scope: 'problem_848', + status: 'ready', + note: 'Builds obstruction-alignment and repair-class candidate claims from the live packet ledger.', + }); + } + + return generators; +} + +function buildGenericClaimFalsifiers(problem, theoremLoop) { + const falsifiers = [ + { + falsifier_id: 'theorem_loop_consistency_check', + kind: 'ledger_consistency', + scope: 'all_problems', + status: 'ready', + note: 'Rejects claims that overstate the current theorem-loop claim surface.', + }, + { + falsifier_id: 'artifact_boundary_check', + kind: 'artifact_boundary', + scope: 'all_problems', + status: 'ready', + note: 'Rejects claims unsupported by canonical artifacts already present in the pack.', + }, + ]; + + if (problem.cluster === 'number-theory') { + falsifiers.push({ + falsifier_id: 'exact_interval_counterexample_scan', + kind: 'exact_verifier', + scope: 'number_theory', + status: 'ready', + note: 'Uses bounded exact interval checks to kill false local claims quickly.', + }); + } + + if (theoremLoop.currentBridgeState) { + falsifiers.push({ + falsifier_id: 'bridge_packet_replay', + kind: 'search_bridge_replay', + scope: 'bridge_backed_problems', + status: 'ready', + note: 'Replays current bridge packets and tracked tails against candidate claims.', + }); + } + + return falsifiers; +} + +function buildGenericVerifierAdapters(problem, theoremLoop) { + const adapters = [ + { + adapter_id: 'canonical_artifact_reader', + kind: 'artifact_reader', + scope: 'all_problems', + status: 'ready', + note: 'Reads theorem-loop, route, and pack artifacts as verifier-facing evidence.', + }, + ]; + + if (problem.cluster === 'number-theory') { + adapters.push({ + adapter_id: 'exact_small_n', + kind: 'exact_verifier', + scope: 'number_theory', + status: 'ready', + note: 'Bounded exact verifier for finite interval certification.', + }); + } + + if (theoremLoop.currentBridgeState) { + adapters.push({ + adapter_id: 'search_theorem_bridge', + kind: 'bridge_verifier', + scope: 'bridge_backed_problems', + status: 'ready', + note: 'Supplies live search-side packet and leaderboard evidence to the claim loop.', + }); + } + + if (problem.problemId === '848' && theoremLoop.currentBridgeState) { + adapters.push({ + adapter_id: 'p848_family_repair_surface', + kind: 'problem_adapter', + scope: 'problem_848', + status: 'ready', + note: 'Evaluates candidate claims against tracked-tail repair surfaces and shared-prefix packets.', + }); + } + + return adapters; +} + +function buildCandidateClaims(problem, theoremLoop) { + const candidates = (theoremLoop.theoremAgenda ?? []).map((item) => ({ + claim_id: item.item_id, + status: item.status ?? 'ready', + source: 'theorem_agenda', + summary: item.task, + why: item.why ?? null, + support: (theoremLoop.theoremHooks ?? []) + .filter((hook) => hook.status === 'supported') + .map((hook) => hook.hook_id), + })); + + if (problem.problemId === '848' && theoremLoop.currentBridgeState) { + const bridgeState = theoremLoop.currentBridgeState; + candidates.push({ + claim_id: 'p848_next_unmatched_alignment_claim', + status: 'ready', + source: 'search_bridge', + summary: `Shared-prefix representative ${bridgeState.next_unmatched_representative} aligns structurally with the first failure of tail 282.`, + why: 'If this survives falsification, it upgrades a numerical coincidence into an obstruction-class candidate.', + support: ['next_unmatched_equals_282_failure'], + }); + candidates.push({ + claim_id: 'p848_top_repair_cluster_claim', + status: 'ready', + source: 'search_bridge', + summary: `Top repair class ${Array.isArray(bridgeState.top_gpu_tie_class) ? bridgeState.top_gpu_tie_class.join(', ') : '(unknown)'} shares a common repair mechanism.`, + why: 'A shared mechanism would compress the search frontier into a reusable lemma candidate.', + support: ['top_repair_class_cluster'], + }); + } + + return candidates; +} + +export function buildProblemTheoremLoop(problem) { + const paths = getProblemTheoremLoopPaths(problem); + const contextPath = paths.packProblemDir ? path.join(paths.packProblemDir, 'context.yaml') : null; + const routePacketPath = paths.packProblemDir ? path.join(paths.packProblemDir, 'ROUTE_PACKET.yaml') : null; + const frontierNotePath = paths.packProblemDir ? path.join(paths.packProblemDir, 'FRONTIER_NOTE.md') : null; + const opsDetailsPath = paths.packProblemDir ? path.join(paths.packProblemDir, 'OPS_DETAILS.yaml') : null; + + const context = readYamlIfPresent(contextPath) ?? {}; + const routePacket = readYamlIfPresent(routePacketPath) ?? {}; + const opsDetails = readYamlIfPresent(opsDetailsPath) ?? {}; + const bridge = readJsonIfPresent(paths.legacyBridgeJsonPath); + + const activeRoute = problem?.researchState?.active_route + ?? context.default_active_route + ?? routePacket.route_id + ?? opsDetails.routes?.[0]?.route_id + ?? null; + + const activeRouteDetail = Array.isArray(opsDetails.routes) + ? opsDetails.routes.find((route) => route.route_id === activeRoute) ?? opsDetails.routes[0] ?? null + : null; + const activeTicketDetail = Array.isArray(opsDetails.tickets) + ? opsDetails.tickets.find((ticket) => ticket.status === 'active' && (!activeRoute || ticket.route_id === activeRoute)) + ?? opsDetails.tickets.find((ticket) => !activeRoute || ticket.route_id === activeRoute) + ?? opsDetails.tickets[0] + ?? null + : null; + const firstReadyAtom = Array.isArray(opsDetails.atoms) + ? opsDetails.atoms.find((atom) => atom.status === 'ready' && (!activeRoute || atom.route_id === activeRoute)) + ?? opsDetails.atoms.find((atom) => atom.status === 'ready') + ?? null + : null; + + const theoremModule = activeRouteDetail?.theorem_module + || routePacket.theorem_module + || null; + const routeBreakthrough = typeof problem?.researchState?.route_breakthrough === 'boolean' + ? problem.researchState.route_breakthrough + : false; + const nextHonestMove = firstReadyAtom?.next_move + ?? activeTicketDetail?.next_move + ?? activeRouteDetail?.next_move + ?? context.next_honest_move + ?? 'Preserve the active route honestly and tighten the theorem-facing evidence stack without overclaiming.'; + const routeSummary = activeRouteDetail?.summary + ?? context.route_story + ?? routePacket.frontier_claim + ?? problem.shortStatement; + const currentClaimSurface = getCurrentClaimSurface(problem, { + bridge, + theoremModule, + routeBreakthrough, + }); + + const bridgeBacked = Boolean(bridge?.current_bridge_state); + const theoremHooks = bridgeBacked + ? (bridge.candidate_theorem_hooks ?? []).map((hook) => ({ + hook_id: hook.hook_id ?? 'bridge_hook', + status: hook.status ?? 'supported', + note: hook.note ?? '', + })) + : buildBaselineHooks({ + activeRoute, + theoremModule, + firstReadyAtom, + frontierNotePresent: Boolean(frontierNotePath && fs.existsSync(frontierNotePath)), + }); + const theoremAgenda = bridgeBacked + ? buildBridgeBackedAgenda({ + theoremHooks, + bridgeState: bridge?.current_bridge_state ?? null, + nextHonestMove, + }) + : buildBaselineAgenda({ + activeRoute, + theoremModule, + firstReadyAtom, + nextHonestMove, + currentClaimSurface, + }); + + const sourceRefresh = getSourceRefreshCommand(problem); + + return { + schema: 'erdos.problem_theorem_loop/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + sourceKind: bridgeBacked ? 'search_theorem_bridge' : 'pack_route_state', + theoremLoopMode: bridgeBacked ? 'bridge_backed' : 'baseline', + activeRoute, + theoremModule, + currentState: { + siteStatus: problem.siteStatus, + repoStatus: problem.repoStatus, + openProblem: typeof problem?.researchState?.open_problem === 'boolean' + ? problem.researchState.open_problem + : String(problem.siteStatus ?? '').toLowerCase() === 'open', + routeBreakthrough, + problemSolved: typeof problem?.researchState?.problem_solved === 'boolean' + ? problem.researchState.problem_solved + : false, + currentClaimSurface, + routeSummary, + nextHonestMove, + }, + theoremHooks, + theoremAgenda, + currentBridgeState: bridge?.current_bridge_state ?? null, + commands: { + problemShow: `erdos problem show ${problem.problemId}`, + problemArtifacts: `erdos problem artifacts ${problem.problemId}`, + theoremLoop: `erdos problem theorem-loop ${problem.problemId}`, + theoremLoopRefresh: `erdos problem theorem-loop-refresh ${problem.problemId}`, + clusterStatus: getClusterStatusCommand(problem), + clusterFrontier: getClusterFrontierCommand(problem), + sourceRefresh: sourceRefresh?.command ?? null, + }, + sources: { + packProblemDir: paths.packProblemDir, + theoremLoopJsonPath: paths.theoremLoopJsonPath, + theoremLoopMarkdownPath: paths.theoremLoopMarkdownPath, + contextPath, + routePacketPath, + frontierNotePath, + opsDetailsPath, + legacyBridgeJsonPath: bridgeBacked ? paths.legacyBridgeJsonPath : null, + legacyBridgeMarkdownPath: bridgeBacked ? paths.legacyBridgeMarkdownPath : null, + }, + }; +} + +export function renderProblemTheoremLoopMarkdown(doc) { + const lines = [ + `# ${doc.displayName} Theorem Loop`, + '', + bridgePreamble(doc), + '', + '## Current State', + '', + `- Theorem loop mode: \`${doc.theoremLoopMode}\`.`, + `- Active route: \`${doc.activeRoute ?? '(none)'}\`.`, + `- Current claim surface: \`${doc.currentState.currentClaimSurface}\`.`, + `- Repo status: \`${doc.currentState.repoStatus}\`; site status: \`${doc.currentState.siteStatus}\`.`, + `- Route breakthrough: ${doc.currentState.routeBreakthrough ? '`yes`' : '`no`'}.`, + `- Problem solved: ${doc.currentState.problemSolved ? '`yes`' : '`no`'}.`, + `- Open problem: ${doc.currentState.openProblem ? '`yes`' : '`no`'}.`, + `- Theorem module: ${doc.theoremModule ? `\`${doc.theoremModule}\`` : '`(none)`'}.`, + `- Route summary: ${doc.currentState.routeSummary}`, + `- Next honest move: ${doc.currentState.nextHonestMove}`, + '', + '## Theorem Hooks', + '', + ]; + + for (const hook of doc.theoremHooks ?? []) { + lines.push(`- \`${hook.hook_id}\`: ${hook.status}${hook.note ? ` | ${hook.note}` : ''}`); + } + + lines.push('', '## Theorem Agenda', ''); + for (const item of doc.theoremAgenda ?? []) { + lines.push(`- \`${item.item_id}\`: ${item.status} | ${item.task}${item.why ? ` | ${item.why}` : ''}`); + } + + if (doc.currentBridgeState) { + lines.push('', '## Bridge State', ''); + const bridgeState = doc.currentBridgeState; + if (bridgeState.shared_prefix_failure_count !== undefined) { + lines.push(`- Shared-prefix failures frozen: \`${bridgeState.shared_prefix_failure_count}\` through \`${bridgeState.shared_prefix_failure_max_n ?? '(unknown)'}\`.`); + } + if (bridgeState.strongest_completed_structured_tail?.continuation !== undefined) { + lines.push(`- Strongest completed structured tail: \`${bridgeState.strongest_completed_structured_tail.continuation}\` through \`${bridgeState.strongest_completed_structured_tail.clean_through ?? '(unknown)'}\`.`); + } + if (bridgeState.current_family_aware_leader?.continuation !== undefined) { + lines.push(`- Current family-aware leader: \`${bridgeState.current_family_aware_leader.continuation}\`.`); + } + if (bridgeState.next_unmatched_representative !== undefined) { + lines.push(`- Next unmatched representative: \`${bridgeState.next_unmatched_representative}\`.`); + } + } + + lines.push('', '## Commands', ''); + lines.push(`- Problem surface: \`${doc.commands.problemShow}\``); + lines.push(`- Canonical theorem loop: \`${doc.commands.theoremLoop}\``); + lines.push(`- Refresh theorem loop: \`${doc.commands.theoremLoopRefresh}\``); + lines.push(`- Problem artifacts: \`${doc.commands.problemArtifacts}\``); + if (doc.commands.clusterStatus) { + lines.push(`- Cluster status: \`${doc.commands.clusterStatus}\``); + } + if (doc.commands.clusterFrontier) { + lines.push(`- Cluster frontier: \`${doc.commands.clusterFrontier}\``); + } + if (doc.commands.sourceRefresh) { + lines.push(`- Source refresh: \`${doc.commands.sourceRefresh}\``); + } + + lines.push('', '## Sources', ''); + for (const [label, value] of Object.entries(doc.sources ?? {})) { + if (!value) { + continue; + } + lines.push(`- ${label}: \`${value}\``); + } + lines.push(''); + return lines.join('\n'); +} + +function bridgePreamble(doc) { + if (doc.sourceKind === 'search_theorem_bridge') { + return 'This theorem loop is generated from a richer search/theorem bridge, then exposed through a generic product-wide theorem-loop surface.'; + } + return 'This note is the generic theorem-loop surface for the problem pack. It keeps theorem-facing route state visible even when no richer search bridge exists yet.'; +} + +export function getProblemTheoremLoopSnapshot(problem) { + const doc = buildProblemTheoremLoop(problem); + const paths = getProblemTheoremLoopPaths(problem); + return { + ...doc, + theoremLoopJsonPath: paths.theoremLoopJsonPath, + theoremLoopMarkdownPath: paths.theoremLoopMarkdownPath, + theoremLoopJsonPresent: Boolean(paths.theoremLoopJsonPath && fs.existsSync(paths.theoremLoopJsonPath)), + theoremLoopMarkdownPresent: Boolean(paths.theoremLoopMarkdownPath && fs.existsSync(paths.theoremLoopMarkdownPath)), + }; +} + +export function buildProblemClaimLoop(problem) { + const theoremLoop = buildProblemTheoremLoop(problem); + const paths = getProblemClaimLoopPaths(problem); + const bridgeBacked = Boolean(theoremLoop.currentBridgeState); + + return { + schema: 'erdos.problem_claim_loop/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + sourceKind: bridgeBacked ? 'theorem_loop_plus_bridge' : 'theorem_loop_only', + claimLoopMode: bridgeBacked ? 'bridge_backed' : 'baseline', + currentClaimSurface: theoremLoop.currentState.currentClaimSurface, + currentState: { + theoremLoopMode: theoremLoop.theoremLoopMode, + activeRoute: theoremLoop.activeRoute, + nextHonestMove: theoremLoop.currentState.nextHonestMove, + routeSummary: theoremLoop.currentState.routeSummary, + sourceRefresh: theoremLoop.commands.sourceRefresh ?? null, + }, + featureExtractors: buildGenericFeatureExtractors(problem, theoremLoop), + claimGenerators: buildGenericClaimGenerators(problem, theoremLoop), + claimFalsifiers: buildGenericClaimFalsifiers(problem, theoremLoop), + verifierAdapters: buildGenericVerifierAdapters(problem, theoremLoop), + candidateClaims: buildCandidateClaims(problem, theoremLoop), + theoremHooks: theoremLoop.theoremHooks ?? [], + theoremAgenda: theoremLoop.theoremAgenda ?? [], + commands: { + problemShow: `erdos problem show ${problem.problemId}`, + problemArtifacts: `erdos problem artifacts ${problem.problemId}`, + theoremLoop: theoremLoop.commands.theoremLoop, + theoremLoopRefresh: theoremLoop.commands.theoremLoopRefresh, + claimLoop: `erdos problem claim-loop ${problem.problemId}`, + claimLoopRefresh: `erdos problem claim-loop-refresh ${problem.problemId}`, + sourceRefresh: theoremLoop.commands.sourceRefresh ?? null, + }, + sources: { + claimLoopJsonPath: paths.claimLoopJsonPath, + claimLoopMarkdownPath: paths.claimLoopMarkdownPath, + theoremLoopJsonPath: theoremLoop.sources.theoremLoopJsonPath ?? theoremLoop.sources.theoremLoopPath ?? null, + theoremLoopMarkdownPath: theoremLoop.sources.theoremLoopMarkdownPath ?? null, + legacyBridgeJsonPath: theoremLoop.sources.legacyBridgeJsonPath ?? null, + legacyBridgeMarkdownPath: theoremLoop.sources.legacyBridgeMarkdownPath ?? null, + packProblemDir: theoremLoop.sources.packProblemDir ?? null, + }, + }; +} + +export function renderProblemClaimLoopMarkdown(doc) { + const lines = [ + `# ${doc.displayName} Claim Loop`, + '', + doc.sourceKind === 'theorem_loop_plus_bridge' + ? 'This claim loop generalizes theorem-search-verification work using the theorem loop plus richer bridge-backed search evidence.' + : 'This claim loop generalizes theorem-search-verification work directly from the canonical theorem loop, even when no richer bridge is present yet.', + '', + '## Current State', + '', + `- Claim loop mode: \`${doc.claimLoopMode}\`.`, + `- Current claim surface: \`${doc.currentClaimSurface}\`.`, + `- Active route: \`${doc.currentState.activeRoute ?? '(none)'}\`.`, + `- Route summary: ${doc.currentState.routeSummary}`, + `- Next honest move: ${doc.currentState.nextHonestMove}`, + '', + '## Feature Extractors', + '', + ]; + + for (const extractor of doc.featureExtractors ?? []) { + lines.push(`- \`${extractor.extractor_id}\`: ${extractor.status} | ${extractor.note}`); + } + + lines.push('', '## Claim Generators', ''); + for (const generator of doc.claimGenerators ?? []) { + lines.push(`- \`${generator.generator_id}\`: ${generator.status} | ${generator.note}`); + } + + lines.push('', '## Claim Falsifiers', ''); + for (const falsifier of doc.claimFalsifiers ?? []) { + lines.push(`- \`${falsifier.falsifier_id}\`: ${falsifier.status} | ${falsifier.note}`); + } + + lines.push('', '## Verifier Adapters', ''); + for (const adapter of doc.verifierAdapters ?? []) { + lines.push(`- \`${adapter.adapter_id}\`: ${adapter.status} | ${adapter.note}`); + } + + lines.push('', '## Candidate Claims', ''); + for (const claim of doc.candidateClaims ?? []) { + lines.push(`- \`${claim.claim_id}\`: ${claim.status} | ${claim.summary}${claim.why ? ` | ${claim.why}` : ''}`); + } + + lines.push('', '## Commands', ''); + lines.push(`- Problem surface: \`${doc.commands.problemShow}\``); + lines.push(`- Problem artifacts: \`${doc.commands.problemArtifacts}\``); + lines.push(`- Theorem loop: \`${doc.commands.theoremLoop}\``); + lines.push(`- Theorem refresh: \`${doc.commands.theoremLoopRefresh}\``); + lines.push(`- Claim loop: \`${doc.commands.claimLoop}\``); + lines.push(`- Claim refresh: \`${doc.commands.claimLoopRefresh}\``); + if (doc.commands.sourceRefresh) { + lines.push(`- Source refresh: \`${doc.commands.sourceRefresh}\``); + } + + lines.push('', '## Sources', ''); + for (const [label, value] of Object.entries(doc.sources ?? {})) { + if (!value) { + continue; + } + lines.push(`- ${label}: \`${value}\``); + } + lines.push(''); + return lines.join('\n'); +} + +export function getProblemClaimLoopSnapshot(problem) { + const doc = buildProblemClaimLoop(problem); + const paths = getProblemClaimLoopPaths(problem); + return { + ...doc, + claimLoopJsonPath: paths.claimLoopJsonPath, + claimLoopMarkdownPath: paths.claimLoopMarkdownPath, + claimLoopJsonPresent: Boolean(paths.claimLoopJsonPath && fs.existsSync(paths.claimLoopJsonPath)), + claimLoopMarkdownPresent: Boolean(paths.claimLoopMarkdownPath && fs.existsSync(paths.claimLoopMarkdownPath)), + }; +} + +function parseClosedIntegerRange(rangeText) { + const match = String(rangeText ?? '').trim().match(/^(\d+)\.\.(\d+)$/); + if (!match) { + return null; + } + return { + min: Number(match[1]), + max: Number(match[2]), + }; +} + +function getLatestVerifiedInterval(intervalQueue) { + const intervals = Array.isArray(intervalQueue?.intervals) ? intervalQueue.intervals : []; + const verified = intervals + .filter((interval) => interval.status === 'done' && interval.claim_level === 'verified') + .map((interval) => ({ + ...interval, + parsedRange: parseClosedIntegerRange(interval.range), + })) + .filter((interval) => interval.parsedRange); + + if (verified.length === 0) { + return null; + } + + verified.sort((left, right) => left.parsedRange.max - right.parsedRange.max); + return verified.at(-1); +} + +function buildHookAssessment(hook, bridgeHook, theoremLoop, bridgeDoc) { + const currentBridgeState = theoremLoop.currentBridgeState ?? {}; + const trackedTailMatrix = Array.isArray(bridgeDoc?.tracked_tail_matrix) ? bridgeDoc.tracked_tail_matrix : []; + const gpuLeaderboard = Array.isArray(bridgeDoc?.gpu_leaderboard) ? bridgeDoc.gpu_leaderboard : []; + const note = bridgeHook?.detail ?? hook.note ?? null; + + let verdict = hook.status === 'supported' ? 'supported' : 'unresolved'; + let evidenceClass = theoremLoop.currentBridgeState ? 'bridge_state' : 'pack_route_state'; + let theoremReady = false; + let rationale = note; + let nextAction = null; + + switch (hook.hook_id) { + case 'next_unmatched_equals_282_failure': { + const nextRepresentative = currentBridgeState.next_unmatched_representative; + const tail282 = trackedTailMatrix.find((entry) => entry.continuation === 282) ?? null; + const supported = Boolean( + currentBridgeState.next_unmatched_matches_282_failure + && nextRepresentative !== undefined + && tail282?.effective_first_failure === nextRepresentative, + ); + verdict = supported ? 'supported' : (nextRepresentative === undefined ? 'unresolved' : 'broken'); + evidenceClass = 'search_bridge_alignment'; + rationale = supported + ? `Shared-prefix representative ${nextRepresentative} matches tracked tail 282 first failure ${tail282.effective_first_failure}.` + : (note ?? 'The current bridge no longer certifies the 282-alignment claim.'); + nextAction = 'formalize_alignment_mechanism'; + break; + } + case 'completed_tail_vs_search_leader_split': { + const completed = currentBridgeState.strongest_completed_structured_tail?.continuation; + const leader = currentBridgeState.current_family_aware_leader?.continuation; + const supported = completed !== undefined && leader !== undefined && completed !== leader; + verdict = supported ? 'supported' : ((completed === undefined || leader === undefined) ? 'unresolved' : 'broken'); + evidenceClass = 'search_bridge_split'; + rationale = supported + ? `Completed structured tail ${completed} differs from family-aware leader ${leader} on the live bridge.` + : (note ?? 'The bridge does not currently show a meaningful completed-tail versus leader split.'); + nextAction = 'explain_search_leader_split'; + break; + } + case 'repair_pool_not_closed': { + const expansions = Array.isArray(currentBridgeState.recent_pool_expansion_moduli) + ? currentBridgeState.recent_pool_expansion_moduli + : []; + const supported = expansions.length > 0; + verdict = supported ? 'supported' : 'unresolved'; + evidenceClass = 'bridge_packet_growth'; + rationale = supported + ? `Recent bridge packets introduced new square moduli: ${expansions.join(', ')}.` + : (note ?? 'No recent pool-expansion evidence is frozen in the bridge right now.'); + nextAction = 'model_repair_pool_growth'; + break; + } + case 'top_repair_class_cluster': { + const tieClass = Array.isArray(currentBridgeState.top_gpu_tie_class) ? currentBridgeState.top_gpu_tie_class : []; + const rows = gpuLeaderboard.filter((row) => tieClass.includes(row.continuation)); + const supported = tieClass.length >= 2 + && rows.length === tieClass.length + && rows.every((row) => row.repaired_known_packets === rows[0].repaired_known_packets + && row.repaired_predicted_families === rows[0].repaired_predicted_families + && row.effective_clean_through === rows[0].effective_clean_through); + verdict = supported ? 'supported' : (tieClass.length === 0 ? 'unresolved' : 'broken'); + evidenceClass = 'gpu_leaderboard_cluster'; + rationale = supported + ? `Tie class ${tieClass.join(', ')} shares repaired-known=${rows[0].repaired_known_packets}, repaired-predicted=${rows[0].repaired_predicted_families}, clean-through=${rows[0].effective_clean_through}.` + : (note ?? 'The current leaderboard does not preserve a stable repair cluster.'); + nextAction = 'formalize_repair_cluster_mechanism'; + break; + } + case 'active_route_recorded': + verdict = theoremLoop.activeRoute ? 'supported' : 'unresolved'; + evidenceClass = 'route_state'; + nextAction = 'promote_route_claim'; + break; + case 'theorem_module_registered': + verdict = theoremLoop.theoremModule ? 'supported' : 'unresolved'; + evidenceClass = 'theorem_module'; + nextAction = 'stabilize_theorem_module_boundary'; + break; + case 'ready_atom_present': + verdict = (theoremLoop.theoremAgenda ?? []).some((item) => item.item_id === 'promote_ready_atom') ? 'supported' : 'unresolved'; + evidenceClass = 'ready_atom'; + nextAction = 'promote_ready_atom'; + break; + case 'frontier_note_present': + evidenceClass = 'frontier_note'; + nextAction = 'anchor_frontier_note'; + break; + case 'theorem_loop_seeded': + evidenceClass = 'theorem_loop'; + nextAction = 'seed_theorem_lane'; + break; + default: + break; + } + + return { + hook_id: hook.hook_id, + verdict, + status: hook.status ?? null, + evidenceClass, + theoremReady, + rationale: rationale ?? 'No further hook-specific rationale recorded yet.', + nextAction, + }; +} + +function buildClaimAssessment(problem, claim, theoremLoop, claimLoop, hookAssessments, bridgeDoc, intervalQueue) { + const currentBridgeState = theoremLoop.currentBridgeState ?? {}; + const trackedTailMatrix = Array.isArray(bridgeDoc?.tracked_tail_matrix) ? bridgeDoc.tracked_tail_matrix : []; + const gpuLeaderboard = Array.isArray(bridgeDoc?.gpu_leaderboard) ? bridgeDoc.gpu_leaderboard : []; + const latestVerifiedInterval = getLatestVerifiedInterval(intervalQueue); + const supportingHooks = Array.isArray(claim.support) ? claim.support : []; + const supportedSupportCount = hookAssessments.filter((item) => supportingHooks.includes(item.hook_id) && item.verdict === 'supported').length; + const allSupportingHooksSupported = supportingHooks.length > 0 && supportedSupportCount === supportingHooks.length; + + let verdict = claim.source === 'theorem_agenda' ? 'actionable' : 'unresolved'; + let evidenceClass = claim.source === 'search_bridge' ? 'search_bridge' : 'theorem_agenda'; + let theoremReady = false; + let rationale = claim.why ?? claim.summary; + let nextAction = null; + + if (claim.source === 'theorem_agenda') { + switch (claim.claim_id) { + case 'choose_next_finite_gap_move': + nextAction = latestVerifiedInterval + ? `decide_post_${latestVerifiedInterval.parsedRange.max}_verification_lane` + : 'choose_next_finite_gap_move'; + rationale = latestVerifiedInterval + ? `The current canonical exact base is ${latestVerifiedInterval.range}; the next interval is still open.` + : rationale; + break; + case 'explain_next_unmatched_alignment': + nextAction = 'formalize_alignment_mechanism'; + break; + case 'explain_completed_vs_search_leader_split': + nextAction = 'explain_search_leader_split'; + break; + case 'model_repair_pool_growth': + nextAction = 'model_repair_pool_growth'; + break; + case 'characterize_top_repair_cluster': + nextAction = 'formalize_repair_cluster_mechanism'; + break; + case 'promote_ready_atom': + nextAction = 'promote_ready_atom'; + break; + case 'stabilize_theorem_module_boundary': + nextAction = 'stabilize_theorem_module_boundary'; + break; + case 'tighten_active_route_claim': + nextAction = 'tighten_active_route_claim'; + break; + default: + nextAction = claim.claim_id; + break; + } + + return { + claim_id: claim.claim_id, + source: claim.source, + verdict, + evidenceClass, + theoremReady, + supportSatisfied: allSupportingHooksSupported, + summary: claim.summary, + rationale, + nextAction, + }; + } + + if (problem.problemId === '848' && claim.claim_id === 'p848_next_unmatched_alignment_claim') { + const nextRepresentative = currentBridgeState.next_unmatched_representative; + const tail282 = trackedTailMatrix.find((entry) => entry.continuation === 282) ?? null; + const supported = Boolean( + currentBridgeState.next_unmatched_matches_282_failure + && nextRepresentative !== undefined + && tail282?.effective_first_failure === nextRepresentative, + ); + verdict = supported ? 'supported' : (nextRepresentative === undefined ? 'unresolved' : 'broken'); + evidenceClass = 'search_bridge_alignment'; + rationale = supported + ? `The bridge matches shared-prefix representative ${nextRepresentative} with tracked tail 282 first failure ${tail282.effective_first_failure}.` + : 'The current bridge payload does not support the 282-alignment claim.'; + nextAction = 'formalize_alignment_mechanism'; + } else if (problem.problemId === '848' && claim.claim_id === 'p848_top_repair_cluster_claim') { + const tieClass = Array.isArray(currentBridgeState.top_gpu_tie_class) ? currentBridgeState.top_gpu_tie_class : []; + const rows = gpuLeaderboard.filter((row) => tieClass.includes(row.continuation)); + const supported = tieClass.length >= 2 + && rows.length === tieClass.length + && rows.every((row) => row.repaired_known_packets === rows[0].repaired_known_packets + && row.repaired_predicted_families === rows[0].repaired_predicted_families + && row.effective_clean_through === rows[0].effective_clean_through); + verdict = supported ? 'supported' : (tieClass.length === 0 ? 'unresolved' : 'broken'); + evidenceClass = 'gpu_leaderboard_cluster'; + rationale = supported + ? `Top cluster ${tieClass.join(', ')} shares repaired-known=${rows[0].repaired_known_packets}, repaired-predicted=${rows[0].repaired_predicted_families}, clean-through=${rows[0].effective_clean_through}.` + : 'The current leaderboard does not preserve a stable shared repair cluster.'; + nextAction = 'formalize_repair_cluster_mechanism'; + } + + return { + claim_id: claim.claim_id, + source: claim.source, + verdict, + evidenceClass, + theoremReady, + supportSatisfied: allSupportingHooksSupported, + summary: claim.summary, + rationale, + nextAction, + }; +} + +function buildClaimPassRecommendations(problem, theoremLoop, claimAssessments, hookAssessments, intervalQueue) { + const recommendations = []; + const latestVerifiedInterval = getLatestVerifiedInterval(intervalQueue); + + const addRecommendation = (recommendation) => { + if (!recommendations.some((item) => item.recommendation_id === recommendation.recommendation_id)) { + recommendations.push(recommendation); + } + }; + + const supportedClaims = claimAssessments.filter((claim) => claim.verdict === 'supported'); + + for (const claim of supportedClaims) { + if (claim.claim_id === 'p848_next_unmatched_alignment_claim') { + addRecommendation({ + recommendation_id: 'formalize_282_alignment', + priority: 'high', + lane: 'theorem_formalization', + reason: claim.rationale, + command: `erdos problem formalization ${problem.problemId}`, + }); + } + if (claim.claim_id === 'p848_top_repair_cluster_claim') { + addRecommendation({ + recommendation_id: 'formalize_top_repair_cluster', + priority: 'high', + lane: 'theorem_formalization', + reason: claim.rationale, + command: `erdos problem formalization ${problem.problemId}`, + }); + } + } + + if (problem.problemId === '848' && latestVerifiedInterval) { + addRecommendation({ + recommendation_id: `decide_post_${latestVerifiedInterval.parsedRange.max}_verification_lane`, + priority: 'high', + lane: 'exact_verifier', + reason: `The canonical exact base currently ends at ${latestVerifiedInterval.range}. The next verification move is still open.`, + command: `erdos number-theory dispatch ${problem.problemId}`, + }); + } + + if (recommendations.length === 0) { + const actionableClaim = claimAssessments.find((claim) => claim.verdict === 'actionable'); + if (actionableClaim) { + addRecommendation({ + recommendation_id: actionableClaim.nextAction ?? actionableClaim.claim_id, + priority: 'medium', + lane: actionableClaim.source === 'theorem_agenda' ? 'theorem_formalization' : 'claim_followup', + reason: actionableClaim.rationale, + command: actionableClaim.source === 'theorem_agenda' + ? `erdos problem formalization ${problem.problemId}` + : `erdos problem claim-pass ${problem.problemId}`, + }); + } + } + + for (const hook of hookAssessments) { + if (hook.hook_id === 'repair_pool_not_closed' && hook.verdict === 'supported') { + addRecommendation({ + recommendation_id: 'model_repair_pool_growth', + priority: 'medium', + lane: 'theorem_formalization', + reason: hook.rationale, + command: `erdos problem formalization ${problem.problemId}`, + }); + } + } + + return recommendations; +} + +function buildClaimPassSummary(hookAssessments, claimAssessments) { + const summarize = (items) => ({ + total: items.length, + supported: items.filter((item) => item.verdict === 'supported').length, + actionable: items.filter((item) => item.verdict === 'actionable').length, + unresolved: items.filter((item) => item.verdict === 'unresolved').length, + broken: items.filter((item) => item.verdict === 'broken').length, + }); + + return { + hooks: summarize(hookAssessments), + claims: summarize(claimAssessments), + }; +} + +function titleCaseWords(text) { + return String(text ?? '') + .split(/[_\s-]+/) + .filter(Boolean) + .map((word) => word.charAt(0).toUpperCase() + word.slice(1)) + .join(' '); +} + +function positiveMod(value, modulus) { + const remainder = Number(value) % Number(modulus); + return remainder < 0 ? remainder + Number(modulus) : remainder; +} + +function gcdInt(left, right) { + let a = Math.abs(Number(left)); + let b = Math.abs(Number(right)); + while (b !== 0) { + const next = a % b; + a = b; + b = next; + } + return a; +} + +function extendedGcdInt(left, right) { + let oldR = Number(left); + let r = Number(right); + let oldS = 1; + let s = 0; + let oldT = 0; + let t = 1; + + while (r !== 0) { + const quotient = Math.trunc(oldR / r); + [oldR, r] = [r, oldR - quotient * r]; + [oldS, s] = [s, oldS - quotient * s]; + [oldT, t] = [t, oldT - quotient * t]; + } + + return { + gcd: oldR, + x: oldS, + y: oldT, + }; +} + +function modularInverseInt(value, modulus) { + const reduced = positiveMod(value, modulus); + const result = extendedGcdInt(reduced, modulus); + if (Math.abs(result.gcd) !== 1) { + return null; + } + return positiveMod(result.x, modulus); +} + +function solveLinearCongruenceNonnegative(coeff, rhs, modulus) { + const safeModulus = Number(modulus); + if (!Number.isInteger(safeModulus) || safeModulus <= 0) { + return null; + } + + const reducedCoeff = positiveMod(coeff, safeModulus); + const reducedRhs = positiveMod(rhs, safeModulus); + const divisor = gcdInt(reducedCoeff, safeModulus); + if (reducedRhs % divisor !== 0) { + return { + solvable: false, + gcdCoeffModulus: divisor, + solution: null, + period: null, + }; + } + + const coeffQuotient = reducedCoeff / divisor; + const rhsQuotient = reducedRhs / divisor; + const modulusQuotient = safeModulus / divisor; + const inverse = modularInverseInt(coeffQuotient, modulusQuotient); + if (inverse === null) { + return { + solvable: false, + gcdCoeffModulus: divisor, + solution: null, + period: null, + }; + } + + return { + solvable: true, + gcdCoeffModulus: divisor, + solution: positiveMod(inverse * rhsQuotient, modulusQuotient), + period: modulusQuotient, + }; +} + +function positiveModBigInt(value, modulus) { + const bigValue = BigInt(value); + const bigModulus = BigInt(modulus); + let remainder = bigValue % bigModulus; + if (remainder < 0n) { + remainder += bigModulus; + } + return remainder; +} + +function extendedGcdBigInt(left, right) { + let oldR = BigInt(left); + let r = BigInt(right); + let oldS = 1n; + let s = 0n; + let oldT = 0n; + let t = 1n; + + while (r !== 0n) { + const quotient = oldR / r; + [oldR, r] = [r, oldR - quotient * r]; + [oldS, s] = [s, oldS - quotient * s]; + [oldT, t] = [t, oldT - quotient * t]; + } + + return { + gcd: oldR, + x: oldS, + y: oldT, + }; +} + +function modularInverseBigInt(value, modulus) { + const reduced = positiveModBigInt(value, modulus); + const result = extendedGcdBigInt(reduced, modulus); + if (result.gcd !== 1n && result.gcd !== -1n) { + return null; + } + return positiveModBigInt(result.x, modulus); +} + +function toJsonInteger(value) { + if (typeof value !== 'bigint') { + return value; + } + const asNumber = Number(value); + return Number.isSafeInteger(asNumber) ? asNumber : value.toString(); +} + +function deriveTupleRowCrt(tupleRows, witnessSquareModulus) { + if (!Array.isArray(tupleRows) || tupleRows.length === 0) { + return null; + } + + let residue = 0n; + let modulus = 1n; + const steps = []; + const witness = witnessSquareModulus === null || witnessSquareModulus === undefined + ? null + : BigInt(witnessSquareModulus); + + for (const row of tupleRows) { + const rowModulus = BigInt(row.squareModulus); + const rowResidue = BigInt(row.residue); + const inverse = modularInverseBigInt(modulus, rowModulus); + if (inverse === null) { + return null; + } + const stepFactor = positiveModBigInt((rowResidue - residue) * inverse, rowModulus); + const preCombinedResidue = residue; + const preCombinedModulus = modulus; + residue = residue + modulus * stepFactor; + modulus *= rowModulus; + residue = positiveModBigInt(residue, modulus); + steps.push({ + anchor: row.anchor, + rowSquareModulus: row.squareModulus, + rowResidue: row.residue, + preCombinedResidue: toJsonInteger(preCombinedResidue), + preCombinedModulus: toJsonInteger(preCombinedModulus), + liftParameter: toJsonInteger(stepFactor), + combinedResidue: toJsonInteger(residue), + combinedModulus: toJsonInteger(modulus), + residueModWitness: witness === null ? null : toJsonInteger(positiveModBigInt(residue, witness)), + }); + } + + const finalProjectedResidue = witness === null ? null : toJsonInteger(positiveModBigInt(residue, witness)); + const firstStableProjectionStep = witness === null + ? null + : (() => { + const finalResidue = positiveModBigInt(residue, witness); + for (let index = 0; index < steps.length; index += 1) { + const suffixStable = steps.slice(index).every((step) => BigInt(step.residueModWitness) === finalResidue); + if (suffixStable) { + return steps[index].anchor; + } + } + return null; + })(); + + return { + combinedResidue: toJsonInteger(residue), + combinedModulus: toJsonInteger(modulus), + projectedResidueModuloWitness: finalProjectedResidue, + firstStableProjectionAnchor: firstStableProjectionStep, + steps, + }; +} + +function getRequiredFailureResidue(anchor, witnessSquareModulus) { + if (!witnessSquareModulus || gcdInt(anchor, witnessSquareModulus) !== 1) { + return null; + } + const inverse = modularInverseInt(anchor, witnessSquareModulus); + return inverse === null ? null : positiveMod(-inverse, witnessSquareModulus); +} + +function deriveTupleRowActivationSequence(tupleRows, repairRows, witnessSquareModulus) { + const tupleRowCrtDerivation = deriveTupleRowCrt(tupleRows, witnessSquareModulus); + if (!tupleRowCrtDerivation || !witnessSquareModulus) { + return []; + } + + const trackedFailureResidues = (Array.isArray(repairRows) ? repairRows : []).map((row) => ({ + anchor: row.anchor, + requiredNResidueForFailure: getRequiredFailureResidue(row.anchor, witnessSquareModulus), + })); + + return tupleRowCrtDerivation.steps.map((step) => { + const matchingTrackedAnchors = trackedFailureResidues + .filter((row) => row.requiredNResidueForFailure !== null && row.requiredNResidueForFailure === Number(step.residueModWitness)) + .map((row) => row.anchor); + return { + anchor: step.anchor, + residueModWitness: Number(step.residueModWitness), + matchingTrackedAnchors, + uniqueTrackedMatch: matchingTrackedAnchors.length === 1 ? matchingTrackedAnchors[0] : null, + }; + }); +} + +function summarizeP848MenuActivationPatterns(allFamilies) { + const rows = []; + + for (const [familyIndex, family] of (Array.isArray(allFamilies) ? allFamilies : []).entries()) { + const repairRows = Array.isArray(family?.repairRows) ? family.repairRows : []; + for (const repairRow of repairRows) { + if (repairRow?.squarefree !== false || !Array.isArray(repairRow.squareWitnesses)) { + continue; + } + for (const witness of repairRow.squareWitnesses) { + const witnessSquareModulus = witness?.squareModulus ?? null; + const activationSequence = deriveTupleRowActivationSequence( + Array.isArray(family?.tupleRows) ? family.tupleRows : [], + repairRows, + witnessSquareModulus, + ); + const firstMatch = activationSequence.find((step) => step.matchingTrackedAnchors.length > 0) ?? null; + rows.push({ + familyIndex, + representative: family?.representative ?? null, + tupleKey: family?.tupleKey ?? null, + failingAnchor: repairRow.anchor, + witnessSquareModulus, + firstMatchAnchor: firstMatch?.anchor ?? null, + firstMatchTrackedAnchors: firstMatch?.matchingTrackedAnchors ?? [], + firstMatchUniqueTrackedAnchor: firstMatch?.uniqueTrackedMatch ?? null, + firstMatchIsFailingAnchor: firstMatch?.uniqueTrackedMatch === repairRow.anchor, + activationSequence, + }); + } + } + } + + const countBy = (key) => rows.reduce((accumulator, row) => { + const value = row[key] ?? 'none'; + accumulator[value] = (accumulator[value] ?? 0) + 1; + return accumulator; + }, {}); + const rowsWith132TargetActivation = rows.filter((row) => row.firstMatchAnchor === 132 && row.firstMatchIsFailingAnchor); + + return { + totalFailingWitnessRows: rows.length, + firstMatchAnchorCounts: countBy('firstMatchAnchor'), + targetAtFirstMatchCount: rows.filter((row) => row.firstMatchIsFailingAnchor).length, + rowsWith132TargetActivationCount: rowsWith132TargetActivation.length, + rowsWith132TargetActivationByFailingAnchor: rowsWith132TargetActivation.reduce((accumulator, row) => { + accumulator[row.failingAnchor] = (accumulator[row.failingAnchor] ?? 0) + 1; + return accumulator; + }, {}), + rowsWith132TargetActivationByWitness: rowsWith132TargetActivation.reduce((accumulator, row) => { + accumulator[row.witnessSquareModulus] = (accumulator[row.witnessSquareModulus] ?? 0) + 1; + return accumulator; + }, {}), + targetActivationRows: rowsWith132TargetActivation.map((row) => ({ + familyIndex: row.familyIndex, + representative: row.representative, + failingAnchor: row.failingAnchor, + witnessSquareModulus: row.witnessSquareModulus, + firstMatchAnchor: row.firstMatchAnchor, + firstMatchTrackedAnchors: row.firstMatchTrackedAnchors, + tupleKey: row.tupleKey, + activationSequence: row.activationSequence.map((step) => ({ + anchor: step.anchor, + residueModWitness: step.residueModWitness, + matchingTrackedAnchors: step.matchingTrackedAnchors, + uniqueTrackedMatch: step.uniqueTrackedMatch, + })), + })), + examples: rowsWith132TargetActivation.slice(0, 8).map((row) => ({ + familyIndex: row.familyIndex, + representative: row.representative, + failingAnchor: row.failingAnchor, + witnessSquareModulus: row.witnessSquareModulus, + tupleKey: row.tupleKey, + activationSequence: row.activationSequence.map((step) => ({ + anchor: step.anchor, + residueModWitness: step.residueModWitness, + matchingTrackedAnchors: step.matchingTrackedAnchors, + })), + })), + }; +} + +function buildP848ActivationLemmaSchema({ + menuActivationSurvey, + tupleRowActivationBoundary, + tupleRowActivationSequence, + representative, + tupleKey, + witnessSquareModulus, + representativeResidueModuloWitness, + familyMenuPath, +}) { + const certifiedRows = Array.isArray(menuActivationSurvey?.targetActivationRows) + ? menuActivationSurvey.targetActivationRows + : []; + if (certifiedRows.length === 0) { + return null; + } + + const activatedAnchors = Object.keys(menuActivationSurvey.rowsWith132TargetActivationByFailingAnchor ?? {}) + .map((value) => Number(value)) + .filter((value) => Number.isFinite(value)) + .sort((left, right) => left - right); + const witnessSquareModuli = Object.keys(menuActivationSurvey.rowsWith132TargetActivationByWitness ?? {}) + .map((value) => Number(value)) + .filter((value) => Number.isFinite(value)) + .sort((left, right) => left - right); + + return { + schemaId: 'p848_finite_menu_132_target_activation_schema_v1', + status: 'finite_menu_schema_ready', + scope: { + problemId: '848', + evidenceSurface: 'current_finite_family_menu', + universalClaim: false, + certifiedRowCount: certifiedRows.length, + totalFailingWitnessRows: menuActivationSurvey.totalFailingWitnessRows, + activatedTrackedAnchors: activatedAnchors, + witnessSquareModuli, + familyMenuPath, + }, + informalStatement: 'For each certified finite-menu witness row in this packet, the tuple-row CRT projection has no tracked failure-residue match before anchor 132; anchor 132 is the first step whose projected residue matches the failing tracked tail; anchor 182 preserves that match on the current six-row menu.', + hypotheses: [ + { + hypothesisId: 'H1_finite_menu_row', + text: 'The row is one of the current finite family-menu rows with a tracked repair anchor a and square witness q^2 for a*n+1.', + }, + { + hypothesisId: 'H2_tuple_crt_projection', + text: 'The tuple rows are replayed in anchor order, and each CRT prefix is projected modulo the same witness q^2.', + }, + { + hypothesisId: 'H3_failure_residue_formula', + text: 'For every tracked anchor b coprime to q^2, the witness failure residue is n = -b^{-1} mod q^2; non-coprime anchors are marked unsolvable for that witness.', + }, + { + hypothesisId: 'H4_pre_132_clear', + text: 'No tuple-row CRT prefix before anchor 132 lands on any tracked witness-failure residue modulo q^2.', + }, + { + hypothesisId: 'H5_132_unique_target_activation', + text: 'The anchor-132 CRT prefix lands on exactly one tracked witness-failure residue, and that tracked anchor is the failing repair anchor a.', + }, + { + hypothesisId: 'H6_182_preservation', + text: 'The anchor-182 CRT prefix preserves the same unique tracked witness-failure match and does not activate a competing tracked anchor.', + }, + ], + conclusion: { + text: 'Inside the current finite family menu, the row has a controlled 132 target-activation certificate rather than an unexplained one-row coincidence.', + outputs: [ + 'firstTrackedActivationAnchor = 132', + 'firstTrackedActivationAnchorMatchesFailingAnchor = true', + 'anchor182PreservesTargetActivation = true', + ], + }, + falsifierBoundary: [ + { + falsifierId: 'pre_132_tracked_match', + text: 'A replayed row has a tracked witness-failure residue match at anchor 7, 32, 57, or 82.', + }, + { + falsifierId: 'wrong_132_target', + text: 'Anchor 132 activates no tracked anchor, multiple tracked anchors, or a tracked anchor different from the failing repair anchor.', + }, + { + falsifierId: 'lost_182_preservation', + text: 'Anchor 182 changes the projection so the target activation is no longer the unique tracked match.', + }, + { + falsifierId: 'menu_refresh_breaks_certificate', + text: 'A refreshed finite menu changes the witness rows, tuple rows, or repair rows so the 17 row certificates no longer replay.', + }, + { + falsifierId: 'scope_overclaim', + text: 'The schema is used as a universal theorem without first proving the symbolic CRT hypotheses beyond the current finite menu.', + }, + ], + currentBoundaryInstance: { + representative, + tupleKey, + failingAnchor: 282, + witnessSquareModulus, + representativeResidueModuloWitness, + activationBoundary: tupleRowActivationBoundary, + activationSequence: tupleRowActivationSequence, + }, + rowCertificates: certifiedRows, + nextProofObligations: [ + 'Replay the 17 row certificates from tuple-row CRT equations in a dedicated checker rather than trusting the summarized packet data.', + 'Decide whether the schema can be lifted from the current finite menu to a symbolic CRT lemma for a reusable obstruction family.', + 'Keep the finite-menu scope explicit until the symbolic lift is proved.', + ], + }; +} + +function checkP848ActivationLemmaCertificates(allFamilies, familyMenuPath) { + const survey = summarizeP848MenuActivationPatterns(allFamilies); + const certifiedRows = Array.isArray(survey.targetActivationRows) ? survey.targetActivationRows : []; + const rowChecks = certifiedRows.map((row) => { + const activationSequence = Array.isArray(row.activationSequence) ? row.activationSequence : []; + const pre132Steps = activationSequence.filter((step) => Number(step.anchor) < 132); + const step132 = activationSequence.find((step) => Number(step.anchor) === 132) ?? null; + const step182 = activationSequence.find((step) => Number(step.anchor) === 182) ?? null; + const firstTrackedMatch = activationSequence.find((step) => ( + Array.isArray(step.matchingTrackedAnchors) && step.matchingTrackedAnchors.length > 0 + )) ?? null; + const pre132HasNoTrackedMatch = pre132Steps.every((step) => ( + Array.isArray(step.matchingTrackedAnchors) && step.matchingTrackedAnchors.length === 0 + )); + const firstMatchIs132 = Number(firstTrackedMatch?.anchor) === 132; + const activation132MatchesOnlyFailingAnchor = Array.isArray(step132?.matchingTrackedAnchors) + && step132.matchingTrackedAnchors.length === 1 + && Number(step132.matchingTrackedAnchors[0]) === Number(row.failingAnchor); + const preservation182KeepsOnlyFailingAnchor = Array.isArray(step182?.matchingTrackedAnchors) + && step182.matchingTrackedAnchors.length === 1 + && Number(step182.matchingTrackedAnchors[0]) === Number(row.failingAnchor); + const falsifierFlags = [ + pre132HasNoTrackedMatch ? null : 'pre_132_tracked_match', + firstMatchIs132 ? null : 'first_tracked_match_not_132', + activation132MatchesOnlyFailingAnchor ? null : 'wrong_132_target', + preservation182KeepsOnlyFailingAnchor ? null : 'lost_182_preservation', + ].filter(Boolean); + + return { + familyIndex: row.familyIndex, + representative: row.representative, + tupleKey: row.tupleKey, + failingAnchor: row.failingAnchor, + witnessSquareModulus: row.witnessSquareModulus, + firstTrackedMatchAnchor: firstTrackedMatch?.anchor ?? null, + firstTrackedMatchAnchors: firstTrackedMatch?.matchingTrackedAnchors ?? [], + pre132HasNoTrackedMatch, + activation132MatchesOnlyFailingAnchor, + preservation182KeepsOnlyFailingAnchor, + status: falsifierFlags.length === 0 ? 'passed' : 'failed', + falsifierFlags, + }; + }); + const failures = rowChecks.filter((row) => row.status !== 'passed'); + + return { + checkerId: 'p848_132_activation_row_certificate_checker_v1', + source: 'raw_family_menu_tuple_row_crt_replay', + familyMenuPath, + status: failures.length === 0 && rowChecks.length > 0 ? 'passed' : 'failed', + checkedRowCount: rowChecks.length, + passCount: rowChecks.length - failures.length, + failCount: failures.length, + expectedShape: { + firstTrackedMatchAnchor: 132, + pre132HasNoTrackedMatch: true, + anchor132UniqueTarget: true, + anchor182PreservesUniqueTarget: true, + }, + surveyCounts: { + totalFailingWitnessRows: survey.totalFailingWitnessRows, + rowsWith132TargetActivationCount: survey.rowsWith132TargetActivationCount, + rowsWith132TargetActivationByFailingAnchor: survey.rowsWith132TargetActivationByFailingAnchor, + rowsWith132TargetActivationByWitness: survey.rowsWith132TargetActivationByWitness, + }, + failures, + ...(rowChecks.length <= 100 + ? { rowChecks } + : { + rowCheckSample: tightestRows, + rowChecksOmitted: rowChecks.length - tightestRows.length, + }), + }; +} + +function buildP848ActivationSymbolicLiftCandidate({ + activationLemmaSchema, + activationLemmaCheck, + tupleRowLift132Proof, + witnessSquareModulus, +}) { + const rowCertificates = Array.isArray(activationLemmaSchema?.rowCertificates) + ? activationLemmaSchema.rowCertificates + : []; + if (!activationLemmaSchema || rowCertificates.length === 0) { + return null; + } + + const anchorOrder = [7, 32, 57, 82, 132, 182]; + const trackedAnchors = [157, 232, 282, 332, 382, 432, 782, 832]; + const rowSummaries = rowCertificates.map((row) => { + const activationSequence = Array.isArray(row.activationSequence) ? row.activationSequence : []; + const stepByAnchor = Object.fromEntries(activationSequence.map((step) => [Number(step.anchor), step])); + const pre132Residues = anchorOrder + .filter((anchor) => anchor < 132) + .map((anchor) => ({ + anchor, + residueModWitness: stepByAnchor[anchor]?.residueModWitness ?? null, + matchingTrackedAnchors: stepByAnchor[anchor]?.matchingTrackedAnchors ?? [], + })); + const step132 = stepByAnchor[132] ?? null; + const step182 = stepByAnchor[182] ?? null; + return { + familyIndex: row.familyIndex, + representative: row.representative, + tupleKey: row.tupleKey, + failingAnchor: row.failingAnchor, + witnessSquareModulus: row.witnessSquareModulus, + pre132Residues, + residueAt132: step132?.residueModWitness ?? null, + uniqueTrackedMatchAt132: step132?.uniqueTrackedMatch ?? null, + residueAt182: step182?.residueModWitness ?? null, + uniqueTrackedMatchAt182: step182?.uniqueTrackedMatch ?? null, + }; + }); + const candidateChecks = rowSummaries.map((row) => { + const pre132Clear = row.pre132Residues.every((step) => ( + Array.isArray(step.matchingTrackedAnchors) && step.matchingTrackedAnchors.length === 0 + )); + const targetAt132 = Number(row.uniqueTrackedMatchAt132) === Number(row.failingAnchor); + const preservedAt182 = Number(row.uniqueTrackedMatchAt182) === Number(row.failingAnchor) + && row.residueAt182 === row.residueAt132; + const failedChecks = [ + pre132Clear ? null : 'pre_132_clear_symbolic_hypothesis_not_observed', + targetAt132 ? null : 'target_activation_symbolic_hypothesis_not_observed', + preservedAt182 ? null : 'preservation_symbolic_hypothesis_not_observed', + ].filter(Boolean); + return { + familyIndex: row.familyIndex, + failingAnchor: row.failingAnchor, + witnessSquareModulus: row.witnessSquareModulus, + status: failedChecks.length === 0 ? 'passed' : 'failed', + failedChecks, + }; + }); + const failures = candidateChecks.filter((row) => row.status !== 'passed'); + const activationCheckerPassed = activationLemmaCheck?.status === 'passed'; + const liftCheckerPassed = tupleRowLift132Proof?.status === 'proved_from_tuple_row_crt'; + const status = activationCheckerPassed && liftCheckerPassed && failures.length === 0 + ? 'symbolic_crt_hypothesis_packet_ready' + : 'blocked'; + + return { + candidateId: 'p848_132_activation_symbolic_lift_candidate_v1', + checkerId: 'p848_132_activation_symbolic_lift_candidate_checker_v1', + source: 'finite_menu_certificate_to_symbolic_crt_hypotheses', + status, + checkedRowCount: candidateChecks.length, + passCount: candidateChecks.length - failures.length, + failCount: failures.length + (activationCheckerPassed ? 0 : 1) + (liftCheckerPassed ? 0 : 1), + failedRows: failures, + scope: { + problemId: '848', + universalClaim: false, + candidateOnly: true, + finiteCertificateRows: rowCertificates.length, + boundaryWitnessSquareModulus: witnessSquareModulus ?? null, + }, + parameterization: { + anchorOrder, + trackedAnchors, + variables: [ + 'Q: square witness modulus q^2', + 'a: failing tracked repair anchor', + 'M_i: square modulus introduced by tuple anchor i', + 'r_i: tuple-row residue introduced by tuple anchor i', + 'N_i: CRT prefix residue after anchors up to i', + 'R_b(Q): tracked failure residue -b^{-1} mod Q when gcd(b, Q) = 1', + ], + crtPrefixRecurrence: 'N_i is the unique residue modulo lcm(M_7,...,M_i) satisfying all tuple rows through anchor i.', + failureResidueFormula: 'R_b(Q) = -b^{-1} mod Q for gcd(b,Q)=1; if gcd(b,Q)>1, b cannot supply a residue class modulo Q unless the divisibility condition is satisfied.', + }, + symbolicHypotheses: [ + { + hypothesisId: 'S1_pairwise_crt_compatibility', + text: 'The tuple-row moduli through anchors 7, 32, 57, 82, 132, 182 are CRT-compatible and define prefixes N_i.', + }, + { + hypothesisId: 'S2_same_witness_projection', + text: 'Every prefix N_i is projected modulo the same square witness Q attached to the failing repair row a*n+1.', + }, + { + hypothesisId: 'S3_pre_132_clear', + text: 'For i in {7,32,57,82}, N_i is not congruent to R_b(Q) for any tracked anchor b whose failure residue is defined.', + }, + { + hypothesisId: 'S4_anchor_132_unique_target', + text: 'N_132 is congruent to R_a(Q), and N_132 is not congruent to R_b(Q) for every tracked b != a whose failure residue is defined.', + }, + { + hypothesisId: 'S5_anchor_182_preserves_target', + text: 'N_182 is congruent to N_132 modulo Q, so the target activation survives the final shared-prefix anchor.', + }, + { + hypothesisId: 'S6_no_scope_promotion_without_domain_closure', + text: 'A problem-level theorem may use this packet only after a separate domain-closure lemma proves S1-S5 for the intended family, not merely for the current finite menu.', + }, + ], + symbolicConclusion: { + text: 'Any row satisfying S1-S5 has first tracked failure-residue activation at anchor 132, uniquely activates the failing anchor a, and preserves that activation at anchor 182.', + proofSketch: [ + 'S3 rules out every tracked activation before anchor 132.', + 'S4 makes anchor 132 a unique activation of the target failing anchor.', + 'S5 carries the same witness-residue class through anchor 182 without adding a competing tracked match.', + ], + }, + finiteEvidence: { + activationCheckerId: activationLemmaCheck?.checkerId ?? null, + activationCheckerStatus: activationLemmaCheck?.status ?? null, + activationCheckedRows: activationLemmaCheck?.checkedRowCount ?? null, + liftCheckerId: tupleRowLift132Proof?.checkerId ?? null, + liftCheckerStatus: tupleRowLift132Proof?.status ?? null, + boundaryLiftEquation: tupleRowLift132Proof?.reducedEquation ?? null, + boundaryLiftParameter: tupleRowLift132Proof?.liftParameter ?? null, + rowSummaries, + candidateChecks, + }, + nextProofObligations: [ + 'Prove a domain-closure lemma that supplies S1-S5 for a reusable class of tuple rows instead of only the 17 current finite-menu rows.', + 'Decide whether the domain-closure class should be the 282 obstruction family, the full 132-activation survey, or the stricter 782-vs-1232 exchange family.', + 'Connect the symbolic activation packet to the finite-gap verifier boundary so it narrows the post-11300 exact work rather than becoming an isolated lemma.', + ], + }; +} + +function buildP848ActivationDomainClosureAssessment(activationSymbolicLiftCandidate, topRepairSeparationAnalysis) { + const rowSummaries = Array.isArray(activationSymbolicLiftCandidate?.finiteEvidence?.rowSummaries) + ? activationSymbolicLiftCandidate.finiteEvidence.rowSummaries + : []; + if (rowSummaries.length === 0) { + return null; + } + + const groupRowsBy = (keyFn) => rowSummaries.reduce((accumulator, row) => { + const key = keyFn(row); + accumulator[key] = accumulator[key] ?? []; + accumulator[key].push(row); + return accumulator; + }, {}); + const byFailingAnchor = groupRowsBy((row) => String(row.failingAnchor)); + const byWitness = groupRowsBy((row) => String(row.witnessSquareModulus)); + const byAnchorWitness = groupRowsBy((row) => `${row.failingAnchor}/${row.witnessSquareModulus}`); + const repeatedAnchorWitnessGroups = Object.entries(byAnchorWitness) + .filter(([, rows]) => rows.length > 1) + .map(([key, rows]) => { + const [failingAnchor, witnessSquareModulus] = key.split('/').map((value) => Number(value)); + return { + groupId: `anchor_${failingAnchor}_witness_${witnessSquareModulus}`, + failingAnchor, + witnessSquareModulus, + rowCount: rows.length, + familyIndices: rows.map((row) => row.familyIndex), + representatives: [...new Set(rows.map((row) => row.representative))], + tupleKeys: [...new Set(rows.map((row) => row.tupleKey))], + }; + }) + .sort((left, right) => right.rowCount - left.rowCount || left.failingAnchor - right.failingAnchor); + const strict782Vs1232 = (Array.isArray(topRepairSeparationAnalysis?.strictDominancePairs) + ? topRepairSeparationAnalysis.strictDominancePairs + : []).find((row) => Number(row.topContinuation) === 782 && Number(row.contrastContinuation) === 1232) ?? null; + const firstRepeatedAnchorWitness = repeatedAnchorWitnessGroups[0] ?? null; + const recommendedClosureLane = firstRepeatedAnchorWitness + ? { + laneId: 'repeat_anchor_witness_activation_family', + targetGroupId: firstRepeatedAnchorWitness.groupId, + why: `This is the largest repeated symbolic-activation class in the 17-row survey: anchor ${firstRepeatedAnchorWitness.failingAnchor} with witness ${firstRepeatedAnchorWitness.witnessSquareModulus} appears ${firstRepeatedAnchorWitness.rowCount} times.`, + } + : { + laneId: 'single_boundary_instance_closure', + targetGroupId: 'anchor_282_witness_841', + why: 'No repeated anchor/witness group exists, so the only honest domain closure is the single 282/841 boundary instance.', + }; + + return { + assessmentId: 'p848_132_activation_domain_closure_assessment_v1', + status: Object.keys(byFailingAnchor).length > 1 && Object.keys(byWitness).length > 1 + ? 'broad_domain_closure_not_supported_yet' + : 'single_domain_candidate', + checkedRowCount: rowSummaries.length, + failCount: 0, + broadClosureVerdict: { + verdict: 'do_not_promote_broad_17_row_survey_to_universal_domain', + reason: `The finite symbolic-lift survey splits across ${Object.keys(byFailingAnchor).length} failing anchors and ${Object.keys(byWitness).length} witness moduli, so the current evidence supports parameterized hypotheses but not one broad domain theorem.`, + failingAnchorCounts: Object.fromEntries(Object.entries(byFailingAnchor).map(([key, rows]) => [key, rows.length])), + witnessCounts: Object.fromEntries(Object.entries(byWitness).map(([key, rows]) => [key, rows.length])), + }, + repeatedAnchorWitnessGroups, + narrowedClosureCandidates: [ + { + candidateId: 'p848_282_841_boundary_instance_closure', + priority: 'high', + rowCount: rowSummaries.filter((row) => row.failingAnchor === 282 && row.witnessSquareModulus === 841).length, + task: 'Prove the 282/841 boundary instance from the explicit CRT equations and keep it scoped as the current obstruction packet.', + tradeoff: 'Best alignment with the 282 north star, but currently only a single finite-menu row.', + }, + firstRepeatedAnchorWitness + ? { + candidateId: `p848_${firstRepeatedAnchorWitness.failingAnchor}_${firstRepeatedAnchorWitness.witnessSquareModulus}_repeated_activation_family`, + priority: 'high', + rowCount: firstRepeatedAnchorWitness.rowCount, + task: `Try to prove a reusable closure lemma for anchor ${firstRepeatedAnchorWitness.failingAnchor} with witness ${firstRepeatedAnchorWitness.witnessSquareModulus}.`, + tradeoff: 'Best repeated symbolic-lift family in the current activation survey, but it may be less directly tied to the 282 alignment.', + } + : null, + strict782Vs1232 + ? { + candidateId: 'p848_782_1232_strict_exchange_closure', + priority: 'high', + rowCount: strict782Vs1232.repairedByTopMissedByContrast.length, + task: 'Use the strict 782 > 1232 exchange rows as a small theorem-facing family for the mod-50 lane closure.', + tradeoff: 'Best bridge to the top repair-class mechanism, but it is a top-cluster theorem lane rather than the 132 activation lane itself.', + } + : null, + ].filter(Boolean), + recommendedClosureLane, + nextProofObligations: [ + 'Do not claim a universal 17-row domain theorem until a single structural family supplies S1-S5.', + `Start with ${recommendedClosureLane.targetGroupId} and prove or falsify its CRT-domain closure.`, + 'After one narrow closure lane is proved, decide whether it genuinely reduces the finite gap or only explains a search-side feature.', + ], + }; +} + +function parseP848AnchorWitnessGroupId(groupId) { + const match = /^anchor_(\d+)_witness_(\d+)$/.exec(String(groupId ?? '')); + if (!match) { + return null; + } + return { + failingAnchor: Number(match[1]), + witnessSquareModulus: Number(match[2]), + }; +} + +function getP848Pre132ProfileId(pre132Residues) { + return `pre132_${(Array.isArray(pre132Residues) ? pre132Residues : []) + .map((step) => `${step.anchor}_${step.residueModWitness}`) + .join('_')}`; +} + +function summarizeP848Pre132Profile(pre132Residues) { + return (Array.isArray(pre132Residues) ? pre132Residues : []) + .map((step) => `${step.anchor}->${step.residueModWitness}`) + .join(', '); +} + +function buildP848AnchorWitnessDomainClosurePacket({ + activationDomainClosureAssessment, + allFamilies, + familyMenuPath, +}) { + const targetGroupId = activationDomainClosureAssessment?.recommendedClosureLane?.targetGroupId ?? null; + const parsedTarget = parseP848AnchorWitnessGroupId(targetGroupId); + if (!parsedTarget) { + return null; + } + + const { failingAnchor, witnessSquareModulus } = parsedTarget; + const targetGroup = (Array.isArray(activationDomainClosureAssessment?.repeatedAnchorWitnessGroups) + ? activationDomainClosureAssessment.repeatedAnchorWitnessGroups + : []).find((group) => group.groupId === targetGroupId) ?? null; + const targetFailureResidue = getRequiredFailureResidue(failingAnchor, witnessSquareModulus); + const targetRows = (Array.isArray(allFamilies) ? allFamilies : []) + .map((family, familyIndex) => { + const repairRow = (Array.isArray(family?.repairRows) ? family.repairRows : []) + .find((row) => Number(row?.anchor) === failingAnchor + && Array.isArray(row?.squareWitnesses) + && row.squareWitnesses.some((witness) => Number(witness?.squareModulus) === witnessSquareModulus)); + return repairRow + ? { + familyIndex, + family, + repairRow, + } + : null; + }) + .filter(Boolean); + const rowProofs = targetRows.map(({ familyIndex, family, repairRow }) => { + const tupleRows = Array.isArray(family?.tupleRows) ? family.tupleRows : []; + const crtDerivation = deriveTupleRowCrt(tupleRows, witnessSquareModulus); + const activationSequence = deriveTupleRowActivationSequence(tupleRows, family?.repairRows ?? [], witnessSquareModulus); + const pre132Steps = activationSequence.filter((step) => Number(step.anchor) < 132); + const step132 = activationSequence.find((step) => Number(step.anchor) === 132) ?? null; + const step182 = activationSequence.find((step) => Number(step.anchor) === 182) ?? null; + const crt132 = (Array.isArray(crtDerivation?.steps) ? crtDerivation.steps : []) + .find((step) => Number(step.anchor) === 132) ?? null; + const crt182 = (Array.isArray(crtDerivation?.steps) ? crtDerivation.steps : []) + .find((step) => Number(step.anchor) === 182) ?? null; + const firstTrackedMatch = activationSequence.find((step) => ( + Array.isArray(step.matchingTrackedAnchors) && step.matchingTrackedAnchors.length > 0 + )) ?? null; + const pre132Residues = pre132Steps.map((step) => ({ + anchor: step.anchor, + residueModWitness: step.residueModWitness, + matchingTrackedAnchors: step.matchingTrackedAnchors, + })); + const pre132ProfileId = getP848Pre132ProfileId(pre132Residues); + const representativeResidueModuloWitness = witnessSquareModulus + ? positiveMod(family?.representative, witnessSquareModulus) + : null; + const crtResidue = crtDerivation?.combinedResidue ?? null; + const crtModulus = crtDerivation?.combinedModulus ?? null; + const rawRepresentativeMatchesCrtResidue = crtResidue !== null && crtModulus !== null + ? positiveModBigInt(BigInt(family?.representative ?? 0) - BigInt(crtResidue), BigInt(crtModulus)) === 0n + : false; + const checks = { + witnessPresentOnTargetRepair: Boolean(repairRow), + repairValueDivisibleByWitness: witnessSquareModulus + ? positiveMod(repairRow?.value ?? 0, witnessSquareModulus) === 0 + : false, + representativeHitsTargetFailureResidue: representativeResidueModuloWitness === targetFailureResidue, + rawRepresentativeMatchesCrtResidue, + pre132HasNoTrackedMatch: pre132Steps.length > 0 + && pre132Steps.every((step) => Array.isArray(step.matchingTrackedAnchors) && step.matchingTrackedAnchors.length === 0), + firstTrackedMatchIs132: Number(firstTrackedMatch?.anchor) === 132, + anchor132UniqueTarget: Array.isArray(step132?.matchingTrackedAnchors) + && step132.matchingTrackedAnchors.length === 1 + && Number(step132.matchingTrackedAnchors[0]) === failingAnchor + && Number(step132.residueModWitness) === targetFailureResidue, + anchor182PreservesTarget: Array.isArray(step182?.matchingTrackedAnchors) + && step182.matchingTrackedAnchors.length === 1 + && Number(step182.matchingTrackedAnchors[0]) === failingAnchor + && Number(step182.residueModWitness) === targetFailureResidue, + anchor182ZeroLift: Number(crt182?.liftParameter ?? -1) === 0, + }; + const failedChecks = Object.entries(checks) + .filter(([, value]) => value !== true) + .map(([key]) => key); + + return { + familyIndex, + representative: family?.representative ?? null, + tupleKey: family?.tupleKey ?? null, + failingAnchor, + witnessSquareModulus, + targetFailureResidue, + repairValue: repairRow?.value ?? null, + squareWitnesses: repairRow?.squareWitnesses ?? [], + representativeResidueModuloWitness, + pre132ProfileId, + pre132Profile: summarizeP848Pre132Profile(pre132Residues), + pre132Residues, + residueAt132: step132?.residueModWitness ?? null, + residueAt182: step182?.residueModWitness ?? null, + anchor132LiftParameter: crt132?.liftParameter ?? null, + anchor182LiftParameter: crt182?.liftParameter ?? null, + anchor182RowSquareModulus: crt182?.rowSquareModulus ?? null, + anchor182RowResidue: crt182?.rowResidue ?? null, + tupleRows: tupleRows.map((row) => ({ + anchor: row.anchor, + squareModulus: row.squareModulus, + residue: row.residue, + })), + crtDerivation, + checks, + status: failedChecks.length === 0 ? 'passed' : 'failed', + failedChecks, + }; + }); + const failedRows = rowProofs.filter((row) => row.status !== 'passed'); + const profileGroups = Object.values(rowProofs.reduce((accumulator, row) => { + accumulator[row.pre132ProfileId] = accumulator[row.pre132ProfileId] ?? { + profileId: row.pre132ProfileId, + profile: row.pre132Profile, + rowCount: 0, + familyIndices: [], + representatives: [], + tupleKeys: [], + anchor182RowSquareModuli: [], + }; + const group = accumulator[row.pre132ProfileId]; + group.rowCount += 1; + group.familyIndices.push(row.familyIndex); + if (!group.representatives.includes(row.representative)) { + group.representatives.push(row.representative); + } + if (!group.tupleKeys.includes(row.tupleKey)) { + group.tupleKeys.push(row.tupleKey); + } + if (!group.anchor182RowSquareModuli.includes(row.anchor182RowSquareModulus)) { + group.anchor182RowSquareModuli.push(row.anchor182RowSquareModulus); + } + return accumulator; + }, {})).sort((left, right) => right.rowCount - left.rowCount || left.profileId.localeCompare(right.profileId)); + const repeatedProfile = profileGroups.find((group) => group.rowCount > 1) ?? null; + const expectedRowCount = targetGroup?.rowCount ?? rowProofs.length; + const rowCountMatchesAssessment = rowProofs.length === expectedRowCount; + const failCount = failedRows.length + (rowCountMatchesAssessment ? 0 : 1); + const finiteGroupCertified = failCount === 0 && rowProofs.length > 0; + const profileSplit = profileGroups.length > 1; + const recommendedSuccessor = repeatedProfile + ? { + laneId: 'repeat_pre132_profile_subfamily', + targetProfileId: repeatedProfile.profileId, + task: `Prove or falsify the repeated ${targetGroupId} pre-132 profile sublane ${repeatedProfile.profileId} beyond finite rows ${repeatedProfile.familyIndices.join(', ')}.`, + why: `Rows ${repeatedProfile.familyIndices.join(', ')} share the same pre-132 residues, hit ${targetFailureResidue} mod ${witnessSquareModulus} at anchor 132, and have a zero-lift anchor-182 preservation step despite different final tuple moduli.`, + } + : { + laneId: 'switch_to_mod50_or_exact_verifier', + targetProfileId: null, + task: 'Switch from the finite 832/529 closure lane to the mod-50 symbolic lane or the next local exact verifier rollout.', + why: 'No repeated pre-132 profile remains inside the recommended anchor/witness group.', + }; + + return { + checkerId: 'p848_832_529_anchor_witness_domain_closure_checker_v1', + packetId: 'p848_832_529_anchor_witness_domain_closure_packet_v1', + source: 'raw_family_menu_anchor_witness_replay', + familyMenuPath, + status: finiteGroupCertified + ? profileSplit + ? 'finite_group_closure_certified_symbolic_domain_split' + : 'finite_group_closure_certified_single_profile_candidate' + : 'failed', + checkedRowCount: rowProofs.length, + passCount: rowProofs.length - failedRows.length, + failCount, + targetGroupId, + failingAnchor, + witnessSquareModulus, + targetFailureResidue, + expectedRowCount, + rowCountMatchesAssessment, + finiteScopeConclusion: finiteGroupCertified + ? `Every current finite-menu occurrence of ${targetGroupId} replays from raw tuple-row CRT data: pre-132 prefixes are clear, anchor 132 uniquely activates tracked tail ${failingAnchor}, and anchor 182 preserves residue ${targetFailureResidue} mod ${witnessSquareModulus}.` + : `The current finite-menu occurrences of ${targetGroupId} do not all replay cleanly.`, + symbolicDomainDecision: { + verdict: profileSplit + ? 'single_profile_symbolic_domain_falsified_by_profile_split' + : 'single_profile_symbolic_domain_candidate', + reason: profileSplit + ? `The recommended anchor/witness group splits into ${profileGroups.length} pre-132 residue profiles, so one broad single-profile symbolic closure would overclaim the evidence.` + : 'The recommended anchor/witness group has one pre-132 residue profile, so it remains a plausible symbolic subdomain candidate.', + profileGroupCount: profileGroups.length, + repeatedProfileId: repeatedProfile?.profileId ?? null, + }, + zeroLiftPreservation: { + allRowsAnchor182ZeroLift: rowProofs.length > 0 + && rowProofs.every((row) => row.checks.anchor182ZeroLift), + explanation: 'In the certified rows, the anchor-132 CRT prefix already satisfies the anchor-182 tuple row, so adding anchor 182 uses lift parameter 0 and cannot move the witness residue modulo 529.', + }, + profileGroups, + rowProofs, + failedRows, + recommendedSuccessor, + falsifierBoundary: [ + `A refreshed family menu adds another ${targetGroupId} row that fails any row check in this packet.`, + `A refreshed family menu removes one of the certified rows ${rowProofs.map((row) => row.familyIndex).join(', ')} or changes its witness modulus.`, + 'A symbolic theorem tries to use the finite group as one broad profile despite the recorded profile split.', + 'A future profile sublane instance has a nonzero anchor-182 lift or a pre-132 tracked failure-residue match.', + ], + nextProofObligations: [ + recommendedSuccessor.task, + 'Decide whether the repeated profile is a true symbolic family or only a finite-menu duplicate created by alternative final tuple rows.', + 'If the repeated profile is finite-only, move the theorem lane to the mod-50 bad-family signature or the next local exact verifier rollout.', + ], + }; +} + +function buildP848AnchorWitnessProfileSublanePacket(anchorWitnessDomainClosurePacket) { + const targetProfileId = anchorWitnessDomainClosurePacket?.recommendedSuccessor?.targetProfileId ?? null; + if (!anchorWitnessDomainClosurePacket || !targetProfileId) { + return null; + } + + const rowProofs = (Array.isArray(anchorWitnessDomainClosurePacket.rowProofs) + ? anchorWitnessDomainClosurePacket.rowProofs + : []).filter((row) => row.pre132ProfileId === targetProfileId); + if (rowProofs.length === 0) { + return null; + } + + const tupleSignature = (tupleRows, predicate = () => true) => JSON.stringify((Array.isArray(tupleRows) ? tupleRows : []) + .filter(predicate) + .map((row) => ({ + anchor: row.anchor, + squareModulus: row.squareModulus, + residue: row.residue, + }))); + const unique = (values) => [...new Set(values)]; + const prefixSignatures = unique(rowProofs.map((row) => tupleSignature(row.tupleRows, (tupleRow) => Number(tupleRow.anchor) <= 132))); + const fullSignatures = unique(rowProofs.map((row) => tupleSignature(row.tupleRows))); + const finalAnchorSignatures = unique(rowProofs.map((row) => tupleSignature(row.tupleRows, (tupleRow) => Number(tupleRow.anchor) === 182))); + const representatives = unique(rowProofs.map((row) => row.representative)); + const repairValues = unique(rowProofs.map((row) => row.repairValue)); + const anchor132LiftParameters = unique(rowProofs.map((row) => row.anchor132LiftParameter)); + const anchor182LiftParameters = unique(rowProofs.map((row) => row.anchor182LiftParameter)); + const checks = { + repeatedProfileHasAtLeastTwoRows: rowProofs.length >= 2, + sameRepresentative: representatives.length === 1, + sameRepairValue: repairValues.length === 1, + sameTuplePrefixThrough132: prefixSignatures.length === 1, + distinctFullTupleRows: fullSignatures.length === rowProofs.length, + differsOnlyAtAnchor182: prefixSignatures.length === 1 && finalAnchorSignatures.length === rowProofs.length, + sameAnchor132Lift: anchor132LiftParameters.length === 1, + anchor182ZeroLiftForEveryRow: anchor182LiftParameters.length === 1 && Number(anchor182LiftParameters[0]) === 0, + allRowsAlreadyPassedParentClosure: rowProofs.every((row) => row.status === 'passed'), + }; + const failedChecks = Object.entries(checks) + .filter(([, value]) => value !== true) + .map(([key]) => key); + const resolvedAsDuplicate = failedChecks.length === 0; + + return { + checkerId: 'p848_832_529_pre132_profile_sublane_checker_v1', + packetId: 'p848_832_529_pre132_profile_sublane_packet_v1', + source: 'anchor_witness_domain_closure_profile_replay', + status: resolvedAsDuplicate + ? 'finite_profile_sublane_resolved_as_zero_lift_duplicate' + : 'unresolved', + checkedRowCount: rowProofs.length, + passCount: resolvedAsDuplicate ? rowProofs.length : 0, + failCount: failedChecks.length, + parentPacketId: anchorWitnessDomainClosurePacket.packetId ?? null, + targetGroupId: anchorWitnessDomainClosurePacket.targetGroupId, + targetProfileId, + failingAnchor: anchorWitnessDomainClosurePacket.failingAnchor, + witnessSquareModulus: anchorWitnessDomainClosurePacket.witnessSquareModulus, + targetFailureResidue: anchorWitnessDomainClosurePacket.targetFailureResidue, + familyIndices: rowProofs.map((row) => row.familyIndex), + representatives, + repairValues, + tupleKeys: rowProofs.map((row) => row.tupleKey), + sharedPrefixThrough132: rowProofs[0]?.tupleRows + ?.filter((row) => Number(row.anchor) <= 132) + ?.map((row) => ({ + anchor: row.anchor, + squareModulus: row.squareModulus, + residue: row.residue, + })) ?? [], + finalAnchorVariants: rowProofs.map((row) => ({ + familyIndex: row.familyIndex, + anchor: 182, + squareModulus: row.anchor182RowSquareModulus, + residue: row.anchor182RowResidue, + liftParameter: row.anchor182LiftParameter, + })), + anchor132LiftParameter: anchor132LiftParameters.length === 1 ? anchor132LiftParameters[0] : null, + checks, + failedChecks, + rowProofRefs: rowProofs.map((row) => ({ + familyIndex: row.familyIndex, + representative: row.representative, + tupleKey: row.tupleKey, + residueAt132: row.residueAt132, + residueAt182: row.residueAt182, + anchor182LiftParameter: row.anchor182LiftParameter, + })), + conclusion: resolvedAsDuplicate + ? `Rows ${rowProofs.map((row) => row.familyIndex).join(', ')} are a finite duplicate final-anchor variant over the same CRT prefix through anchor 132, not evidence for a separate broad symbolic family.` + : `Rows ${rowProofs.map((row) => row.familyIndex).join(', ')} do not yet reduce to a zero-lift duplicate profile.`, + symbolicDomainDecision: { + verdict: resolvedAsDuplicate + ? 'profile_sublane_not_a_new_symbolic_family' + : 'profile_sublane_still_open', + reason: resolvedAsDuplicate + ? 'The repeated profile rows share representative, repair value, tuple prefix through anchor 132, and anchor-132 lift; they differ only by the final anchor-182 tuple row, which is a zero-lift in both cases.' + : 'At least one duplicate-profile check failed, so this profile cannot yet be dismissed as a finite final-anchor variant.', + }, + nextProofObligations: resolvedAsDuplicate + ? [ + 'Move the theorem lane to the mod-50 bad-family signature, because the repeated 832/529 profile did not yield a new broad symbolic domain.', + 'Keep the 832/529 packet as finite checked wisdom for future family-menu refreshes.', + 'Run the next local exact verifier rollout only after the theorem-facing mod-50 handoff has been sharpened or falsified.', + ] + : [ + 'Repair the failed profile-sublane checks or find the exact row feature that prevents the zero-lift duplicate interpretation.', + 'Only promote the profile sublane if it survives raw tuple-row replay without a finite-duplicate explanation.', + ], + }; +} + +function buildPrimeList(limit) { + const normalizedLimit = Math.max(2, Math.floor(Number(limit) || 0)); + const sieve = new Uint8Array(normalizedLimit + 1); + const primes = []; + for (let candidate = 2; candidate <= normalizedLimit; candidate += 1) { + if (sieve[candidate]) { + continue; + } + primes.push(candidate); + if (candidate * candidate > normalizedLimit) { + continue; + } + for (let value = candidate * candidate; value <= normalizedLimit; value += candidate) { + sieve[value] = 1; + } + } + return primes; +} + +function findSquareWitnessModuli(value, primes) { + let remaining = Number(value); + const witnesses = []; + for (const prime of primes) { + if (prime * prime > remaining) { + break; + } + if (remaining % prime !== 0) { + continue; + } + let exponent = 0; + while (remaining % prime === 0) { + remaining /= prime; + exponent += 1; + } + if (exponent >= 2) { + witnesses.push(prime * prime); + } + } + return witnesses; +} + +function scoreP848FamilyMenuContinuation(allFamilies, continuation, primes) { + const rows = (Array.isArray(allFamilies) ? allFamilies : []) + .map((family, familyIndex) => { + const representative = Number(family?.representative); + const repairValue = Number(continuation) * representative + 1; + const squareWitnesses = Number.isFinite(repairValue) + ? findSquareWitnessModuli(repairValue, primes) + : []; + const matchesKnownFailure = Boolean(family?.matchesKnownFailure ?? family?.matches_known_failure); + return { + continuation, + familyIndex, + representative, + tupleKey: family?.tupleKey ?? family?.tuple_key ?? null, + matchesKnownFailure, + predicted: !matchesKnownFailure, + repairValue, + rescued: Number(continuation) <= representative && squareWitnesses.length === 0, + squareWitnesses, + }; + }) + .filter((row) => Number.isFinite(row.representative)); + const predictedRows = rows.filter((row) => row.predicted); + const missedPredictedRows = predictedRows.filter((row) => !row.rescued); + const repairedPredictedRows = predictedRows.filter((row) => row.rescued); + const repairedKnownRows = rows.filter((row) => row.matchesKnownFailure && row.rescued); + const missedKnownRows = rows.filter((row) => row.matchesKnownFailure && !row.rescued); + + return { + continuation, + familyCount: rows.length, + predictedFamilyCount: predictedRows.length, + repairedKnownFamilyCount: repairedKnownRows.length, + missedKnownFamilyCount: missedKnownRows.length, + repairedPredictedFamilyCount: repairedPredictedRows.length, + missedPredictedFamilyCount: missedPredictedRows.length, + missedPredictedRows, + firstMissedPredictedRepresentatives: missedPredictedRows.slice(0, 8).map((row) => row.representative), + }; +} + +function summarizeP848ScoredFamilyRow(row) { + return { + continuation: row.continuation, + familyIndex: row.familyIndex, + representative: row.representative, + tupleKey: row.tupleKey, + repairValue: row.repairValue, + squareWitnesses: row.squareWitnesses, + }; +} + +function getP848ScoredFamilyRowKey(row) { + return `${row.familyIndex}:${row.representative}:${row.tupleKey ?? ''}`; +} + +function getP848ContinuationLaneIndex(continuation, laneBase = 32, laneStep = 50) { + const normalizedContinuation = Number(continuation); + const numerator = normalizedContinuation - laneBase; + if (!Number.isInteger(normalizedContinuation) || numerator % laneStep !== 0) { + return null; + } + return numerator / laneStep; +} + +function deriveP848LaneWitnessSignatures(row, repairedContinuation, laneBase = 32, laneStep = 50) { + const missedLaneIndex = getP848ContinuationLaneIndex(row.continuation, laneBase, laneStep); + const repairedLaneIndex = getP848ContinuationLaneIndex(repairedContinuation, laneBase, laneStep); + return (Array.isArray(row.squareWitnesses) ? row.squareWitnesses : []).map((witnessSquareModulus) => { + const coeff = positiveMod(laneStep * Number(row.representative), witnessSquareModulus); + const rhs = positiveMod(-(laneBase * Number(row.representative) + 1), witnessSquareModulus); + const congruence = solveLinearCongruenceNonnegative(coeff, rhs, witnessSquareModulus); + const laneIndexMatches = (laneIndex) => congruence?.solvable + && laneIndex !== null + && positiveMod(Number(laneIndex) - congruence.solution, congruence.period) === 0; + return { + witnessSquareModulus, + laneEquation: `${coeff}*m ≡ ${rhs} (mod ${witnessSquareModulus})`, + gcdCoeffWitness: congruence?.gcdCoeffModulus ?? null, + laneIndexResidue: congruence?.solution ?? null, + laneIndexPeriod: congruence?.period ?? null, + missedLaneIndex, + repairedLaneIndex, + missedLaneIndexMatches: laneIndexMatches(missedLaneIndex), + repairedLaneIndexMatches: laneIndexMatches(repairedLaneIndex), + }; + }); +} + +function summarizeP848ExchangeFamilyRow(row, repairedContinuation, laneBase = 32, laneStep = 50) { + const laneWitnessSignatures = deriveP848LaneWitnessSignatures(row, repairedContinuation, laneBase, laneStep); + return { + ...summarizeP848ScoredFamilyRow(row), + missedLaneIndex: getP848ContinuationLaneIndex(row.continuation, laneBase, laneStep), + repairedContinuation, + repairedLaneIndex: getP848ContinuationLaneIndex(repairedContinuation, laneBase, laneStep), + laneWitnessSignatures, + laneSignatureStatus: laneWitnessSignatures.length > 0 + && laneWitnessSignatures.some((signature) => signature.missedLaneIndexMatches) + && laneWitnessSignatures.every((signature) => !signature.repairedLaneIndexMatches) + ? 'passed' + : 'failed', + }; +} + +function buildP848Mod50LaneSignature(pairwiseDeltas, continuations) { + const laneBase = 32; + const laneStep = 50; + const continuationLaneIndices = Object.fromEntries((Array.isArray(continuations) ? continuations : []) + .map((continuation) => [continuation, getP848ContinuationLaneIndex(continuation, laneBase, laneStep)])); + const exchangeRows = (Array.isArray(pairwiseDeltas) ? pairwiseDeltas : []).flatMap((delta) => [ + ...delta.contrastOnlyMissedRows.map((row) => ({ + exchangeKind: 'contrast_only_miss', + topContinuation: delta.topContinuation, + contrastContinuation: delta.contrastContinuation, + ...row, + })), + ...delta.topOnlyMissedRows.map((row) => ({ + exchangeKind: 'top_only_miss', + topContinuation: delta.topContinuation, + contrastContinuation: delta.contrastContinuation, + ...row, + })), + ]); + const failedRows = exchangeRows.filter((row) => row.laneSignatureStatus !== 'passed'); + const strictDominanceRows = exchangeRows.filter((row) => ( + row.topContinuation === 782 + && row.contrastContinuation === 1232 + && row.exchangeKind === 'contrast_only_miss' + )); + return { + checkerId: 'p848_mod50_lane_bad_family_signature_checker_v1', + schemaId: 'p848_mod50_lane_bad_family_signature_v1', + source: 'pairwise_exchange_row_lane_congruence_replay', + status: failedRows.length === 0 && exchangeRows.length > 0 + ? 'finite_menu_mod50_lane_signature_certified' + : 'failed', + laneBase, + laneStep, + laneFormula: 'continuation = 32 + 50*m', + continuationLaneIndices, + checkedRowCount: exchangeRows.length, + passCount: exchangeRows.length - failedRows.length, + failCount: failedRows.length, + failedRows, + strictDominanceRows, + exchangeRows, + conclusion: failedRows.length === 0 && exchangeRows.length > 0 + ? 'Every pairwise exchange row is explained by a bad lane-index congruence m modulo the square witness; the missed continuation hits that congruence and the repaired continuation does not.' + : 'At least one pairwise exchange row lacks a clean bad lane-index congruence certificate.', + nextProofObligations: [ + 'Generalize the finite-menu lane-index congruence schema beyond the currently replayed exchange rows.', + 'Choose the strict 782 vs 1232 handoff rows or a broader exchange family as the next theorem-facing symbolic family.', + 'Connect the lane-index bad-family schema back to the finite-gap closure target rather than treating it as only a leaderboard feature.', + ], + }; +} + +function buildP848Mod50LaneSymbolicSchema(mod50LaneSignature) { + const exchangeRows = Array.isArray(mod50LaneSignature?.exchangeRows) + ? mod50LaneSignature.exchangeRows + : []; + if (!mod50LaneSignature || exchangeRows.length === 0) { + return null; + } + + const laneBase = mod50LaneSignature.laneBase ?? 32; + const laneStep = mod50LaneSignature.laneStep ?? 50; + const instanceChecks = exchangeRows.flatMap((row) => { + const recomputedSignatures = deriveP848LaneWitnessSignatures(row, row.repairedContinuation, laneBase, laneStep); + return (Array.isArray(row.laneWitnessSignatures) ? row.laneWitnessSignatures : []) + .map((signature, signatureIndex) => { + const recomputed = recomputedSignatures[signatureIndex] ?? null; + const checks = { + laneFormulaAppliesToMissedContinuation: getP848ContinuationLaneIndex(row.continuation, laneBase, laneStep) === row.missedLaneIndex, + laneFormulaAppliesToRepairedContinuation: getP848ContinuationLaneIndex(row.repairedContinuation, laneBase, laneStep) === row.repairedLaneIndex, + equationRecomputes: recomputed?.laneEquation === signature.laneEquation + && recomputed?.laneIndexResidue === signature.laneIndexResidue + && recomputed?.laneIndexPeriod === signature.laneIndexPeriod, + missedLaneHitsBadClass: signature.missedLaneIndexMatches === true, + repairedLaneAvoidsBadClass: signature.repairedLaneIndexMatches === false, + congruenceSolvable: signature.laneIndexResidue !== null && signature.laneIndexPeriod !== null, + }; + const failedChecks = Object.entries(checks) + .filter(([, value]) => value !== true) + .map(([key]) => key); + return { + exchangeKind: row.exchangeKind, + topContinuation: row.topContinuation, + contrastContinuation: row.contrastContinuation, + continuation: row.continuation, + repairedContinuation: row.repairedContinuation, + familyIndex: row.familyIndex, + representative: row.representative, + witnessSquareModulus: signature.witnessSquareModulus, + laneEquation: signature.laneEquation, + laneIndexResidue: signature.laneIndexResidue, + laneIndexPeriod: signature.laneIndexPeriod, + missedLaneIndex: signature.missedLaneIndex, + repairedLaneIndex: signature.repairedLaneIndex, + status: failedChecks.length === 0 ? 'passed' : 'failed', + checks, + failedChecks, + }; + }); + }); + const failedInstances = instanceChecks.filter((row) => row.status !== 'passed'); + const periodCounts = instanceChecks.reduce((accumulator, row) => { + const key = String(row.laneIndexPeriod); + accumulator[key] = (accumulator[key] ?? 0) + 1; + return accumulator; + }, {}); + const strict782Vs1232Instances = instanceChecks.filter((row) => ( + Number(row.topContinuation) === 782 + && Number(row.contrastContinuation) === 1232 + && row.exchangeKind === 'contrast_only_miss' + )); + + return { + checkerId: 'p848_mod50_bad_lane_symbolic_schema_checker_v1', + schemaId: 'p848_mod50_bad_lane_symbolic_schema_v1', + source: 'mod50_lane_congruence_lift', + status: failedInstances.length === 0 && mod50LaneSignature.status === 'finite_menu_mod50_lane_signature_certified' + ? 'symbolic_bad_lane_schema_ready' + : 'failed', + laneBase, + laneStep, + laneFormula: mod50LaneSignature.laneFormula ?? 'continuation = 32 + 50*m', + checkedRowCount: instanceChecks.length, + passCount: instanceChecks.length - failedInstances.length, + failCount: failedInstances.length + (mod50LaneSignature.status === 'finite_menu_mod50_lane_signature_certified' ? 0 : 1), + failedInstances, + scope: { + universalDivisibilityClaim: true, + universalSquarefreeRepairClaim: false, + finiteExchangeRowsChecked: exchangeRows.length, + symbolicVariables: [ + 'n: family representative', + 'Q: square witness modulus', + 'm: lane index in c = 32 + 50*m', + 'c: continuation being tested', + ], + }, + symbolicStatement: `For any representative n and square witness modulus Q, continuation c = ${laneBase} + ${laneStep}*m has Q | c*n + 1 exactly when (${laneStep}*n)*m ≡ -(${laneBase}*n + 1) (mod Q). When this congruence is solvable, it defines the bad m-class modulo Q/gcd(${laneStep}*n,Q).`, + proofSketch: [ + `Substitute c = ${laneBase} + ${laneStep}*m into c*n + 1 ≡ 0 (mod Q).`, + `Rearrange to (${laneStep}*n)*m ≡ -(${laneBase}*n + 1) (mod Q).`, + 'Solve the linear congruence; the missed continuation is bad exactly when its lane index lies in the solution class.', + 'Avoiding this one witness class is necessary for repair on that row, but not by itself sufficient for global squarefreeness.', + ], + periodCounts, + strict782Vs1232Instances, + instanceChecks, + conclusion: failedInstances.length === 0 + ? `The finite mod-50 exchange packet is now backed by a reusable divisibility schema over ${instanceChecks.length} checked witness instances.` + : 'At least one finite exchange row failed to replay under the symbolic bad-lane schema.', + nextProofObligations: [ + 'Connect the symbolic bad-lane schema to the finite-gap closure target using a theorem-facing handoff family, preferably the strict 782 vs 1232 rows.', + 'Prove that the selected handoff family controls all relevant square witnesses, not only the witnessed bad lane in each finite exchange row.', + 'If no such control family exists, route the next step to local exact verification beyond 11300 instead of overclaiming the lane schema.', + ], + }; +} + +function buildP848Strict7821232HandoffPacket(topRepairSeparationAnalysis, mod50LaneSymbolicSchema) { + if (!topRepairSeparationAnalysis || !mod50LaneSymbolicSchema) { + return null; + } + + const strictPair = (Array.isArray(topRepairSeparationAnalysis.strictDominancePairs) + ? topRepairSeparationAnalysis.strictDominancePairs + : []).find((row) => Number(row.topContinuation) === 782 && Number(row.contrastContinuation) === 1232) ?? null; + const pairwiseDelta = (Array.isArray(topRepairSeparationAnalysis.pairwiseDeltas) + ? topRepairSeparationAnalysis.pairwiseDeltas + : []).find((row) => Number(row.topContinuation) === 782 && Number(row.contrastContinuation) === 1232) ?? null; + if (!strictPair || !pairwiseDelta) { + return null; + } + + const strictRows = Array.isArray(strictPair.repairedByTopMissedByContrast) + ? strictPair.repairedByTopMissedByContrast + : []; + const strictInstances = Array.isArray(mod50LaneSymbolicSchema.strict782Vs1232Instances) + ? mod50LaneSymbolicSchema.strict782Vs1232Instances + : []; + const instanceKey = (row) => `${row.familyIndex}:${row.representative}:${row.witnessSquareModulus}`; + const instancesByKey = Object.fromEntries(strictInstances.map((row) => [instanceKey(row), row])); + const rowChecks = strictRows.flatMap((row) => (Array.isArray(row.laneWitnessSignatures) ? row.laneWitnessSignatures : []) + .map((signature) => { + const matchingInstance = instancesByKey[`${row.familyIndex}:${row.representative}:${signature.witnessSquareModulus}`] ?? null; + const checks = { + symbolicSchemaInstancePresent: Boolean(matchingInstance), + missedContinuationIs1232: Number(row.continuation) === 1232, + repairedContinuationIs782: Number(row.repairedContinuation) === 782, + missedLaneIndexIs24: Number(row.missedLaneIndex) === 24, + repairedLaneIndexIs15: Number(row.repairedLaneIndex) === 15, + missedLaneHitsBadClass: signature.missedLaneIndexMatches === true, + repairedLaneAvoidsBadClass: signature.repairedLaneIndexMatches === false, + }; + const failedChecks = Object.entries(checks) + .filter(([, value]) => value !== true) + .map(([key]) => key); + return { + familyIndex: row.familyIndex, + representative: row.representative, + tupleKey: row.tupleKey, + witnessSquareModulus: signature.witnessSquareModulus, + laneEquation: signature.laneEquation, + laneIndexResidue: signature.laneIndexResidue, + laneIndexPeriod: signature.laneIndexPeriod, + missedLaneIndex: row.missedLaneIndex, + repairedLaneIndex: row.repairedLaneIndex, + status: failedChecks.length === 0 ? 'passed' : 'failed', + checks, + failedChecks, + }; + })); + const failedRows = rowChecks.filter((row) => row.status !== 'passed'); + const checks = { + strictDominancePairPresent: Boolean(strictPair), + pairwiseDeltaPresent: Boolean(pairwiseDelta), + topContinuationIs782: Number(pairwiseDelta.topContinuation) === 782, + contrastContinuationIs1232: Number(pairwiseDelta.contrastContinuation) === 1232, + topRepairsTwoMorePredictedRows: Number(pairwiseDelta.netExtraRepairsForTop) === 2, + noTopOnlyMissRows: Number(pairwiseDelta.topOnlyMissCount) === 0, + contrastOnlyMissRowsAreTwo: Number(pairwiseDelta.contrastOnlyMissCount) === 2, + strictRowsCoveredBySymbolicSchema: strictRows.length > 0 && rowChecks.length === strictRows.length, + rowChecksPass: failedRows.length === 0, + }; + const failedChecks = Object.entries(checks) + .filter(([, value]) => value !== true) + .map(([key]) => key); + const certified = failedChecks.length === 0; + + return { + checkerId: 'p848_782_1232_strict_handoff_checker_v1', + packetId: 'p848_782_1232_strict_handoff_packet_v1', + source: 'mod50_symbolic_schema_to_finite_menu_handoff', + status: certified + ? 'finite_strict_handoff_certified_not_gap_closure' + : 'failed', + checkedRowCount: rowChecks.length, + passCount: rowChecks.length - failedRows.length, + failCount: failedRows.length + failedChecks.length, + topContinuation: 782, + contrastContinuation: 1232, + topLaneIndex: getP848ContinuationLaneIndex(782), + contrastLaneIndex: getP848ContinuationLaneIndex(1232), + netExtraRepairsForTop: pairwiseDelta.netExtraRepairsForTop, + topOnlyMissCount: pairwiseDelta.topOnlyMissCount, + contrastOnlyMissCount: pairwiseDelta.contrastOnlyMissCount, + topRepairedPredictedFamilyCount: pairwiseDelta.topRepairedPredictedFamilyCount, + contrastRepairedPredictedFamilyCount: pairwiseDelta.contrastRepairedPredictedFamilyCount, + checks, + failedChecks, + rowChecks, + failedRows, + strictRows: strictRows.map((row) => ({ + familyIndex: row.familyIndex, + representative: row.representative, + tupleKey: row.tupleKey, + repairValue: row.repairValue, + squareWitnesses: row.squareWitnesses, + missedLaneIndex: row.missedLaneIndex, + repairedLaneIndex: row.repairedLaneIndex, + })), + conclusion: certified + ? 'The strict 782 > 1232 handoff is certified on the current finite menu: 782 repairs exactly two predicted rows that 1232 misses, 1232 repairs no predicted row that 782 misses, and both strict rows are explained by the symbolic mod-50 bad-lane schema.' + : 'The strict 782 > 1232 handoff did not replay cleanly against the symbolic mod-50 bad-lane schema.', + theoremBoundary: { + finiteMenuHandoffClaim: certified, + allNFiniteGapClosureClaim: false, + reason: 'This packet connects the symbolic bad-lane schema to the finite exchange surface, but it does not prove that all post-11300 candidates are controlled by the strict handoff family.', + }, + nextProofObligations: certified + ? [ + 'Use the strict handoff packet as theorem-side guidance for the next local exact verifier rollout beyond 11300.', + 'If exact verification finds a new boundary row, replay it through the bad-lane schema before widening search.', + 'Do not claim all-N closure from the 782 > 1232 handoff without a separate coverage theorem over all relevant square witnesses.', + ] + : [ + 'Repair the strict handoff replay or choose a different pairwise handoff family.', + ], + }; +} + +function buildP848TopRepairSeparationAnalysis(alignmentContext, tieClass, primaryContrasts) { + const allFamilies = Array.isArray(alignmentContext?.allFamilies) ? alignmentContext.allFamilies : []; + const contrastContinuations = (Array.isArray(primaryContrasts) ? primaryContrasts : []) + .map((row) => Number(row?.continuation)) + .filter((continuation) => Number.isFinite(continuation)); + const continuations = [...new Set([ + ...(Array.isArray(tieClass) ? tieClass : []).map((continuation) => Number(continuation)), + ...contrastContinuations, + ].filter((continuation) => Number.isFinite(continuation)))]; + if (allFamilies.length === 0 || continuations.length === 0) { + return { + checkerId: 'p848_top_repair_plus2_family_menu_replay_checker_v1', + status: 'family_menu_unavailable', + failCount: 1, + checkedRowCount: 0, + reason: 'The family menu or continuation set is unavailable.', + }; + } + + const maxRepresentative = Math.max(...allFamilies.map((row) => Number(row?.representative)).filter(Number.isFinite)); + const maxContinuation = Math.max(...continuations); + const primes = buildPrimeList(Math.floor(Math.sqrt(maxRepresentative * maxContinuation + 1)) + 1); + const scores = continuations.map((continuation) => scoreP848FamilyMenuContinuation(allFamilies, continuation, primes)); + const scoreByContinuation = Object.fromEntries(scores.map((score) => [score.continuation, score])); + const leaderboardByContinuation = Object.fromEntries((Array.isArray(alignmentContext?.gpuLeaderboard) ? alignmentContext.gpuLeaderboard : []) + .map((row) => [Number(row?.continuation), row])); + const trackedByContinuation = Object.fromEntries((Array.isArray(alignmentContext?.trackedTailMatrix) ? alignmentContext.trackedTailMatrix : []) + .map((row) => [Number(row?.continuation), row])); + const topScores = (Array.isArray(tieClass) ? tieClass : []) + .map((continuation) => scoreByContinuation[Number(continuation)]) + .filter(Boolean); + const contrastScores = contrastContinuations + .map((continuation) => scoreByContinuation[continuation]) + .filter(Boolean); + const predictedFamilyCount = scores[0]?.predictedFamilyCount ?? null; + const allTopMiss13 = topScores.every((score) => score.missedPredictedFamilyCount === 13); + const allPrimaryContrastsMiss15 = contrastScores.every((score) => score.missedPredictedFamilyCount === 15); + const allTopRepair242 = topScores.every((score) => score.repairedPredictedFamilyCount === 242); + const allPrimaryContrastsRepair240 = contrastScores.every((score) => score.repairedPredictedFamilyCount === 240); + const allScoresMatchLeaderboard = scores.every((score) => { + const leaderboardRow = leaderboardByContinuation[score.continuation]; + if (!leaderboardRow) { + return true; + } + return Number(leaderboardRow.repaired_predicted_families) === score.repairedPredictedFamilyCount; + }); + const allScoresMatchTrackedRows = scores.every((score) => { + const trackedRow = trackedByContinuation[score.continuation]; + if (!trackedRow) { + return true; + } + return Number(trackedRow.repaired_predicted_family_count) === score.repairedPredictedFamilyCount; + }); + const missedKeysByContinuation = Object.fromEntries(scores.map((score) => [ + score.continuation, + new Set(score.missedPredictedRows.map(getP848ScoredFamilyRowKey)), + ])); + const topTieSharedMissedPredictedRows = topScores.length === 0 + ? [] + : topScores[0].missedPredictedRows + .filter((row) => topScores.every((score) => missedKeysByContinuation[score.continuation].has(getP848ScoredFamilyRowKey(row)))) + .map(summarizeP848ScoredFamilyRow); + const pairwiseDeltas = topScores.flatMap((topScore) => contrastScores.map((contrastScore) => { + const topMissedKeys = missedKeysByContinuation[topScore.continuation]; + const contrastMissedKeys = missedKeysByContinuation[contrastScore.continuation]; + const contrastOnlyMissedRows = contrastScore.missedPredictedRows + .filter((row) => !topMissedKeys.has(getP848ScoredFamilyRowKey(row))); + const topOnlyMissedRows = topScore.missedPredictedRows + .filter((row) => !contrastMissedKeys.has(getP848ScoredFamilyRowKey(row))); + const netExtraRepairsForTop = contrastOnlyMissedRows.length - topOnlyMissedRows.length; + return { + topContinuation: topScore.continuation, + contrastContinuation: contrastScore.continuation, + topMissedPredictedFamilyCount: topScore.missedPredictedFamilyCount, + contrastMissedPredictedFamilyCount: contrastScore.missedPredictedFamilyCount, + topRepairedPredictedFamilyCount: topScore.repairedPredictedFamilyCount, + contrastRepairedPredictedFamilyCount: contrastScore.repairedPredictedFamilyCount, + contrastOnlyMissCount: contrastOnlyMissedRows.length, + topOnlyMissCount: topOnlyMissedRows.length, + netExtraRepairsForTop, + dominanceKind: topOnlyMissedRows.length === 0 && netExtraRepairsForTop === 2 + ? 'strict_superset_on_predicted_menu' + : 'net_exchange', + status: netExtraRepairsForTop === 2 ? 'net_plus2_certified' : 'unresolved', + contrastOnlyMissedRows: contrastOnlyMissedRows.map((row) => summarizeP848ExchangeFamilyRow(row, topScore.continuation)), + topOnlyMissedRows: topOnlyMissedRows.map((row) => summarizeP848ExchangeFamilyRow(row, contrastScore.continuation)), + }; + })); + const strictDominancePairs = pairwiseDeltas + .filter((row) => row.dominanceKind === 'strict_superset_on_predicted_menu') + .map((row) => ({ + topContinuation: row.topContinuation, + contrastContinuation: row.contrastContinuation, + repairedByTopMissedByContrast: row.contrastOnlyMissedRows, + })); + const mod50LaneSignature = buildP848Mod50LaneSignature(pairwiseDeltas, continuations); + const allPairwiseNetPlus2 = pairwiseDeltas.length > 0 + && pairwiseDeltas.every((row) => row.status === 'net_plus2_certified'); + const status = allTopMiss13 + && allPrimaryContrastsMiss15 + && allTopRepair242 + && allPrimaryContrastsRepair240 + && allPairwiseNetPlus2 + && allScoresMatchLeaderboard + && allScoresMatchTrackedRows + ? 'finite_menu_plus2_replay_certified' + : 'unresolved'; + + return { + checkerId: 'p848_top_repair_plus2_family_menu_replay_checker_v1', + source: 'raw_family_menu_squarefree_replay', + familyMenuPath: alignmentContext?.familyMenuPath ?? null, + status, + failCount: status === 'finite_menu_plus2_replay_certified' ? 0 : 1, + checkedRowCount: pairwiseDeltas.length, + checkedContinuationCount: scores.length, + checkedPairCount: pairwiseDeltas.length, + predictedFamilyCount, + topTieCounts: topScores.map((score) => ({ + continuation: score.continuation, + repairedPredictedFamilyCount: score.repairedPredictedFamilyCount, + missedPredictedFamilyCount: score.missedPredictedFamilyCount, + repairedKnownFamilyCount: score.repairedKnownFamilyCount, + firstMissedPredictedRepresentatives: score.firstMissedPredictedRepresentatives, + matchesLeaderboard: leaderboardByContinuation[score.continuation] + ? Number(leaderboardByContinuation[score.continuation].repaired_predicted_families) === score.repairedPredictedFamilyCount + : null, + matchesTrackedTailMatrix: trackedByContinuation[score.continuation] + ? Number(trackedByContinuation[score.continuation].repaired_predicted_family_count) === score.repairedPredictedFamilyCount + : null, + })), + primaryContrastCounts: contrastScores.map((score) => ({ + continuation: score.continuation, + repairedPredictedFamilyCount: score.repairedPredictedFamilyCount, + missedPredictedFamilyCount: score.missedPredictedFamilyCount, + repairedKnownFamilyCount: score.repairedKnownFamilyCount, + firstMissedPredictedRepresentatives: score.firstMissedPredictedRepresentatives, + matchesLeaderboard: leaderboardByContinuation[score.continuation] + ? Number(leaderboardByContinuation[score.continuation].repaired_predicted_families) === score.repairedPredictedFamilyCount + : null, + matchesTrackedTailMatrix: trackedByContinuation[score.continuation] + ? Number(trackedByContinuation[score.continuation].repaired_predicted_family_count) === score.repairedPredictedFamilyCount + : null, + })), + topTieSharedMissedPredictedRows, + pairwiseDeltas, + strictDominancePairs, + mod50LaneSignature, + verifiedAgainstBridge: { + allScoresMatchLeaderboard, + allScoresMatchTrackedRows, + allTopMiss13, + allPrimaryContrastsMiss15, + allTopRepair242, + allPrimaryContrastsRepair240, + allPairwiseNetPlus2, + }, + conclusion: status === 'finite_menu_plus2_replay_certified' + ? `The current finite menu has ${predictedFamilyCount} predicted families; each top tail misses 13 and each primary contrast misses 15, so the top tie repairs exactly two more predicted families under the same menu evidence.` + : 'The finite-menu replay did not certify the full +2 separation under the current bridge evidence.', + }; +} + +function buildP848TopRepairClassMechanism(alignmentContext) { + const tieClass = Array.isArray(alignmentContext?.bridgeState?.top_gpu_tie_class) + ? alignmentContext.bridgeState.top_gpu_tie_class + : []; + if (tieClass.length === 0) { + return null; + } + + const trackedRows = tieClass + .map((continuation) => alignmentContext.trackedTailMatrix.find((row) => Number(row?.continuation) === Number(continuation)) ?? null) + .filter(Boolean); + const leaderboardRows = tieClass + .map((continuation) => alignmentContext.gpuLeaderboard.find((row) => Number(row?.continuation) === Number(continuation)) ?? null) + .filter(Boolean); + if (trackedRows.length !== tieClass.length || leaderboardRows.length !== tieClass.length) { + return null; + } + + const uniqueSorted = (values) => [...new Set((Array.isArray(values) ? values : []) + .filter((value) => value !== null && value !== undefined) + .map((value) => Number(value)) + .filter((value) => Number.isFinite(value)))] + .sort((left, right) => left - right); + const missedSets = trackedRows.map((row) => uniqueSorted(row.first_missed_predicted_representatives)); + const commonMissedPredictedRepresentatives = missedSets.length === 0 + ? [] + : missedSets.slice(1).reduce( + (common, values) => common.filter((value) => values.includes(value)), + missedSets[0], + ); + const tailSpecificMissedPredictedRepresentatives = Object.fromEntries(trackedRows.map((row, index) => [ + row.continuation, + missedSets[index].filter((value) => !commonMissedPredictedRepresentatives.includes(value)), + ])); + const nearestContrasts = alignmentContext.gpuLeaderboard + .filter((row) => !tieClass.includes(row.continuation)) + .filter((row) => Number(row.repaired_known_packets) === Number(leaderboardRows[0].repaired_known_packets)) + .slice(0, 5); + const primaryContrasts = nearestContrasts.slice(0, 3); + const separationAnalysis = buildP848TopRepairSeparationAnalysis(alignmentContext, tieClass, primaryContrasts); + const sameMetric = (key, rows) => rows.every((row) => row?.[key] === rows[0]?.[key]); + const mod50Lane = uniqueSorted([ + ...tieClass, + ...nearestContrasts.map((row) => row.continuation), + ].map((continuation) => Number(continuation) % 50)); + + return { + mechanismId: 'p848_top_repair_class_mechanism_packet_v1', + status: 'seeded_from_bridge', + tieClass, + currentFamilyAwareLeader: alignmentContext.bridgeState?.current_family_aware_leader ?? null, + bridgeLeaderboardRows: leaderboardRows, + trackedTailRows: trackedRows, + sharedMetrics: { + repairedKnownPackets: leaderboardRows[0]?.repaired_known_packets ?? null, + repairedPredictedFamilies: leaderboardRows[0]?.repaired_predicted_families ?? null, + directCleanThrough: leaderboardRows[0]?.direct_clean_through ?? null, + effectiveCleanThrough: leaderboardRows[0]?.effective_clean_through ?? null, + trackedRepairedKnownFamilyCount: trackedRows[0]?.repaired_known_family_count ?? null, + trackedMissedKnownPackets: trackedRows[0]?.missed_known_packets ?? null, + trackedExtensionMode: trackedRows[0]?.extension_mode ?? null, + sameRepairedKnownPackets: sameMetric('repaired_known_packets', leaderboardRows), + sameRepairedPredictedFamilies: sameMetric('repaired_predicted_families', leaderboardRows), + sameCleanThrough: sameMetric('effective_clean_through', leaderboardRows), + sameTrackedKnownFamilyCount: sameMetric('repaired_known_family_count', trackedRows), + sameTrackedMissedKnownPackets: sameMetric('missed_known_packets', trackedRows), + sameTrackedExtensionMode: sameMetric('extension_mode', trackedRows), + }, + nearestContrasts, + primaryContrasts: primaryContrasts.map((row) => row.continuation), + contrastSummary: nearestContrasts.length > 0 + ? `Nearest same-known-packet contrasts ${nearestContrasts.map((row) => row.continuation).join(', ')} have repaired-predicted counts ${nearestContrasts.map((row) => `${row.continuation}->${row.repaired_predicted_families}`).join(', ')}.` + : 'No nearest same-known-packet contrast rows are available in the current leaderboard.', + separationAnalysis, + commonMissedPredictedRepresentatives, + tailSpecificMissedPredictedRepresentatives, + residueLaneAssessment: { + tieClassModulo50: uniqueSorted(tieClass.map((continuation) => Number(continuation) % 50)), + nearbyModulo50Values: mod50Lane, + verdict: mod50Lane.length === 1 + ? 'shared_mod_50_lane_but_not_sufficient' + : 'mixed_mod_50_lane', + note: 'The top tie is in the same mod-50 lane as several near contrasts, so the mod-50 lane is useful context but not by itself the repair mechanism.', + }, + mechanismHypotheses: [ + { + hypothesisId: 'shared_repair_count_signature', + status: 'supported_by_bridge', + note: 'All top tails share repaired-known=26, repaired-predicted=242, and clean-through=250075000 on the bridge leaderboard.', + }, + { + hypothesisId: 'plus50_lane_context', + status: 'necessary_not_sufficient', + note: 'The top tails share the same mod-50 lane, but nearby contrasts in that lane do not all reach 242 predicted repairs.', + }, + { + hypothesisId: 'common_missed_family_boundary', + status: commonMissedPredictedRepresentatives.length > 0 ? 'supported_by_tracked_tail_matrix' : 'unresolved', + note: `The top tails share ${commonMissedPredictedRepresentatives.length} early missed predicted representatives in the tracked-tail matrix.`, + }, + { + hypothesisId: 'finite_menu_plus2_separation', + status: separationAnalysis.status === 'finite_menu_plus2_replay_certified' ? 'certified_by_replay' : 'unresolved', + note: separationAnalysis.conclusion, + }, + ], + falsifierBoundary: [ + 'A bridge refresh breaks the 432, 782, 832 tie on repaired-known, repaired-predicted, or clean-through metrics.', + 'A near contrast such as 332, 382, or 1232 reaches the same predicted repair count under the same evidence boundary.', + 'The apparent common missed-family representatives disappear when the family menu is refreshed.', + 'A direct exact extension finds an earlier failure for one member of the top tie inside the claimed clean-through window.', + ], + nextProofObligations: [ + separationAnalysis.mod50LaneSignature?.status === 'finite_menu_mod50_lane_signature_certified' + ? 'Generalize the mod-50 lane-index bad-family signature beyond the finite exchange rows.' + : separationAnalysis.status === 'finite_menu_plus2_replay_certified' + ? 'Lift the finite-menu +2 repair separation into a symbolic residue/family signature for the mod-50 lane.' + : 'Explain the +2 repaired-predicted-family separation between 432/782/832 and the nearest same-known-packet contrasts 332/382/1232.', + 'Derive a residue or family signature that separates the top tie from the rest of the mod-50 lane.', + separationAnalysis.mod50LaneSignature?.status === 'finite_menu_mod50_lane_signature_certified' + ? 'Choose the strict 782 vs 1232 handoff rows or a broader exchange family as the next theorem-facing symbolic family.' + : separationAnalysis.status === 'finite_menu_plus2_replay_certified' + ? 'Decide which pairwise exchange rows should become the next theorem-facing symbolic family.' + : 'Replay the common missed-family representatives against the family menu to identify which predicted repairs distinguish the tie.', + ], + }; +} + +function summarizeChecklist(items) { + const rows = Array.isArray(items) ? items : []; + return { + total: rows.length, + ready: rows.filter((item) => item?.status === 'ready').length, + inProgress: rows.filter((item) => item?.status === 'in_progress').length, + blocked: rows.filter((item) => item?.status === 'blocked').length, + done: rows.filter((item) => item?.status === 'done').length, + }; +} + +function renderChecklistItem(item) { + if (typeof item === 'string') { + return item; + } + const parts = []; + if (item?.task) { + parts.push(item.task); + } + if (item?.why) { + parts.push(item.why); + } + if (item?.dischargeWith) { + parts.push(`discharge: ${item.dischargeWith}`); + } + if (item?.command) { + parts.push(`command: ${item.command}`); + } + const body = parts.join(' | '); + if (item?.obligationId || item?.checkId || item?.criterionId) { + const id = item.obligationId ?? item.checkId ?? item.criterionId; + return `\`${id}\`: ${item.status ?? 'ready'}${body ? ` | ${body}` : ''}`; + } + return body || '(unspecified)'; +} + +function escapeXml(value) { + return String(value ?? '') + .replaceAll('&', '&') + .replaceAll('<', '<') + .replaceAll('>', '>') + .replaceAll('"', '"') + .replaceAll("'", '''); +} + +function wrapSvgText(text, maxLength = 44) { + const source = String(text ?? '').trim(); + if (!source) { + return []; + } + + const words = source.split(/\s+/); + const lines = []; + let current = ''; + for (const word of words) { + const candidate = current ? `${current} ${word}` : word; + if (candidate.length <= maxLength) { + current = candidate; + continue; + } + if (current) { + lines.push(current); + } + current = word; + } + if (current) { + lines.push(current); + } + return lines; +} + +function renderP848FormalizationWorkDiagram(doc) { + const target = doc?.currentWork ?? {}; + const packet = target.packetData ?? {}; + const rowTable = Array.isArray(packet.rowProgressionAnchorTable) ? packet.rowProgressionAnchorTable : []; + const anchorTable = Array.isArray(packet.anchorCongruenceTable) ? packet.anchorCongruenceTable : []; + const priorRows = Array.isArray(packet.priorRowsModuloWitness) ? packet.priorRowsModuloWitness : []; + const period = Math.max(...rowTable.map((row) => Number(row.rowIndexPeriod)).filter(Number.isFinite), Number(packet.witnessSquareModulus) || 1); + const witness = packet.witnessSquareModulus ?? '(unknown)'; + const representative = packet.representative ?? '(unknown)'; + const nextSameRowWitness = packet.nextSameRowWitnessFor282 ?? null; + const crtDerivation = packet.tupleRowCrtDerivation ?? null; + const width = 1440; + const height = 980; + const chartLeft = 90; + const chartTop = 280; + const chartWidth = 760; + const chartHeight = 420; + const rowSpacing = chartHeight / Math.max(rowTable.length, 1); + const neverX = chartLeft + chartWidth + 95; + const tickValues = [0, Math.floor(period / 4), Math.floor(period / 2), Math.floor((3 * period) / 4), period]; + + const lines = [ + ``, + `${escapeXml(doc.displayName)} formalization work diagram`, + `Diagram of the 848 shared-prefix row progression showing when tracked anchors hit witness ${escapeXml(witness)} and why anchor 282 is special at row index 0.`, + '', + '', + '', + '', + '', + '', + '', + '', + '', + '', + '', + '', + '', + ``, + '', + `${escapeXml(doc.displayName)}: 282 / 841 Mechanism`, + `Representative ${escapeXml(representative)} on tuple ${escapeXml(packet.tupleKey ?? '(unknown tuple)')}`, + `Witness ${escapeXml(witness)} is the extra repair witness; the row progression itself still traverses all residues modulo ${escapeXml(witness)}.`, + crtDerivation + ? `Tuple-row CRT projects to ${escapeXml(crtDerivation.projectedResidueModuloWitness)} mod ${escapeXml(witness)}${crtDerivation.firstStableProjectionAnchor ? `, stabilizing when anchor ${escapeXml(crtDerivation.firstStableProjectionAnchor)} is added` : ''}.` + : '', + ]; + + const cards = [ + { x: 88, y: 184, w: 220, h: 72, label: 'Verdict', value: target.mechanismAssessment?.verdict ?? 'unresolved', accent: '#0f766e' }, + { x: 326, y: 184, w: 220, h: 72, label: 'Representative residue', value: `${packet.representativeResidueModuloWitness ?? '(unknown)'} mod ${witness}`, accent: '#1d4ed8' }, + { x: 564, y: 184, w: 220, h: 72, label: '282 row start', value: 't = 0', accent: '#b91c1c' }, + { x: 802, y: 184, w: 270, h: 72, label: 'Next same-row 282 hit', value: nextSameRowWitness ?? '(unknown)', accent: '#7c3aed' }, + { x: 1090, y: 184, w: 260, h: 72, label: 'Verified base', value: doc.currentState?.latestVerifiedInterval ?? '(unknown)', accent: '#9a3412' }, + ]; + + for (const card of cards) { + lines.push(``); + lines.push(``); + lines.push(`${escapeXml(card.label)}`); + lines.push(`${escapeXml(card.value)}`); + } + + lines.push(``); + lines.push(`Shared-Prefix Row Progression`); + lines.push(`Each point shows the first row index t where a tracked anchor can hit witness ${escapeXml(witness)} along n = residue + modulus * t.`); + lines.push(``); + lines.push(``); + lines.push(``); + lines.push(`never`); + + for (const tick of tickValues) { + const x = chartLeft + (chartWidth * tick) / period; + lines.push(``); + lines.push(`${escapeXml(tick)}`); + } + + rowTable.forEach((row, index) => { + const y = chartTop + rowSpacing * index + rowSpacing / 2; + const is282 = row.anchor === 282; + const fill = is282 ? '#b91c1c' : row.solvableAlongRowProgression ? '#0f766e' : '#9a3412'; + const radius = is282 ? 9 : 7; + lines.push(``); + lines.push(`${escapeXml(row.anchor)}`); + if (row.solvableAlongRowProgression && Number.isInteger(row.rowIndexForWitness)) { + const x = chartLeft + (chartWidth * row.rowIndexForWitness) / period; + lines.push(``); + lines.push(`t=${escapeXml(row.rowIndexForWitness)}`); + } else { + lines.push(``); + lines.push(`no solution`); + } + }); + + const congruencePanelX = 920; + const congruencePanelY = 330; + const congruenceRows = anchorTable.slice(0, 8); + lines.push(`Residue Match Slice`); + lines.push(`Representative residue 504 matches only the 282 failure residue class.`); + congruenceRows.forEach((row, index) => { + const y = congruencePanelY + index * 42; + const active = row.matchesRepresentativeResidue; + const bg = active ? '#fdecec' : row.solvableModuloWitness ? '#eef7f4' : '#fff4ea'; + const stroke = active ? '#b91c1c' : row.solvableModuloWitness ? '#cfe3dc' : '#f1c7a3'; + lines.push(``); + lines.push(`${escapeXml(row.anchor)}`); + lines.push(`needs ${escapeXml(row.requiredNResidueForFailure ?? 'none')}`); + lines.push(`${escapeXml(active ? 'matches rep' : row.solvableModuloWitness ? 'later/other residue' : 'unsolvable')}`); + lines.push(`res=${escapeXml(row.residueCheck)}`); + }); + + const priorPanelX = 920; + const priorPanelY = 710; + lines.push(`Earlier Boundary Rows`); + lines.push(`Earlier rows stay nonzero mod ${escapeXml(witness)} before the first 282 failure lands.`); + priorRows.forEach((row, index) => { + const y = priorPanelY + 26 + index * 34; + lines.push(``); + lines.push(`${escapeXml(row.representative)}`); + lines.push(`res=${escapeXml(row.residueModuloWitness)}`); + lines.push(`${escapeXml(row.tupleKey)}`); + }); + + if (crtDerivation && Array.isArray(crtDerivation.steps) && crtDerivation.steps.length > 0) { + const crtPanelX = 88; + const crtPanelY = 784; + lines.push(`Tuple-Row CRT Projection`); + lines.push(`As tuple congruences are added, the projected residue modulo ${escapeXml(witness)} evolves toward the boundary value ${escapeXml(crtDerivation.projectedResidueModuloWitness)}.`); + crtDerivation.steps.slice(0, 6).forEach((step, index) => { + const x = crtPanelX + index * 120; + const y = crtPanelY + 54; + const active = step.residueModWitness === crtDerivation.projectedResidueModuloWitness; + lines.push(``); + lines.push(`a=${escapeXml(step.anchor)}`); + lines.push(`mod ${escapeXml(step.combinedModulus)}`); + lines.push(`res ${escapeXml(step.residueModWitness)}`); + }); + } + + lines.push(`North-star reading: the row does not force 841 by itself, but the boundary representative is the unique tracked start-point of the 282 witness class inside that row progression.`); + lines.push(''); + return lines.join(''); +} + +function renderGenericFormalizationWorkDiagram(doc) { + const target = doc?.currentWork ?? {}; + const width = 1200; + const height = 780; + const lines = [ + ``, + `${escapeXml(doc.displayName)} formalization work diagram`, + `Generic visual summary of the current formalization-work packet.`, + '', + '', + `${escapeXml(doc.displayName)} Formalization Work`, + `${escapeXml(target.title ?? '(no current work)')}`, + `Status: ${escapeXml(target.status ?? '(unknown)')} | Route: ${escapeXml(doc.currentState?.activeRoute ?? '(none)')}`, + '', + '', + 'Working Definition', + 'Current Evidence', + ]; + + (target.workingDefinition ?? []).slice(0, 8).forEach((item, index) => { + const y = 274 + index * 48; + wrapSvgText(item, 48).forEach((line, lineIndex) => { + lines.push(`• ${escapeXml(line)}`); + }); + }); + (target.currentEvidence ?? []).slice(0, 8).forEach((item, index) => { + const y = 274 + index * 48; + wrapSvgText(item, 46).forEach((line, lineIndex) => { + lines.push(`• ${escapeXml(line)}`); + }); + }); + + lines.push(`Canonical files: ${escapeXml(doc.sources?.formalizationWorkJsonPath ?? '(none)')} and ${escapeXml(doc.sources?.formalizationWorkMarkdownPath ?? '(none)')}`); + lines.push(''); + return lines.join(''); +} + +export function renderProblemFormalizationWorkSvg(doc) { + const target = doc?.currentWork ?? {}; + if (Array.isArray(target?.packetData?.rowProgressionAnchorTable) && target.packetData.rowProgressionAnchorTable.length > 0) { + return renderP848FormalizationWorkDiagram(doc); + } + return renderGenericFormalizationWorkDiagram(doc); +} + +function buildP848AlignmentContext(theoremLoop) { + const bridgePath = theoremLoop?.sources?.legacyBridgeJsonPath ?? null; + const bridgeDoc = bridgePath ? readJsonIfPresent(bridgePath) : null; + const bridgeState = bridgeDoc?.current_bridge_state ?? null; + const nextRepresentative = bridgeState?.next_unmatched_representative ?? null; + const familyMenuPath = bridgeDoc?.sources?.family_menu_source_path ?? null; + const familyMenu = familyMenuPath ? readJsonIfPresent(familyMenuPath) : null; + const familyRow = Array.isArray(familyMenu?.families) && nextRepresentative !== null + ? familyMenu.families.find((row) => row?.representative === nextRepresentative) ?? null + : null; + const trackedTailMatrix = Array.isArray(bridgeDoc?.tracked_tail_matrix) ? bridgeDoc.tracked_tail_matrix : []; + const gpuLeaderboard = Array.isArray(bridgeDoc?.gpu_leaderboard) ? bridgeDoc.gpu_leaderboard : []; + const trackedTail282 = trackedTailMatrix.find((row) => row?.continuation === 282) ?? null; + const allFamilies = Array.isArray(familyMenu?.families) ? familyMenu.families : []; + const sameTupleFamilies = familyRow?.tupleKey + ? allFamilies.filter((row) => row?.tupleKey === familyRow.tupleKey) + : []; + const failing282Families = allFamilies + .filter((row) => Array.isArray(row?.repairRows) && row.repairRows.some((repairRow) => repairRow?.anchor === 282 && repairRow.squarefree === false)) + .sort((left, right) => Number(left?.representative ?? Number.MAX_SAFE_INTEGER) - Number(right?.representative ?? Number.MAX_SAFE_INTEGER)); + const firstFailing282Family = failing282Families[0] ?? null; + const repairRows = Array.isArray(familyRow?.repairRows) ? familyRow.repairRows : []; + const stableRepairRows = repairRows.filter((row) => row?.squarefree); + const failingRepairRows = repairRows.filter((row) => row && row.squarefree === false); + const failing282 = repairRows.find((row) => row?.anchor === 282 && row.squarefree === false) ?? null; + const only282Fails = failingRepairRows.length === 1 && failingRepairRows[0]?.anchor === 282; + const witnessSquareModulus = failing282?.squareWitnesses?.[0]?.squareModulus ?? null; + const tupleRowCrtDerivation = deriveTupleRowCrt(Array.isArray(familyRow?.tupleRows) ? familyRow.tupleRows : [], witnessSquareModulus); + const representativeModulus = familyRow?.modulus ?? null; + const representativeResidue = familyRow?.residue ?? null; + const rowProgressionModuloWitness = representativeModulus && witnessSquareModulus + ? { + gcdModulusWitness: gcdInt(representativeModulus, witnessSquareModulus), + modulusModWitness: positiveMod(representativeModulus, witnessSquareModulus), + residueModWitness: representativeResidue !== null ? positiveMod(representativeResidue, witnessSquareModulus) : null, + traversesAllWitnessResidues: gcdInt(representativeModulus, witnessSquareModulus) === 1, + } + : null; + const rowProgressionAnchorTable = representativeModulus && representativeResidue !== null && witnessSquareModulus + ? repairRows.map((row) => { + const progressionCoeff = positiveMod(Number(row.anchor) * Number(representativeModulus), witnessSquareModulus); + const progressionRhs = positiveMod(-(Number(row.anchor) * Number(representativeResidue) + 1), witnessSquareModulus); + const congruence = solveLinearCongruenceNonnegative(progressionCoeff, progressionRhs, witnessSquareModulus); + return { + anchor: row.anchor, + progressionCoeffModuloWitness: progressionCoeff, + progressionRhsModuloWitness: progressionRhs, + gcdCoeffWitness: congruence?.gcdCoeffModulus ?? null, + rowIndexForWitness: congruence?.solvable ? congruence.solution : null, + rowIndexPeriod: congruence?.solvable ? congruence.period : null, + witnessOccursAtCurrentRepresentative: congruence?.solvable ? congruence.solution === 0 : false, + solvableAlongRowProgression: Boolean(congruence?.solvable), + squarefree: row.squarefree, + }; + }) + : []; + const rowProgressionAnchor282 = rowProgressionAnchorTable.find((row) => row.anchor === 282) ?? null; + const nextSameRowWitnessFor282 = rowProgressionAnchor282 + && rowProgressionAnchor282.solvableAlongRowProgression + && representativeResidue !== null + && representativeModulus + && rowProgressionAnchor282.rowIndexPeriod + ? Number(representativeResidue) + Number(representativeModulus) * ( + rowProgressionAnchor282.rowIndexForWitness === 0 + ? rowProgressionAnchor282.rowIndexPeriod + : rowProgressionAnchor282.rowIndexForWitness + ) + : null; + const repairRow282ForFamily = (family) => Array.isArray(family?.repairRows) + ? family.repairRows.find((row) => row?.anchor === 282) ?? null + : null; + const prior282Rows = firstFailing282Family && witnessSquareModulus + ? allFamilies + .filter((row) => Number(row?.representative) < Number(firstFailing282Family.representative)) + .map((row) => ({ + representative: row.representative, + tupleKey: row.tupleKey ?? null, + repairRow: repairRow282ForFamily(row), + })) + .filter((row) => row.repairRow && Number.isInteger(row.repairRow.value)) + .sort((left, right) => Number(left.representative) - Number(right.representative)) + : []; + const priorRowsModuloWitness = witnessSquareModulus + ? prior282Rows.slice(-3).map((row) => ({ + representative: row.representative, + tupleKey: row.tupleKey, + residueModuloWitness: Number(row.repairRow.value % witnessSquareModulus), + squarefree: row.repairRow.squarefree, + })) + : []; + const witnessFirstOccurrence = witnessSquareModulus + ? (() => { + const matchingFamilies = allFamilies + .map((row) => ({ + representative: row?.representative ?? null, + tupleKey: row?.tupleKey ?? null, + repairRow: repairRow282ForFamily(row), + })) + .filter((row) => row.repairRow && Array.isArray(row.repairRow.squareWitnesses) + && row.repairRow.squareWitnesses.some((witness) => witness?.squareModulus === witnessSquareModulus)) + .sort((left, right) => Number(left.representative) - Number(right.representative)); + const first = matchingFamilies[0] ?? null; + return first + ? { + squareModulus: witnessSquareModulus, + firstRepresentative: first.representative, + firstTupleKey: first.tupleKey, + earlierRowCount: prior282Rows.length, + earlierZeroResidueCount: prior282Rows.filter((row) => Number(row.repairRow.value % witnessSquareModulus) === 0).length, + } + : null; + })() + : null; + const witnessTimeline = failing282Families + .map((row) => { + const repairRow = repairRow282ForFamily(row); + const squareModulus = repairRow?.squareWitnesses?.[0]?.squareModulus ?? null; + return squareModulus + ? { + representative: row.representative, + tupleKey: row.tupleKey ?? null, + witnessSquareModulus: squareModulus, + } + : null; + }) + .filter(Boolean); + + return { + bridgeDoc, + bridgeState, + trackedTailMatrix, + gpuLeaderboard, + familyMenuPath, + familyMenu, + allFamilies, + familyRow, + nextRepresentative, + trackedTail282, + failing282Families, + firstFailing282Family, + repairRows, + stableRepairRows, + failingRepairRows, + failing282, + only282Fails, + witnessSquareModulus, + tupleRowCrtDerivation, + sameTupleCount: sameTupleFamilies.length, + rowProgressionModuloWitness, + rowProgressionAnchorTable, + nextSameRowWitnessFor282, + prior282Rows, + priorRowsModuloWitness, + witnessFirstOccurrence, + witnessTimeline, + }; +} + +function findP848StructuralLiftChecklistStep(checklist, stepId) { + for (const phase of checklist?.phases ?? []) { + const step = (phase?.steps ?? []).find((item) => item?.stepId === stepId); + if (step) { + return { phase, step }; + } + } + return null; +} + +function buildP848SameSideBaseCliqueProof() { + const residueChecks = [ + { + sideId: 'B7', + residue: 7, + productResidueModulo25: positiveMod(7 * 7, 25), + productPlusOneResidueModulo25: positiveMod((7 * 7) + 1, 25), + }, + { + sideId: 'B18', + residue: 18, + productResidueModulo25: positiveMod(18 * 18, 25), + productPlusOneResidueModulo25: positiveMod((18 * 18) + 1, 25), + }, + ]; + const failedRows = residueChecks.filter((row) => row.productPlusOneResidueModulo25 !== 0); + + return { + checkerId: 'p848_C1_same_side_base_clique_checker_v1', + obligationId: 'C1_same_side_base_clique', + status: failedRows.length === 0 ? 'proved_by_mod25_identity' : 'failed', + checkedRowCount: residueChecks.length, + passCount: residueChecks.length - failedRows.length, + failCount: failedRows.length, + statement: 'Inside one principal base side, compatible base vertices form a clique for the fixed outsider graph considered by the verifier.', + scope: { + problemId: '848', + universalSameSideClaim: true, + dependsOnOutsider: false, + dependsOnN: false, + principalBaseResiduesModulo25: [7, 18], + }, + hypotheses: [ + 'u and v are both in the 7 mod 25 principal base side, or both in the 18 mod 25 principal base side.', + 'The verifier graph uses non-squarefree pair compatibility: an edge is present when u*v + 1 is not squarefree.', + ], + proof: [ + 'If u and v are both 7 mod 25, then u*v + 1 is congruent to 7^2 + 1 = 50, hence 0 mod 25.', + 'If u and v are both 18 mod 25, then u*v + 1 is congruent to 18^2 + 1 = 325, hence 0 mod 25.', + 'Because 25 = 5^2 is a square divisor, u*v + 1 is not squarefree in either same-side case.', + 'Therefore every pair of same-side principal base vertices has an edge, so each same-side compatible vertex set is a clique.', + ], + residueChecks, + failedRows, + conclusion: 'The same-side parts of the mixed-base compatibility graph are cliques; only cross-side edges need the missing-cross graph analysis.', + falsifierBoundary: failedRows.length === 0 + ? 'A falsifier would need a pair of same-side principal base residues whose product plus one is not divisible by 25, but both residue checks are 0 mod 25.' + : 'At least one principal same-side residue check failed.', + }; +} + +function buildP848TwoCliquesPlusCrossEdgesProof(sameSideBaseCliqueProof, miner, fullVerifier) { + const verifierBoundaryText = [ + fullVerifier?.boundary?.cliqueReduction, + miner?.sourceVerifier?.method, + miner?.summary?.nextTheoremLane, + ].filter(Boolean).join(' '); + const proofChecks = [ + { + checkId: 'C1_dependency_discharged', + passed: sameSideBaseCliqueProof?.status === 'proved_by_mod25_identity' + && Number(sameSideBaseCliqueProof?.failCount ?? 1) === 0, + evidence: sameSideBaseCliqueProof?.checkerId ?? null, + }, + { + checkId: 'principal_side_partition', + passed: true, + evidence: { + leftSide: 'B7-compatible vertices', + rightSide: 'B18-compatible vertices', + principalResiduesModulo25: [7, 18], + }, + }, + { + checkId: 'same_side_edges_complete_by_C1', + passed: sameSideBaseCliqueProof?.residueChecks?.every((row) => row.productPlusOneResidueModulo25 === 0) === true, + evidence: sameSideBaseCliqueProof?.residueChecks ?? [], + }, + { + checkId: 'cross_edges_are_the_only_unfixed_edges', + passed: true, + evidence: 'After partitioning into B7 and B18 sides and applying C1 on each side, the only pair relations not forced complete are B7 x B18 cross pairs.', + }, + { + checkId: 'verifier_boundary_uses_two_clique_reduction', + passed: verifierBoundaryText.includes('two cliques') + || verifierBoundaryText.includes('mixed_base') + || verifierBoundaryText.includes('mixed-base'), + evidence: verifierBoundaryText || null, + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + + return { + checkerId: 'p848_C2_two_cliques_plus_cross_edges_checker_v1', + obligationId: 'C2_two_cliques_plus_cross_edges', + status: failedChecks.length === 0 ? 'proved_by_c1_partition_decomposition' : 'failed', + checkedRowCount: proofChecks.length, + passCount: proofChecks.length - failedChecks.length, + failCount: failedChecks.length, + statement: 'For fixed outsider x, the compatible mixed-base graph is one clique on B7-compatible vertices, one clique on B18-compatible vertices, plus arbitrary cross edges.', + scope: { + problemId: '848', + universalInN: true, + universalInOutsider: true, + principalBaseResiduesModulo25: [7, 18], + boundedVerifierEvidenceRange: fullVerifier?.summary?.assessedRange ?? miner?.summary?.assessedRange ?? null, + }, + dependencies: [ + sameSideBaseCliqueProof?.checkerId ?? 'p848_C1_same_side_base_clique_checker_v1', + 'definition_of_mixed_base_compatible_vertex_sets', + ], + hypotheses: [ + 'For fixed outsider x and cutoff N, L is the set of x-compatible principal base vertices congruent to 7 mod 25.', + 'For fixed outsider x and cutoff N, R is the set of x-compatible principal base vertices congruent to 18 mod 25.', + 'The mixed-base graph has vertex set L union R and an edge exactly when the corresponding pair relation is compatible in the verifier graph.', + 'C1 has proved that every same-side pair inside L or inside R is an edge.', + ], + proof: [ + 'The vertex set is partitioned into the two principal compatible sides L and R by residue modulo 25.', + 'By C1, every pair of vertices inside L is adjacent, and every pair of vertices inside R is adjacent.', + 'No additional same-side obstruction remains after C1; all non-forced edge information lies between L and R.', + 'Therefore the graph is exactly two cliques, L and R, plus whatever cross edges the pair compatibility relation supplies.', + ], + proofChecks, + failedChecks, + conclusion: 'The mixed-base compatible graph is a two-clique/co-bipartite graph; the next theorem atom only needs to name the missing cross-edge bipartite graph.', + falsifierBoundary: failedChecks.length === 0 + ? 'A falsifier must either break C1 on a same-side pair or exhibit a compatible mixed-base vertex outside the B7/B18 partition.' + : 'At least one decomposition check failed.', + }; +} + +function buildP848MissingCrossGraphDefinitionProof(twoCliquesPlusCrossEdgesProof, miner, fullVerifier) { + const verifierBoundaryText = [ + fullVerifier?.boundary?.cliqueReduction, + miner?.liftObligations?.find((obligation) => obligation.obligationId === 'p848_cross_side_matching_bound')?.statementTemplate, + ].filter(Boolean).join(' '); + const proofChecks = [ + { + checkId: 'C2_dependency_discharged', + passed: twoCliquesPlusCrossEdgesProof?.status === 'proved_by_c1_partition_decomposition' + && Number(twoCliquesPlusCrossEdgesProof?.failCount ?? 1) === 0, + evidence: twoCliquesPlusCrossEdgesProof?.checkerId ?? null, + }, + { + checkId: 'missing_cross_graph_is_bipartite_by_definition', + passed: true, + evidence: { + leftPartition: 'L = B7-compatible vertices', + rightPartition: 'R = B18-compatible vertices', + noSameSideMissingEdgesIncluded: true, + }, + }, + { + checkId: 'edge_sign_is_missing_compatibility', + passed: true, + evidence: 'An edge (l,r) belongs to H_{x,N} exactly when l in L, r in R, and l*r+1 is squarefree, i.e. the cross pair is missing from the compatible graph.', + }, + { + checkId: 'verifier_boundary_names_missing_cross_edges', + passed: verifierBoundaryText.includes('missing cross') + || verifierBoundaryText.includes('missing cross-edge') + || verifierBoundaryText.includes('missing-cross'), + evidence: verifierBoundaryText || null, + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + + return { + checkerId: 'p848_C3_missing_cross_graph_definition_checker_v1', + obligationId: 'C3_missing_cross_graph_definition', + status: failedChecks.length === 0 ? 'proved_by_definition' : 'failed', + checkedRowCount: proofChecks.length, + passCount: proofChecks.length - failedChecks.length, + failCount: failedChecks.length, + statement: 'Define H_{x,N} as the bipartite graph whose edges are precisely missing cross edges between compatible B7 and B18 vertices.', + scope: { + problemId: '848', + universalInN: true, + universalInOutsider: true, + graphPartitions: ['B7-compatible vertices', 'B18-compatible vertices'], + boundedVerifierEvidenceRange: fullVerifier?.summary?.assessedRange ?? miner?.summary?.assessedRange ?? null, + }, + dependencies: [ + twoCliquesPlusCrossEdgesProof?.checkerId ?? 'p848_C2_two_cliques_plus_cross_edges_checker_v1', + ], + hypotheses: [ + 'C2 has decomposed the mixed-base compatible graph into two same-side cliques L and R plus cross edges.', + 'Cross compatibility is evaluated only for pairs (l,r) with l in L and r in R.', + 'A missing cross edge means that the pair (l,r) is not an edge of the compatible graph.', + ], + definition: { + vertexSet: 'V(H_{x,N}) = L union R', + edgeSet: 'E(H_{x,N}) = {{l,r}: l in L, r in R, and {l,r} is not a compatible cross edge}', + equivalentArithmeticSign: 'Because compatible edges are non-squarefree pair relations, H contains (l,r) exactly when l*r+1 is squarefree for the verifier relation.', + }, + proof: [ + 'C2 leaves only cross pairs between L and R as possible obstructions to cliquehood.', + 'Put exactly those obstructing cross pairs into H_{x,N}.', + 'Every edge of H has one endpoint in L and one endpoint in R, so H is bipartite by construction.', + 'The sign convention is explicit: H records missing compatible cross edges, not present compatible cross edges.', + ], + proofChecks, + failedChecks, + conclusion: 'The missing-cross graph H_{x,N} is a well-defined bipartite graph on the B7/B18 compatible partition with edges exactly opposite to cross compatibility.', + falsifierBoundary: failedChecks.length === 0 + ? 'A falsifier must show a same-side H edge or a cross pair whose H membership uses the wrong compatibility sign.' + : 'At least one missing-cross graph definition check failed.', + }; +} + +function buildP848CliqueVertexCoverDualityProof(missingCrossGraphDefinitionProof) { + const proofChecks = [ + { + checkId: 'C3_dependency_discharged', + passed: missingCrossGraphDefinitionProof?.status === 'proved_by_definition' + && Number(missingCrossGraphDefinitionProof?.failCount ?? 1) === 0, + evidence: missingCrossGraphDefinitionProof?.checkerId ?? null, + }, + { + checkId: 'clique_complement_hits_every_missing_cross_edge', + passed: true, + evidence: 'If a clique kept both endpoints of a missing cross edge, those endpoints would be a non-edge in the compatible graph.', + }, + { + checkId: 'vertex_cover_complement_is_clique', + passed: true, + evidence: 'If removed vertices cover every missing cross edge, then no missing cross edge remains among kept vertices; same-side pairs are already cliques by C2.', + }, + { + checkId: 'max_min_cardinality_duality', + passed: true, + evidence: 'Maximizing kept vertices is equivalent to minimizing removed vertices over vertex covers of H_{x,N}.', + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + + return { + checkerId: 'p848_C4_clique_to_vertex_cover_duality_checker_v1', + obligationId: 'C4_clique_to_vertex_cover_duality', + status: failedChecks.length === 0 ? 'proved_by_clique_vertex_cover_complement' : 'failed', + checkedRowCount: proofChecks.length, + passCount: proofChecks.length - failedChecks.length, + failCount: failedChecks.length, + statement: 'A mixed-base clique equals all compatible vertices minus a vertex cover of H_{x,N}; hence max clique size is |L| + |R| minus minimum vertex cover size.', + dependencies: [ + missingCrossGraphDefinitionProof?.checkerId ?? 'p848_C3_missing_cross_graph_definition_checker_v1', + ], + hypotheses: [ + 'The mixed-base compatible graph is two cliques L and R plus cross edges.', + 'H_{x,N} is the bipartite graph of missing cross edges between L and R.', + 'A vertex cover of H_{x,N} is a set of vertices meeting every missing cross edge.', + ], + proof: [ + 'Let K be a clique in the compatible graph and S be the complement of K in L union R.', + 'If an H edge had both endpoints outside S, then both endpoints would lie in K but would be a missing compatible cross edge, contradicting cliquehood.', + 'Thus S is a vertex cover of H.', + 'Conversely, if S is a vertex cover of H, then K = (L union R) minus S contains no missing cross edge, and same-side pairs are already complete, so K is a clique.', + 'The correspondence reverses cardinality, giving maxClique = |L| + |R| - minVertexCover(H).', + ], + proofChecks, + failedChecks, + conclusion: 'Mixed-base clique maximization is equivalent to deleting a minimum vertex cover from the missing-cross graph.', + falsifierBoundary: failedChecks.length === 0 + ? 'A falsifier must exhibit a clique whose complement misses an H edge, or a vertex cover whose complement is not a clique.' + : 'At least one clique/vertex-cover duality check failed.', + }; +} + +function buildP848KonigMatchingReductionProof(missingCrossGraphDefinitionProof) { + const proofChecks = [ + { + checkId: 'C3_dependency_discharged', + passed: missingCrossGraphDefinitionProof?.status === 'proved_by_definition' + && Number(missingCrossGraphDefinitionProof?.failCount ?? 1) === 0, + evidence: missingCrossGraphDefinitionProof?.checkerId ?? null, + }, + { + checkId: 'H_is_bipartite', + passed: true, + evidence: 'Every H edge runs between the B7-compatible side L and the B18-compatible side R.', + }, + { + checkId: 'konig_theorem_applies', + passed: true, + evidence: 'For every finite bipartite graph, minimum vertex cover size equals maximum matching size.', + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + + return { + checkerId: 'p848_C5_konig_matching_reduction_checker_v1', + obligationId: 'C5_konig_matching_reduction', + status: failedChecks.length === 0 ? 'proved_by_konig_theorem' : 'failed', + checkedRowCount: proofChecks.length, + passCount: proofChecks.length - failedChecks.length, + failCount: failedChecks.length, + statement: "Because H_{x,N} is bipartite, minimum vertex cover size equals maximum matching size.", + dependencies: [ + missingCrossGraphDefinitionProof?.checkerId ?? 'p848_C3_missing_cross_graph_definition_checker_v1', + "Konig's theorem for finite bipartite graphs", + ], + hypotheses: [ + 'H_{x,N} is finite because it is built from vertices <= N.', + 'H_{x,N} is bipartite with parts L and R by C3.', + "Konig's theorem is available as a standard graph-theory lemma for finite bipartite graphs.", + ], + proof: [ + 'C3 constructs H with all edges crossing between L and R.', + 'Therefore H satisfies the finite bipartite hypotheses of Konig\'s theorem.', + "Apply Konig's theorem to replace minVertexCover(H) with maxMatching(H).", + ], + proofChecks, + failedChecks, + conclusion: 'The minimum vertex cover term in C4 may be replaced by the maximum matching size of H_{x,N}.', + falsifierBoundary: failedChecks.length === 0 + ? "A falsifier must show H is not bipartite/finite or that the invoked Konig theorem dependency is unavailable." + : 'At least one Konig-reduction check failed.', + }; +} + +function buildP848MixedCliqueMatchingFormulaProof(cliqueVertexCoverDualityProof, konigMatchingReductionProof, fullVerifier) { + const worstExact = fullVerifier?.worstExactMixedRow ?? null; + const rowChecks = worstExact?.worstThreat + ? [{ + checkId: 'worst_exact_row_matches_formula', + N: worstExact.N, + p: worstExact.p, + outsider: worstExact.worstThreat.outsider, + leftSize: worstExact.worstThreat.compatibleSide7Count, + rightSize: worstExact.worstThreat.compatibleSide18Count, + maxMatchingSize: worstExact.worstThreat.matchingSizeInMissingCrossGraph, + verifierCliqueSize: worstExact.worstThreat.mixedBaseCliqueSize, + formulaCliqueSize: Number(worstExact.worstThreat.compatibleSide7Count ?? 0) + + Number(worstExact.worstThreat.compatibleSide18Count ?? 0) + - Number(worstExact.worstThreat.matchingSizeInMissingCrossGraph ?? 0), + }] + : []; + for (const row of rowChecks) { + row.passed = row.formulaCliqueSize === row.verifierCliqueSize; + } + const proofChecks = [ + { + checkId: 'C4_dependency_discharged', + passed: cliqueVertexCoverDualityProof?.status === 'proved_by_clique_vertex_cover_complement' + && Number(cliqueVertexCoverDualityProof?.failCount ?? 1) === 0, + evidence: cliqueVertexCoverDualityProof?.checkerId ?? null, + }, + { + checkId: 'C5_dependency_discharged', + passed: konigMatchingReductionProof?.status === 'proved_by_konig_theorem' + && Number(konigMatchingReductionProof?.failCount ?? 1) === 0, + evidence: konigMatchingReductionProof?.checkerId ?? null, + }, + { + checkId: 'formula_composes_C4_and_C5', + passed: true, + evidence: 'maxClique = |L| + |R| - minVertexCover(H) and minVertexCover(H) = maxMatching(H).', + }, + { + checkId: 'verifier_row_formula_replay_available', + passed: rowChecks.length > 0 ? rowChecks.every((row) => row.passed) : true, + evidence: rowChecks, + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + const failedRows = rowChecks.filter((row) => !row.passed); + + return { + checkerId: 'p848_C6_mixed_clique_matching_formula_checker_v1', + obligationId: 'C6_mixed_clique_matching_formula', + status: failedChecks.length === 0 && failedRows.length === 0 + ? 'proved_by_vertex_cover_konig_composition' + : 'failed', + checkedRowCount: proofChecks.length + rowChecks.length, + passCount: proofChecks.length + rowChecks.length - failedChecks.length - failedRows.length, + failCount: failedChecks.length + failedRows.length, + statement: 'sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).', + dependencies: [ + cliqueVertexCoverDualityProof?.checkerId ?? 'p848_C4_clique_to_vertex_cover_duality_checker_v1', + konigMatchingReductionProof?.checkerId ?? 'p848_C5_konig_matching_reduction_checker_v1', + ], + hypotheses: [ + 'C4 proves max mixed clique size equals |L| + |R| minus minVertexCover(H).', + 'C5 proves minVertexCover(H) equals maxMatching(H).', + ], + proof: [ + 'Start from the C4 identity maxClique = |L| + |R| - minVertexCover(H).', + 'Substitute minVertexCover(H) = maxMatching(H) from C5.', + 'The resulting identity is sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).', + ], + ...(rowChecks.length <= 100 + ? { rowChecks } + : { + rowCheckSample: tightestRows, + rowChecksOmitted: rowChecks.length - tightestRows.length, + }), + proofChecks, + failedChecks, + failedRows, + conclusion: 'The verifier Hopcroft-Karp quantity has now been promoted to a theorem-facing graph formula.', + falsifierBoundary: failedChecks.length === 0 && failedRows.length === 0 + ? 'A falsifier must break C4, break C5, or find a verifier row where |L| + |R| - matching disagrees with sMixed.' + : 'At least one mixed-clique formula check failed.', + }; +} + +function buildP848MatchingSaturationBoundProof(mixedCliqueMatchingFormulaProof, fullVerifier) { + const threateningOutsiderRows = (fullVerifier?.threatLiftMiningRows ?? []) + .filter((row) => row?.certificateMode === 'exact_mixed_base'); + const worstRows = (fullVerifier?.liftMiningRows ?? []) + .filter((row) => row?.certificateMode === 'exact_mixed_base'); + const exactMixedRows = threateningOutsiderRows.length > 0 ? threateningOutsiderRows : worstRows; + const sourceRowKind = threateningOutsiderRows.length > 0 + ? 'all_bounded_threatening_outsiders' + : 'worst_threat_per_structural_row'; + const rowChecks = exactMixedRows.map((row) => { + const leftSize = Number(row.compatibleSide7Count); + const rightSize = Number(row.compatibleSide18Count); + const strictBaseThreshold = Number(row.strictBaseThreshold); + const actualMatching = Number(row.matchingSizeInMissingCrossGraph); + const verifierMixedCliqueSize = Number(row.mixedBaseCliqueSize ?? row.sMaxMixed ?? row.worstMixedCliqueSize); + const numericFieldsPresent = [ + Number(row.N), + Number(row.p), + leftSize, + rightSize, + strictBaseThreshold, + actualMatching, + verifierMixedCliqueSize, + ].every(Number.isFinite); + const totalCompatible = leftSize + rightSize; + const smallerSideSize = Math.min(leftSize, rightSize); + const requiredMatchingLowerBound = Number.isFinite(Number(row.requiredMatchingLowerBound)) + ? Number(row.requiredMatchingLowerBound) + : totalCompatible - strictBaseThreshold + 1; + const formulaCliqueSize = totalCompatible - actualMatching; + const matchingSlack = actualMatching - requiredMatchingLowerBound; + const lowerBoundPassed = numericFieldsPresent && actualMatching >= requiredMatchingLowerBound; + const saturationPassed = numericFieldsPresent && actualMatching === smallerSideSize; + const formulaReplayPassed = numericFieldsPresent && formulaCliqueSize === verifierMixedCliqueSize; + + return { + checkId: `D1_matching_saturation_${row.N}_${row.p}_${row.outsider ?? row.worstOutsider ?? row.sMaxMixedWitness ?? 'unknown'}`, + N: Number(row.N), + p: Number(row.p), + outsider: Number(row.outsider ?? row.worstOutsider ?? row.sMaxMixedWitness ?? NaN), + outsiderMod25: row.outsiderMod25 ?? row.worstOutsiderMod25 ?? row.sMaxMixedWitnessMod25 ?? null, + leftSize, + rightSize, + smallerSideSize, + totalCompatible, + strictBaseThreshold, + requiredMatchingLowerBound, + actualMatching, + matchingSlack, + formulaCliqueSize, + verifierMixedCliqueSize, + numericFieldsPresent, + lowerBoundPassed, + saturationPassed, + formulaReplayPassed, + passed: numericFieldsPresent && lowerBoundPassed && saturationPassed && formulaReplayPassed, + }; + }); + const primeSummaries = Array.from(new Set(rowChecks.map((row) => row.p))).sort((a, b) => a - b) + .map((p) => { + const rows = rowChecks.filter((row) => row.p === p); + const minRequiredMatchingLowerBound = Math.min(...rows.map((row) => row.requiredMatchingLowerBound)); + const maxRequiredMatchingLowerBound = Math.max(...rows.map((row) => row.requiredMatchingLowerBound)); + const minActualMatching = Math.min(...rows.map((row) => row.actualMatching)); + const maxActualMatching = Math.max(...rows.map((row) => row.actualMatching)); + const minMatchingSlack = Math.min(...rows.map((row) => row.matchingSlack)); + return { + p, + rowCount: rows.length, + minRequiredMatchingLowerBound, + maxRequiredMatchingLowerBound, + minActualMatching, + maxActualMatching, + minMatchingSlack, + allRowsSaturateSmallerSide: rows.every((row) => row.saturationPassed), + allRowsMeetRequiredLowerBound: rows.every((row) => row.lowerBoundPassed), + }; + }); + const tightestRows = [...rowChecks] + .sort((a, b) => a.matchingSlack - b.matchingSlack || a.N - b.N || a.p - b.p) + .slice(0, 5) + .map((row) => ({ + N: row.N, + p: row.p, + outsider: row.outsider, + requiredMatchingLowerBound: row.requiredMatchingLowerBound, + actualMatching: row.actualMatching, + matchingSlack: row.matchingSlack, + smallerSideSize: row.smallerSideSize, + })); + const observedPrimes = Array.from(new Set(rowChecks.map((row) => row.p))).sort((a, b) => a - b); + const proofChecks = [ + { + checkId: 'C6_dependency_discharged', + passed: mixedCliqueMatchingFormulaProof?.status === 'proved_by_vertex_cover_konig_composition' + && Number(mixedCliqueMatchingFormulaProof?.failCount ?? 1) === 0, + evidence: mixedCliqueMatchingFormulaProof?.checkerId ?? null, + }, + { + checkId: 'exact_mixed_lift_rows_available', + passed: rowChecks.length > 0, + evidence: { + rowCount: rowChecks.length, + verifierLiftMiningRowCount: fullVerifier?.summary?.liftMiningRowCount ?? null, + verifierThreatLiftMiningRowCount: fullVerifier?.summary?.threatLiftMiningRowCount ?? null, + sourceRowKind, + }, + }, + { + checkId: 'primary_exact_primes_are_current_D_lane', + passed: rowChecks.length > 0 && observedPrimes.every((p) => [13, 17].includes(p)), + evidence: observedPrimes, + }, + { + checkId: 'matching_lower_bound_formula_extracted', + passed: rowChecks.length > 0 + && rowChecks.every((row) => Number.isFinite(row.requiredMatchingLowerBound)), + evidence: 'K(N,x) = |L| + |R| - strictBaseThreshold + 1 is the matching lower bound needed for strict mixed-clique margin.', + }, + { + checkId: 'all_rows_meet_required_matching_bound', + passed: rowChecks.length > 0 && rowChecks.every((row) => row.lowerBoundPassed), + evidence: { + primeSummaries, + tightestRows, + }, + }, + { + checkId: 'all_rows_saturate_smaller_side', + passed: rowChecks.length > 0 && rowChecks.every((row) => row.saturationPassed), + evidence: primeSummaries, + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + const failedRows = rowChecks.filter((row) => !row.passed); + + return { + checkerId: 'p848_D1_matching_saturation_bound_checker_v1', + obligationId: 'D1_residue_block_matching_injection', + status: failedChecks.length === 0 && failedRows.length === 0 + ? 'bounded_matching_saturation_extraction_certified' + : 'failed', + checkedRowCount: proofChecks.length + rowChecks.length, + passCount: proofChecks.length + rowChecks.length - failedChecks.length - failedRows.length, + failCount: failedChecks.length + failedRows.length, + statement: 'Extract the current D-lane matching target: each bounded exact mixed-base threatening-outsider row has matching at least K(N,x), and the verifier matching saturates the smaller compatible side.', + scope: { + problemId: '848', + universalInN: false, + promotesAllNClaim: false, + boundedVerifierEvidenceRange: fullVerifier?.summary?.assessedRange ?? null, + boundedRowCount: rowChecks.length, + sourceRowKind, + observedPrimes, + role: 'bounded_extraction_packet_for_symbolic_D2_D3', + }, + dependencies: [ + mixedCliqueMatchingFormulaProof?.checkerId ?? 'p848_C6_mixed_clique_matching_formula_checker_v1', + 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.liftMiningRows', + ], + hypotheses: [ + 'C6 has promoted the mixed-base clique size to |L| + |R| - maxMatching(H_{x,N}).', + 'A strict mixed-base pass needs |L| + |R| - maxMatching(H_{x,N}) <= strictBaseThreshold - 1.', + 'Equivalently, it is enough to prove maxMatching(H_{x,N}) >= |L| + |R| - strictBaseThreshold + 1.', + 'The current packet is bounded to the exact mixed-base threatening-outsider rows emitted by the repo-owned full mixed-base structural verifier.', + ], + proof: [ + 'For each exact mixed-base threatening-outsider row, compute K(N,x) = |L| + |R| - strictBaseThreshold + 1.', + 'Replay the C6 formula against the verifier row to ensure |L| + |R| - matching equals the recorded mixed clique size.', + 'Check that the recorded maximum matching is at least K(N,x).', + 'Check the stronger bounded pattern that the recorded maximum matching saturates the smaller of the two compatible sides.', + 'This certifies the bounded extraction target and routes the all-N burden to symbolic lower-bound packets D2 and D3.', + ], + ...(rowChecks.length <= 100 + ? { rowChecks } + : { + rowCheckSample: tightestRows, + rowChecksOmitted: rowChecks.length - tightestRows.length, + }), + proofChecks, + failedChecks, + failedRows, + primeSummaries, + tightestRows, + conclusion: failedChecks.length === 0 && failedRows.length === 0 + ? `All ${rowChecks.length} current exact mixed-base threatening-outsider rows meet the required matching lower bound; the matching saturates the smaller compatible side in every checked row.` + : 'At least one current exact mixed-base threatening-outsider row failed the bounded D1 matching extraction.', + falsifierBoundary: failedChecks.length === 0 && failedRows.length === 0 + ? 'A refreshed verifier row falsifies this bounded extraction if matching < |L| + |R| - strictBaseThreshold + 1, if the C6 formula replay disagrees, or if the smaller-side saturation pattern fails. This is not yet the all-N symbolic matching proof.' + : 'Inspect failedChecks and failedRows; D2/D3 must not be promoted until D1 is repaired.', + }; +} + +function buildP848P13MatchingLowerBoundCandidate(matchingSaturationBoundProof, miner, matchingPatternMiner) { + const p13Profile = (miner?.threatMatchingProfiles ?? []).find((profile) => Number(profile?.p) === 13) ?? null; + if (!p13Profile) { + return null; + } + const tightestThreat = p13Profile.tightestThreats?.[0] ?? null; + const p13MatchingPattern = Number(matchingPatternMiner?.parameters?.targetPrime ?? NaN) === 13 + ? matchingPatternMiner + : null; + const matchingWitnessSample = (p13MatchingPattern?.witnesses ?? []).slice(0, 2).map((witness) => ({ + N: witness.N, + outsider: witness.outsider, + requiredMatchingLowerBound: witness.requiredMatchingLowerBound, + reconstructedMatchingSize: witness.reconstructedMatchingSize, + matchingSlack: witness.matchingSlack, + smallerSide: witness.smallerSide, + saturatesSmallerSide: witness.saturatesSmallerSide, + pairSample: (witness.matchingPairSample ?? []).slice(0, 6), + })); + + return { + candidateId: 'p848_D2_p13_matching_lower_bound_candidate_v1', + obligationId: 'D2_p13_matching_lower_bound', + status: matchingSaturationBoundProof?.status === 'bounded_matching_saturation_extraction_certified' + ? 'bounded_p13_threat_profile_ready_symbolic_proof_needed' + : 'blocked_by_D1', + scope: { + problemId: '848', + universalInN: false, + promotesAllNClaim: false, + boundedVerifierEvidenceRange: miner?.summary?.assessedRange ?? null, + threatRowCount: p13Profile.threatRowCount, + structuralRowCount: p13Profile.structuralRowCount, + source: 'STRUCTURAL_LIFT_MINER.threatMatchingProfiles[p=13]', + }, + extractedTarget: { + requiredMatchingLowerBoundRange: [ + p13Profile.minRequiredMatchingLowerBound, + p13Profile.maxRequiredMatchingLowerBound, + ], + actualMatchingRange: [ + p13Profile.minActualMatching, + p13Profile.maxActualMatching, + ], + minMatchingSlack: p13Profile.minMatchingSlack, + allThreatsMeetRequiredLowerBound: p13Profile.allThreatsMeetRequiredLowerBound, + allThreatsSaturateSmallerSide: p13Profile.allThreatsSaturateSmallerSide, + tightestThreat, + }, + matchingPatternEvidence: p13MatchingPattern + ? { + status: p13MatchingPattern.status ?? null, + targetPrime: p13MatchingPattern.parameters?.targetPrime ?? null, + witnessRowCount: p13MatchingPattern.summary?.witnessRowCount ?? null, + allReconstructedMatchesAgree: p13MatchingPattern.summary?.allReconstructedMatchesAgree ?? null, + allWitnessesSaturateSmallerSide: p13MatchingPattern.summary?.allWitnessesSaturateSmallerSide ?? null, + minMatchingSlack: p13MatchingPattern.summary?.minMatchingSlack ?? null, + patternSummary: p13MatchingPattern.patternSummary + ? { + totalWitnessMatchingPairs: p13MatchingPattern.patternSummary.totalWitnessMatchingPairs ?? null, + commonMatchingPairCountAcrossWitnesses: p13MatchingPattern.patternSummary.commonMatchingPairCountAcrossWitnesses ?? null, + outsiderResidueGroups: p13MatchingPattern.patternSummary.outsiderResidueGroups ?? [], + splitProfiles: (p13MatchingPattern.patternSummary.splitProfiles ?? []).slice(0, 4).map((profile) => ({ + groupKey: profile.groupKey, + witnessCount: profile.witnessCount, + minN: profile.minN, + maxN: profile.maxN, + minMatchingSlack: profile.minMatchingSlack, + commonMatchingPairCount: profile.commonMatchingPairCount, + rightMinusLeftModuloP2Distribution: (profile.rightMinusLeftModuloP2Distribution ?? []).slice(0, 6), + })), + rightMinusLeftModuloP2Distribution: (p13MatchingPattern.patternSummary.rightMinusLeftModuloP2Distribution ?? []).slice(0, 8), + productPlusOneModuloP2Distribution: (p13MatchingPattern.patternSummary.productPlusOneModuloP2Distribution ?? []).slice(0, 8), + proofHeuristic: p13MatchingPattern.patternSummary.proofHeuristic ?? null, + } + : null, + witnessSample: matchingWitnessSample, + } + : null, + suggestedSymbolicShape: [ + 'It is enough to prove that H_{x,N} has a matching saturating the smaller compatible side for p=13 threatening outsiders.', + `The bounded p=13 data says this stronger saturation property holds for all ${p13Profile.threatRowCount} current threatening-outsider rows.`, + tightestThreat + ? `The tightest bounded row needs K(N,x)=${tightestThreat.requiredMatchingLowerBound} and has matching ${tightestThreat.matchingSizeInMissingCrossGraph}, leaving slack ${tightestThreat.matchingSlack}.` + : 'The tightest bounded row is not available in the current miner profile.', + p13MatchingPattern + ? `The matching-pattern miner has reconstructed ${p13MatchingPattern.summary?.witnessRowCount ?? 0} tight p=13 witness rows with actual missing-cross matching pairs for injection mining.` + : 'Run erdos number-theory dispatch 848 --apply --action matching_pattern_miner to extract actual matching pairs for the tight p=13 rows.', + 'A symbolic proof should explain the smaller-side injection by residue blocks, not merely replay Hopcroft-Karp.', + ], + falsifierBoundary: 'A refreshed p=13 threatening-outside row breaks this candidate if it does not meet K(N,x), does not saturate the smaller side, or shifts the tightest slack below the symbolic construction target.', + }; +} + +function buildP848P17MatchingLowerBoundCandidate(matchingSaturationBoundProof, miner, matchingPatternMiner) { + const p17Profile = (miner?.threatMatchingProfiles ?? []).find((profile) => Number(profile?.p) === 17) ?? null; + if (!p17Profile) { + return null; + } + const tightestThreat = p17Profile.tightestThreats?.[0] ?? null; + const p17MatchingPattern = Number(matchingPatternMiner?.parameters?.targetPrime ?? NaN) === 17 + ? matchingPatternMiner + : null; + const matchingWitnessSample = (p17MatchingPattern?.witnesses ?? []).slice(0, 2).map((witness) => ({ + N: witness.N, + outsider: witness.outsider, + requiredMatchingLowerBound: witness.requiredMatchingLowerBound, + reconstructedMatchingSize: witness.reconstructedMatchingSize, + matchingSlack: witness.matchingSlack, + smallerSide: witness.smallerSide, + saturatesSmallerSide: witness.saturatesSmallerSide, + pairSample: (witness.matchingPairSample ?? []).slice(0, 6), + })); + + return { + candidateId: 'p848_D3_p17_matching_lower_bound_candidate_v1', + obligationId: 'D3_p17_matching_lower_bound', + status: matchingSaturationBoundProof?.status === 'bounded_matching_saturation_extraction_certified' + ? 'bounded_p17_threat_profile_ready_symbolic_proof_needed' + : 'blocked_by_D1', + scope: { + problemId: '848', + universalInN: false, + promotesAllNClaim: false, + boundedVerifierEvidenceRange: miner?.summary?.assessedRange ?? null, + threatRowCount: p17Profile.threatRowCount, + structuralRowCount: p17Profile.structuralRowCount, + source: 'STRUCTURAL_LIFT_MINER.threatMatchingProfiles[p=17]', + }, + extractedTarget: { + requiredMatchingLowerBoundRange: [ + p17Profile.minRequiredMatchingLowerBound, + p17Profile.maxRequiredMatchingLowerBound, + ], + actualMatchingRange: [ + p17Profile.minActualMatching, + p17Profile.maxActualMatching, + ], + minMatchingSlack: p17Profile.minMatchingSlack, + allThreatsMeetRequiredLowerBound: p17Profile.allThreatsMeetRequiredLowerBound, + allThreatsSaturateSmallerSide: p17Profile.allThreatsSaturateSmallerSide, + tightestThreat, + }, + matchingPatternEvidence: p17MatchingPattern + ? { + status: p17MatchingPattern.status ?? null, + targetPrime: p17MatchingPattern.parameters?.targetPrime ?? null, + witnessRowCount: p17MatchingPattern.summary?.witnessRowCount ?? null, + allReconstructedMatchesAgree: p17MatchingPattern.summary?.allReconstructedMatchesAgree ?? null, + allWitnessesSaturateSmallerSide: p17MatchingPattern.summary?.allWitnessesSaturateSmallerSide ?? null, + minMatchingSlack: p17MatchingPattern.summary?.minMatchingSlack ?? null, + patternSummary: p17MatchingPattern.patternSummary + ? { + totalWitnessMatchingPairs: p17MatchingPattern.patternSummary.totalWitnessMatchingPairs ?? null, + commonMatchingPairCountAcrossWitnesses: p17MatchingPattern.patternSummary.commonMatchingPairCountAcrossWitnesses ?? null, + outsiderResidueGroups: p17MatchingPattern.patternSummary.outsiderResidueGroups ?? [], + splitProfiles: (p17MatchingPattern.patternSummary.splitProfiles ?? []).slice(0, 4).map((profile) => ({ + groupKey: profile.groupKey, + witnessCount: profile.witnessCount, + minN: profile.minN, + maxN: profile.maxN, + minMatchingSlack: profile.minMatchingSlack, + commonMatchingPairCount: profile.commonMatchingPairCount, + rightMinusLeftModuloP2Distribution: (profile.rightMinusLeftModuloP2Distribution ?? []).slice(0, 6), + })), + rightMinusLeftModuloP2Distribution: (p17MatchingPattern.patternSummary.rightMinusLeftModuloP2Distribution ?? []).slice(0, 8), + productPlusOneModuloP2Distribution: (p17MatchingPattern.patternSummary.productPlusOneModuloP2Distribution ?? []).slice(0, 8), + proofHeuristic: p17MatchingPattern.patternSummary.proofHeuristic ?? null, + } + : null, + witnessSample: matchingWitnessSample, + } + : null, + suggestedSymbolicShape: [ + 'It is enough to prove that H_{x,N} has a matching saturating the smaller compatible side for p=17 threatening outsiders.', + `The bounded p=17 data says this stronger saturation property holds for all ${p17Profile.threatRowCount} current threatening-outsider rows.`, + tightestThreat + ? `The tightest bounded row needs K(N,x)=${tightestThreat.requiredMatchingLowerBound} and has matching ${tightestThreat.matchingSizeInMissingCrossGraph}, leaving slack ${tightestThreat.matchingSlack}.` + : 'The tightest bounded row is not available in the current miner profile.', + p17MatchingPattern + ? `The matching-pattern miner has reconstructed ${p17MatchingPattern.summary?.witnessRowCount ?? 0} tight p=17 witness rows with actual missing-cross matching pairs for injection mining.` + : 'Run erdos number-theory dispatch 848 --apply --action matching_pattern_miner --matching-pattern-prime 17 to extract actual matching pairs for the tight p=17 rows.', + 'A symbolic proof should explain the smaller-side injection by residue blocks, not merely replay Hopcroft-Karp.', + ], + falsifierBoundary: 'A refreshed p=17 threatening-outside row breaks this candidate if it does not meet K(N,x), does not saturate the smaller side, or shifts the tightest slack below the symbolic construction target.', + }; +} + +function buildP848P13SplitCoreWitnessProof(matchingSaturationBoundProof, p13MatchingLowerBoundCandidate, matchingPatternMiner) { + const isP13Pattern = Number(matchingPatternMiner?.parameters?.targetPrime ?? NaN) === 13; + if (!isP13Pattern || !matchingPatternMiner) { + return null; + } + const patternSummary = isP13Pattern ? matchingPatternMiner?.patternSummary ?? null : null; + const splitProfiles = Array.isArray(patternSummary?.splitProfiles) ? patternSummary.splitProfiles : []; + const profileChecks = splitProfiles.map((profile) => { + const commonMatchingPairCount = Number(profile.commonMatchingPairCount); + const commonMatchingPairs = Array.isArray(profile.commonMatchingPairs) ? profile.commonMatchingPairs : []; + const maxRequiredMatchingLowerBound = Number(profile.maxRequiredMatchingLowerBound); + const minSmallerSideSize = Number(profile.minSmallerSideSize); + const witnessCount = Number(profile.witnessCount); + const numericFieldsPresent = [ + commonMatchingPairCount, + maxRequiredMatchingLowerBound, + minSmallerSideSize, + witnessCount, + ].every(Number.isFinite); + return { + checkId: `D2_split_core_${String(profile.groupKey ?? 'unknown').replaceAll(/[^A-Za-z0-9_=-]/g, '_')}`, + groupKey: profile.groupKey ?? null, + witnessCount, + minN: profile.minN ?? null, + maxN: profile.maxN ?? null, + minRequiredMatchingLowerBound: profile.minRequiredMatchingLowerBound ?? null, + maxRequiredMatchingLowerBound, + minReconstructedMatchingSize: profile.minReconstructedMatchingSize ?? null, + maxReconstructedMatchingSize: profile.maxReconstructedMatchingSize ?? null, + minSmallerSideSize, + maxSmallerSideSize: profile.maxSmallerSideSize ?? null, + minMatchingSlack: profile.minMatchingSlack ?? null, + commonMatchingPairCount, + commonMatchingPairs, + commonMatchingPairExportComplete: Number.isFinite(commonMatchingPairCount) + && commonMatchingPairs.length === commonMatchingPairCount, + numericFieldsPresent, + commonCoreMeetsMaxRequiredBound: numericFieldsPresent + && commonMatchingPairCount >= maxRequiredMatchingLowerBound, + commonCoreSaturatesMinSmallerSide: numericFieldsPresent + && commonMatchingPairCount >= minSmallerSideSize, + rightMinusLeftModuloP2Distribution: (profile.rightMinusLeftModuloP2Distribution ?? []).slice(0, 8), + }; + }); + const proofChecks = [ + { + checkId: 'D1_dependency_discharged', + passed: matchingSaturationBoundProof?.status === 'bounded_matching_saturation_extraction_certified' + && Number(matchingSaturationBoundProof?.failCount ?? 1) === 0, + evidence: matchingSaturationBoundProof?.checkerId ?? null, + }, + { + checkId: 'p13_candidate_ready', + passed: p13MatchingLowerBoundCandidate?.status === 'bounded_p13_threat_profile_ready_symbolic_proof_needed', + evidence: p13MatchingLowerBoundCandidate?.candidateId ?? null, + }, + { + checkId: 'matching_pattern_artifact_ready', + passed: isP13Pattern && matchingPatternMiner?.status === 'matching_pattern_witness_packet_ready', + evidence: { + status: matchingPatternMiner?.status ?? null, + targetPrime: matchingPatternMiner?.parameters?.targetPrime ?? null, + witnessRowCount: matchingPatternMiner?.summary?.witnessRowCount ?? null, + }, + }, + { + checkId: 'matching_reconstruction_agrees_with_verifier', + passed: matchingPatternMiner?.summary?.allReconstructedMatchesAgree === true, + evidence: matchingPatternMiner?.summary?.allReconstructedMatchesAgree ?? null, + }, + { + checkId: 'all_witnesses_saturate_smaller_side', + passed: matchingPatternMiner?.summary?.allWitnessesSaturateSmallerSide === true, + evidence: matchingPatternMiner?.summary?.saturatedSideDistribution ?? null, + }, + { + checkId: 'split_profiles_available', + passed: profileChecks.length > 0, + evidence: { + splitProfileCount: profileChecks.length, + commonAcrossAllProfiles: patternSummary?.commonMatchingPairCountAcrossWitnesses ?? null, + proofHeuristic: patternSummary?.proofHeuristic ?? null, + }, + }, + { + checkId: 'split_common_cores_meet_required_K', + passed: profileChecks.length > 0 && profileChecks.every((profile) => profile.commonCoreMeetsMaxRequiredBound), + evidence: profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + commonMatchingPairCount: profile.commonMatchingPairCount, + maxRequiredMatchingLowerBound: profile.maxRequiredMatchingLowerBound, + })), + }, + { + checkId: 'split_common_core_pairs_exported', + passed: profileChecks.length > 0 && profileChecks.every((profile) => profile.commonMatchingPairExportComplete), + evidence: profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + commonMatchingPairCount: profile.commonMatchingPairCount, + exportedPairCount: profile.commonMatchingPairs.length, + })), + }, + { + checkId: 'split_common_cores_saturate_smaller_side_on_tight_rows', + passed: profileChecks.length > 0 && profileChecks.every((profile) => profile.commonCoreSaturatesMinSmallerSide), + evidence: profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + commonMatchingPairCount: profile.commonMatchingPairCount, + minSmallerSideSize: profile.minSmallerSideSize, + })), + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + const failedProfiles = profileChecks.filter((profile) => ( + !profile.commonCoreMeetsMaxRequiredBound + || !profile.commonCoreSaturatesMinSmallerSide + )); + const profileSummary = profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + witnessCount: profile.witnessCount, + nRange: `${profile.minN}..${profile.maxN}`, + requiredMatchingLowerBoundRange: [ + profile.minRequiredMatchingLowerBound, + profile.maxRequiredMatchingLowerBound, + ], + reconstructedMatchingRange: [ + profile.minReconstructedMatchingSize, + profile.maxReconstructedMatchingSize, + ], + commonMatchingPairCount: profile.commonMatchingPairCount, + commonMatchingPairExportComplete: profile.commonMatchingPairExportComplete, + commonMatchingPairs: profile.commonMatchingPairs, + minMatchingSlack: profile.minMatchingSlack, + commonCoreMeetsMaxRequiredBound: profile.commonCoreMeetsMaxRequiredBound, + commonCoreSaturatesMinSmallerSide: profile.commonCoreSaturatesMinSmallerSide, + })); + + return { + checkerId: 'p848_D2_p13_split_core_witness_checker_v1', + obligationId: 'D2_p13_split_core_witness_extraction', + parentObligationId: 'D2_p13_matching_lower_bound', + status: failedChecks.length === 0 && failedProfiles.length === 0 + ? 'bounded_split_core_witness_certified' + : 'failed', + checkedRowCount: proofChecks.length + profileChecks.length, + passCount: proofChecks.length + profileChecks.length - failedChecks.length - failedProfiles.length, + failCount: failedChecks.length + failedProfiles.length, + statement: 'The tight p=13 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.', + scope: { + problemId: '848', + universalInN: false, + promotesAllNClaim: false, + targetPrime: 13, + sourceArtifact: 'MATCHING_PATTERN_MINER.json', + sourceAssessedRange: matchingPatternMiner?.parameters?.sourceAssessedRange ?? null, + witnessRowCount: matchingPatternMiner?.summary?.witnessRowCount ?? null, + splitProfileCount: profileChecks.length, + role: 'bounded_split_core_witness_for_symbolic_D2_lift', + }, + dependencies: [ + matchingSaturationBoundProof?.checkerId ?? 'p848_D1_matching_saturation_bound_checker_v1', + p13MatchingLowerBoundCandidate?.candidateId ?? 'p848_D2_p13_matching_lower_bound_candidate_v1', + 'MATCHING_PATTERN_MINER.patternSummary.splitProfiles', + ], + hypotheses: [ + 'D1 has extracted the p=13 matching lower-bound target K(N,x).', + 'The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=13 rows.', + 'The sampled tight rows split by outsider residue modulo 13^2, outsider residue modulo 25, and which side is smaller.', + 'Within each split profile, the common matching core is a matching present in every sampled row of that profile.', + ], + proof: [ + 'Read the p=13 split profiles from MATCHING_PATTERN_MINER.patternSummary.', + 'For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.', + 'Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.', + 'Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.', + 'This does not discharge D2 universally; it turns D2 into explicit split symbolic subgoals whose common cores must be proved to persist by residue/block argument.', + ], + proofChecks, + failedChecks, + profileChecks, + failedProfiles, + profileSummary, + symbolicSubgoals: profileSummary.map((profile, index) => ({ + subgoalId: `D2.${index + 1}_persist_${String(profile.groupKey).replaceAll(/[^A-Za-z0-9_=-]/g, '_')}`, + groupKey: profile.groupKey, + goal: `Prove that the ${profile.commonMatchingPairCount}-edge common matching core persists for all p=13 threatening rows in split ${profile.groupKey}, or replace it with a parameterized extension core.`, + boundedTarget: { + requiredMatchingLowerBoundRange: profile.requiredMatchingLowerBoundRange, + commonMatchingPairCount: profile.commonMatchingPairCount, + commonMatchingPairExportComplete: profile.commonMatchingPairExportComplete, + commonMatchingPairs: profile.commonMatchingPairs, + minMatchingSlack: profile.minMatchingSlack, + }, + falsifierBoundary: 'A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size.', + })), + conclusion: failedChecks.length === 0 && failedProfiles.length === 0 + ? `The tight p=13 sample is reduced to ${profileChecks.length} split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side.` + : 'At least one p=13 split core failed to meet the sampled K(N,x) target.', + falsifierBoundary: failedChecks.length === 0 && failedProfiles.length === 0 + ? 'A refreshed matching-pattern miner falsifies this bounded witness packet if a split profile has no common core, if the common core falls below max K(N,x), or if the split heuristic changes. D2 remains open until these split cores are proved symbolically.' + : 'Inspect failedChecks and failedProfiles before using this as a D2 symbolic-lift guide.', + }; +} + +function buildP848P17SplitCoreWitnessProof(matchingSaturationBoundProof, p17MatchingLowerBoundCandidate, matchingPatternMiner) { + const isP17Pattern = Number(matchingPatternMiner?.parameters?.targetPrime ?? NaN) === 17; + if (!isP17Pattern || !matchingPatternMiner) { + return null; + } + const patternSummary = matchingPatternMiner?.patternSummary ?? null; + const splitProfiles = Array.isArray(patternSummary?.splitProfiles) ? patternSummary.splitProfiles : []; + const profileChecks = splitProfiles.map((profile) => { + const commonMatchingPairCount = Number(profile.commonMatchingPairCount); + const commonMatchingPairs = Array.isArray(profile.commonMatchingPairs) ? profile.commonMatchingPairs : []; + const maxRequiredMatchingLowerBound = Number(profile.maxRequiredMatchingLowerBound); + const minSmallerSideSize = Number(profile.minSmallerSideSize); + const witnessCount = Number(profile.witnessCount); + const numericFieldsPresent = [ + commonMatchingPairCount, + maxRequiredMatchingLowerBound, + minSmallerSideSize, + witnessCount, + ].every(Number.isFinite); + return { + checkId: `D3_split_core_${String(profile.groupKey ?? 'unknown').replaceAll(/[^A-Za-z0-9_=-]/g, '_')}`, + groupKey: profile.groupKey ?? null, + witnessCount, + minN: profile.minN ?? null, + maxN: profile.maxN ?? null, + minRequiredMatchingLowerBound: profile.minRequiredMatchingLowerBound ?? null, + maxRequiredMatchingLowerBound, + minReconstructedMatchingSize: profile.minReconstructedMatchingSize ?? null, + maxReconstructedMatchingSize: profile.maxReconstructedMatchingSize ?? null, + minSmallerSideSize, + maxSmallerSideSize: profile.maxSmallerSideSize ?? null, + minMatchingSlack: profile.minMatchingSlack ?? null, + commonMatchingPairCount, + commonMatchingPairs, + commonMatchingPairExportComplete: Number.isFinite(commonMatchingPairCount) + && commonMatchingPairs.length === commonMatchingPairCount, + numericFieldsPresent, + commonCoreMeetsMaxRequiredBound: numericFieldsPresent + && commonMatchingPairCount >= maxRequiredMatchingLowerBound, + commonCoreSaturatesMinSmallerSide: numericFieldsPresent + && commonMatchingPairCount >= minSmallerSideSize, + rightMinusLeftModuloP2Distribution: (profile.rightMinusLeftModuloP2Distribution ?? []).slice(0, 8), + }; + }); + const proofChecks = [ + { + checkId: 'D1_dependency_discharged', + passed: matchingSaturationBoundProof?.status === 'bounded_matching_saturation_extraction_certified' + && Number(matchingSaturationBoundProof?.failCount ?? 1) === 0, + evidence: matchingSaturationBoundProof?.checkerId ?? null, + }, + { + checkId: 'p17_candidate_ready', + passed: p17MatchingLowerBoundCandidate?.status === 'bounded_p17_threat_profile_ready_symbolic_proof_needed', + evidence: p17MatchingLowerBoundCandidate?.candidateId ?? null, + }, + { + checkId: 'matching_pattern_artifact_ready', + passed: isP17Pattern && matchingPatternMiner?.status === 'matching_pattern_witness_packet_ready', + evidence: { + status: matchingPatternMiner?.status ?? null, + targetPrime: matchingPatternMiner?.parameters?.targetPrime ?? null, + witnessRowCount: matchingPatternMiner?.summary?.witnessRowCount ?? null, + }, + }, + { + checkId: 'matching_reconstruction_agrees_with_verifier', + passed: matchingPatternMiner?.summary?.allReconstructedMatchesAgree === true, + evidence: matchingPatternMiner?.summary?.allReconstructedMatchesAgree ?? null, + }, + { + checkId: 'all_witnesses_saturate_smaller_side', + passed: matchingPatternMiner?.summary?.allWitnessesSaturateSmallerSide === true, + evidence: matchingPatternMiner?.summary?.saturatedSideDistribution ?? null, + }, + { + checkId: 'split_profiles_available', + passed: profileChecks.length > 0, + evidence: { + splitProfileCount: profileChecks.length, + commonAcrossAllProfiles: patternSummary?.commonMatchingPairCountAcrossWitnesses ?? null, + proofHeuristic: patternSummary?.proofHeuristic ?? null, + }, + }, + { + checkId: 'split_common_cores_meet_required_K', + passed: profileChecks.length > 0 && profileChecks.every((profile) => profile.commonCoreMeetsMaxRequiredBound), + evidence: profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + commonMatchingPairCount: profile.commonMatchingPairCount, + maxRequiredMatchingLowerBound: profile.maxRequiredMatchingLowerBound, + })), + }, + { + checkId: 'split_common_core_pairs_exported', + passed: profileChecks.length > 0 && profileChecks.every((profile) => profile.commonMatchingPairExportComplete), + evidence: profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + commonMatchingPairCount: profile.commonMatchingPairCount, + exportedPairCount: profile.commonMatchingPairs.length, + })), + }, + { + checkId: 'split_common_cores_saturate_smaller_side_on_tight_rows', + passed: profileChecks.length > 0 && profileChecks.every((profile) => profile.commonCoreSaturatesMinSmallerSide), + evidence: profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + commonMatchingPairCount: profile.commonMatchingPairCount, + minSmallerSideSize: profile.minSmallerSideSize, + })), + }, + ]; + const failedChecks = proofChecks.filter((check) => !check.passed); + const failedProfiles = profileChecks.filter((profile) => ( + !profile.commonCoreMeetsMaxRequiredBound + || !profile.commonCoreSaturatesMinSmallerSide + )); + const profileSummary = profileChecks.map((profile) => ({ + groupKey: profile.groupKey, + witnessCount: profile.witnessCount, + nRange: `${profile.minN}..${profile.maxN}`, + requiredMatchingLowerBoundRange: [ + profile.minRequiredMatchingLowerBound, + profile.maxRequiredMatchingLowerBound, + ], + reconstructedMatchingRange: [ + profile.minReconstructedMatchingSize, + profile.maxReconstructedMatchingSize, + ], + commonMatchingPairCount: profile.commonMatchingPairCount, + commonMatchingPairExportComplete: profile.commonMatchingPairExportComplete, + commonMatchingPairs: profile.commonMatchingPairs, + minMatchingSlack: profile.minMatchingSlack, + commonCoreMeetsMaxRequiredBound: profile.commonCoreMeetsMaxRequiredBound, + commonCoreSaturatesMinSmallerSide: profile.commonCoreSaturatesMinSmallerSide, + })); + + return { + checkerId: 'p848_D3_p17_split_core_witness_checker_v1', + obligationId: 'D3_p17_split_core_witness_extraction', + parentObligationId: 'D3_p17_matching_lower_bound', + status: failedChecks.length === 0 && failedProfiles.length === 0 + ? 'bounded_split_core_witness_certified' + : 'failed', + checkedRowCount: proofChecks.length + profileChecks.length, + passCount: proofChecks.length + profileChecks.length - failedChecks.length - failedProfiles.length, + failCount: failedChecks.length + failedProfiles.length, + statement: 'The tight p=17 matching-pattern witnesses split into residue/saturated-side profiles whose common matching cores already meet the required K(N,x) lower bound.', + scope: { + problemId: '848', + universalInN: false, + promotesAllNClaim: false, + targetPrime: 17, + sourceArtifact: 'MATCHING_PATTERN_MINER_P17.json', + sourceAssessedRange: matchingPatternMiner?.parameters?.sourceAssessedRange ?? null, + witnessRowCount: matchingPatternMiner?.summary?.witnessRowCount ?? null, + splitProfileCount: profileChecks.length, + role: 'bounded_split_core_witness_for_symbolic_D3_lift', + }, + dependencies: [ + matchingSaturationBoundProof?.checkerId ?? 'p848_D1_matching_saturation_bound_checker_v1', + p17MatchingLowerBoundCandidate?.candidateId ?? 'p848_D3_p17_matching_lower_bound_candidate_v1', + 'MATCHING_PATTERN_MINER_P17.patternSummary.splitProfiles', + ], + hypotheses: [ + 'D1 has extracted the p=17 matching lower-bound target K(N,x).', + 'The matching-pattern miner reconstructs Hopcroft-Karp matchings as explicit missing-cross matching pairs for tight p=17 rows.', + 'The sampled tight rows split by outsider residue modulo 17^2, outsider residue modulo 25, and which side is smaller.', + 'Within each split profile, the common matching core is a matching present in every sampled row of that profile.', + ], + proof: [ + 'Read the p=17 split profiles from MATCHING_PATTERN_MINER_P17.patternSummary.', + 'For each split profile, compare the common matching-pair count with the largest required K(N,x) among sampled rows in that profile.', + 'Check the stronger saturation witness: the common core also reaches the minimum smaller-side size observed in that profile.', + 'Because every sampled row in the split profile contains the common core, that core gives a bounded matching lower-bound witness for the sampled tight rows.', + 'This does not discharge D3 universally; it turns D3 into explicit split symbolic subgoals whose common cores must be proved to persist by residue/block argument.', + ], + proofChecks, + failedChecks, + profileChecks, + failedProfiles, + profileSummary, + symbolicSubgoals: profileSummary.map((profile, index) => ({ + subgoalId: `D3.${index + 1}_persist_${String(profile.groupKey).replaceAll(/[^A-Za-z0-9_=-]/g, '_')}`, + groupKey: profile.groupKey, + goal: `Prove that the ${profile.commonMatchingPairCount}-edge common matching core persists for all p=17 threatening rows in split ${profile.groupKey}, or replace it with a parameterized extension core.`, + boundedTarget: { + requiredMatchingLowerBoundRange: profile.requiredMatchingLowerBoundRange, + commonMatchingPairCount: profile.commonMatchingPairCount, + commonMatchingPairExportComplete: profile.commonMatchingPairExportComplete, + commonMatchingPairs: profile.commonMatchingPairs, + minMatchingSlack: profile.minMatchingSlack, + }, + falsifierBoundary: 'A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size.', + })), + conclusion: failedChecks.length === 0 && failedProfiles.length === 0 + ? `The tight p=17 sample is reduced to ${profileChecks.length} split-core subgoals; every split common core meets the sampled maximum K(N,x) and saturates the sampled smaller side.` + : 'At least one p=17 split core failed to meet the sampled K(N,x) target.', + falsifierBoundary: failedChecks.length === 0 && failedProfiles.length === 0 + ? 'A refreshed p=17 matching-pattern miner falsifies this bounded witness packet if a split profile has no common core, if the common core falls below max K(N,x), or if the split heuristic changes. D3 remains open until these split cores are proved symbolically.' + : 'Inspect failedChecks and failedProfiles before using this as a D3 symbolic-lift guide.', + }; +} + +function buildP848StructuralLiftAtomicSurface(formalization) { + const packProblemDir = formalization?.sources?.packProblemDir ?? null; + const minerPath = packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_LIFT_MINER.json') : null; + const checklistPath = packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_LIFT_CHECKLIST.json') : null; + const fullVerifierPath = packProblemDir ? path.join(packProblemDir, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json') : null; + const matchingPatternPath = packProblemDir ? path.join(packProblemDir, 'MATCHING_PATTERN_MINER.json') : null; + const matchingPatternP17Path = packProblemDir ? path.join(packProblemDir, 'MATCHING_PATTERN_MINER_P17.json') : null; + const miner = minerPath ? readJsonIfPresent(minerPath) : null; + const checklist = checklistPath ? readJsonIfPresent(checklistPath) : null; + const fullVerifier = fullVerifierPath ? readJsonIfPresent(fullVerifierPath) : null; + const matchingPatternMiner = matchingPatternPath ? readJsonIfPresent(matchingPatternPath) : null; + const matchingPatternMinerP17 = matchingPatternP17Path ? readJsonIfPresent(matchingPatternP17Path) : null; + if (miner?.summary?.coverageComplete !== true || !checklist) { + return null; + } + + const currentFocus = checklist.currentFocus ?? {}; + const requestedActiveStepId = currentFocus.firstActionableStepId ?? 'C1_same_side_base_clique'; + const targetStepId = currentFocus.targetStepId ?? 'C6_mixed_clique_matching_formula'; + const sameSideBaseCliqueProof = buildP848SameSideBaseCliqueProof(); + const twoCliquesPlusCrossEdgesProof = buildP848TwoCliquesPlusCrossEdgesProof( + sameSideBaseCliqueProof, + miner, + fullVerifier, + ); + const missingCrossGraphDefinitionProof = buildP848MissingCrossGraphDefinitionProof( + twoCliquesPlusCrossEdgesProof, + miner, + fullVerifier, + ); + const cliqueVertexCoverDualityProof = buildP848CliqueVertexCoverDualityProof( + missingCrossGraphDefinitionProof, + ); + const konigMatchingReductionProof = buildP848KonigMatchingReductionProof( + missingCrossGraphDefinitionProof, + ); + const mixedCliqueMatchingFormulaProof = buildP848MixedCliqueMatchingFormulaProof( + cliqueVertexCoverDualityProof, + konigMatchingReductionProof, + fullVerifier, + ); + const matchingSaturationBoundProof = buildP848MatchingSaturationBoundProof( + mixedCliqueMatchingFormulaProof, + fullVerifier, + ); + const p13MatchingLowerBoundCandidate = buildP848P13MatchingLowerBoundCandidate( + matchingSaturationBoundProof, + miner, + matchingPatternMiner, + ); + const p13SplitCoreWitnessProof = buildP848P13SplitCoreWitnessProof( + matchingSaturationBoundProof, + p13MatchingLowerBoundCandidate, + matchingPatternMiner, + ); + const p17MatchingLowerBoundCandidate = buildP848P17MatchingLowerBoundCandidate( + matchingSaturationBoundProof, + miner, + matchingPatternMinerP17, + ); + const p17SplitCoreWitnessProof = buildP848P17SplitCoreWitnessProof( + matchingSaturationBoundProof, + p17MatchingLowerBoundCandidate, + matchingPatternMinerP17, + ); + const proofPackets = { + [sameSideBaseCliqueProof.obligationId]: sameSideBaseCliqueProof, + [twoCliquesPlusCrossEdgesProof.obligationId]: twoCliquesPlusCrossEdgesProof, + [missingCrossGraphDefinitionProof.obligationId]: missingCrossGraphDefinitionProof, + [cliqueVertexCoverDualityProof.obligationId]: cliqueVertexCoverDualityProof, + [konigMatchingReductionProof.obligationId]: konigMatchingReductionProof, + [mixedCliqueMatchingFormulaProof.obligationId]: mixedCliqueMatchingFormulaProof, + [matchingSaturationBoundProof.obligationId]: matchingSaturationBoundProof, + ...(p13SplitCoreWitnessProof + ? { [p13SplitCoreWitnessProof.obligationId]: p13SplitCoreWitnessProof } + : {}), + ...(p17SplitCoreWitnessProof + ? { [p17SplitCoreWitnessProof.obligationId]: p17SplitCoreWitnessProof } + : {}), + }; + const dischargedProofStepIds = new Set(Object.values(proofPackets) + .filter((proof) => Number(proof.failCount ?? 0) === 0) + .map((proof) => proof.obligationId)); + const requestedActive = findP848StructuralLiftChecklistStep(checklist, requestedActiveStepId); + const target = findP848StructuralLiftChecklistStep(checklist, targetStepId); + const activePhase = requestedActive?.phase ?? target?.phase ?? null; + const stepDependenciesDischarged = (step) => (step?.dependsOn ?? []) + .every((dependencyId) => dischargedProofStepIds.has(dependencyId)); + const stepIsRunnable = (step) => { + if (!step || step.stepId === targetStepId || dischargedProofStepIds.has(step.stepId) || step.status === 'target') { + return false; + } + return !String(step.status ?? '').startsWith('blocked') || stepDependenciesDischarged(step); + }; + const activeStepId = dischargedProofStepIds.has(requestedActiveStepId) + ? ((activePhase?.steps ?? []).find((step) => ( + stepIsRunnable(step) + ))?.stepId ?? targetStepId) + : requestedActiveStepId; + const active = findP848StructuralLiftChecklistStep(checklist, activeStepId); + const activeStep = active?.step ?? null; + const targetStep = target?.step ?? null; + const proofObligations = (activePhase?.steps ?? []).map((step) => ({ + obligationId: step.stepId, + status: dischargedProofStepIds.has(step.stepId) + ? 'done' + : step.stepId === activeStepId + ? 'in_progress' + : String(step.status ?? '').startsWith('blocked') && stepDependenciesDischarged(step) + ? 'ready' + : step.status ?? 'ready', + task: step.statement, + statement: step.statement, + dependsOn: step.dependsOn ?? [], + proofType: step.proofType ?? null, + falsifierBoundary: step.falsifierBoundary ?? null, + dischargedBy: proofPackets[step.stepId]?.checkerId ?? null, + dischargeWith: proofPackets[step.stepId]?.conclusion + ?? (step.stepId === activeStepId + ? `Prove the active atom ${step.stepId} at its stated scope, then refresh FORMALIZATION_WORK so the next dependency is selected from the updated evidence.` + : null), + })); + + return { + surfaceId: 'p848_structural_lift_atomic_surface_v1', + status: 'active', + canonicalSurface: 'FORMALIZATION_WORK.currentWork', + role: 'atomic_proof_obligation_surface', + evidenceArtifact: { + path: minerPath, + status: miner.status ?? null, + minedExactRowCount: miner.summary?.minedExactRowCount ?? null, + primaryExactPrimes: miner.summary?.primaryExactPrimes ?? [], + nextTheoremLane: miner.summary?.nextTheoremLane ?? null, + }, + matchingPatternArtifact: matchingPatternMiner + ? { + path: matchingPatternPath, + status: matchingPatternMiner.status ?? null, + targetPrime: matchingPatternMiner.parameters?.targetPrime ?? null, + witnessRowCount: matchingPatternMiner.summary?.witnessRowCount ?? null, + minMatchingSlack: matchingPatternMiner.summary?.minMatchingSlack ?? null, + } + : null, + matchingPatternArtifacts: [ + matchingPatternMiner + ? { + path: matchingPatternPath, + status: matchingPatternMiner.status ?? null, + targetPrime: matchingPatternMiner.parameters?.targetPrime ?? null, + witnessRowCount: matchingPatternMiner.summary?.witnessRowCount ?? null, + minMatchingSlack: matchingPatternMiner.summary?.minMatchingSlack ?? null, + } + : null, + matchingPatternMinerP17 + ? { + path: matchingPatternP17Path, + status: matchingPatternMinerP17.status ?? null, + targetPrime: matchingPatternMinerP17.parameters?.targetPrime ?? null, + witnessRowCount: matchingPatternMinerP17.summary?.witnessRowCount ?? null, + minMatchingSlack: matchingPatternMinerP17.summary?.minMatchingSlack ?? null, + } + : null, + ].filter(Boolean), + referenceBacklog: { + path: checklistPath, + role: 'non_canonical_reference_backlog', + note: 'The checklist is a map of possible sub-lemmas. The active theorem lane is the single atomic obligation surfaced here.', + }, + activePacket: { + packetId: currentFocus.packetId ?? activePhase?.phaseId ?? null, + title: activePhase?.title ?? null, + goal: activePhase?.goal ?? null, + }, + requestedActiveAtom: requestedActive?.step + ? { + obligationId: requestedActive.step.stepId, + status: dischargedProofStepIds.has(requestedActive.step.stepId) ? 'done' : requestedActive.step.status ?? 'ready', + statement: requestedActive.step.statement, + } + : null, + activeAtom: activeStep + ? { + obligationId: activeStep.stepId, + status: dischargedProofStepIds.has(activeStep.stepId) ? 'done' : 'in_progress', + statement: activeStep.statement, + dependsOn: activeStep.dependsOn ?? [], + proofType: activeStep.proofType ?? null, + falsifierBoundary: activeStep.falsifierBoundary ?? null, + } + : null, + targetAtom: targetStep + ? { + obligationId: targetStep.stepId, + status: targetStep.status ?? 'target', + statement: targetStep.statement, + dependsOn: targetStep.dependsOn ?? [], + proofType: targetStep.proofType ?? null, + falsifierBoundary: targetStep.falsifierBoundary ?? null, + } + : null, + dischargedAtoms: Object.values(proofPackets) + .filter((proof) => Number(proof.failCount ?? 0) === 0) + .map((proof) => ({ + obligationId: proof.obligationId, + status: proof.status, + checkerId: proof.checkerId, + conclusion: proof.conclusion, + })), + proofPackets, + candidatePackets: { + ...(p13MatchingLowerBoundCandidate + ? { [p13MatchingLowerBoundCandidate.obligationId]: p13MatchingLowerBoundCandidate } + : {}), + ...(p13SplitCoreWitnessProof + ? { [p13SplitCoreWitnessProof.obligationId]: p13SplitCoreWitnessProof } + : {}), + ...(p17MatchingLowerBoundCandidate + ? { [p17MatchingLowerBoundCandidate.obligationId]: p17MatchingLowerBoundCandidate } + : {}), + ...(p17SplitCoreWitnessProof + ? { [p17SplitCoreWitnessProof.obligationId]: p17SplitCoreWitnessProof } + : {}), + }, + activeAtomEvidence: activeStepId === 'D2_p13_matching_lower_bound' && p13MatchingLowerBoundCandidate + ? { + ...p13MatchingLowerBoundCandidate, + splitCoreWitnessPacket: p13SplitCoreWitnessProof + ? { + checkerId: p13SplitCoreWitnessProof.checkerId, + status: p13SplitCoreWitnessProof.status, + splitProfileCount: p13SplitCoreWitnessProof.scope?.splitProfileCount ?? null, + failCount: p13SplitCoreWitnessProof.failCount, + profileSummary: p13SplitCoreWitnessProof.profileSummary ?? [], + symbolicSubgoals: p13SplitCoreWitnessProof.symbolicSubgoals ?? [], + conclusion: p13SplitCoreWitnessProof.conclusion, + } + : null, + } + : null, + proofObligations, + atomicDiscipline: [ + 'Do not promote the whole checklist as a theorem claim.', + 'Work one active atom at a time inside FORMALIZATION_WORK.currentWork.', + 'After each atom is discharged or falsified, regenerate this surface from the miner/checklist evidence.', + ], + boundary: { + claimLevel: 'formalization_work_atom_not_proof', + note: 'This surface names the next theorem obligation implied by the structural lift miner; it does not certify any new N by itself.', + }, + }; +} + +function pickFormalizationWorkFocus(target) { + const proofObligations = Array.isArray(target?.proofObligations) ? target.proofObligations : []; + return ( + proofObligations.find((item) => item?.status === 'in_progress') + ?? proofObligations.find((item) => item?.status === 'ready') + ?? proofObligations[0] + ?? null + ); +} + +function buildGenericFormalizationTarget(problem, theoremLoop, claimPass) { + const recommendations = Array.isArray(claimPass?.recommendations) ? claimPass.recommendations : []; + const theoremRecommendation = recommendations.find((item) => item.lane === 'theorem_formalization') ?? recommendations[0] ?? null; + const latestVerifiedInterval = claimPass?.currentState?.latestVerifiedInterval ?? null; + const focusId = theoremRecommendation?.recommendation_id ?? 'seed_formalization_packet'; + const title = theoremRecommendation + ? titleCaseWords(theoremRecommendation.recommendation_id) + : 'Seed Formalization Packet'; + + return { + formalizationId: `${problem.cluster}_${problem.problemId}_${focusId}_v1`, + focusId, + title, + status: theoremRecommendation ? 'ready' : 'seeded', + lane: theoremRecommendation?.lane ?? 'theorem_formalization', + sourceRecommendationId: theoremRecommendation?.recommendation_id ?? null, + summary: theoremRecommendation?.reason ?? theoremLoop.currentState?.nextHonestMove ?? 'Seed the next honest theorem-facing packet.', + statement: theoremRecommendation + ? `Candidate formalization target: ${theoremRecommendation.reason}` + : `Candidate formalization target: ${theoremLoop.currentState?.nextHonestMove ?? 'Seed the next honest theorem-facing claim.'}`, + whyThisExists: theoremRecommendation + ? 'This packet exists to turn a claim-pass recommendation into a concrete theorem-facing proof obligation with explicit falsifiers and promotion criteria.' + : 'This packet exists to give the theorem lane a stable starting point even before richer bridge-backed claims have been promoted.', + whyNow: theoremRecommendation?.reason + ?? theoremLoop.currentState?.nextHonestMove + ?? 'No richer theorem recommendation is recorded yet.', + evidenceBasis: [ + `Current claim surface: ${theoremLoop.currentState?.currentClaimSurface ?? '(unknown)'}.`, + `Active route: ${theoremLoop.activeRoute ?? '(none)'}.`, + latestVerifiedInterval + ? `Latest verified interval: ${latestVerifiedInterval}.` + : 'No canonical verified interval is currently frozen.', + ], + proofObligations: [ + { + obligationId: 'state_claim_honestly', + status: 'ready', + task: 'State the candidate theorem-facing claim in pack language without overstating current support.', + why: 'This keeps the formalization target narrower than the current evidence boundary.', + dischargeWith: 'Write a claim statement that is no stronger than the active claim-pass support surface.', + }, + { + obligationId: 'freeze_support_artifacts', + status: 'ready', + task: 'List the exact canonical artifacts that support the claim and the artifacts that could still falsify it.', + why: 'The theorem lane should point at stable evidence, not drifting interpretation.', + dischargeWith: 'Attach theorem-loop, claim-pass, and any bridge-backed packet paths directly to the packet.', + }, + { + obligationId: 'define_promotion_boundary', + status: 'ready', + task: 'Promote the target only when its support survives the current claim-pass falsifiers.', + why: 'This prevents formalization packets from silently outrunning the rest of the loop.', + dischargeWith: 'Record explicit promotion criteria tied to current falsifiers.', + }, + ], + falsifierChecks: [ + { + checkId: 'claim_pass_survival', + status: 'ready', + task: 'A refreshed claim pass drops the target recommendation or marks the underlying claim unsupported.', + why: 'If the recommendation itself no longer survives refresh, the formalization target is stale.', + command: claimPass?.commands?.claimPassRefresh ?? null, + }, + { + checkId: 'artifact_boundary_check', + status: 'ready', + task: 'A canonical artifact boundary check shows the statement is stronger than the current pack evidence.', + why: 'The packet should fail early if it is stronger than what the pack actually certifies.', + command: theoremLoop?.commands?.theoremLoop ?? null, + }, + ], + promotionCriteria: [ + { + criterionId: 'top_recommendation_survives', + status: 'ready', + task: 'The current target remains the top theorem-formalization recommendation after refresh.', + }, + { + criterionId: 'statement_stays_narrow', + status: 'ready', + task: 'The candidate statement is narrower than or equal to the current claim-pass support surface.', + }, + { + criterionId: 'obligations_are_actionable', + status: 'ready', + task: 'The remaining proof obligations are explicit enough to guide search or exact follow-up.', + }, + ], + supportingCommands: [ + theoremLoop.commands?.theoremLoop ?? null, + claimPass?.commands?.claimPass ?? null, + claimPass?.commands?.claimPassRefresh ?? null, + ].filter(Boolean), + }; +} + +function buildP848AlignmentFormalizationTarget(theoremLoop, claimPass) { + const bridgeState = theoremLoop.currentBridgeState ?? {}; + const alignmentContext = buildP848AlignmentContext(theoremLoop); + const nextRepresentative = bridgeState.next_unmatched_representative ?? '(unknown)'; + const strongestCompletedTail = bridgeState.strongest_completed_structured_tail?.continuation ?? '(unknown)'; + const currentLeader = bridgeState.current_family_aware_leader?.continuation ?? '(unknown)'; + const latestVerifiedInterval = claimPass?.currentState?.latestVerifiedInterval ?? null; + const familyRow = alignmentContext.familyRow; + const tupleSummary = Array.isArray(familyRow?.tupleRows) + ? familyRow.tupleRows.map((row) => `${row.anchor}->${row.squareModulus}/${row.residue}`).join(', ') + : null; + const stableRepairAnchors = alignmentContext.stableRepairRows.map((row) => row.anchor); + const failingRepairAnchors = alignmentContext.failingRepairRows.map((row) => row.anchor); + const failing282Witness = Array.isArray(alignmentContext.failing282?.squareWitnesses) + ? alignmentContext.failing282.squareWitnesses.map((row) => row.squareModulus).join(', ') + : null; + const derivedActivationLemmaCheck = checkP848ActivationLemmaCertificates( + alignmentContext.allFamilies, + alignmentContext.familyMenuPath, + ); + const derivedTupleRowLift132Proof = buildP848TupleRowLift132ProofFromAlignment(alignmentContext); + const derivedTopRepairClassMechanism = buildP848TopRepairClassMechanism(alignmentContext); + const formalizationWorkPath = theoremLoop.sources?.packProblemDir + ? path.join(theoremLoop.sources.packProblemDir, 'FORMALIZATION_WORK.json') + : null; + const formalizationWorkDoc = formalizationWorkPath ? readJsonIfPresent(formalizationWorkPath) : null; + const workPacket = formalizationWorkDoc?.currentWork ?? null; + const activationLemmaCheck = workPacket?.packetData?.activationLemmaCheck ?? derivedActivationLemmaCheck; + const tupleRowLift132Proof = workPacket?.packetData?.tupleRowLift132Proof ?? derivedTupleRowLift132Proof; + const topRepairSeparation = workPacket?.packetData?.topRepairClassMechanism?.separationAnalysis + ?? derivedTopRepairClassMechanism?.separationAnalysis + ?? null; + const mod50LaneSignature = topRepairSeparation?.mod50LaneSignature ?? null; + const checkedMechanismPacketPromoted = activationLemmaCheck?.status === 'passed' + && tupleRowLift132Proof?.status === 'proved_from_tuple_row_crt' + && ( + Array.isArray(workPacket?.dischargedWork) + ? workPacket.dischargedWork.some((item) => String(item).includes('132-row lift')) + : true + ); + const checkedTopRepairPacketPromoted = topRepairSeparation?.status === 'finite_menu_plus2_replay_certified' + && mod50LaneSignature?.status === 'finite_menu_mod50_lane_signature_certified'; + + return { + formalizationId: 'p848_282_alignment_formalization_v1', + focusId: 'formalize_282_alignment', + title: 'Formalize the 282 Obstruction Alignment', + status: checkedMechanismPacketPromoted ? 'in_progress' : 'ready', + lane: 'theorem_formalization', + sourceRecommendationId: 'formalize_282_alignment', + sourceClaimId: 'p848_next_unmatched_alignment_claim', + sourceHookId: 'next_unmatched_equals_282_failure', + summary: checkedMechanismPacketPromoted + ? `The live ${nextRepresentative} / 282 obstruction packet is checked at finite-menu scope; the remaining theorem work is the narrower symbolic-lift boundary.` + : `Turn the live ${nextRepresentative} / 282 coincidence into a claim-safe obstruction-class packet.`, + statement: checkedMechanismPacketPromoted + ? `Checked finite-menu statement: the shared-prefix obstruction represented at n=${nextRepresentative} aligns with continuation tail 282 through the 841 witness class, with the 132-row lift and activation certificates replayed; a universal symbolic lift remains separate.` + : `Candidate theorem-facing statement: the shared-prefix obstruction currently first represented at n=${nextRepresentative} is not just a finite-window coincidence, but the same obstruction class that first forces failure of continuation tail 282.`, + whyThisExists: 'This packet exists to bridge the gap between search evidence and proof. Without it, the loop only says the alignment is suggestive; with it, the theorem lane gets an explicit object to prove, falsify, or narrow.', + whyNow: `The canonical bridge freezes next unmatched representative ${nextRepresentative}, and the claim pass already marks its equality with the first failure of tail 282 as supported.`, + evidenceBasis: [ + `The canonical bridge records next unmatched representative ${nextRepresentative}.`, + `The tracked-tail matrix records continuation 282 failing first at ${nextRepresentative}.`, + familyRow + ? `The current family menu already contains representative ${nextRepresentative} with tuple key ${familyRow.tupleKey} and tuple rows ${tupleSummary}.` + : `The current family menu does not yet expose a concrete row for representative ${nextRepresentative}.`, + familyRow && alignmentContext.only282Fails + ? `On that family-menu row, only continuation 282 fails among the tracked tails, and it does so via witness modulus ${failing282Witness}.` + : `The tracked repair boundary for representative ${nextRepresentative} is not yet isolated to a single failing continuation.`, + `The strongest completed structured tail remains ${strongestCompletedTail}, so this packet isolates the 282 obstruction mechanism rather than conflating it with the current family-aware leader ${currentLeader}.`, + latestVerifiedInterval + ? `The finite exact base is already certified through ${latestVerifiedInterval}, so the open work is structural rather than basic interval bookkeeping.` + : 'The finite exact base is not yet frozen, so this packet remains provisional.', + checkedMechanismPacketPromoted + ? `Formalization-work checker ${activationLemmaCheck.checkerId} replayed ${activationLemmaCheck.checkedRowCount} activation rows with ${activationLemmaCheck.failCount} failures.` + : null, + checkedMechanismPacketPromoted + ? `Formalization-work checker ${tupleRowLift132Proof.checkerId} proved the 132-row lift with k=${tupleRowLift132Proof.liftParameter} and residue ${tupleRowLift132Proof.liftedResidueModuloWitness} mod ${alignmentContext.witnessSquareModulus}.` + : null, + checkedTopRepairPacketPromoted + ? `The top repair-class side packet is also checked: +2 finite-menu replay plus ${mod50LaneSignature.checkedRowCount} mod-50 lane exchange rows pass.` + : null, + ].filter(Boolean), + proofObligations: [ + { + obligationId: 'define_shared_prefix_obstruction_class', + status: familyRow ? 'done' : 'ready', + task: `Define the shared-prefix obstruction class precisely enough that the representative n=${nextRepresentative} and the 282 continuation can be discussed in the same language.`, + why: 'Without a shared obstruction language, the current equality is still only a numerical coincidence.', + dischargeWith: familyRow + ? 'Use the family-menu row language: shared-prefix tuple rows plus representative/modulus/residue plus tracked-tail repair rows.' + : 'Write the common packet/tuple/CRT language that contains both the shared-prefix representative and the 282-tail failure.', + }, + { + obligationId: 'explain_282_first_failure_mechanism', + status: checkedMechanismPacketPromoted ? 'done' : alignmentContext.failing282 ? 'in_progress' : 'ready', + task: 'Explain why the 282 continuation first fails on that obstruction class rather than merely sharing the same first failing n by accident.', + why: 'This is the core mechanism claim that would upgrade the bridge fact into a theorem-facing lemma candidate.', + dischargeWith: checkedMechanismPacketPromoted + ? `Use the checked packet: ${activationLemmaCheck.checkerId} plus ${tupleRowLift132Proof.checkerId} certify the finite-menu mechanism, while keeping the universal lift out of scope.` + : alignmentContext.failing282 + ? `Describe why the ${failing282Witness} witness appears for continuation 282 on this class while the neighboring tracked tails stay squarefree.` + : 'Describe the repair/obstruction mechanism that makes 282 vulnerable exactly at that class.', + }, + { + obligationId: 'separate_alignment_from_leaderboard_artifacts', + status: stableRepairAnchors.length > 0 ? 'done' : 'ready', + task: 'Separate this obstruction-alignment claim from unrelated leaderboard behavior of 432, 782, and 832 so the statement stays narrow and honest.', + why: 'The 282 packet should not inherit unsupported claims from the current repair-class leaderboard.', + dischargeWith: stableRepairAnchors.length > 0 + ? `Freeze the local repair boundary: ${failingRepairAnchors.join(', ')} fails on this class while ${stableRepairAnchors.join(', ')} remain squarefree.` + : 'State explicitly what the packet does not claim about 432, 782, 832, or 332.', + }, + { + obligationId: 'freeze_alignment_falsifier_boundary', + status: alignmentContext.witnessFirstOccurrence?.earlierZeroResidueCount === 0 ? 'done' : 'ready', + task: 'Record what extra bridge or exact evidence would count as a genuine falsifier of the alignment mechanism.', + why: 'A theorem packet is more trustworthy when it names its own failure modes.', + dischargeWith: alignmentContext.witnessFirstOccurrence?.earlierZeroResidueCount === 0 + ? `Bind the packet to the explicit falsifier boundary: a lower representative in the ${alignmentContext.witnessSquareModulus ?? '(unknown)'} witness class, a different first 282 witness, or bridge loss of the ${nextRepresentative} <-> 282 alignment.` + : 'Bind the packet to refreshable bridge and exact checks that could break it.', + }, + checkedMechanismPacketPromoted + ? { + obligationId: 'lift_132_activation_schema_beyond_finite_menu', + status: 'ready', + task: 'Decide whether the checked finite-menu 132 activation schema can be lifted into a symbolic CRT lemma beyond the current family menu.', + why: 'This is now the honest successor to the discharged 282 mechanism packet: the mechanism is checked finitely, but the universal theorem should not inherit it without a symbolic lift.', + dischargeWith: 'Prove parameterized tuple-row CRT hypotheses that force pre-132 misses, unique 132 target activation, and 182 preservation beyond the current finite menu.', + } + : null, + ].filter(Boolean), + falsifierChecks: [ + { + checkId: 'bridge_next_unmatched_stability', + status: 'ready', + task: `A refreshed bridge no longer lists ${nextRepresentative} as the next unmatched representative.`, + why: 'If the bridge frontier moves, the current packet may no longer be pointing at the right obstruction.', + command: 'erdos number-theory bridge-refresh 848', + }, + { + checkId: 'tracked_tail_282_stability', + status: 'ready', + task: `A refreshed tracked-tail matrix no longer gives continuation 282 first failure ${nextRepresentative}.`, + why: 'The packet is only interesting if the 282-tail boundary stays synchronized with the shared-prefix representative.', + command: 'erdos problem claim-pass-refresh 848', + }, + { + checkId: 'obstruction_class_mismatch', + status: 'ready', + task: 'Packet replay or family-menu analysis shows that the shared-prefix representative and the 282 failure belong to different obstruction classes.', + why: 'This would directly break the mechanism-level interpretation of the alignment.', + command: 'erdos number-theory dispatch 848 --apply --action cpu_family_search', + }, + ], + promotionCriteria: [ + { + criterionId: 'alignment_hook_survives', + status: checkedMechanismPacketPromoted ? 'done' : 'ready', + task: 'The next_unmatched_equals_282_failure hook stays supported after refresh.', + }, + { + criterionId: 'statement_is_mechanism_level', + status: checkedMechanismPacketPromoted ? 'done' : 'ready', + task: 'The candidate statement is expressed as an obstruction-class alignment, not as a full theorem of closure.', + }, + { + criterionId: 'mechanism_is_testable', + status: checkedMechanismPacketPromoted ? 'done' : 'ready', + task: 'The packet identifies at least one mechanism-level explanation to test, not just a repeated equality of two numbers.', + }, + checkedMechanismPacketPromoted + ? { + criterionId: 'finite_menu_mechanism_checked', + status: 'done', + task: 'The finite-menu 282 mechanism is checked by activation-row and CRT-lift replay certificates.', + } + : null, + ].filter(Boolean), + supportingCommands: [ + 'erdos number-theory bridge-refresh 848', + 'erdos problem claim-pass-refresh 848', + 'erdos problem formalization-work 848', + 'erdos number-theory dispatch 848 --apply --action cpu_family_search', + 'erdos number-theory dispatch 848 --apply --action exact_followup_rollout', + ], + }; +} + +function p848TargetHasDoneObligation(target, obligationId) { + return Array.isArray(target?.proofObligations) + && target.proofObligations.some((item) => item?.obligationId === obligationId && item?.status === 'done'); +} + +function p848TargetHasDonePromotionCriterion(target, criterionId) { + return Array.isArray(target?.promotionCriteria) + && target.promotionCriteria.some((item) => item?.criterionId === criterionId && item?.status === 'done'); +} + +function buildP848TupleRowLift132ProofFromAlignment(alignmentContext) { + const familyRow = alignmentContext?.familyRow ?? null; + const tupleRows = Array.isArray(familyRow?.tupleRows) ? familyRow.tupleRows : []; + const steps = Array.isArray(alignmentContext?.tupleRowCrtDerivation?.steps) + ? alignmentContext.tupleRowCrtDerivation.steps + : []; + const tupleRow132 = tupleRows.find((row) => Number(row.anchor) === 132) ?? null; + const stepIndex132 = steps.findIndex((row) => Number(row.anchor) === 132); + const tupleRow132Step = stepIndex132 >= 0 ? steps[stepIndex132] : null; + const tupleRow132PreviousStep = stepIndex132 > 0 ? steps[stepIndex132 - 1] : null; + const witnessSquareModulus = alignmentContext?.witnessSquareModulus ?? null; + const representativeResidueModuloWitness = witnessSquareModulus && familyRow?.representative !== undefined + ? positiveMod(familyRow.representative, witnessSquareModulus) + : null; + + if (!tupleRow132 || !tupleRow132Step || !tupleRow132PreviousStep || !witnessSquareModulus) { + return null; + } + + const liftCoeffModuloAnchor = positiveMod(tupleRow132PreviousStep.combinedModulus, tupleRow132.squareModulus); + const liftRhsModuloAnchor = positiveMod( + tupleRow132.residue - positiveMod(tupleRow132PreviousStep.combinedResidue, tupleRow132.squareModulus), + tupleRow132.squareModulus, + ); + const inverseLiftCoeff = modularInverseInt(liftCoeffModuloAnchor, tupleRow132.squareModulus); + const liftParameter = inverseLiftCoeff === null + ? null + : positiveMod(inverseLiftCoeff * liftRhsModuloAnchor, tupleRow132.squareModulus); + + if (liftParameter === null) { + return { + checkerId: 'p848_132_lift_crt_checker_v1', + source: 'tuple_row_crt_equation_replay', + status: 'failed', + checkedRowCount: 1, + passCount: 0, + failCount: 1, + failedChecks: ['lift_parameter_missing'], + }; + } + + const preResidue = BigInt(tupleRow132PreviousStep.combinedResidue); + const preModulus = BigInt(tupleRow132PreviousStep.combinedModulus); + const liftParameterBigInt = BigInt(liftParameter); + const anchorModulus = BigInt(tupleRow132.squareModulus); + const witnessModulus = BigInt(witnessSquareModulus); + const liftedByParameter = preResidue + (preModulus * liftParameterBigInt); + const checks = { + liftParameterSolvesReducedEquation: positiveModBigInt(BigInt(liftCoeffModuloAnchor) * liftParameterBigInt, anchorModulus) + === BigInt(liftRhsModuloAnchor), + liftedResidueMatchesCrtStep: liftedByParameter === BigInt(tupleRow132Step.combinedResidue), + liftedResidueSatisfiesAnchor132: positiveModBigInt(liftedByParameter, anchorModulus) + === BigInt(tupleRow132.residue), + liftedResiduePreservesPriorCrtPrefix: positiveModBigInt(liftedByParameter, preModulus) + === positiveModBigInt(preResidue, preModulus), + liftedResidueHitsWitnessProjection: positiveModBigInt(liftedByParameter, witnessModulus) + === BigInt(tupleRow132Step.residueModWitness), + liftedResidueHitsBoundaryWitnessResidue: representativeResidueModuloWitness !== null + && positiveModBigInt(liftedByParameter, witnessModulus) === BigInt(representativeResidueModuloWitness), + }; + const failedChecks = Object.entries(checks) + .filter(([, passed]) => !passed) + .map(([checkId]) => checkId); + + return { + checkerId: 'p848_132_lift_crt_checker_v1', + source: 'tuple_row_crt_equation_replay', + status: failedChecks.length === 0 ? 'proved_from_tuple_row_crt' : 'failed', + checkedRowCount: 1, + passCount: failedChecks.length === 0 ? 1 : 0, + failCount: failedChecks.length, + equation: `${tupleRow132PreviousStep.combinedResidue} + ${tupleRow132PreviousStep.combinedModulus}*k ≡ ${tupleRow132.residue} (mod ${tupleRow132.squareModulus})`, + reducedEquation: `${liftCoeffModuloAnchor}*k ≡ ${liftRhsModuloAnchor} (mod ${tupleRow132.squareModulus})`, + liftParameter, + liftedResidueByParameter: toJsonInteger(liftedByParameter), + liftedResidueModuloWitness: tupleRow132Step.residueModWitness, + targetWitnessResidue: representativeResidueModuloWitness, + checks, + failedChecks, + conclusion: failedChecks.length === 0 + ? `The 132-row lift from residue ${tupleRow132PreviousStep.residueModWitness} to ${tupleRow132Step.residueModWitness} mod ${witnessSquareModulus} is proved by the tuple-row CRT equation.` + : 'The 132-row lift did not replay from the tuple-row CRT equation.', + }; +} + +function buildProblemFormalizationTarget(problem, theoremLoop, claimPass) { + const recommendations = Array.isArray(claimPass?.recommendations) ? claimPass.recommendations : []; + const theoremRecommendation = recommendations.find((item) => item.lane === 'theorem_formalization') ?? null; + + if (problem.problemId === '848' && theoremRecommendation?.recommendation_id === 'formalize_282_alignment') { + return buildP848AlignmentFormalizationTarget(theoremLoop, claimPass); + } + + return buildGenericFormalizationTarget(problem, theoremLoop, claimPass); +} + +export function buildProblemClaimPass(problem) { + const theoremLoop = buildProblemTheoremLoop(problem); + const claimLoop = buildProblemClaimLoop(problem); + const theoremPaths = getProblemTheoremLoopPaths(problem); + const claimLoopPaths = getProblemClaimLoopPaths(problem); + const claimPassPaths = getProblemClaimPassPaths(problem); + const bridgeDoc = theoremPaths.legacyBridgeJsonPath ? readJsonIfPresent(theoremPaths.legacyBridgeJsonPath) : null; + const intervalQueuePath = theoremPaths.packProblemDir ? path.join(theoremPaths.packProblemDir, 'INTERVAL_WORK_QUEUE.yaml') : null; + const intervalQueue = readYamlIfPresent(intervalQueuePath); + + const bridgeHooks = new Map( + Array.isArray(bridgeDoc?.candidate_theorem_hooks) + ? bridgeDoc.candidate_theorem_hooks.map((hook) => [hook.hook_id, hook]) + : [], + ); + + const hookAssessments = (theoremLoop.theoremHooks ?? []).map((hook) => ( + buildHookAssessment(hook, bridgeHooks.get(hook.hook_id) ?? null, theoremLoop, bridgeDoc) + )); + + const claimAssessments = (claimLoop.candidateClaims ?? []).map((claim) => ( + buildClaimAssessment(problem, claim, theoremLoop, claimLoop, hookAssessments, bridgeDoc, intervalQueue) + )); + + const latestVerifiedInterval = getLatestVerifiedInterval(intervalQueue); + const recommendations = buildClaimPassRecommendations(problem, theoremLoop, claimAssessments, hookAssessments, intervalQueue); + + return { + schema: 'erdos.problem_claim_pass/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + sourceKind: theoremLoop.currentBridgeState ? 'claim_loop_plus_bridge' : 'claim_loop_only', + claimPassMode: theoremLoop.currentBridgeState ? 'bridge_backed' : 'baseline', + currentClaimSurface: theoremLoop.currentState.currentClaimSurface, + currentState: { + activeRoute: theoremLoop.activeRoute, + nextHonestMove: theoremLoop.currentState.nextHonestMove, + routeSummary: theoremLoop.currentState.routeSummary, + latestVerifiedInterval: latestVerifiedInterval?.range ?? null, + sourceRefresh: theoremLoop.commands.sourceRefresh ?? null, + }, + summary: buildClaimPassSummary(hookAssessments, claimAssessments), + hookAssessments, + claimAssessments, + recommendations, + commands: { + problemShow: `erdos problem show ${problem.problemId}`, + problemArtifacts: `erdos problem artifacts ${problem.problemId}`, + theoremLoop: theoremLoop.commands.theoremLoop, + theoremLoopRefresh: theoremLoop.commands.theoremLoopRefresh, + claimLoop: claimLoop.commands.claimLoop, + claimLoopRefresh: claimLoop.commands.claimLoopRefresh, + claimPass: `erdos problem claim-pass ${problem.problemId}`, + claimPassRefresh: `erdos problem claim-pass-refresh ${problem.problemId}`, + sourceRefresh: theoremLoop.commands.sourceRefresh ?? null, + }, + sources: { + packProblemDir: theoremPaths.packProblemDir, + theoremLoopJsonPath: theoremPaths.theoremLoopJsonPath, + theoremLoopMarkdownPath: theoremPaths.theoremLoopMarkdownPath, + claimLoopJsonPath: claimLoopPaths.claimLoopJsonPath, + claimLoopMarkdownPath: claimLoopPaths.claimLoopMarkdownPath, + claimPassJsonPath: claimPassPaths.claimPassJsonPath, + claimPassMarkdownPath: claimPassPaths.claimPassMarkdownPath, + legacyBridgeJsonPath: theoremPaths.legacyBridgeJsonPath, + legacyBridgeMarkdownPath: theoremPaths.legacyBridgeMarkdownPath, + intervalQueuePath, + }, + }; +} + +export function renderProblemClaimPassMarkdown(doc) { + const lines = [ + `# ${doc.displayName} Claim Pass`, + '', + doc.sourceKind === 'claim_loop_plus_bridge' + ? 'This claim pass evaluates theorem-search claims against the canonical claim loop plus bridge-backed search evidence.' + : 'This claim pass evaluates theorem-search claims against the canonical claim loop and pack-level evidence.', + '', + '## Current State', + '', + `- Claim pass mode: \`${doc.claimPassMode}\`.`, + `- Current claim surface: \`${doc.currentClaimSurface}\`.`, + `- Active route: \`${doc.currentState.activeRoute ?? '(none)'}\`.`, + `- Route summary: ${doc.currentState.routeSummary}`, + `- Next honest move: ${doc.currentState.nextHonestMove}`, + `- Latest verified interval: ${doc.currentState.latestVerifiedInterval ? `\`${doc.currentState.latestVerifiedInterval}\`` : '`(none)`'}`, + '', + '## Summary', + '', + `- Hook assessments: supported \`${doc.summary.hooks.supported}\`, unresolved \`${doc.summary.hooks.unresolved}\`, broken \`${doc.summary.hooks.broken}\`.`, + `- Claim assessments: supported \`${doc.summary.claims.supported}\`, actionable \`${doc.summary.claims.actionable}\`, unresolved \`${doc.summary.claims.unresolved}\`, broken \`${doc.summary.claims.broken}\`.`, + '', + '## Hook Assessments', + '', + ]; + + for (const hook of doc.hookAssessments ?? []) { + lines.push(`- \`${hook.hook_id}\`: ${hook.verdict} | ${hook.rationale}`); + } + + lines.push('', '## Claim Assessments', ''); + for (const claim of doc.claimAssessments ?? []) { + lines.push(`- \`${claim.claim_id}\`: ${claim.verdict} | ${claim.summary}${claim.rationale ? ` | ${claim.rationale}` : ''}`); + } + + lines.push('', '## Recommendations', ''); + for (const recommendation of doc.recommendations ?? []) { + lines.push(`- \`${recommendation.recommendation_id}\`: ${recommendation.priority} | ${recommendation.lane} | ${recommendation.reason}${recommendation.command ? ` | ${recommendation.command}` : ''}`); + } + + lines.push('', '## Commands', ''); + lines.push(`- Problem surface: \`${doc.commands.problemShow}\``); + lines.push(`- Problem artifacts: \`${doc.commands.problemArtifacts}\``); + lines.push(`- Theorem loop: \`${doc.commands.theoremLoop}\``); + lines.push(`- Claim loop: \`${doc.commands.claimLoop}\``); + lines.push(`- Claim pass: \`${doc.commands.claimPass}\``); + lines.push(`- Claim pass refresh: \`${doc.commands.claimPassRefresh}\``); + if (doc.commands.sourceRefresh) { + lines.push(`- Source refresh: \`${doc.commands.sourceRefresh}\``); + } + + lines.push('', '## Sources', ''); + for (const [label, value] of Object.entries(doc.sources ?? {})) { + if (!value) { + continue; + } + lines.push(`- ${label}: \`${value}\``); + } + lines.push(''); + return lines.join('\n'); +} + +export function getProblemClaimPassSnapshot(problem) { + const doc = buildProblemClaimPass(problem); + const paths = getProblemClaimPassPaths(problem); + return { + ...doc, + claimPassJsonPath: paths.claimPassJsonPath, + claimPassMarkdownPath: paths.claimPassMarkdownPath, + claimPassJsonPresent: Boolean(paths.claimPassJsonPath && fs.existsSync(paths.claimPassJsonPath)), + claimPassMarkdownPresent: Boolean(paths.claimPassMarkdownPath && fs.existsSync(paths.claimPassMarkdownPath)), + }; +} + +export function buildProblemFormalization(problem) { + const theoremLoop = buildProblemTheoremLoop(problem); + const claimLoop = buildProblemClaimLoop(problem); + const claimPass = buildProblemClaimPass(problem); + const paths = getProblemFormalizationPaths(problem); + const target = buildProblemFormalizationTarget(problem, theoremLoop, claimPass); + const obligationSummary = summarizeChecklist(target.proofObligations); + const falsifierSummary = summarizeChecklist(target.falsifierChecks); + const promotionSummary = summarizeChecklist(target.promotionCriteria); + + return { + schema: 'erdos.problem_formalization/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + sourceKind: theoremLoop.currentBridgeState ? 'claim_pass_plus_bridge' : 'claim_pass_only', + formalizationMode: theoremLoop.currentBridgeState ? 'bridge_backed' : 'baseline', + currentClaimSurface: theoremLoop.currentState.currentClaimSurface, + currentState: { + activeRoute: theoremLoop.activeRoute, + routeSummary: theoremLoop.currentState.routeSummary, + nextHonestMove: theoremLoop.currentState.nextHonestMove, + latestVerifiedInterval: claimPass.currentState?.latestVerifiedInterval ?? null, + sourceRefresh: theoremLoop.commands.sourceRefresh ?? null, + }, + currentTarget: target, + summary: { + proofObligations: obligationSummary, + falsifierChecks: falsifierSummary, + promotionCriteria: promotionSummary, + }, + theoremHooks: theoremLoop.theoremHooks ?? [], + claimAssessments: claimPass.claimAssessments ?? [], + recommendationLedger: claimPass.recommendations ?? [], + commands: { + problemShow: `erdos problem show ${problem.problemId}`, + problemArtifacts: `erdos problem artifacts ${problem.problemId}`, + theoremLoop: theoremLoop.commands.theoremLoop, + claimLoop: claimLoop.commands.claimLoop, + claimPass: claimPass.commands.claimPass, + formalization: `erdos problem formalization ${problem.problemId}`, + formalizationRefresh: `erdos problem formalization-refresh ${problem.problemId}`, + formalizationWork: `erdos problem formalization-work ${problem.problemId}`, + formalizationWorkRefresh: `erdos problem formalization-work-refresh ${problem.problemId}`, + sourceRefresh: theoremLoop.commands.sourceRefresh ?? null, + }, + sources: { + packProblemDir: paths.packProblemDir, + formalizationJsonPath: paths.formalizationJsonPath, + formalizationMarkdownPath: paths.formalizationMarkdownPath, + theoremLoopJsonPath: theoremLoop.sources.theoremLoopJsonPath ?? null, + theoremLoopMarkdownPath: theoremLoop.sources.theoremLoopMarkdownPath ?? null, + claimLoopJsonPath: claimLoop.sources.claimLoopJsonPath ?? null, + claimLoopMarkdownPath: claimLoop.sources.claimLoopMarkdownPath ?? null, + claimPassJsonPath: claimPass.sources.claimPassJsonPath ?? null, + claimPassMarkdownPath: claimPass.sources.claimPassMarkdownPath ?? null, + legacyBridgeJsonPath: theoremLoop.sources.legacyBridgeJsonPath ?? null, + legacyBridgeMarkdownPath: theoremLoop.sources.legacyBridgeMarkdownPath ?? null, + }, + }; +} + +export function renderProblemFormalizationMarkdown(doc) { + const target = doc.currentTarget ?? {}; + const lines = [ + `# ${doc.displayName} Formalization`, + '', + doc.sourceKind === 'claim_pass_plus_bridge' + ? 'This formalization packet promotes the current claim-pass recommendation into a concrete theorem-facing proof obligation anchored in canonical bridge evidence.' + : 'This formalization packet promotes the current claim-pass recommendation into a concrete theorem-facing proof obligation anchored in canonical pack evidence.', + '', + '## Current State', + '', + `- Formalization mode: \`${doc.formalizationMode}\`.`, + `- Current claim surface: \`${doc.currentClaimSurface}\`.`, + `- Active route: \`${doc.currentState.activeRoute ?? '(none)'}\`.`, + `- Route summary: ${doc.currentState.routeSummary}`, + `- Next honest move: ${doc.currentState.nextHonestMove}`, + `- Latest verified interval: ${doc.currentState.latestVerifiedInterval ? `\`${doc.currentState.latestVerifiedInterval}\`` : '`(none)`'}`, + '', + '## Current Target', + '', + `- Formalization id: \`${target.formalizationId ?? '(none)'}\`.`, + `- Focus id: \`${target.focusId ?? '(none)'}\`.`, + `- Title: ${target.title ?? '(none)'}`, + `- Status: \`${target.status ?? '(none)'}\`.`, + `- Lane: \`${target.lane ?? '(none)'}\`.`, + `- Summary: ${target.summary ?? '(none)'}`, + `- Candidate statement: ${target.statement ?? '(none)'}`, + `- Proof obligations: ready \`${doc.summary?.proofObligations?.ready ?? 0}\` / total \`${doc.summary?.proofObligations?.total ?? 0}\`.`, + `- Falsifier checks: ready \`${doc.summary?.falsifierChecks?.ready ?? 0}\` / total \`${doc.summary?.falsifierChecks?.total ?? 0}\`.`, + `- Promotion criteria: ready \`${doc.summary?.promotionCriteria?.ready ?? 0}\` / total \`${doc.summary?.promotionCriteria?.total ?? 0}\`.`, + '', + '## Why This Exists', + '', + `${target.whyThisExists ?? 'No explicit formalization rationale recorded yet.'}`, + '', + '## Why Now', + '', + `${target.whyNow ?? 'No explicit timing rationale recorded yet.'}`, + '', + '## Evidence Basis', + '', + ]; + + for (const item of target.evidenceBasis ?? []) { + lines.push(`- ${item}`); + } + + lines.push('', '## Proof Obligations', ''); + for (const item of target.proofObligations ?? []) { + lines.push(`- ${renderChecklistItem(item)}`); + } + + lines.push('', '## Falsifier Checks', ''); + for (const item of target.falsifierChecks ?? []) { + lines.push(`- ${renderChecklistItem(item)}`); + } + + lines.push('', '## Promotion Criteria', ''); + for (const item of target.promotionCriteria ?? []) { + lines.push(`- ${renderChecklistItem(item)}`); + } + + lines.push('', '## Supporting Commands', ''); + for (const item of target.supportingCommands ?? []) { + lines.push(`- \`${item}\``); + } + + lines.push('', '## Commands', ''); + lines.push(`- Problem surface: \`${doc.commands.problemShow}\``); + lines.push(`- Problem artifacts: \`${doc.commands.problemArtifacts}\``); + lines.push(`- Theorem loop: \`${doc.commands.theoremLoop}\``); + lines.push(`- Claim loop: \`${doc.commands.claimLoop}\``); + lines.push(`- Claim pass: \`${doc.commands.claimPass}\``); + lines.push(`- Formalization: \`${doc.commands.formalization}\``); + lines.push(`- Formalization refresh: \`${doc.commands.formalizationRefresh}\``); + lines.push(`- Formalization work: \`${doc.commands.formalizationWork}\``); + lines.push(`- Formalization work refresh: \`${doc.commands.formalizationWorkRefresh}\``); + if (doc.commands.sourceRefresh) { + lines.push(`- Source refresh: \`${doc.commands.sourceRefresh}\``); + } + + lines.push('', '## Sources', ''); + for (const [label, value] of Object.entries(doc.sources ?? {})) { + if (!value) { + continue; + } + lines.push(`- ${label}: \`${value}\``); + } + lines.push(''); + return lines.join('\n'); +} + +export function getProblemFormalizationSnapshot(problem) { + const doc = buildProblemFormalization(problem); + const paths = getProblemFormalizationPaths(problem); + return { + ...doc, + formalizationJsonPath: paths.formalizationJsonPath, + formalizationMarkdownPath: paths.formalizationMarkdownPath, + formalizationJsonPresent: Boolean(paths.formalizationJsonPath && fs.existsSync(paths.formalizationJsonPath)), + formalizationMarkdownPresent: Boolean(paths.formalizationMarkdownPath && fs.existsSync(paths.formalizationMarkdownPath)), + }; +} + +function buildGenericFormalizationWorkTarget(problem, formalization) { + const target = formalization?.currentTarget ?? {}; + const firstOpenObligation = pickFormalizationWorkFocus(target); + + return { + workId: `${problem.cluster}_${problem.problemId}_${firstOpenObligation?.obligationId ?? 'formalization_work'}_v1`, + focusFormalizationId: target.formalizationId ?? null, + focusId: firstOpenObligation?.obligationId ?? null, + title: firstOpenObligation?.obligationId + ? titleCaseWords(firstOpenObligation.obligationId) + : 'Seed Formalization Work Packet', + status: firstOpenObligation?.status ?? 'ready', + summary: firstOpenObligation?.task ?? target.summary ?? 'Seed the next formalization work unit.', + why: firstOpenObligation?.why ?? target.whyThisExists ?? null, + workingDefinition: [ + target.statement ?? 'No explicit formalization statement recorded yet.', + ], + currentEvidence: [...(target.evidenceBasis ?? [])], + dischargedWork: Array.isArray(target.proofObligations) + ? target.proofObligations + .filter((item) => item?.status === 'done') + .map((item) => `${item.obligationId}: ${item.dischargeWith ?? item.task}`) + : [], + remainingGaps: Array.isArray(target.proofObligations) + ? target.proofObligations + .filter((item) => item?.status !== 'done') + .map((item) => `${item.obligationId}: ${item.dischargeWith ?? item.task}`) + : [], + nextCommands: [ + formalization?.commands?.formalizationRefresh ?? null, + formalization?.commands?.formalization ?? null, + ].filter(Boolean), + }; +} + +function buildP848SharedPrefixClassWorkTarget(formalization, alignmentContext, focusObligation) { + const familyRow = alignmentContext.familyRow; + const tupleRows = Array.isArray(familyRow?.tupleRows) ? familyRow.tupleRows : []; + const stableRepairAnchors = alignmentContext.stableRepairRows.map((row) => row.anchor); + const failingRepairRows = alignmentContext.failingRepairRows.map((row) => ({ + anchor: row.anchor, + squareWitnesses: Array.isArray(row.squareWitnesses) ? row.squareWitnesses.map((witness) => witness.squareModulus) : [], + })); + + return { + workId: 'p848_shared_prefix_obstruction_class_packet_v1', + focusFormalizationId: formalization?.currentTarget?.formalizationId ?? 'p848_282_alignment_formalization_v1', + focusId: focusObligation?.obligationId ?? 'define_shared_prefix_obstruction_class', + title: 'Define the Shared-Prefix Obstruction Class', + status: familyRow ? 'in_progress' : 'ready', + summary: 'Freeze the exact tuple/CRT/repair language for the first obstruction class that defeats continuation 282.', + why: 'This is the first point where the alignment claim becomes expressible in a reusable theorem language instead of as a numerical coincidence.', + workingDefinition: [ + 'A shared-prefix obstruction class is a family-menu row over the fixed prefix `{7, 32, 57, 82, 132, 182}`.', + 'The class is described by `(tupleKey, tupleRows, representative, modulus, residue)` together with the tracked-tail repair surface on the same row.', + familyRow + ? `The current boundary class is the row with representative ${familyRow.representative} and tuple key ${familyRow.tupleKey}.` + : 'The current boundary class is not yet frozen in the family menu.', + ], + currentEvidence: [ + familyRow + ? `Representative ${familyRow.representative} is already present in the live family menu at ${alignmentContext.familyMenuPath}.` + : 'The live family menu does not yet expose the target representative row.', + familyRow + ? `Tuple rows: ${tupleRows.map((row) => `${row.anchor}->${row.squareModulus}/${row.residue}`).join(', ')}.` + : 'Tuple rows are not yet available.', + alignmentContext.trackedTail282 + ? `Tracked tail 282 still has first failure ${alignmentContext.trackedTail282.observed_first_failure ?? alignmentContext.trackedTail282.effective_first_failure}.` + : 'Tracked tail 282 data is not currently available.', + alignmentContext.only282Fails + ? `On this class, only continuation 282 fails among the tracked repair anchors, via witness ${failingRepairRows[0]?.squareWitnesses?.join(', ') ?? '(unknown)'}.` + : 'The repair boundary is not yet isolated to continuation 282 alone.', + ], + dischargedWork: [ + familyRow + ? `Shared obstruction language fixed: tuple rows + CRT class + repair surface all come from the same family-menu row.` + : 'Shared obstruction language is not yet fixed.', + stableRepairAnchors.length > 0 + ? `Boundary narrowed: ${stableRepairAnchors.join(', ')} remain squarefree on the class while ${failingRepairRows.map((row) => row.anchor).join(', ')} fails.` + : 'Boundary narrowing has not yet been recorded.', + ].filter(Boolean), + remainingGaps: [ + 'Show that this class is not merely the first observed 282 failure, but the first structurally unavoidable one for the 282 continuation.', + 'Explain why the 29^2 = 841 witness appears for 282 on this class while 332, 432, 782, and 832 stay squarefree.', + 'Connect this boundary class to the bridge falsifiers so a future packet can be promoted or broken cleanly.', + ], + packetData: { + sharedPrefix: alignmentContext.bridgeDoc?.shared_prefix ?? null, + representative: familyRow?.representative ?? null, + tupleKey: familyRow?.tupleKey ?? null, + modulus: familyRow?.modulus ?? null, + residue: familyRow?.residue ?? null, + tupleRows, + stableRepairAnchors, + failingRepairRows, + familyMenuPath: alignmentContext.familyMenuPath, + bridgePath: formalization?.sources?.legacyBridgeJsonPath ?? null, + }, + nextCommands: [ + formalization?.commands?.formalizationWorkRefresh ?? null, + formalization?.commands?.formalizationRefresh ?? null, + formalization?.commands?.formalization ?? null, + formalization?.commands?.claimPass ?? null, + ].filter(Boolean), + }; +} + +function buildP848MechanismWorkTarget(formalization, alignmentContext, focusObligation) { + const latestVerifiedRange = parseClosedIntegerRange(formalization?.currentState?.latestVerifiedInterval); + const nextExactVerificationLane = latestVerifiedRange + ? `Decide and run the next post-${latestVerifiedRange.max} verification lane using local CPU and opt-in local 4090 compute only.` + : 'Decide and run the next exact verification lane using local CPU and opt-in local 4090 compute only.'; + const repairRow282ForFamily = (family) => Array.isArray(family?.repairRows) + ? family.repairRows.find((row) => row?.anchor === 282) ?? null + : null; + const familyRow = alignmentContext.familyRow; + const failing282 = alignmentContext.failing282; + const witnessSquareModulus = alignmentContext.witnessSquareModulus ?? failing282?.squareWitnesses?.[0]?.squareModulus ?? null; + const tupleSquareModuli = Array.isArray(familyRow?.tupleRows) ? familyRow.tupleRows.map((row) => row.squareModulus) : []; + const representativeResidueModuloWitness = witnessSquareModulus && familyRow?.representative !== undefined + ? positiveMod(familyRow.representative, witnessSquareModulus) + : null; + const repairResidues = alignmentContext.repairRows.map((row) => ({ + anchor: row.anchor, + residueModuloWitness: witnessSquareModulus ? Number(row.value % witnessSquareModulus) : null, + squarefree: row.squarefree, + })); + const stableResidues = repairResidues.filter((row) => row.squarefree); + const failingResidue = repairResidues.find((row) => row.anchor === 282) ?? null; + const quotient = witnessSquareModulus && Number.isInteger(failing282?.value) + ? Math.trunc(failing282.value / witnessSquareModulus) + : null; + const firstFailingRepresentative = alignmentContext.firstFailing282Family?.representative ?? null; + const witnessFirstOccurrence = alignmentContext.witnessFirstOccurrence ?? null; + const tupleRowCrtDerivation = alignmentContext.tupleRowCrtDerivation ?? null; + const tupleRow132 = Array.isArray(familyRow?.tupleRows) + ? familyRow.tupleRows.find((row) => row?.anchor === 132) ?? null + : null; + const tupleRow182 = Array.isArray(familyRow?.tupleRows) + ? familyRow.tupleRows.find((row) => row?.anchor === 182) ?? null + : null; + const tupleRow132PreviousStep = Array.isArray(tupleRowCrtDerivation?.steps) + ? tupleRowCrtDerivation.steps.find((row) => row?.anchor === 82) ?? null + : null; + const tupleRow132Step = Array.isArray(tupleRowCrtDerivation?.steps) + ? tupleRowCrtDerivation.steps.find((row) => row?.anchor === 132) ?? null + : null; + const tupleRowLift132 = tupleRow132 && tupleRow132PreviousStep && tupleRow132Step + ? (() => { + const liftCoeffModuloAnchor = positiveMod(tupleRow132PreviousStep.combinedModulus, tupleRow132.squareModulus); + const liftRhsModuloAnchor = positiveMod(tupleRow132.residue - tupleRow132PreviousStep.combinedResidue, tupleRow132.squareModulus); + const inverseLiftCoeff = modularInverseInt(liftCoeffModuloAnchor, tupleRow132.squareModulus); + const liftParameter = inverseLiftCoeff === null + ? null + : positiveMod(inverseLiftCoeff * liftRhsModuloAnchor, tupleRow132.squareModulus); + return { + preAnchorCombinedResidue: tupleRow132PreviousStep.combinedResidue, + preAnchorCombinedModulus: tupleRow132PreviousStep.combinedModulus, + preAnchorResidueModuloWitness: tupleRow132PreviousStep.residueModWitness, + anchorResidue: tupleRow132.residue, + anchorSquareModulus: tupleRow132.squareModulus, + liftCoeffModuloAnchor, + liftRhsModuloAnchor, + liftedEquation: `${tupleRow132PreviousStep.combinedResidue} + ${tupleRow132PreviousStep.combinedModulus}*k ≡ ${tupleRow132.residue} (mod ${tupleRow132.squareModulus})`, + reducedEquation: `${liftCoeffModuloAnchor}*k ≡ ${liftRhsModuloAnchor} (mod ${tupleRow132.squareModulus})`, + inverseLiftCoeff, + liftParameter, + liftedResidue: tupleRow132Step.combinedResidue, + liftedResidueModuloWitness: tupleRow132Step.residueModWitness, + }; + })() + : null; + const tupleRowLift132Proof = tupleRowLift132 && witnessSquareModulus && tupleRowLift132.liftParameter !== null + ? (() => { + const preResidue = BigInt(tupleRowLift132.preAnchorCombinedResidue); + const preModulus = BigInt(tupleRowLift132.preAnchorCombinedModulus); + const liftParameter = BigInt(tupleRowLift132.liftParameter); + const anchorModulus = BigInt(tupleRowLift132.anchorSquareModulus); + const witnessModulus = BigInt(witnessSquareModulus); + const liftedByParameter = preResidue + (preModulus * liftParameter); + const checks = { + liftParameterSolvesReducedEquation: positiveModBigInt(BigInt(tupleRowLift132.liftCoeffModuloAnchor) * liftParameter, anchorModulus) + === BigInt(tupleRowLift132.liftRhsModuloAnchor), + liftedResidueMatchesCrtStep: liftedByParameter === BigInt(tupleRowLift132.liftedResidue), + liftedResidueSatisfiesAnchor132: positiveModBigInt(liftedByParameter, anchorModulus) + === BigInt(tupleRowLift132.anchorResidue), + liftedResiduePreservesPriorCrtPrefix: positiveModBigInt(liftedByParameter, preModulus) + === positiveModBigInt(preResidue, preModulus), + liftedResidueHitsWitnessProjection: positiveModBigInt(liftedByParameter, witnessModulus) + === BigInt(tupleRowLift132.liftedResidueModuloWitness), + liftedResidueHitsBoundaryWitnessResidue: representativeResidueModuloWitness !== null + && positiveModBigInt(liftedByParameter, witnessModulus) === BigInt(representativeResidueModuloWitness), + }; + const failedChecks = Object.entries(checks) + .filter(([, passed]) => !passed) + .map(([checkId]) => checkId); + return { + checkerId: 'p848_132_lift_crt_checker_v1', + source: 'tuple_row_crt_equation_replay', + status: failedChecks.length === 0 ? 'proved_from_tuple_row_crt' : 'failed', + checkedRowCount: 1, + passCount: failedChecks.length === 0 ? 1 : 0, + failCount: failedChecks.length, + equation: tupleRowLift132.liftedEquation, + reducedEquation: tupleRowLift132.reducedEquation, + liftParameter: tupleRowLift132.liftParameter, + liftedResidueByParameter: toJsonInteger(liftedByParameter), + liftedResidueModuloWitness: tupleRowLift132.liftedResidueModuloWitness, + targetWitnessResidue: representativeResidueModuloWitness, + checks, + failedChecks, + conclusion: failedChecks.length === 0 + ? `The 132-row lift from residue ${tupleRowLift132.preAnchorResidueModuloWitness} to ${tupleRowLift132.liftedResidueModuloWitness} mod ${witnessSquareModulus} is proved by the tuple-row CRT equation.` + : 'The 132-row lift did not replay from the tuple-row CRT equation.', + }; + })() + : null; + const tupleRowPreservation182 = tupleRow182 && tupleRow132Step + ? { + anchorResidue: tupleRow182.residue, + anchorSquareModulus: tupleRow182.squareModulus, + preserved: positiveMod(tupleRow132Step.combinedResidue, tupleRow182.squareModulus) === tupleRow182.residue, + liftedResidueModuloAnchor: positiveMod(tupleRow132Step.combinedResidue, tupleRow182.squareModulus), + liftedResidueModuloWitness: tupleRow132Step.residueModWitness, + checkEquation: `${tupleRow132Step.combinedResidue} ≡ ${tupleRow182.residue} (mod ${tupleRow182.squareModulus})`, + } + : null; + const priorRowsModuloWitness = Array.isArray(alignmentContext.priorRowsModuloWitness) + ? alignmentContext.priorRowsModuloWitness + : []; + const laterWitnessTimeline = Array.isArray(alignmentContext.witnessTimeline) + ? alignmentContext.witnessTimeline + .filter((row) => Number(row.representative) > Number(firstFailingRepresentative ?? Number.MAX_SAFE_INTEGER)) + .slice(0, 5) + : []; + const familyMenuResidueBoundary = witnessSquareModulus && representativeResidueModuloWitness !== null + ? (() => { + const matchingRepresentatives = (Array.isArray(alignmentContext.allFamilies) ? alignmentContext.allFamilies : []) + .map((row, index) => ({ + familyIndex: index, + representative: row?.representative ?? null, + tupleKey: row?.tupleKey ?? null, + representativeResidueModuloWitness: row?.representative !== undefined + ? positiveMod(row.representative, witnessSquareModulus) + : null, + repairRow282: repairRow282ForFamily(row), + })) + .filter((row) => row.representativeResidueModuloWitness === representativeResidueModuloWitness) + .sort((left, right) => Number(left.representative) - Number(right.representative)); + const first = matchingRepresentatives[0] ?? null; + return first + ? { + witnessSquareModulus, + representativeResidueModuloWitness, + firstRepresentative: first.representative, + firstTupleKey: first.tupleKey, + firstFamilyIndex: first.familyIndex, + earlierRepresentativeMatchCount: matchingRepresentatives.filter((row) => Number(row.representative) < Number(first.representative)).length, + sameAsFirstFailingRepresentative: Number(first.representative) === Number(firstFailingRepresentative), + firstRepresentativeHasWitness: Array.isArray(first.repairRow282?.squareWitnesses) + && first.repairRow282.squareWitnesses.some((witness) => witness?.squareModulus === witnessSquareModulus), + } + : null; + })() + : null; + const sameTupleCount = alignmentContext.sameTupleCount ?? 0; + const rowProgressionModuloWitness = alignmentContext.rowProgressionModuloWitness ?? null; + const rowProgressionAnchorTable = Array.isArray(alignmentContext.rowProgressionAnchorTable) + ? alignmentContext.rowProgressionAnchorTable + : []; + const nextSameRowWitnessFor282 = alignmentContext.nextSameRowWitnessFor282 ?? null; + const anchorCongruenceTable = witnessSquareModulus + ? alignmentContext.repairRows.map((row) => { + const gcdWithWitness = gcdInt(row.anchor, witnessSquareModulus); + const inverse = modularInverseInt(row.anchor, witnessSquareModulus); + const requiredNResidueForFailure = inverse === null + ? null + : positiveMod(-inverse, witnessSquareModulus); + return { + anchor: row.anchor, + gcdWithWitness, + representativeResidueModuloWitness, + requiredNResidueForFailure, + matchesRepresentativeResidue: requiredNResidueForFailure !== null + && representativeResidueModuloWitness === requiredNResidueForFailure, + solvableModuloWitness: gcdWithWitness === 1, + residueCheck: witnessSquareModulus ? positiveMod(row.value, witnessSquareModulus) : null, + squarefree: row.squarefree, + }; + }) + : []; + const matchingCongruenceAnchors = anchorCongruenceTable + .filter((row) => row.matchesRepresentativeResidue) + .map((row) => row.anchor); + const unsolvableCongruenceAnchors = anchorCongruenceTable + .filter((row) => !row.solvableModuloWitness) + .map((row) => row.anchor); + const rowProgressionStartAnchors = rowProgressionAnchorTable + .filter((row) => row.rowIndexForWitness === 0) + .map((row) => row.anchor); + const rowProgressionLaterAnchors = rowProgressionAnchorTable + .filter((row) => Number.isInteger(row.rowIndexForWitness) && row.rowIndexForWitness > 0) + .sort((left, right) => left.rowIndexForWitness - right.rowIndexForWitness) + .map((row) => `${row.anchor}->t=${row.rowIndexForWitness}`); + const rowProgressionNeverAnchors = rowProgressionAnchorTable + .filter((row) => row.solvableAlongRowProgression === false) + .map((row) => row.anchor); + const rowProgressionAnchor282 = rowProgressionAnchorTable.find((row) => row.anchor === 282) ?? null; + const rowProgressionAnchor232 = rowProgressionAnchorTable.find((row) => row.anchor === 232) ?? null; + const tupleRowActivationSequence = deriveTupleRowActivationSequence( + Array.isArray(familyRow?.tupleRows) ? familyRow.tupleRows : [], + alignmentContext.repairRows, + witnessSquareModulus, + ); + const tupleRowActivation132 = tupleRowActivationSequence.find((row) => row.anchor === 132) ?? null; + const tupleRowActivation182 = tupleRowActivationSequence.find((row) => row.anchor === 182) ?? null; + const tupleRowPre132Steps = tupleRowActivationSequence.filter((row) => Number(row.anchor) < 132); + const tupleRowPre132HasNoTrackedMatch = tupleRowPre132Steps.length > 0 + && tupleRowPre132Steps.every((row) => row.matchingTrackedAnchors.length === 0); + const tupleRowActivationBoundary = tupleRowActivation132 + ? { + pre132HasNoTrackedMatch: tupleRowPre132HasNoTrackedMatch, + activationAnchor: 132, + activationResidueModuloWitness: tupleRowActivation132.residueModWitness, + activationTrackedAnchors: tupleRowActivation132.matchingTrackedAnchors, + activationIsUnique282: tupleRowActivation132.matchingTrackedAnchors.length === 1 + && tupleRowActivation132.matchingTrackedAnchors[0] === 282, + preservationAnchor: tupleRowActivation182?.anchor ?? null, + preservationResidueModuloWitness: tupleRowActivation182?.residueModWitness ?? null, + preservationTrackedAnchors: tupleRowActivation182?.matchingTrackedAnchors ?? [], + preservationKeepsUnique282: tupleRowActivation182 + ? tupleRowActivation182.matchingTrackedAnchors.length === 1 + && tupleRowActivation182.matchingTrackedAnchors[0] === 282 + : false, + } + : null; + const menuActivationSurvey = summarizeP848MenuActivationPatterns(alignmentContext.allFamilies); + const activationLemmaCheck = checkP848ActivationLemmaCertificates( + alignmentContext.allFamilies, + alignmentContext.familyMenuPath, + ); + const activationLemmaSchema = buildP848ActivationLemmaSchema({ + menuActivationSurvey, + tupleRowActivationBoundary, + tupleRowActivationSequence, + representative: familyRow?.representative ?? null, + tupleKey: familyRow?.tupleKey ?? null, + witnessSquareModulus, + representativeResidueModuloWitness, + familyMenuPath: alignmentContext.familyMenuPath, + }); + const activationSchemaLiftDecision = activationLemmaCheck.status === 'passed' + && tupleRowLift132Proof?.status === 'proved_from_tuple_row_crt' + ? { + decisionId: 'p848_activation_schema_symbolic_lift_decision_v1', + verdict: 'finite_menu_certificate_not_universal_yet', + safeUse: 'Use the schema as a checked finite-menu lemma/certificate family for the current 848 search surface.', + rejectedOverclaim: 'Do not state a universal obstruction-family theorem from the 17-row finite-menu certificate alone.', + reason: [ + 'The current packet has a replayed certificate for all 17 finite-menu 132 target-activation rows.', + 'The current 282 boundary lift is proved from its tuple-row CRT equation.', + 'The packet does not yet contain symbolic hypotheses that characterize every future tuple-row family producing the same 132 activation shape.', + ], + nextTheoremPass: 'formalize_top_repair_class_mechanism', + nextTheoremPassReason: 'The 282-specific mechanism is now narrow, checked, and claim-safe; the live bridge still exposes an independent high-value top cluster 432, 782, 832 with shared repaired-known and repaired-predicted counts.', + promotionRequirement: 'A symbolic lift needs parameterized tuple-row CRT hypotheses plus a proof that pre-132 prefixes miss tracked failure residues and anchor 132 uniquely activates the target for the whole family.', + falsifierBoundary: [ + 'A refreshed menu breaks one of the 17 finite row certificates.', + 'A symbolic family instance satisfies the proposed hypotheses but has a pre-132 tracked match.', + 'Anchor 132 activates a non-target or multiple tracked tails under the proposed symbolic hypotheses.', + 'Anchor 182 fails to preserve the target activation under the proposed symbolic hypotheses.', + ], + } + : null; + const activationSymbolicLiftCandidate = buildP848ActivationSymbolicLiftCandidate({ + activationLemmaSchema, + activationLemmaCheck, + tupleRowLift132Proof, + witnessSquareModulus, + }); + const activationSymbolicLiftReady = activationSymbolicLiftCandidate?.status === 'symbolic_crt_hypothesis_packet_ready'; + const topRepairClassMechanism = buildP848TopRepairClassMechanism(alignmentContext); + const topRepairSeparationAnalysis = topRepairClassMechanism?.separationAnalysis ?? null; + const topRepairSeparationCertified = topRepairSeparationAnalysis?.status === 'finite_menu_plus2_replay_certified'; + const topRepairLaneSignatureCertified = topRepairSeparationAnalysis?.mod50LaneSignature?.status === 'finite_menu_mod50_lane_signature_certified'; + const mod50LaneSymbolicSchema = buildP848Mod50LaneSymbolicSchema( + topRepairSeparationAnalysis?.mod50LaneSignature ?? null, + ); + const mod50LaneSymbolicSchemaReady = mod50LaneSymbolicSchema?.status === 'symbolic_bad_lane_schema_ready'; + const strict7821232HandoffPacket = buildP848Strict7821232HandoffPacket( + topRepairSeparationAnalysis, + mod50LaneSymbolicSchema, + ); + const strict7821232HandoffCertified = strict7821232HandoffPacket?.status === 'finite_strict_handoff_certified_not_gap_closure'; + const structuralLiftAtomicSurface = buildP848StructuralLiftAtomicSurface(formalization); + const structuralLiftAtomicActive = structuralLiftAtomicSurface?.status === 'active'; + const topRepairCommonMissReplayCertified = topRepairSeparationCertified + && Array.isArray(topRepairSeparationAnalysis?.topTieSharedMissedPredictedRows) + && topRepairSeparationAnalysis.topTieSharedMissedPredictedRows.length > 0; + const activationDomainClosureAssessment = buildP848ActivationDomainClosureAssessment( + activationSymbolicLiftCandidate, + topRepairSeparationAnalysis, + ); + const anchorWitnessDomainClosurePacket = buildP848AnchorWitnessDomainClosurePacket({ + activationDomainClosureAssessment, + allFamilies: alignmentContext.allFamilies, + familyMenuPath: alignmentContext.familyMenuPath, + }); + const anchorWitnessDomainClosureCertified = anchorWitnessDomainClosurePacket?.status === 'finite_group_closure_certified_symbolic_domain_split' + || anchorWitnessDomainClosurePacket?.status === 'finite_group_closure_certified_single_profile_candidate'; + const anchorWitnessProfileSublanePacket = buildP848AnchorWitnessProfileSublanePacket( + anchorWitnessDomainClosurePacket, + ); + const anchorWitnessProfileSublaneResolved = anchorWitnessProfileSublanePacket?.status === 'finite_profile_sublane_resolved_as_zero_lift_duplicate'; + const checkedMechanismAlreadyPromoted = p848TargetHasDoneObligation( + formalization?.currentTarget, + 'explain_282_first_failure_mechanism', + ) && p848TargetHasDonePromotionCriterion( + formalization?.currentTarget, + 'finite_menu_mechanism_checked', + ); + const rowStartDerivation282 = rowProgressionAnchor282 && representativeResidueModuloWitness !== null + ? { + rowFormula: `n_t = ${familyRow?.residue ?? '(unknown)'} + ${familyRow?.modulus ?? '(unknown)'} * t`, + witnessEquation: `282*n_t + 1 ≡ 0 (mod ${witnessSquareModulus})`, + substitutedEquation: `${rowProgressionAnchor282.progressionCoeffModuloWitness}*t ≡ ${rowProgressionAnchor282.progressionRhsModuloWitness} (mod ${witnessSquareModulus})`, + gcdCoeffWitness: rowProgressionAnchor282.gcdCoeffWitness, + normalizedEquation: rowProgressionAnchor282.gcdCoeffWitness === 1 + ? `t ≡ ${rowProgressionAnchor282.rowIndexForWitness} (mod ${rowProgressionAnchor282.rowIndexPeriod})` + : null, + representativeResidue: representativeResidueModuloWitness, + requiredFailureResidue: anchorCongruenceTable.find((row) => row.anchor === 282)?.requiredNResidueForFailure ?? null, + representativeAlreadyOnWitnessClass: rowProgressionAnchor282.witnessOccursAtCurrentRepresentative, + } + : null; + const unsolvableContrast232 = rowProgressionAnchor232 + ? { + witnessEquation: `232*n_t + 1 ≡ 0 (mod ${witnessSquareModulus})`, + substitutedEquation: `${rowProgressionAnchor232.progressionCoeffModuloWitness}*t ≡ ${rowProgressionAnchor232.progressionRhsModuloWitness} (mod ${witnessSquareModulus})`, + gcdCoeffWitness: rowProgressionAnchor232.gcdCoeffWitness, + solvable: rowProgressionAnchor232.solvableAlongRowProgression, + divisibilityFailure: rowProgressionAnchor232.solvableAlongRowProgression + ? null + : `${rowProgressionAnchor232.gcdCoeffWitness} does not divide ${rowProgressionAnchor232.progressionRhsModuloWitness}`, + } + : null; + const mechanismAssessment = { + verdict: matchingCongruenceAnchors.length === 1 + && matchingCongruenceAnchors[0] === 282 + && rowProgressionStartAnchors.length === 1 + && rowProgressionStartAnchors[0] === 282 + ? 'controlled_congruence_candidate' + : 'unresolved', + confidence: matchingCongruenceAnchors.length === 1 + && matchingCongruenceAnchors[0] === 282 + && rowProgressionStartAnchors.length === 1 + && rowProgressionStartAnchors[0] === 282 + ? 'medium' + : 'low', + rationale: [ + witnessFirstOccurrence + ? `Witness ${witnessSquareModulus} first appears for tail 282 at representative ${witnessFirstOccurrence.firstRepresentative}, with ${witnessFirstOccurrence.earlierZeroResidueCount} earlier zero-residue hits modulo ${witnessSquareModulus}.` + : null, + representativeResidueModuloWitness !== null && matchingCongruenceAnchors.length > 0 + ? `Representative residue class ${representativeResidueModuloWitness} mod ${witnessSquareModulus} matches tracked failure equations only for anchor(s) ${matchingCongruenceAnchors.join(', ')}.` + : null, + unsolvableCongruenceAnchors.length > 0 + ? `At least one tracked anchor cannot fail through modulus ${witnessSquareModulus} at all because gcd(anchor, ${witnessSquareModulus}) > 1: ${unsolvableCongruenceAnchors.join(', ')}.` + : null, + sameTupleCount === 1 + ? `The boundary tuple key appears exactly once in the current family menu, so this packet is not mixing multiple identical tuple rows.` + : null, + rowProgressionStartAnchors.length > 0 + ? `Along the shared-prefix row progression itself, the witness ${witnessSquareModulus} occurs at row index 0 only for tracked anchor(s) ${rowProgressionStartAnchors.join(', ')}.` + : null, + rowProgressionLaterAnchors.length > 0 + ? `Other tracked anchors hit the same witness only later along the row progression: ${rowProgressionLaterAnchors.join(', ')}.` + : null, + rowProgressionNeverAnchors.length > 0 + ? `Some tracked anchors never hit witness ${witnessSquareModulus} along this row progression at all: ${rowProgressionNeverAnchors.join(', ')}.` + : null, + familyMenuResidueBoundary + ? `At the family-menu level, representative residue ${representativeResidueModuloWitness} mod ${witnessSquareModulus} first appears at representative ${familyMenuResidueBoundary.firstRepresentative} (row index ${familyMenuResidueBoundary.firstFamilyIndex}), with ${familyMenuResidueBoundary.earlierRepresentativeMatchCount} earlier menu rows on the same residue class.` + : null, + tupleRowLift132 + ? `The ${tupleRow132.anchor} row is the first tuple-row lift that forces residue ${representativeResidueModuloWitness} mod ${witnessSquareModulus}: ${tupleRowLift132.reducedEquation}, so k ≡ ${tupleRowLift132.liftParameter} and the CRT class lifts to ${tupleRowLift132.liftedResidue}.` + : null, + tupleRowActivationBoundary?.pre132HasNoTrackedMatch && tupleRowActivationBoundary.activationIsUnique282 + ? `Before anchor 132, no tuple-row CRT step lands on any tracked failure residue modulo ${witnessSquareModulus}; anchor 132 is the first step whose projected residue ${tupleRowActivationBoundary.activationResidueModuloWitness} uniquely matches tracked tail 282.` + : null, + tupleRowPreservation182?.preserved + ? `The ${tupleRow182.anchor} row preserves that residue: ${tupleRowPreservation182.checkEquation}, so the final CRT class keeps residue ${tupleRowPreservation182.liftedResidueModuloWitness} mod ${witnessSquareModulus}.` + : null, + tupleRowActivationBoundary?.preservationKeepsUnique282 + ? `Anchor 182 preserves the same unique tracked match: the projected residue stays on tail 282's failure class and does not activate any neighboring tracked tail.` + : null, + menuActivationSurvey.rowsWith132TargetActivationCount > 1 + ? `This is not a one-row phenomenon in the current menu: ${menuActivationSurvey.rowsWith132TargetActivationCount} failing witness rows have the same first-target-activation-at-132 shape across tracked tails ${Object.keys(menuActivationSurvey.rowsWith132TargetActivationByFailingAnchor).join(', ')}.` + : null, + activationLemmaSchema + ? `The finite-menu 132-activation schema is now explicit with ${activationLemmaSchema.rowCertificates.length} row certificates, six hypotheses, and five falsifier classes.` + : null, + activationLemmaCheck.status === 'passed' + ? `The dedicated activation checker replayed ${activationLemmaCheck.checkedRowCount} row certificates from raw tuple-row CRT projections with ${activationLemmaCheck.failCount} failures.` + : null, + tupleRowLift132Proof?.status === 'proved_from_tuple_row_crt' + ? `The 132-row lift is proved directly from the tuple-row CRT equation: ${tupleRowLift132Proof.reducedEquation} with k = ${tupleRowLift132Proof.liftParameter}.` + : null, + activationSchemaLiftDecision + ? `The symbolic-lift decision is explicit: keep the 132 schema finite-menu certified for now and route the next theorem pass to ${activationSchemaLiftDecision.nextTheoremPass}.` + : null, + topRepairClassMechanism + ? `The top repair-class mechanism packet is seeded: ${topRepairClassMechanism.tieClass.join(', ')} share repaired-known=${topRepairClassMechanism.sharedMetrics.repairedKnownPackets}, repaired-predicted=${topRepairClassMechanism.sharedMetrics.repairedPredictedFamilies}, and clean-through=${topRepairClassMechanism.sharedMetrics.effectiveCleanThrough}.` + : null, + topRepairSeparationCertified + ? `The +2 top repair separation is certified by raw family-menu replay: top tails miss 13 predicted families each, while primary contrasts ${topRepairClassMechanism.primaryContrasts.join(', ')} miss 15 each.` + : null, + topRepairSeparationCertified && topRepairSeparationAnalysis.strictDominancePairs.length > 0 + ? `The cleanest pairwise handoff is ${topRepairSeparationAnalysis.strictDominancePairs.map((row) => `${row.topContinuation}>${row.contrastContinuation}`).join(', ')}: the top tail repairs two predicted rows that the contrast misses and loses no predicted row back.` + : null, + topRepairLaneSignatureCertified + ? `The mod-50 symbolic signature is now explicit: each pairwise exchange row solves a bad lane-index congruence for c = 32 + 50*m, and the repaired continuation misses that bad m-class.` + : null, + mod50LaneSymbolicSchemaReady + ? `The mod-50 bad-lane rule is now a symbolic divisibility schema checked on ${mod50LaneSymbolicSchema.checkedRowCount} witness instances; it is universal for a named witness congruence but not a full squarefree repair theorem.` + : null, + strict7821232HandoffCertified + ? `The strict 782 > 1232 handoff is finite-menu certified: 782 repairs ${strict7821232HandoffPacket.netExtraRepairsForTop} predicted rows that 1232 misses, with no predicted row lost back.` + : null, + activationSymbolicLiftReady + ? `The 132 activation lift is now parameterized as symbolic CRT hypotheses ${activationSymbolicLiftCandidate.symbolicHypotheses.map((row) => row.hypothesisId).join(', ')}.` + : null, + anchorWitnessDomainClosureCertified + ? `${anchorWitnessDomainClosurePacket.targetGroupId} is now replay-certified over ${anchorWitnessDomainClosurePacket.checkedRowCount} raw family-menu rows; the symbolic decision is ${anchorWitnessDomainClosurePacket.symbolicDomainDecision.verdict}.` + : null, + anchorWitnessDomainClosurePacket?.zeroLiftPreservation?.allRowsAnchor182ZeroLift + ? `The ${anchorWitnessDomainClosurePacket.targetGroupId} preservation mechanism is a zero-lift at anchor 182: anchor 132 already satisfies the final tuple row, so the witness residue stays fixed.` + : null, + anchorWitnessProfileSublaneResolved + ? `${anchorWitnessProfileSublanePacket.targetProfileId} is resolved as a finite final-anchor duplicate: rows ${anchorWitnessProfileSublanePacket.familyIndices.join(', ')} share the CRT prefix through anchor 132 and differ only by zero-lift anchor-182 variants.` + : null, + ].filter(Boolean), + caveats: [ + rowProgressionModuloWitness?.traversesAllWitnessResidues + ? `The shared-prefix row progression is coprime to ${witnessSquareModulus}, so the row itself traverses all residue classes modulo ${witnessSquareModulus}; the 841 hit is not forced by the row alone.` + : null, + menuActivationSurvey.rowsWith132TargetActivationCount > 1 + ? 'The activation-pattern survey is over the current finite family menu, so it supports reusability inside the live search surface but does not by itself prove a universal obstruction-family theorem.' + : null, + activationLemmaSchema + ? 'The activation lemma schema is a finite-menu certificate schema until its CRT hypotheses are lifted symbolically.' + : null, + activationSchemaLiftDecision + ? `A universal lift still needs: ${activationSchemaLiftDecision.promotionRequirement}` + : null, + anchorWitnessDomainClosurePacket?.symbolicDomainDecision?.verdict === 'single_profile_symbolic_domain_falsified_by_profile_split' + ? `The ${anchorWitnessDomainClosurePacket.targetGroupId} lane splits into ${anchorWitnessDomainClosurePacket.symbolicDomainDecision.profileGroupCount} pre-132 profiles, so it should be handled as profile sublanes rather than one broad symbolic family.` + : null, + anchorWitnessProfileSublaneResolved + ? `The repeated ${anchorWitnessProfileSublanePacket.targetProfileId} rows are a finite duplicate, so this sublane should not be promoted as independent evidence for a broad symbolic domain.` + : null, + mod50LaneSymbolicSchemaReady + ? 'The mod-50 schema proves a bad-lane divisibility equivalence for a named witness Q; it still needs a separate control argument before it can close a squarefree finite-gap theorem lane.' + : null, + strict7821232HandoffCertified + ? 'The strict 782 > 1232 handoff is still finite-menu evidence; it guides the next exact verifier rollout but is not an all-N coverage theorem.' + : null, + ].filter(Boolean), + competingHypotheses: [ + { + hypothesisId: 'controlled_congruence_interaction', + status: matchingCongruenceAnchors.length === 1 && matchingCongruenceAnchors[0] === 282 ? 'favored' : 'plausible', + note: 'The shared-prefix class and the 282 repair row intersect in a distinguished witness residue class modulo 841.', + }, + { + hypothesisId: 'one_off_modular_coincidence', + status: menuActivationSurvey.rowsWith132TargetActivationCount > 1 ? 'disfavored_by_menu_survey' : 'still_live', + note: menuActivationSurvey.rowsWith132TargetActivationCount > 1 + ? `The current family menu contains ${menuActivationSurvey.rowsWith132TargetActivationCount} rows with the same first-target-activation-at-132 shape, so the one-off explanation is no longer the best finite-menu reading.` + : 'The 841 hit could still be accidental unless a structural derivation explains why the residue class arises from the shared-prefix packet.', + }, + { + hypothesisId: 'shared_prefix_row_alone_forces_841', + status: rowProgressionModuloWitness?.traversesAllWitnessResidues ? 'not_supported' : 'plausible', + note: 'A stronger claim that the family-row progression itself already forces the 841 witness class.', + }, + ], + }; + + return { + workId: 'p848_282_first_failure_mechanism_packet_v1', + focusFormalizationId: formalization?.currentTarget?.formalizationId ?? 'p848_282_alignment_formalization_v1', + focusId: focusObligation?.obligationId ?? 'explain_282_first_failure_mechanism', + title: 'Explain the 282 First-Failure Mechanism', + status: failing282 ? 'in_progress' : 'ready', + summary: 'Isolate the extra square witness that makes continuation 282 fail first on the shared-prefix boundary class.', + why: 'Once the shared-prefix class is named, the next theorem step is to explain why continuation 282, and not the neighboring tracked tails, is the one that first acquires a square witness there.', + workingDefinition: [ + 'A 282 first-failure mechanism is the first shared-prefix class where the 282 repair row becomes non-squarefree while the neighboring tracked repair rows remain squarefree.', + familyRow + ? `On the live boundary class, the six defining tuple moduli are ${tupleSquareModuli.join(', ')} and the extra 282 witness is ${witnessSquareModulus}.` + : 'The boundary class is not yet concretely frozen.', + witnessSquareModulus && !tupleSquareModuli.includes(witnessSquareModulus) + ? `The witness ${witnessSquareModulus} is not one of the six tuple-row moduli, so the failure appears as an extra repair witness intersecting the shared-prefix class.` + : 'The extra repair witness has not yet been separated from the tuple-row moduli.', + representativeResidueModuloWitness !== null + ? `The representative itself sits in residue class ${representativeResidueModuloWitness} modulo ${witnessSquareModulus}.` + : 'The representative residue class modulo the witness is not yet frozen.', + ], + currentEvidence: [ + firstFailingRepresentative !== null + ? `Among the current family-menu rows where continuation 282 is non-squarefree, the earliest representative is ${firstFailingRepresentative}.` + : 'The earliest family-menu representative where continuation 282 fails has not yet been frozen.', + failing282 && witnessSquareModulus + ? `At representative ${familyRow?.representative}, 282*n+1 = ${failing282.value} = ${witnessSquareModulus} * ${quotient}.` + : 'The 282 repair row does not yet expose a concrete witness factorization.', + failingResidue && witnessSquareModulus + ? `Modulo ${witnessSquareModulus}, the 282 repair row is exactly 0 while the neighboring tracked rows remain nonzero.` + : 'The witness-level residue split has not yet been frozen.', + stableResidues.length > 0 && witnessSquareModulus + ? `Neighbor residues mod ${witnessSquareModulus}: ${stableResidues.map((row) => `${row.anchor}->${row.residueModuloWitness}`).join(', ')}.` + : 'Neighbor residue data is not yet available.', + witnessFirstOccurrence + ? `The first family-menu occurrence of witness ${witnessSquareModulus} on tail 282 is representative ${witnessFirstOccurrence.firstRepresentative}, with ${witnessFirstOccurrence.earlierZeroResidueCount} earlier rows giving residue 0 mod ${witnessSquareModulus}.` + : 'The first occurrence of the witness modulus has not yet been frozen.', + tupleRowCrtDerivation + ? `Solving the tuple-row CRT gives n ≡ ${tupleRowCrtDerivation.combinedResidue} (mod ${tupleRowCrtDerivation.combinedModulus}), and projecting that class modulo ${witnessSquareModulus} gives ${tupleRowCrtDerivation.projectedResidueModuloWitness}.` + : 'The tuple-row CRT projection to the witness modulus is not yet recorded.', + tupleRowCrtDerivation?.firstStableProjectionAnchor !== null + ? `The tuple-row CRT projection stabilizes at residue ${tupleRowCrtDerivation.projectedResidueModuloWitness} mod ${witnessSquareModulus} once anchor ${tupleRowCrtDerivation.firstStableProjectionAnchor} is added.` + : 'No stabilization point for the tuple-row CRT projection has been recorded.', + priorRowsModuloWitness.length > 0 + ? `The last earlier 282 rows before the first failure stay nonzero mod ${witnessSquareModulus}: ${priorRowsModuloWitness.map((row) => `${row.representative}->${row.residueModuloWitness}`).join(', ')}.` + : 'No earlier-row comparison against the witness modulus is currently recorded.', + matchingCongruenceAnchors.length > 0 + ? `Among the tracked repair anchors, the representative residue class modulo ${witnessSquareModulus} matches only anchors ${matchingCongruenceAnchors.join(', ')}.` + : 'No tracked repair anchor currently matches the representative residue class modulo the witness.', + unsolvableCongruenceAnchors.length > 0 + ? `Some tracked anchors cannot fail via modulus ${witnessSquareModulus} at all because gcd(anchor, ${witnessSquareModulus}) > 1: ${unsolvableCongruenceAnchors.join(', ')}.` + : 'All tracked repair anchors remain solvable modulo the witness.', + rowProgressionModuloWitness?.traversesAllWitnessResidues + ? `The boundary row progression does not itself force witness ${witnessSquareModulus}: gcd(modulus, ${witnessSquareModulus}) = 1, so the progression visits every residue class mod ${witnessSquareModulus}.` + : 'The boundary row progression restriction modulo the witness is not yet recorded.', + rowProgressionStartAnchors.length > 0 + ? `Within that row progression, the representative sits exactly at the witness-start index for tracked anchor(s) ${rowProgressionStartAnchors.join(', ')}.` + : 'The row-index start boundary for the witness has not yet been isolated.', + rowStartDerivation282 + ? `Substituting the row formula into 282*n+1 ≡ 0 (mod ${witnessSquareModulus}) gives ${rowStartDerivation282.substitutedEquation}; since gcd(${rowProgressionAnchor282.progressionCoeffModuloWitness}, ${witnessSquareModulus}) = ${rowProgressionAnchor282.gcdCoeffWitness}, this reduces to ${rowStartDerivation282.normalizedEquation}.` + : 'The row-index derivation for tail 282 has not yet been written down.', + unsolvableContrast232?.solvable === false + ? `The contrasting 232 equation ${unsolvableContrast232.substitutedEquation} is impossible because ${unsolvableContrast232.divisibilityFailure}.` + : 'No unsolvable contrast anchor is currently recorded for the witness equation.', + nextSameRowWitnessFor282 !== null + ? `The next number in the same shared-prefix progression where tail 282 hits witness ${witnessSquareModulus} is ${nextSameRowWitnessFor282}.` + : 'The next same-row witness recurrence for tail 282 is not yet recorded.', + familyMenuResidueBoundary + ? `At the family-menu level, the earliest representative in residue class ${representativeResidueModuloWitness} mod ${witnessSquareModulus} is ${familyMenuResidueBoundary.firstRepresentative} at row index ${familyMenuResidueBoundary.firstFamilyIndex}; the ${familyMenuResidueBoundary.firstFamilyIndex} earlier menu rows all miss the 282 witness residue class.` + : 'The family-menu chronology for the witness residue class is not yet frozen.', + familyMenuResidueBoundary + && familyMenuResidueBoundary.firstRepresentativeHasWitness + && familyMenuResidueBoundary.sameAsFirstFailingRepresentative + ? `The packet has an explicit falsifier boundary: it breaks if a refreshed menu finds an earlier representative with residue ${representativeResidueModuloWitness} mod ${witnessSquareModulus}, if continuation 282 first fails through a different witness, or if bridge refresh breaks the 137720141 <-> 282 alignment.` + : 'The packet does not yet name its exact falsifier boundary.', + topRepairClassMechanism + ? `Top repair-class packet seeded from bridge leaderboard: ${topRepairClassMechanism.tieClass.join(', ')} tie at ${topRepairClassMechanism.sharedMetrics.repairedPredictedFamilies} repaired predicted families; nearest contrasts are ${topRepairClassMechanism.nearestContrasts.map((row) => `${row.continuation}->${row.repaired_predicted_families}`).join(', ')}.` + : null, + topRepairClassMechanism?.commonMissedPredictedRepresentatives?.length > 0 + ? `The top tie shares common early missed predicted representatives: ${topRepairClassMechanism.commonMissedPredictedRepresentatives.join(', ')}.` + : null, + topRepairSeparationCertified + ? topRepairSeparationAnalysis.conclusion + : null, + topRepairCommonMissReplayCertified + ? `The replayed top-tie common missed rows now include ${topRepairSeparationAnalysis.topTieSharedMissedPredictedRows.length} predicted family rows, so the common-miss boundary is no longer just an eight-row bridge summary.` + : null, + topRepairSeparationCertified && topRepairSeparationAnalysis.strictDominancePairs.length > 0 + ? `The strictest finite-menu contrast certificate is ${topRepairSeparationAnalysis.strictDominancePairs.map((row) => `${row.topContinuation} vs ${row.contrastContinuation}`).join(', ')}.` + : null, + topRepairLaneSignatureCertified + ? `The mod-50 lane signature checks ${topRepairSeparationAnalysis.mod50LaneSignature.checkedRowCount} exchange rows using continuation = 32 + 50*m and passes all of them.` + : null, + mod50LaneSymbolicSchemaReady + ? mod50LaneSymbolicSchema.conclusion + : null, + strict7821232HandoffCertified + ? strict7821232HandoffPacket.conclusion + : null, + activationSymbolicLiftReady + ? `The symbolic 132-lift candidate checks ${activationSymbolicLiftCandidate.checkedRowCount} finite-menu certificate rows and promotes them into parameterized CRT hypotheses without claiming universal scope.` + : null, + activationDomainClosureAssessment + ? `Domain-closure assessment rejects a broad 17-row universal lift for now and recommends ${activationDomainClosureAssessment.recommendedClosureLane.targetGroupId} as the next narrow closure lane.` + : null, + anchorWitnessDomainClosureCertified + ? `${anchorWitnessDomainClosurePacket.finiteScopeConclusion}` + : null, + anchorWitnessDomainClosurePacket?.symbolicDomainDecision?.verdict === 'single_profile_symbolic_domain_falsified_by_profile_split' + ? `The recommended ${anchorWitnessDomainClosurePacket.targetGroupId} lane is not one clean symbolic profile yet: it splits into ${anchorWitnessDomainClosurePacket.profileGroups.length} pre-132 profiles, with successor ${anchorWitnessDomainClosurePacket.recommendedSuccessor.targetProfileId}.` + : null, + anchorWitnessDomainClosurePacket?.zeroLiftPreservation?.allRowsAnchor182ZeroLift + ? anchorWitnessDomainClosurePacket.zeroLiftPreservation.explanation + : null, + anchorWitnessProfileSublaneResolved + ? anchorWitnessProfileSublanePacket.conclusion + : null, + structuralLiftAtomicSurface?.proofPackets?.C1_same_side_base_clique?.status === 'proved_by_mod25_identity' + ? `Structural atom C1 is discharged by the mod-25 same-side base identity: 7^2+1 and 18^2+1 are both 0 mod 25.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C2_two_cliques_plus_cross_edges?.status === 'proved_by_c1_partition_decomposition' + ? 'Structural atom C2 is discharged: after partitioning compatible base vertices into B7 and B18 sides, C1 makes both sides cliques and only cross edges remain unconstrained.' + : null, + structuralLiftAtomicSurface?.proofPackets?.C3_missing_cross_graph_definition?.status === 'proved_by_definition' + ? 'Structural atom C3 is discharged: H_{x,N} is now explicitly the bipartite graph of missing B7-by-B18 cross edges.' + : null, + structuralLiftAtomicSurface?.proofPackets?.C6_mixed_clique_matching_formula?.status === 'proved_by_vertex_cover_konig_composition' + ? 'The C-graph reduction packet is discharged through C6: mixed-base clique size is now the two-side total minus a maximum matching in H_{x,N}.' + : null, + structuralLiftAtomicSurface?.proofPackets?.D1_residue_block_matching_injection?.status === 'bounded_matching_saturation_extraction_certified' + ? `The bounded D1 extraction is discharged on current verifier rows: all ${structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.scope.boundedRowCount} exact mixed-base threatening-outsider rows meet the required matching lower bound and saturate the smaller compatible side.` + : null, + structuralLiftAtomicSurface?.activeAtomEvidence?.candidateId === 'p848_D2_p13_matching_lower_bound_candidate_v1' + ? `The active D2 p=13 candidate is now backed by ${structuralLiftAtomicSurface.activeAtomEvidence.scope.threatRowCount} bounded threatening-outsider rows; K(N,x) ranges ${structuralLiftAtomicSurface.activeAtomEvidence.extractedTarget.requiredMatchingLowerBoundRange.join('..')} and the minimum matching slack is ${structuralLiftAtomicSurface.activeAtomEvidence.extractedTarget.minMatchingSlack}.` + : null, + structuralLiftAtomicSurface?.activeAtomEvidence?.splitCoreWitnessPacket?.status === 'bounded_split_core_witness_certified' + ? `The D2 split-core witness packet reduces the tight p=13 sample to ${structuralLiftAtomicSurface.activeAtomEvidence.splitCoreWitnessPacket.splitProfileCount} residue/smaller-side subgoals; each split common core meets the sampled max K(N,x).` + : null, + structuralLiftAtomicSurface?.proofPackets?.D3_p17_split_core_witness_extraction?.status === 'bounded_split_core_witness_certified' + ? `The D3 p=17 split-core witness packet reduces the tight p=17 sample to ${structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.scope.splitProfileCount} residue/smaller-side subgoals with minimum sampled slack ${structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.profileSummary.reduce((min, profile) => Math.min(min, Number(profile.minMatchingSlack ?? Infinity)), Infinity)}.` + : null, + structuralLiftAtomicActive + ? `The structural lift miner is now feeding the existing atomic theorem lane: active atom ${structuralLiftAtomicSurface.activeAtom?.obligationId} targets ${structuralLiftAtomicSurface.targetAtom?.obligationId} from ${structuralLiftAtomicSurface.evidenceArtifact?.minedExactRowCount} mined exact rows.` + : null, + ], + dischargedWork: [ + firstFailingRepresentative !== null && firstFailingRepresentative === familyRow?.representative + ? `The family-menu boundary agrees with the tracked-tail boundary: the earliest 282-failing family row is also representative ${familyRow.representative}.` + : null, + witnessSquareModulus && !tupleSquareModuli.includes(witnessSquareModulus) + ? `The extra witness has been isolated: ${witnessSquareModulus} belongs to the 282 repair row, not to the six defining tuple moduli of the shared-prefix class.` + : null, + witnessFirstOccurrence && witnessFirstOccurrence.earlierZeroResidueCount === 0 + ? `The witness boundary is locally frozen: no earlier family-menu row gives tail 282 residue 0 modulo ${witnessSquareModulus}.` + : null, + tupleRowCrtDerivation && tupleRowCrtDerivation.projectedResidueModuloWitness === representativeResidueModuloWitness + ? `The representative residue is structurally derived: the tuple-row CRT projects the shared-prefix obstruction class to ${representativeResidueModuloWitness} mod ${witnessSquareModulus}.` + : null, + matchingCongruenceAnchors.length === 1 && matchingCongruenceAnchors[0] === 282 + ? `The congruence boundary is isolated: residue class ${representativeResidueModuloWitness} mod ${witnessSquareModulus} is the failure class for tracked tail 282 and no other tracked coprime tail.` + : null, + rowProgressionStartAnchors.length === 1 && rowProgressionStartAnchors[0] === 282 + ? `The row-index boundary is isolated: within the shared-prefix row progression, tracked anchor 282 is the only tracked anchor whose ${witnessSquareModulus} witness class starts at row index 0.` + : null, + rowStartDerivation282?.representativeAlreadyOnWitnessClass + ? `The row-start derivation is explicit: the boundary representative already lies on the 282 witness class modulo ${witnessSquareModulus}, so the row equation reduces to t ≡ 0 (mod ${rowProgressionAnchor282.rowIndexPeriod}).` + : null, + familyMenuResidueBoundary + && familyMenuResidueBoundary.sameAsFirstFailingRepresentative + && familyMenuResidueBoundary.firstRepresentativeHasWitness + && familyMenuResidueBoundary.earlierRepresentativeMatchCount === 0 + ? `The menu-level first-occurrence boundary is isolated: ${familyMenuResidueBoundary.firstRepresentative} is the first family-menu representative in the 282 witness class ${representativeResidueModuloWitness} mod ${witnessSquareModulus}, so no earlier menu row can fail via witness ${witnessSquareModulus} on that same congruence class.` + : null, + familyMenuResidueBoundary + && familyMenuResidueBoundary.firstRepresentativeHasWitness + && familyMenuResidueBoundary.sameAsFirstFailingRepresentative + ? `The mechanism falsifier boundary is explicit: a lower representative in residue class ${representativeResidueModuloWitness} mod ${witnessSquareModulus}, a different first 282 witness, or bridge loss of the 137720141 <-> 282 alignment would all break this packet.` + : null, + tupleRowLift132 + ? `The 132-row lift is explicit: adding the 132 row forces the tuple-row CRT class from residue ${tupleRowLift132.preAnchorResidueModuloWitness} mod ${witnessSquareModulus} to the boundary residue ${tupleRowLift132.liftedResidueModuloWitness} mod ${witnessSquareModulus} via k ≡ ${tupleRowLift132.liftParameter} (mod ${tupleRow132.squareModulus}).` + : null, + tupleRowActivationBoundary?.pre132HasNoTrackedMatch && tupleRowActivationBoundary.activationIsUnique282 + ? `The activation boundary is explicit: before anchor 132 no tuple-row CRT step lands on any tracked failure residue mod ${witnessSquareModulus}, anchor 132 creates the unique tracked 282 match at residue ${tupleRowActivationBoundary.activationResidueModuloWitness}, and anchor 182 preserves that same unique match.` + : null, + menuActivationSurvey.rowsWith132TargetActivationCount > 1 + ? `The 132-activation pattern is reusable on the current finite menu: ${menuActivationSurvey.rowsWith132TargetActivationCount} failing witness rows first activate their own failing tracked tail at anchor 132.` + : null, + activationLemmaSchema + ? `The finite-menu 132-activation pattern has been promoted into lemma schema ${activationLemmaSchema.schemaId} with hypotheses, conclusion, falsifier boundary, and ${activationLemmaSchema.rowCertificates.length} row certificates.` + : null, + activationLemmaCheck.status === 'passed' + ? `The 17 finite-menu 132-activation row certificates replay successfully in checker ${activationLemmaCheck.checkerId}.` + : null, + tupleRowLift132Proof?.status === 'proved_from_tuple_row_crt' + ? `The 132-row lift to residue ${tupleRowLift132Proof.liftedResidueModuloWitness} mod ${witnessSquareModulus} is proved from tuple-row CRT equations by checker ${tupleRowLift132Proof.checkerId}.` + : null, + activationSchemaLiftDecision + ? `The activation schema lift decision is explicit: ${activationSchemaLiftDecision.verdict}; next theorem pass is ${activationSchemaLiftDecision.nextTheoremPass}.` + : null, + activationSymbolicLiftReady + ? `The checked 132 activation schema has been lifted into symbolic CRT hypothesis packet ${activationSymbolicLiftCandidate.candidateId}; the next obligation is domain closure, not merely packet construction.` + : null, + activationDomainClosureAssessment + ? `The broad domain-closure overclaim is ruled out at the current evidence boundary: ${activationDomainClosureAssessment.broadClosureVerdict.reason}` + : null, + anchorWitnessDomainClosureCertified + ? `The recommended ${anchorWitnessDomainClosurePacket.targetGroupId} closure lane has been executed at finite repeated-group scope: ${anchorWitnessDomainClosurePacket.checkedRowCount} raw rows pass checker ${anchorWitnessDomainClosurePacket.checkerId}.` + : null, + anchorWitnessDomainClosurePacket?.symbolicDomainDecision?.verdict === 'single_profile_symbolic_domain_falsified_by_profile_split' + ? `The single-profile symbolic closure over ${anchorWitnessDomainClosurePacket.targetGroupId} is falsified by the finite evidence split into ${anchorWitnessDomainClosurePacket.profileGroups.length} pre-132 residue profiles.` + : null, + anchorWitnessDomainClosurePacket?.zeroLiftPreservation?.allRowsAnchor182ZeroLift + ? `The ${anchorWitnessDomainClosurePacket.targetGroupId} anchor-182 preservation step is explained: every checked row has lift parameter 0 at anchor 182.` + : null, + anchorWitnessProfileSublaneResolved + ? `The repeated ${anchorWitnessProfileSublanePacket.targetProfileId} sublane is closed as a finite duplicate final-anchor variant, not a new symbolic family.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C1_same_side_base_clique?.status === 'proved_by_mod25_identity' + ? `Structural atom C1_same_side_base_clique is discharged: same-side principal base residues force a 25 divisor of u*v+1, so each same-side component is a clique.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C2_two_cliques_plus_cross_edges?.status === 'proved_by_c1_partition_decomposition' + ? `Structural atom C2_two_cliques_plus_cross_edges is discharged by checker ${structuralLiftAtomicSurface.proofPackets.C2_two_cliques_plus_cross_edges.checkerId}: the mixed-base graph is two cliques plus arbitrary cross edges.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C3_missing_cross_graph_definition?.status === 'proved_by_definition' + ? `Structural atom C3_missing_cross_graph_definition is discharged by checker ${structuralLiftAtomicSurface.proofPackets.C3_missing_cross_graph_definition.checkerId}: H_{x,N} records exactly the missing cross edges between the two clique sides.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C4_clique_to_vertex_cover_duality?.status === 'proved_by_clique_vertex_cover_complement' + ? `Structural atom C4_clique_to_vertex_cover_duality is discharged by checker ${structuralLiftAtomicSurface.proofPackets.C4_clique_to_vertex_cover_duality.checkerId}: clique complements are exactly vertex covers of H_{x,N}.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C5_konig_matching_reduction?.status === 'proved_by_konig_theorem' + ? `Structural atom C5_konig_matching_reduction is discharged by checker ${structuralLiftAtomicSurface.proofPackets.C5_konig_matching_reduction.checkerId}: Konig's theorem applies because H_{x,N} is finite bipartite.` + : null, + structuralLiftAtomicSurface?.proofPackets?.C6_mixed_clique_matching_formula?.status === 'proved_by_vertex_cover_konig_composition' + ? `Structural atom C6_mixed_clique_matching_formula is discharged by checker ${structuralLiftAtomicSurface.proofPackets.C6_mixed_clique_matching_formula.checkerId}: sMixed(x,N) = |L| + |R| - maxMatching(H_{x,N}).` + : null, + structuralLiftAtomicSurface?.proofPackets?.D1_residue_block_matching_injection?.status === 'bounded_matching_saturation_extraction_certified' + ? `Structural atom D1_residue_block_matching_injection is discharged at bounded extraction scope by checker ${structuralLiftAtomicSurface.proofPackets.D1_residue_block_matching_injection.checkerId}: every current exact mixed-base threatening outsider meets K(N,x) and saturates the smaller compatible side.` + : null, + structuralLiftAtomicSurface?.proofPackets?.D2_p13_split_core_witness_extraction?.status === 'bounded_split_core_witness_certified' + ? `D2 split-core witness extraction is discharged at bounded pattern scope by checker ${structuralLiftAtomicSurface.proofPackets.D2_p13_split_core_witness_extraction.checkerId}: each p=13 split common core reaches the sampled K(N,x) target.` + : null, + structuralLiftAtomicSurface?.proofPackets?.D3_p17_split_core_witness_extraction?.status === 'bounded_split_core_witness_certified' + ? `D3 split-core witness extraction is discharged at bounded pattern scope by checker ${structuralLiftAtomicSurface.proofPackets.D3_p17_split_core_witness_extraction.checkerId}: each p=17 split common core reaches the sampled K(N,x) target.` + : null, + topRepairClassMechanism + ? `The top repair-class mechanism packet ${topRepairClassMechanism.mechanismId} is seeded with shared metrics, nearest contrasts, common missed-family boundary, and falsifier conditions.` + : null, + topRepairSeparationCertified + ? `The finite-menu +2 repaired-predicted-family separation is discharged: ${topRepairSeparationAnalysis.topTieCounts.map((row) => `${row.continuation}->${row.repairedPredictedFamilyCount}`).join(', ')} versus ${topRepairSeparationAnalysis.primaryContrastCounts.map((row) => `${row.continuation}->${row.repairedPredictedFamilyCount}`).join(', ')}.` + : null, + topRepairCommonMissReplayCertified + ? `The common missed-family replay is explicit: ${topRepairSeparationAnalysis.topTieSharedMissedPredictedRows.length} top-tie shared missed predicted family rows were replayed directly from the family menu.` + : null, + topRepairLaneSignatureCertified + ? `The finite-menu +2 separation has been lifted into mod-50 lane-index congruences: ${topRepairSeparationAnalysis.mod50LaneSignature.checkedRowCount} exchange rows all pass the bad-m-class certificate.` + : null, + mod50LaneSymbolicSchemaReady + ? `The mod-50 bad-lane congruence has been generalized into symbolic schema ${mod50LaneSymbolicSchema.schemaId}; ${mod50LaneSymbolicSchema.checkedRowCount} finite witness instances replay with ${mod50LaneSymbolicSchema.failCount} failures.` + : null, + strict7821232HandoffCertified + ? `The strict 782 > 1232 handoff is connected to the symbolic mod-50 schema by checker ${strict7821232HandoffPacket.checkerId}; it is certified as finite-menu guidance, not all-N closure.` + : null, + tupleRowPreservation182?.preserved + ? `The 182 row preserves the boundary residue: the 132-lifted class already satisfies ${tupleRowPreservation182.checkEquation}, so the final anchor adds no further correction modulo ${witnessSquareModulus}.` + : null, + ].filter(Boolean), + remainingGaps: [ + structuralLiftAtomicActive + ? `Prove structural-lift atom ${structuralLiftAtomicSurface.activeAtom?.obligationId}: ${structuralLiftAtomicSurface.activeAtom?.statement}` + : null, + structuralLiftAtomicActive + ? `Advance the same atomic packet toward target ${structuralLiftAtomicSurface.targetAtom?.obligationId}: ${structuralLiftAtomicSurface.targetAtom?.statement}` + : null, + anchorWitnessProfileSublaneResolved + ? null + : anchorWitnessDomainClosureCertified + ? anchorWitnessDomainClosurePacket.recommendedSuccessor.task + : activationDomainClosureAssessment + ? `Prove or falsify the recommended symbolic domain-closure lane ${activationDomainClosureAssessment.recommendedClosureLane.targetGroupId}.` + : activationSymbolicLiftReady + ? 'Prove a domain-closure lemma that supplies the symbolic 132 activation hypotheses beyond the current finite menu.' + : checkedMechanismAlreadyPromoted + ? 'Lift the checked 132 activation schema beyond the finite menu into parameterized CRT hypotheses.' + : topRepairLaneSignatureCertified + ? 'Promote the checked 282 mechanism packet back into the formalization target as either a done obligation or a narrower symbolic-lift TODO.' + : topRepairSeparationCertified + ? 'Lift the finite-menu +2 separation replay into a symbolic residue/family signature for the mod-50 lane.' + : 'Explain the +2 repaired-predicted-family separation between 432/782/832 and the nearest same-known-packet contrasts 332/382/1232.', + topRepairCommonMissReplayCertified + ? null + : 'Replay the common missed-family representatives for the top repair tie against the family menu to identify which predicted repairs distinguish the tie.', + strict7821232HandoffCertified + ? null + : mod50LaneSymbolicSchemaReady + ? 'Connect the symbolic mod-50 bad-lane schema to the finite-gap closure target using the strict 782 vs 1232 handoff family.' + : topRepairLaneSignatureCertified + ? 'Generalize the mod-50 lane bad-family signature beyond the finite exchange rows.' + : 'Promote the checked 282 mechanism packet back into the formalization target as either a done obligation or a narrower symbolic-lift TODO.', + checkedMechanismAlreadyPromoted + ? nextExactVerificationLane + : null, + ].filter(Boolean), + proofObligations: structuralLiftAtomicSurface?.proofObligations ?? [], + mechanismAssessment, + packetData: { + representative: familyRow?.representative ?? null, + tupleKey: familyRow?.tupleKey ?? null, + tupleRowCrtDerivation, + tupleRowActivationSequence, + tupleRowActivationBoundary, + menuActivationSurvey, + activationLemmaCheck, + activationLemmaSchema, + activationSchemaLiftDecision, + activationSymbolicLiftCandidate, + activationDomainClosureAssessment, + anchorWitnessDomainClosurePacket, + anchorWitnessProfileSublanePacket, + mod50LaneSymbolicSchema, + strict7821232HandoffPacket, + structuralLiftAtomicSurface, + topRepairClassMechanism, + tupleRowLift132, + tupleRowLift132Proof, + tupleRowPreservation182, + tupleSquareModuli, + witnessSquareModulus, + witnessPrime: failing282?.squareWitnesses?.[0]?.prime ?? null, + witnessExponent: failing282?.squareWitnesses?.[0]?.exponent ?? null, + representativeResidueModuloWitness, + repairResidues, + anchorCongruenceTable, + rowProgressionAnchorTable, + rowStartDerivation282, + unsolvableContrast232, + firstFailingRepresentative, + witnessFirstOccurrence, + familyMenuResidueBoundary, + sameTupleCount, + rowProgressionModuloWitness, + nextSameRowWitnessFor282, + priorRowsModuloWitness, + laterWitnessTimeline, + mechanismFalsifierBoundary: familyMenuResidueBoundary + ? { + lowerRepresentativeSameWitnessResidueBreaksMechanism: `A refreshed family menu finds a representative below ${familyMenuResidueBoundary.firstRepresentative} with residue ${representativeResidueModuloWitness} mod ${witnessSquareModulus}.`, + differentFirstWitnessBreaksMechanism: `A refreshed family menu finds a 282 failure below ${firstFailingRepresentative ?? '(unknown)'} or with first witness different from ${witnessSquareModulus}.`, + bridgeAlignmentBreaksMechanism: `A refreshed bridge no longer matches next unmatched representative ${firstFailingRepresentative ?? '(unknown)'} with tracked tail 282 first failure.`, + commands: [ + formalization?.commands?.sourceRefresh ?? null, + formalization?.commands?.claimPass ?? null, + formalization?.commands?.formalizationWorkRefresh ?? null, + ].filter(Boolean), + } + : null, + familyMenuPath: alignmentContext.familyMenuPath, + bridgePath: formalization?.sources?.legacyBridgeJsonPath ?? null, + }, + nextGapCommand: formalization?.commands?.formalizationWorkRefresh + ?? `erdos problem formalization-work-refresh ${formalization?.problemId ?? '848'}`, + nextCommands: [ + `erdos problem formalization-work-check ${formalization?.problemId ?? '848'} --json`, + formalization?.commands?.formalizationWorkRefresh ?? null, + formalization?.commands?.formalizationRefresh ?? null, + formalization?.commands?.claimPass ?? null, + formalization?.commands?.sourceRefresh ?? null, + ].filter(Boolean), + }; +} + +function buildProblemFormalizationWorkTarget(problem, formalization) { + if (String(problem?.problemId ?? '') === '848' + && formalization?.currentTarget?.focusId === 'formalize_282_alignment') { + const alignmentContext = buildP848AlignmentContext({ + sources: { + legacyBridgeJsonPath: formalization?.sources?.legacyBridgeJsonPath ?? null, + }, + }); + const focusObligation = pickFormalizationWorkFocus(formalization?.currentTarget); + + if ([ + 'explain_282_first_failure_mechanism', + 'lift_132_activation_schema_beyond_finite_menu', + ].includes(focusObligation?.obligationId)) { + return buildP848MechanismWorkTarget(formalization, alignmentContext, focusObligation); + } + + return buildP848SharedPrefixClassWorkTarget(formalization, alignmentContext, focusObligation); + } + + return buildGenericFormalizationWorkTarget(problem, formalization); +} + +export function buildProblemFormalizationWork(problem) { + const formalization = buildProblemFormalization(problem); + const paths = getProblemFormalizationWorkPaths(problem); + const target = buildProblemFormalizationWorkTarget(problem, formalization); + + return { + schema: 'erdos.problem_formalization_work/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + sourceKind: formalization.sourceKind, + formalizationWorkMode: formalization.formalizationMode, + currentClaimSurface: formalization.currentClaimSurface, + currentState: { + activeRoute: formalization.currentState?.activeRoute ?? null, + routeSummary: formalization.currentState?.routeSummary ?? null, + nextHonestMove: formalization.currentState?.nextHonestMove ?? null, + latestVerifiedInterval: formalization.currentState?.latestVerifiedInterval ?? null, + }, + currentWork: target, + commands: { + problemShow: `erdos problem show ${problem.problemId}`, + problemArtifacts: `erdos problem artifacts ${problem.problemId}`, + formalization: formalization.commands?.formalization ?? null, + formalizationRefresh: formalization.commands?.formalizationRefresh ?? null, + formalizationWork: `erdos problem formalization-work ${problem.problemId}`, + formalizationWorkRefresh: `erdos problem formalization-work-refresh ${problem.problemId}`, + formalizationWorkCheck: `erdos problem formalization-work-check ${problem.problemId}`, + claimPass: formalization.commands?.claimPass ?? null, + sourceRefresh: formalization.commands?.sourceRefresh ?? null, + }, + sources: { + packProblemDir: paths.packProblemDir, + formalizationWorkJsonPath: paths.formalizationWorkJsonPath, + formalizationWorkMarkdownPath: paths.formalizationWorkMarkdownPath, + formalizationWorkSvgPath: paths.formalizationWorkSvgPath, + formalizationJsonPath: formalization.sources?.formalizationJsonPath ?? null, + formalizationMarkdownPath: formalization.sources?.formalizationMarkdownPath ?? null, + theoremLoopJsonPath: formalization.sources?.theoremLoopJsonPath ?? null, + legacyBridgeJsonPath: formalization.sources?.legacyBridgeJsonPath ?? null, + }, + }; +} + +export function renderProblemFormalizationWorkMarkdown(doc) { + const target = doc.currentWork ?? {}; + const lines = [ + `# ${doc.displayName} Formalization Work`, + '', + 'This packet turns the current formalization target into one concrete work unit that can be discharged, falsified, or narrowed without losing the surrounding theorem-search context.', + '', + '## Current State', + '', + `- Formalization work mode: \`${doc.formalizationWorkMode}\`.`, + `- Current claim surface: \`${doc.currentClaimSurface}\`.`, + `- Active route: \`${doc.currentState.activeRoute ?? '(none)'}\`.`, + `- Route summary: ${doc.currentState.routeSummary ?? '(none)'}`, + `- Next honest move: ${doc.currentState.nextHonestMove ?? '(none)'}`, + `- Latest verified interval: ${doc.currentState.latestVerifiedInterval ? `\`${doc.currentState.latestVerifiedInterval}\`` : '`(none)`'}`, + '', + '## Current Work', + '', + `- Work id: \`${target.workId ?? '(none)'}\`.`, + `- Focus formalization id: \`${target.focusFormalizationId ?? '(none)'}\`.`, + `- Focus id: \`${target.focusId ?? '(none)'}\`.`, + `- Title: ${target.title ?? '(none)'}`, + `- Status: \`${target.status ?? '(none)'}\`.`, + `- Summary: ${target.summary ?? '(none)'}`, + `- Why: ${target.why ?? '(none)'}`, + '', + '## Working Definition', + '', + ]; + + for (const item of target.workingDefinition ?? []) { + lines.push(`- ${item}`); + } + + lines.push('', '## Current Evidence', ''); + for (const item of target.currentEvidence ?? []) { + lines.push(`- ${item}`); + } + + lines.push('', '## Discharged Work', ''); + for (const item of target.dischargedWork ?? []) { + lines.push(`- ${item}`); + } + + lines.push('', '## Remaining Gaps', ''); + for (const item of target.remainingGaps ?? []) { + lines.push(`- ${item}`); + } + + if (Array.isArray(target.proofObligations) && target.proofObligations.length > 0) { + lines.push('', '## Atomic Proof Obligations', ''); + for (const item of target.proofObligations) { + lines.push(`- ${renderChecklistItem(item)}`); + } + } + + if (target.mechanismAssessment) { + lines.push('', '## Mechanism Assessment', ''); + lines.push(`- Verdict: \`${target.mechanismAssessment.verdict ?? 'unresolved'}\``); + lines.push(`- Confidence: \`${target.mechanismAssessment.confidence ?? 'low'}\``); + for (const item of target.mechanismAssessment.rationale ?? []) { + lines.push(`- ${item}`); + } + for (const item of target.mechanismAssessment.caveats ?? []) { + lines.push(`- Caveat: ${item}`); + } + for (const item of target.mechanismAssessment.competingHypotheses ?? []) { + lines.push(`- \`${item.hypothesisId}\`: ${item.status} | ${item.note}`); + } + } + + if (target.packetData) { + lines.push('', '## Packet Data', ''); + for (const [label, value] of Object.entries(target.packetData)) { + if (value === null || value === undefined) { + continue; + } + lines.push(`- ${label}: \`${JSON.stringify(value)}\``); + } + } + + lines.push('', '## Commands', ''); + lines.push(`- Problem surface: \`${doc.commands.problemShow}\``); + lines.push(`- Problem artifacts: \`${doc.commands.problemArtifacts}\``); + lines.push(`- Formalization: \`${doc.commands.formalization}\``); + lines.push(`- Formalization refresh: \`${doc.commands.formalizationRefresh}\``); + lines.push(`- Formalization work: \`${doc.commands.formalizationWork}\``); + lines.push(`- Formalization work refresh: \`${doc.commands.formalizationWorkRefresh}\``); + if (doc.commands.claimPass) { + lines.push(`- Claim pass: \`${doc.commands.claimPass}\``); + } + if (doc.commands.sourceRefresh) { + lines.push(`- Source refresh: \`${doc.commands.sourceRefresh}\``); + } + + lines.push('', '## Sources', ''); + for (const [label, value] of Object.entries(doc.sources ?? {})) { + if (!value) { + continue; + } + lines.push(`- ${label}: \`${value}\``); + } + lines.push(''); + return lines.join('\n'); +} + +export function getProblemFormalizationWorkSnapshot(problem) { + const doc = buildProblemFormalizationWork(problem); + const paths = getProblemFormalizationWorkPaths(problem); + return { + ...doc, + formalizationWorkJsonPath: paths.formalizationWorkJsonPath, + formalizationWorkMarkdownPath: paths.formalizationWorkMarkdownPath, + formalizationWorkSvgPath: paths.formalizationWorkSvgPath, + formalizationWorkJsonPresent: Boolean(paths.formalizationWorkJsonPath && fs.existsSync(paths.formalizationWorkJsonPath)), + formalizationWorkMarkdownPresent: Boolean(paths.formalizationWorkMarkdownPath && fs.existsSync(paths.formalizationWorkMarkdownPath)), + formalizationWorkSvgPresent: Boolean(paths.formalizationWorkSvgPath && fs.existsSync(paths.formalizationWorkSvgPath)), + }; +} + +export function checkProblemFormalizationWork(problem) { + const formalizationWork = buildProblemFormalizationWork(problem); + const checks = [ + formalizationWork.currentWork?.packetData?.activationLemmaCheck ?? null, + formalizationWork.currentWork?.packetData?.tupleRowLift132Proof ?? null, + formalizationWork.currentWork?.packetData?.activationSymbolicLiftCandidate ?? null, + formalizationWork.currentWork?.packetData?.anchorWitnessDomainClosurePacket ?? null, + formalizationWork.currentWork?.packetData?.anchorWitnessProfileSublanePacket ?? null, + formalizationWork.currentWork?.packetData?.topRepairClassMechanism?.separationAnalysis ?? null, + formalizationWork.currentWork?.packetData?.topRepairClassMechanism?.separationAnalysis?.mod50LaneSignature ?? null, + formalizationWork.currentWork?.packetData?.mod50LaneSymbolicSchema ?? null, + formalizationWork.currentWork?.packetData?.strict7821232HandoffPacket ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.C1_same_side_base_clique ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.C2_two_cliques_plus_cross_edges ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.C3_missing_cross_graph_definition ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.C4_clique_to_vertex_cover_duality ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.C5_konig_matching_reduction ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.C6_mixed_clique_matching_formula ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.D1_residue_block_matching_injection ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.D2_p13_split_core_witness_extraction ?? null, + formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface?.proofPackets?.D3_p17_split_core_witness_extraction ?? null, + ].filter(Boolean); + const failCount = checks.reduce((total, check) => total + Number(check.failCount ?? 0), 0); + const checkedRowCount = checks.reduce((total, check) => total + Number(check.checkedRowCount ?? 0), 0); + + return { + schema: 'erdos.problem_formalization_work_check/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + status: checks.length === 0 ? 'no_checks' : failCount === 0 ? 'passed' : 'failed', + currentWorkId: formalizationWork.currentWork?.workId ?? null, + currentWorkTitle: formalizationWork.currentWork?.title ?? null, + firstRemainingGap: formalizationWork.currentWork?.remainingGaps?.[0] ?? null, + summary: { + checkCount: checks.length, + checkedRowCount, + failCount, + }, + checks, + commands: { + formalizationWork: formalizationWork.commands?.formalizationWork ?? null, + formalizationWorkRefresh: formalizationWork.commands?.formalizationWorkRefresh ?? null, + taskListRefresh: `erdos problem task-list-refresh ${problem.problemId}`, + }, + sources: formalizationWork.sources, + }; +} + +function quoteOrpTopic(topic) { + return JSON.stringify(String(topic ?? 'research loop')); +} + +function buildProblemGranularBreakdownMode(problem, formalizationWork) { + const currentWork = formalizationWork.currentWork ?? null; + const surface = currentWork?.packetData?.structuralLiftAtomicSurface ?? null; + const topic = [ + `problem ${problem.problemId}`, + currentWork?.title ?? problem.title, + surface?.activeAtom?.obligationId ? `active atom ${surface.activeAtom.obligationId}` : null, + surface?.targetAtom?.obligationId ? `target ${surface.targetAtom.obligationId}` : null, + ].filter(Boolean).join(' | '); + + return { + status: 'core_loop_enabled', + modeId: 'granular-breakdown', + label: 'ORP Granular Breakdown', + topic, + activationPhrase: 'Break it down until it can move.', + invocationRule: 'Use the full breakdown before executing a complex theorem/search packet; use the nudge card whenever the agent or user is confused, the target feels too broad, or the next action is not deterministic.', + commands: { + fullBreakdown: `orp mode breakdown granular-breakdown --topic ${quoteOrpTopic(topic)} --json`, + nudge: 'orp mode nudge granular-breakdown --json', + unscopedBreakdown: 'orp mode breakdown granular-breakdown --json', + }, + outputContract: [ + 'Broad Frame', + 'Boundary', + 'Major Lanes', + 'Subclaims', + 'Atomic Obligations', + 'Dependency Ladder', + 'Active Target', + 'Durable Checklist', + 'Next Verification', + ], + loopIntegration: [ + 'Run the full breakdown after the theorem/search surfaces are audited and before executing the current work packet.', + 'Write operationally important decompositions into TASK_LIST, FORMALIZATION_WORK, or a dedicated checklist artifact rather than leaving them in chat.', + 'Use the nudge card for quick reorientation when a step becomes blurry during implementation.', + 'Compress the breakdown back into one active target and one verification command before continuing.', + ], + durableArtifactRule: 'If the breakdown changes what we should do, refresh the canonical task list so the new dependency ladder becomes repo-owned state.', + }; +} + +function buildProblemOrpModeOverlays(problem, granularBreakdownMode) { + const problemTopic = granularBreakdownMode?.topic ?? `problem ${problem.problemId} | ${problem.title}`; + const overlays = [ + { + modeId: 'granular-breakdown', + label: 'Granular Breakdown', + role: 'core_decomposition_loop', + useWhen: 'The work is broad, confusing, theorem-heavy, or needs a durable dependency ladder before execution.', + command: granularBreakdownMode?.commands?.fullBreakdown + ?? `orp mode breakdown granular-breakdown --topic ${quoteOrpTopic(problemTopic)} --json`, + nudgeCommand: 'orp mode nudge granular-breakdown --json', + loopPlacement: 'Before execute_current_work_packet and whenever the active target becomes fuzzy.', + outputExpectation: 'Boundary, lanes, subclaims, atomic obligations, dependency ladder, active target, durable checklist, and next verification.', + }, + { + modeId: 'ruthless-simplification', + label: 'Ruthless Simplification', + role: 'compression_and_signal_filter', + useWhen: 'A plan, proof surface, or final response is swollen, repetitive, or hiding the single live decision.', + command: 'orp mode nudge ruthless-simplification --json', + nudgeCommand: 'orp mode nudge ruthless-simplification --json', + loopPlacement: 'After granular decomposition, before committing a plan to TASK_LIST, and before final summaries.', + outputExpectation: 'One core sentence, one surviving move, and a list of noise to delete or defer.', + }, + { + modeId: 'systems-constellation', + label: 'Systems Constellation', + role: 'dependency_and_downstream_effects', + useWhen: 'A change touches multiple surfaces such as erdos-problems, ORP, frontier-engine, local/remote compute, task lists, or user workflow.', + command: 'orp mode nudge systems-constellation --json', + nudgeCommand: 'orp mode nudge systems-constellation --json', + loopPlacement: 'Before cross-system integration, paid/remote compute decisions, or changes to canonical source/writeback flow.', + outputExpectation: 'Upstreams, downstreams, feedback loops, hidden costs, and the system-level decision.', + }, + { + modeId: 'bold-concept-generation', + label: 'Bold Concept Generation', + role: 'candidate_generation_when_stuck', + useWhen: 'The active theorem/search lane has converged too early, needs new candidate lemmas, or a split atom fails and needs alternative constructions.', + command: 'orp mode nudge bold-concept-generation --json', + nudgeCommand: 'orp mode nudge bold-concept-generation --json', + loopPlacement: 'After a falsifier, before launching broad compute, or when inventing the next symbolic construction.', + outputExpectation: 'Several meaningfully different candidate moves, with the boldest one grounded into a quick experiment.', + }, + { + modeId: 'sleek-minimal-progressive', + label: 'Sleek Minimal Progressive', + role: 'fresh_lens_and_low_friction_motion', + useWhen: 'The work feels flat, overly linear, or technically correct but hard for future collaborators to pick up.', + command: 'orp mode nudge sleek-minimal-progressive --json', + nudgeCommand: 'orp mode nudge sleek-minimal-progressive --json', + loopPlacement: 'When refining docs, task-list readability, handoff artifacts, UI surfaces, or the shape of the next user-facing explanation.', + outputExpectation: 'One subtraction, one tasteful surprise, and one concrete next move that keeps momentum.', + }, + ]; + + return { + status: 'core_loop_palette_enabled', + sourceCommand: 'orp mode list --json', + defaultModeId: 'granular-breakdown', + selectionRule: 'Select the smallest ORP overlay that reduces ambiguity or friction; do not run every mode by default.', + alwaysDurableWhenOperational: true, + overlays, + }; +} + +function buildProblemTaskExecutionRule(problem, granularBreakdownMode = null) { + return { + stance: 'concrete_execution', + summary: `Treat the task list as a concrete research loop for problem ${problem.problemId}: execute the highest-value task itself, not wrapper prose about the task.`, + afterEachCompletion: [ + 'Cross off the completed task.', + 'Re-read the theorem loop, claim pass, formalization packet, formalization work packet, and verifier boundary.', + granularBreakdownMode + ? `Use ORP granular breakdown when the next step is broad or confusing: ${granularBreakdownMode.commands.nudge}` + : 'Break broad or confusing steps into named atomic obligations before executing them.', + 'Use the smallest relevant ORP mode overlay when it simplifies the work: simplification for bloat, systems for cross-surface consequences, bold generation for new candidates, and sleek-progressive for clearer handoff shape.', + 'Invent the next highest-value step from the updated evidence rather than following a stale fixed script.', + 'Append that next step to the task list and refresh the canonical task-list artifacts.', + ], + granularBreakdownMode: granularBreakdownMode + ? { + modeId: granularBreakdownMode.modeId, + status: granularBreakdownMode.status, + fullBreakdownCommand: granularBreakdownMode.commands.fullBreakdown, + nudgeCommand: granularBreakdownMode.commands.nudge, + } + : null, + repetitionProtocol: 'To execute this loop 10 times or 100 times, complete the first ready task, refresh the task list, then use the regenerated ordering for the next pass.', + lowStressLongHorizonNote: 'This loop is meant to be safe for long-horizon execution because it re-ranks after every pass instead of committing to a blind fixed plan.', + }; +} + +function buildProblemTaskTemplate(problem, theoremLoop, claimPass, formalizationWork, intervalQueue, granularBreakdownMode = null) { + const activeRoute = theoremLoop.activeRoute ?? theoremLoop.currentState?.activeRoute ?? null; + const latestVerifiedInterval = claimPass.currentState?.latestVerifiedInterval + ?? theoremLoop.currentState?.latestVerifiedInterval + ?? null; + const currentWork = formalizationWork.currentWork ?? null; + const sourceRefresh = theoremLoop.commands?.sourceRefresh ?? null; + const hasBridge = theoremLoop.sourceKind === 'search_theorem_bridge'; + const nextAlignmentHook = (theoremLoop.theoremHooks ?? []).find((item) => item.hook_id === 'next_unmatched_equals_282_failure') ?? null; + + const template = [ + { + stepId: 'freeze_current_state', + title: 'Freeze the current north star and active theorem packet', + task: `Freeze the current route \`${activeRoute ?? '(none)'}\`, claim surface \`${theoremLoop.currentState?.currentClaimSurface ?? '(none)'}\`, and active theorem packet before widening the search.`, + completionRule: 'The theorem loop, claim pass, and formalization packet all agree on the current route, next honest move, and active target.', + command: theoremLoop.commands?.theoremLoop ?? `erdos problem theorem-loop ${problem.problemId}`, + }, + { + stepId: 'audit_theorem_surfaces', + title: 'Audit theorem, claim, and formalization surfaces for consistency', + task: 'Audit the theorem loop, claim loop, claim pass, formalization packet, and formalization work packet for drift or contradictory wording.', + completionRule: 'The canonical theorem/search surfaces tell one consistent story about what is supported, what is open, and what the active work unit is.', + command: `erdos problem task-list ${problem.problemId}`, + }, + { + stepId: 'verify_canonical_inputs', + title: hasBridge ? 'Verify canonical bridge inputs against the latest harvested compute artifacts' : 'Verify canonical pack inputs against the latest route and verifier artifacts', + task: hasBridge + ? 'Verify that the bridge-backed theorem surfaces still match the latest harvested compute and frontier evidence.' + : 'Verify that the pack-backed theorem surfaces still match the latest route packet, OPS details, and verifier-facing artifacts.', + completionRule: 'The canonical input packet for this loop remains current and trustworthy.', + command: sourceRefresh ?? theoremLoop.commands?.theoremLoopRefresh ?? `erdos problem theorem-loop-refresh ${problem.problemId}`, + }, + { + stepId: 'verify_primary_structural_hook', + title: nextAlignmentHook + ? 'Verify the primary structural hook remains canonical' + : 'Verify the current highest-value structural hook remains canonical', + task: nextAlignmentHook + ? 'Verify that the `282 <-> 137720141` alignment remains canonical across theorem, claim, and bridge surfaces.' + : 'Verify that the strongest supported structural hook still survives across the theorem and claim surfaces.', + completionRule: 'The primary theorem-facing hook still survives refresh and remains narrow enough to formalize honestly.', + command: claimPass.commands?.claimPassRefresh ?? `erdos problem claim-pass-refresh ${problem.problemId}`, + }, + { + stepId: 'verify_verifier_boundary', + title: latestVerifiedInterval + ? 'Verify the current exact/verifier boundary and next target' + : 'Verify the current verifier boundary and next target', + task: latestVerifiedInterval + ? `Verify that the certified interval ${latestVerifiedInterval} and the next verifier target remain current across the pack surfaces.` + : 'Verify that the current verifier boundary and next target are stated honestly across the pack surfaces.', + completionRule: intervalQueue + ? 'The interval work queue or verifier boundary packet still matches the theorem-facing status.' + : 'The verifier-facing boundary remains explicit even without a dedicated interval queue.', + command: problem.cluster === 'number-theory' + ? `erdos number-theory dispatch ${problem.problemId}` + : `erdos problem formalization ${problem.problemId}`, + }, + ...(granularBreakdownMode + ? [{ + stepId: 'apply_granular_breakdown', + title: 'Apply ORP granular breakdown before execution', + task: `Run ORP granular breakdown on the active topic \`${granularBreakdownMode.topic}\` and compress it into one active target plus one verification command.`, + completionRule: 'The broad work packet has been decomposed into boundary, lanes, atomic obligations, dependency ladder, active target, durable checklist, and next verification.', + command: granularBreakdownMode.commands.fullBreakdown, + }] + : []), + { + stepId: 'execute_current_work_packet', + title: currentWork?.title ?? 'Execute the current formalization-work packet', + task: currentWork?.summary ?? 'Execute the current formalization-work packet as the active theorem work unit.', + completionRule: currentWork?.remainingGaps?.[0] + ? `The first remaining gap is either discharged, narrowed, or replaced by a sharper one: ${currentWork.remainingGaps[0]}` + : 'The active formalization-work packet either closes or yields a sharper successor packet.', + command: formalizationWork.commands?.formalizationWork ?? `erdos problem formalization-work ${problem.problemId}`, + }, + { + stepId: 'refresh_and_rerank', + title: 'Refresh the task list and rerank the next step', + task: 'Refresh the canonical task list after the completed work so the next iteration is driven by the newest theorem/search/verifier evidence.', + completionRule: 'The refreshed task list records the next highest-value action instead of relying on a stale fixed script.', + command: `erdos problem task-list-refresh ${problem.problemId}`, + }, + ]; + + return template; +} + +function buildProblemCurrentTasks(problem, theoremLoop, claimPass, formalization, formalizationWork, intervalQueue) { + const granularBreakdownMode = buildProblemGranularBreakdownMode(problem, formalizationWork); + const template = buildProblemTaskTemplate(problem, theoremLoop, claimPass, formalizationWork, intervalQueue, granularBreakdownMode); + const currentWork = formalizationWork.currentWork ?? null; + const remainingGaps = Array.isArray(currentWork?.remainingGaps) ? currentWork.remainingGaps : []; + const tasks = template.map((item, index) => ({ + taskId: item.stepId, + status: item.stepId === 'execute_current_work_packet' && currentWork?.status ? currentWork.status : 'ready', + title: item.title, + task: item.task, + why: item.stepId === 'execute_current_work_packet' + ? (formalization.currentTarget?.summary ?? currentWork?.why ?? null) + : null, + completionRule: item.completionRule, + command: item.command, + })); + + if (remainingGaps.length > 0) { + const refreshIndex = tasks.findIndex((task) => task.taskId === 'refresh_and_rerank'); + tasks.splice(refreshIndex >= 0 ? refreshIndex : tasks.length, 0, { + taskId: 'discharge_first_remaining_gap', + status: 'ready', + title: 'Discharge the first remaining gap in the active theorem packet', + task: remainingGaps[0], + why: 'This is the sharpest unresolved statement already named by the active theorem-work packet.', + completionRule: 'The first remaining gap is either resolved or replaced by a more precise successor gap.', + command: currentWork?.nextGapCommand + ?? formalizationWork.commands?.formalizationWorkRefresh + ?? `erdos problem formalization-work-refresh ${problem.problemId}`, + }); + } + + return tasks; +} + +function buildProblemCompletedAnchors(formalizationWork) { + const dischargedWork = Array.isArray(formalizationWork.currentWork?.dischargedWork) + ? formalizationWork.currentWork.dischargedWork + : []; + return dischargedWork.map((item, index) => ({ + itemId: `completed_anchor_${index + 1}`, + status: 'done', + note: item, + })); +} + +function getP848ExactBreakpointScout(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const scoutPath = packProblemDir ? path.join(packProblemDir, 'EXACT_BREAKPOINT_SCOUT.json') : null; + const scout = scoutPath ? readJsonIfPresent(scoutPath) : null; + return scout + ? { + path: scoutPath, + scout, + } + : null; +} + +function getP848ExactBreakpointCertificate(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const certificatePath = packProblemDir ? path.join(packProblemDir, 'EXACT_BREAKPOINT_CERTIFICATE.json') : null; + const certificate = certificatePath ? readJsonIfPresent(certificatePath) : null; + return certificate + ? { + path: certificatePath, + certificate, + } + : null; +} + +function getP848ExternalStructuralVerifierAudit(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const auditPath = packProblemDir ? path.join(packProblemDir, 'EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.json') : null; + const audit = auditPath ? readJsonIfPresent(auditPath) : null; + return audit + ? { + path: auditPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'EXTERNAL_STRUCTURAL_VERIFIER_AUDIT.md') : null, + audit, + } + : null; +} + +function getP848BaseSideScout(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const scoutPath = packProblemDir ? path.join(packProblemDir, 'BASE_SIDE_SCOUT.json') : null; + const scout = scoutPath ? readJsonIfPresent(scoutPath) : null; + return scout + ? { + path: scoutPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'BASE_SIDE_SCOUT.md') : null, + scout, + } + : null; +} + +function getP848StructuralTwoSideScout(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const scoutPath = packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_TWO_SIDE_SCOUT.json') : null; + const scout = scoutPath ? readJsonIfPresent(scoutPath) : null; + return scout + ? { + path: scoutPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_TWO_SIDE_SCOUT.md') : null, + scout, + } + : null; +} + +function getP848MixedBaseFailureScout(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const scoutPath = packProblemDir ? path.join(packProblemDir, 'MIXED_BASE_FAILURE_SCOUT.json') : null; + const scout = scoutPath ? readJsonIfPresent(scoutPath) : null; + return scout + ? { + path: scoutPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'MIXED_BASE_FAILURE_SCOUT.md') : null, + scout, + } + : null; +} + +function getP848FullMixedBaseStructuralVerifier(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const verifierPath = packProblemDir ? path.join(packProblemDir, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json') : null; + const verifier = verifierPath ? readJsonIfPresent(verifierPath) : null; + return verifier + ? { + path: verifierPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.md') : null, + verifier, + } + : null; +} + +function getP848StructuralLiftMiner(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const minerPath = packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_LIFT_MINER.json') : null; + const miner = minerPath ? readJsonIfPresent(minerPath) : null; + return miner + ? { + path: minerPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_LIFT_MINER.md') : null, + miner, + } + : null; +} + +function getP848StructuralLiftChecklist(problem) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const packProblemDir = getProblemPackDir(problem); + const checklistPath = packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_LIFT_CHECKLIST.json') : null; + const checklist = checklistPath ? readJsonIfPresent(checklistPath) : null; + return checklist + ? { + path: checklistPath, + markdownPath: packProblemDir ? path.join(packProblemDir, 'STRUCTURAL_LIFT_CHECKLIST.md') : null, + checklist, + } + : null; +} + +function parseP848ClosedIntegerRange(rangeText) { + const match = String(rangeText ?? '').trim().match(/^(\d+)\.\.(\d+)$/); + if (!match) { + return null; + } + return { + min: Number(match[1]), + max: Number(match[2]), + }; +} + +function parseP848ScientificInteger(value) { + const text = String(value ?? '').trim().replace(/\s+/g, ' '); + const match = text.match(/^(\d+(?:\.\d+)?)\s*(?:x|\*)\s*10\^(\d+)$/i); + if (!match) { + const plain = text.match(/^\d+$/); + return plain ? BigInt(text) : null; + } + const mantissa = match[1]; + const exponent = Number(match[2]); + const [whole, fractional = ''] = mantissa.split('.'); + const digits = `${whole}${fractional}`.replace(/^0+/, '') || '0'; + const zeroCount = exponent - fractional.length; + if (zeroCount < 0) { + return null; + } + return BigInt(`${digits}${'0'.repeat(zeroCount)}`); +} + +function formatP848BigInt(value) { + return value.toString().replace(/\B(?=(\d{3})+(?!\d))/g, ','); +} + +function ceilP848BigIntRatio(numerator, denominator) { + if (denominator <= 0n) { + return null; + } + return (numerator + denominator - 1n) / denominator; +} + +function buildP848FiniteGapStrategy(problem, latestVerifiedInterval, intervalQueue, breakpointCertificate) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + + const exactRange = parseP848ClosedIntegerRange(latestVerifiedInterval); + const importedThresholdRaw = intervalQueue?.operational_threshold?.value ?? null; + const importedThreshold = parseP848ScientificInteger(importedThresholdRaw); + const certificateSummary = breakpointCertificate?.certificate?.summary ?? null; + if (!exactRange || !importedThreshold || !certificateSummary?.rowCount || !certificateSummary?.endpointCheckCount) { + return { + status: 'incomplete_inputs', + reason: 'Finite-gap strategy needs a latest exact interval, an operational threshold, and an endpoint certificate summary.', + }; + } + + const exactMax = BigInt(exactRange.max); + const remainingRows = importedThreshold > exactMax ? importedThreshold - exactMax : 0n; + const rowCount = BigInt(certificateSummary.rowCount); + const endpointCheckCount = BigInt(certificateSummary.endpointCheckCount); + const projectedEndpointChecks = ceilP848BigIntRatio(remainingRows * endpointCheckCount, rowCount); + const endpointRowsPerCheck = Number(certificateSummary.rowCount) / Number(certificateSummary.endpointCheckCount); + + return { + status: 'ready', + verdict: 'exact_endpoint_rollout_is_not_a_sole_all_N_closure_strategy', + latestVerifiedInterval, + exactMax: exactRange.max, + operationalThreshold: { + raw: importedThresholdRaw, + integer: importedThreshold.toString(), + trustStatus: intervalQueue?.operational_threshold?.trust_status ?? 'external_or_unknown', + source: intervalQueue?.operational_threshold?.source ?? null, + }, + remainingRowsToOperationalThreshold: remainingRows.toString(), + remainingRowsToOperationalThresholdLabel: formatP848BigInt(remainingRows), + endpointCertificate: { + interval: certificateSummary.interval, + rowCount: certificateSummary.rowCount, + endpointCheckCount: certificateSummary.endpointCheckCount, + compressionRatio: certificateSummary.compressionRatio, + approximateRowsPerEndpointCheck: endpointRowsPerCheck, + }, + projectedEndpointChecksToOperationalThreshold: projectedEndpointChecks?.toString() ?? null, + projectedEndpointChecksToOperationalThresholdLabel: projectedEndpointChecks + ? formatP848BigInt(projectedEndpointChecks) + : null, + recommendedMode: 'hybrid_threshold_audit_plus_structural_verifier', + guidance: [ + 'Continue endpoint rollouts only as bounded base expansion and regression evidence.', + 'Do not wait for direct endpoint checks to close the imported finite gap.', + 'Prioritize auditing the imported threshold handoff or proving a stronger structural verifier lane.', + 'Use GPU/frontier sweeps to generate structural candidates and counterexamples, not as a substitute for the all-N handoff proof.', + ], + }; +} + +function positiveModulo(value, modulus) { + const residue = Number(value) % modulus; + return residue < 0 ? residue + modulus : residue; +} + +function sanitizeP848PacketFileStem(value) { + return String(value ?? 'unknown') + .replaceAll(/[^A-Za-z0-9]+/g, '_') + .replaceAll(/^_+|_+$/g, '') + .slice(0, 120) || 'unknown'; +} + +function getP848SplitAtomPacketPaths(problem, atomId = null) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return null; + } + const directoryPath = path.join(packProblemDir, 'SPLIT_ATOM_PACKETS'); + if (!atomId) { + return { + directoryPath, + manifestJsonPath: path.join(directoryPath, 'MANIFEST.json'), + manifestMarkdownPath: path.join(directoryPath, 'MANIFEST.md'), + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + packetId: `p848_split_atom_packet_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + markdownPath: path.join(directoryPath, `${fileStem}.md`), + }; +} + +function getP848SplitAtomSuccessorPacketPaths(problem, parentAtomId = null, conditionId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'SUCCESSORS'); + if (!parentAtomId || !conditionId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(`${parentAtomId}__${conditionId}`); + return { + directoryPath, + fileStem, + packetId: `p848_split_atom_successor_packet_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + markdownPath: path.join(directoryPath, `${fileStem}.md`), + }; +} + +function getP848SideCountFloorPacketPaths(problem, atomId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'SIDE_COUNT_FLOOR'); + if (!atomId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + packetId: `p848_side_count_floor_packet_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + markdownPath: path.join(directoryPath, `${fileStem}.md`), + }; +} + +function getP848DMaxBoundProbePaths(problem, atomId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'DMAX_BOUND_PROBES'); + if (!atomId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + probeId: `p848_dmax_bound_probe_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + }; +} + +function readP848DMaxBoundProbe(problem, atomId) { + const probePaths = getP848DMaxBoundProbePaths(problem, atomId); + if (!probePaths?.jsonPath) { + return null; + } + const probe = readJsonIfPresent(probePaths.jsonPath); + if (!probe) { + return null; + } + return { + ...probe, + probeId: probe.probeId ?? probePaths.probeId, + jsonPath: probePaths.jsonPath, + }; +} + +function getP848DMaxGrowthProfilePaths(problem, atomId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'DMAX_GROWTH_PROFILES'); + if (!atomId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + profileId: `p848_dmax_growth_profile_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + }; +} + +function readP848DMaxGrowthProfile(problem, atomId) { + const profilePaths = getP848DMaxGrowthProfilePaths(problem, atomId); + if (!profilePaths?.jsonPath) { + return null; + } + const profile = readJsonIfPresent(profilePaths.jsonPath); + if (!profile) { + return null; + } + return { + ...profile, + profileId: profile.profileId ?? profilePaths.profileId, + jsonPath: profilePaths.jsonPath, + }; +} + +function getP848DMaxQProgressionProofPaths(problem, atomId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'DMAX_Q_PROGRESSION_PROOFS'); + if (!atomId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + proofId: `p848_dmax_q_progression_proof_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + }; +} + +function readP848DMaxQProgressionProof(problem, atomId) { + const proofPaths = getP848DMaxQProgressionProofPaths(problem, atomId); + if (!proofPaths?.jsonPath) { + return null; + } + const proof = readJsonIfPresent(proofPaths.jsonPath); + if (!proof) { + return null; + } + return { + ...proof, + proofId: proof.proofId ?? proofPaths.proofId, + jsonPath: proofPaths.jsonPath, + }; +} + +function getP848DMaxTailRecombinationProofPaths(problem, atomId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'DMAX_TAIL_RECOMBINATION_PROOFS'); + if (!atomId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + proofId: `p848_dmax_tail_recombination_proof_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + }; +} + +function readP848DMaxTailRecombinationProof(problem, atomId) { + const proofPaths = getP848DMaxTailRecombinationProofPaths(problem, atomId); + if (!proofPaths?.jsonPath) { + return null; + } + const proof = readJsonIfPresent(proofPaths.jsonPath); + if (!proof) { + return null; + } + return { + ...proof, + proofId: proof.proofId ?? proofPaths.proofId, + jsonPath: proofPaths.jsonPath, + }; +} + +function getP848DynamicMarginProofPaths(problem, atomId = null) { + const packetPaths = getP848SplitAtomPacketPaths(problem); + if (!packetPaths) { + return null; + } + const directoryPath = path.join(packetPaths.directoryPath, 'DYNAMIC_MARGIN_PROOFS'); + if (!atomId) { + return { + directoryPath, + }; + } + + const fileStem = sanitizeP848PacketFileStem(atomId); + return { + directoryPath, + fileStem, + proofId: `p848_dynamic_margin_proof_${fileStem}`, + jsonPath: path.join(directoryPath, `${fileStem}.json`), + }; +} + +function readP848DynamicMarginProof(problem, atomId) { + const proofPaths = getP848DynamicMarginProofPaths(problem, atomId); + if (!proofPaths?.jsonPath) { + return null; + } + let proof = readJsonIfPresent(proofPaths.jsonPath); + let jsonPath = proofPaths.jsonPath; + if (!proof && proofPaths.directoryPath && fs.existsSync(proofPaths.directoryPath)) { + const candidateFilenames = fs.readdirSync(proofPaths.directoryPath) + .filter((filename) => filename.endsWith('.json')); + for (const filename of candidateFilenames) { + const candidatePath = path.join(proofPaths.directoryPath, filename); + const candidateProof = readJsonIfPresent(candidatePath); + if (candidateProof?.atomId === atomId) { + proof = candidateProof; + jsonPath = candidatePath; + break; + } + } + } + if (!proof) { + return null; + } + return { + ...proof, + proofId: proof.proofId ?? proofPaths.proofId, + jsonPath, + }; +} + +function buildP848SquarefreeCheck(value) { + const productPlusOne = Number(value); + const squareDivisorWitnesses = []; + const checkedSquareRootFloor = Math.floor(Math.sqrt(productPlusOne)); + for (let divisor = 2; divisor <= checkedSquareRootFloor; divisor += 1) { + const square = divisor * divisor; + if (productPlusOne % square === 0) { + squareDivisorWitnesses.push({ + divisor, + square, + quotient: productPlusOne / square, + }); + } + } + + return { + productPlusOne, + checkedSquareRootFloor, + squareDivisorWitnesses, + isSquarefree: squareDivisorWitnesses.length === 0, + }; +} + +function buildP848SplitKeyForWitness(witness) { + return `outP2=${witness.outsiderModP2}|out25=${witness.outsiderMod25}|smaller=${witness.smallerSide}`; +} + +function getP848SplitAtomWitnessRows(problem, atom) { + const packProblemDir = getProblemPackDir(problem); + if (!packProblemDir) { + return []; + } + const artifactName = Number(atom.prime) === 17 + ? 'MATCHING_PATTERN_MINER_P17.json' + : 'MATCHING_PATTERN_MINER.json'; + const artifact = readJsonIfPresent(path.join(packProblemDir, artifactName)); + return (artifact?.witnesses ?? []) + .filter((witness) => buildP848SplitKeyForWitness(witness) === atom.splitKey) + .map((witness) => ({ + N: witness.N, + outsider: witness.outsider, + outsiderMod25: witness.outsiderMod25, + outsiderModP2: witness.outsiderModP2, + smallerSide: witness.smallerSide, + side7Count: witness.side7Count, + side18Count: witness.side18Count, + requiredMatchingLowerBound: witness.requiredMatchingLowerBound, + reconstructedMatchingSize: witness.reconstructedMatchingSize, + matchingSlack: witness.matchingSlack, + })); +} + +function buildP848VertexPresenceCheck(value, witnessRows, splitModulus) { + const witnessChecks = witnessRows.map((witness) => { + const squareCheck = buildP848SquarefreeCheck(Number(witness.outsider) * Number(value) + 1); + const squareDivisorWitnesses = squareCheck.squareDivisorWitnesses.map((squareWitness) => ({ + ...squareWitness, + stableUnderCurrentSplitModulus: (Number(splitModulus) * Number(value)) % Number(squareWitness.square) === 0, + })); + return { + N: witness.N, + outsider: witness.outsider, + productPlusOne: squareCheck.productPlusOne, + hasAnySquareDivisor: squareDivisorWitnesses.length > 0, + hasStableSplitWitness: squareDivisorWitnesses.some((squareWitness) => squareWitness.stableUnderCurrentSplitModulus), + firstSquareDivisorWitness: squareDivisorWitnesses[0] ?? null, + firstStableSplitWitness: squareDivisorWitnesses.find((squareWitness) => squareWitness.stableUnderCurrentSplitModulus) ?? null, + squareDivisorWitnesses, + }; + }); + const allWitnessRowsCompatible = witnessChecks.length > 0 + && witnessChecks.every((check) => check.hasAnySquareDivisor); + const allWitnessRowsHaveStableSplitWitness = witnessChecks.length > 0 + && witnessChecks.every((check) => check.hasStableSplitWitness); + + return { + status: allWitnessRowsHaveStableSplitWitness + ? 'bounded_presence_supported_by_current_split_modulus' + : allWitnessRowsCompatible + ? 'needs_sharper_split_or_parametric_presence_witness' + : 'failed_vertex_not_compatible_in_witness_row', + allWitnessRowsCompatible, + allWitnessRowsHaveStableSplitWitness, + witnessChecks, + }; +} + +function buildP848VertexPresenceRefinement(atom, witnessRows, splitModulus, { + stableVertexPresenceAtomCount, + unstableVertexPresenceAtoms, + failedVertexPresenceAtoms, +}) { + const conditionsByKey = new Map(); + + for (const vertex of unstableVertexPresenceAtoms) { + const witnessChecks = vertex.presenceCheck?.witnessChecks ?? []; + for (const [witnessIndex, check] of witnessChecks.entries()) { + const squareWitness = check.firstSquareDivisorWitness; + if (!squareWitness) { + continue; + } + + const square = Number(squareWitness.square); + const requiredOutsiderResidue = positiveModulo(check.outsider, square); + const currentSplitResidue = positiveModulo(check.outsider, splitModulus); + const gcdWithCurrentSplitModulus = gcdInt(splitModulus, square); + const compatibleWithCurrentSplit = positiveModulo(currentSplitResidue, gcdWithCurrentSplitModulus) + === positiveModulo(requiredOutsiderResidue, gcdWithCurrentSplitModulus); + const combinedSplitModulus = (splitModulus / gcdWithCurrentSplitModulus) * square; + const conditionKey = `${square}:${requiredOutsiderResidue}`; + + if (!conditionsByKey.has(conditionKey)) { + conditionsByKey.set(conditionKey, { + conditionId: `square_${square}_outsider_${requiredOutsiderResidue}`, + refinementKind: 'square_witness_residue_split', + divisor: Number(squareWitness.divisor), + square, + requiredOutsiderResidueModSquare: requiredOutsiderResidue, + currentSplitCompatibility: { + currentSplitModulus: splitModulus, + currentSplitResidueModCurrentSplitModulus: currentSplitResidue, + gcdWithCurrentSplitModulus, + compatibleWithCurrentSplit, + combinedSplitModulus, + }, + successorSplitKey: `${atom.splitKey}|out${square}=${requiredOutsiderResidue}`, + successorAtomId: `${atom.atomId}.square_${square}_out_${requiredOutsiderResidue}`, + witnessRows: [], + atomIds: [], + examples: [], + }); + } + + const condition = conditionsByKey.get(conditionKey); + if (!condition.atomIds.includes(vertex.atomId)) { + condition.atomIds.push(vertex.atomId); + } + if (!condition.witnessRows.some((row) => row.witnessIndex === witnessIndex)) { + condition.witnessRows.push({ + witnessIndex, + N: check.N, + outsider: check.outsider, + productPlusOne: check.productPlusOne, + quotient: squareWitness.quotient, + }); + } + if (condition.examples.length < 8) { + condition.examples.push({ + atomId: vertex.atomId, + side: vertex.side, + value: vertex.value, + productPlusOne: check.productPlusOne, + }); + } + } + } + + const conditions = [...conditionsByKey.values()] + .map((condition) => ({ + ...condition, + atomCount: condition.atomIds.length, + witnessRowCount: condition.witnessRows.length, + })) + .sort((left, right) => { + if (right.atomCount !== left.atomCount) { + return right.atomCount - left.atomCount; + } + if (left.square !== right.square) { + return left.square - right.square; + } + return left.requiredOutsiderResidueModSquare - right.requiredOutsiderResidueModSquare; + }); + const coveredUnstableAtomIds = new Set(conditions.flatMap((condition) => condition.atomIds)); + const unstableAtomCount = unstableVertexPresenceAtoms.length; + + return { + status: unstableAtomCount > 0 + ? 'literal_core_requires_sharper_square_witness_split' + : failedVertexPresenceAtoms.length > 0 + ? 'literal_core_has_failed_vertex_presence_atoms' + : 'literal_core_stable_under_current_split_modulus', + deterministicMove: unstableAtomCount > 0 + ? 'emit_successor_atoms_by_square_witness_residue' + : 'attempt_symbolic_literal_core_persistence', + splitModulus, + stableAtomCount: stableVertexPresenceAtomCount, + unstableAtomCount, + failedAtomCount: failedVertexPresenceAtoms.length, + conditionCount: conditions.length, + coveredUnstableAtomCount: coveredUnstableAtomIds.size, + uncoveredUnstableAtomCount: Math.max(0, unstableAtomCount - coveredUnstableAtomIds.size), + dominantConditions: conditions.slice(0, 8).map((condition) => ({ + conditionId: condition.conditionId, + square: condition.square, + requiredOutsiderResidueModSquare: condition.requiredOutsiderResidueModSquare, + atomCount: condition.atomCount, + successorSplitKey: condition.successorSplitKey, + })), + conditions, + proofBoundary: 'These square-witness residue classes explain the bounded literal vertex-presence instability; each successor split still needs a theorem-facing persistence proof before it can support an all-N claim.', + }; +} + +function buildP848EdgeObstructionCertificate(atom, edgeObstructionAtoms) { + const edgeAtoms = Array.isArray(edgeObstructionAtoms) ? edgeObstructionAtoms : []; + const squarefreeEdgeAtoms = edgeAtoms.filter((edge) => edge.squarefreeCheck?.isSquarefree === true); + const nonSquarefreeEdgeAtoms = edgeAtoms.filter((edge) => edge.squarefreeCheck?.isSquarefree !== true); + const productPlusOneValues = edgeAtoms + .map((edge) => Number(edge.squarefreeCheck?.productPlusOne)) + .filter((value) => Number.isFinite(value)); + const buildGroups = (groupKeyForEdge, groupSummaryForFirstEdge) => { + const groupsByKey = new Map(); + for (const edge of edgeAtoms) { + const key = groupKeyForEdge(edge); + if (!groupsByKey.has(key)) { + groupsByKey.set(key, { + groupKey: key, + ...groupSummaryForFirstEdge(edge), + edgeAtomIds: [], + examples: [], + }); + } + const group = groupsByKey.get(key); + group.edgeAtomIds.push(edge.atomId); + if (group.examples.length < 6) { + group.examples.push({ + atomId: edge.atomId, + leftValue: edge.pair?.leftValue ?? null, + rightValue: edge.pair?.rightValue ?? null, + productPlusOne: edge.squarefreeCheck?.productPlusOne ?? null, + }); + } + } + return [...groupsByKey.values()] + .map((group) => ({ + ...group, + edgeCount: group.edgeAtomIds.length, + })) + .sort((left, right) => { + if (right.edgeCount !== left.edgeCount) { + return right.edgeCount - left.edgeCount; + } + return String(left.groupKey).localeCompare(String(right.groupKey)); + }); + }; + const mod25Classes = buildGroups( + (edge) => `${edge.pair?.leftMod25 ?? 'unknown'}:${edge.pair?.rightMod25 ?? 'unknown'}`, + (edge) => ({ + leftMod25: edge.pair?.leftMod25 ?? null, + rightMod25: edge.pair?.rightMod25 ?? null, + }), + ); + const primeResidueClasses = buildGroups( + (edge) => { + const leftModP = Number(edge.pair?.leftModP); + const rightModP = Number(edge.pair?.rightModP); + const productPlusOneModP = Number.isFinite(leftModP) && Number.isFinite(rightModP) + ? positiveModulo((leftModP * rightModP) + 1, atom.prime) + : 'unknown'; + return `${edge.pair?.leftModP ?? 'unknown'}:${edge.pair?.rightModP ?? 'unknown'}:${productPlusOneModP}`; + }, + (edge) => { + const leftModP = Number(edge.pair?.leftModP); + const rightModP = Number(edge.pair?.rightModP); + return { + leftModP: edge.pair?.leftModP ?? null, + rightModP: edge.pair?.rightModP ?? null, + productPlusOneModP: Number.isFinite(leftModP) && Number.isFinite(rightModP) + ? positiveModulo((leftModP * rightModP) + 1, atom.prime) + : null, + }; + }, + ); + const primeSquareFingerprints = buildGroups( + (edge) => [ + edge.pair?.leftModP2 ?? 'unknown', + edge.pair?.rightModP2 ?? 'unknown', + edge.pair?.productPlusOneModP2 ?? 'unknown', + ].join(':'), + (edge) => ({ + leftModP2: edge.pair?.leftModP2 ?? null, + rightModP2: edge.pair?.rightModP2 ?? null, + productPlusOneModP2: edge.pair?.productPlusOneModP2 ?? null, + }), + ); + + return { + schema: 'erdos.p848_edge_obstruction_certificate/1', + certificateId: `${atom.atomId}.edge_obstruction_certificate`, + status: edgeAtoms.length > 0 && nonSquarefreeEdgeAtoms.length === 0 + ? 'literal_edge_obstruction_certificate_verified' + : 'literal_edge_obstruction_certificate_needs_recheck', + proofKind: 'literal_product_plus_one_squarefree_missing_edge_certificate', + edgeAtomCount: edgeAtoms.length, + squarefreeEdgeAtomCount: squarefreeEdgeAtoms.length, + nonSquarefreeEdgeAtomCount: nonSquarefreeEdgeAtoms.length, + allSquarefree: edgeAtoms.length > 0 && nonSquarefreeEdgeAtoms.length === 0, + productPlusOneRange: productPlusOneValues.length > 0 + ? { + min: Math.min(...productPlusOneValues), + max: Math.max(...productPlusOneValues), + } + : null, + residueSummary: { + mod25ClassCount: mod25Classes.length, + primeResidueClassCount: primeResidueClasses.length, + primeSquareFingerprintCount: primeSquareFingerprints.length, + }, + mod25Classes, + primeResidueClasses, + firstPrimeSquareFingerprints: primeSquareFingerprints.slice(0, 16), + firstEdgeCertificates: edgeAtoms.slice(0, 10).map((edge) => ({ + atomId: edge.atomId, + leftValue: edge.pair?.leftValue ?? null, + rightValue: edge.pair?.rightValue ?? null, + productPlusOne: edge.squarefreeCheck?.productPlusOne ?? null, + checkedSquareRootFloor: edge.squarefreeCheck?.checkedSquareRootFloor ?? null, + squareDivisorWitnesses: edge.squarefreeCheck?.squareDivisorWitnesses ?? [], + isSquarefree: edge.squarefreeCheck?.isSquarefree === true, + })), + failedEdgeAtoms: nonSquarefreeEdgeAtoms.slice(0, 10).map((edge) => ({ + atomId: edge.atomId, + leftValue: edge.pair?.leftValue ?? null, + rightValue: edge.pair?.rightValue ?? null, + productPlusOne: edge.squarefreeCheck?.productPlusOne ?? null, + squareDivisorWitnesses: edge.squarefreeCheck?.squareDivisorWitnesses ?? [], + })), + proofBoundary: 'This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim.', + nextTheoremAction: 'Promote this literal edge-obstruction certificate into A5 congruence-persistence families, or emit a sharper successor atom for any edge whose obstruction is not implied by the split hypotheses.', + }; +} + +function buildP848EdgeCongruencePersistence(atom, edgeObstructionAtoms, edgeObstructionCertificate, witnessRows) { + const edgeAtoms = Array.isArray(edgeObstructionAtoms) ? edgeObstructionAtoms : []; + const verifiedLiteralCertificate = edgeObstructionCertificate?.status + === 'literal_edge_obstruction_certificate_verified'; + const checks = edgeAtoms.map((edge) => { + const leftValue = Number(edge.pair?.leftValue); + const rightValue = Number(edge.pair?.rightValue); + const productPlusOne = Number(edge.squarefreeCheck?.productPlusOne); + return { + atomId: edge.atomId, + pairIndex: edge.pairIndex, + leftValue: edge.pair?.leftValue ?? null, + rightValue: edge.pair?.rightValue ?? null, + productPlusOne: edge.squarefreeCheck?.productPlusOne ?? null, + productPlusOneRecomputed: Number.isFinite(leftValue) && Number.isFinite(rightValue) + ? (leftValue * rightValue) + 1 + : null, + productPlusOneConstantMatchesCertificate: + Number.isFinite(leftValue) + && Number.isFinite(rightValue) + && Number.isFinite(productPlusOne) + && ((leftValue * rightValue) + 1) === productPlusOne, + squarefreeCertificateVerified: edge.squarefreeCheck?.isSquarefree === true, + dependsOnSampledN: false, + dependsOnWitnessOutsider: false, + impliedBySplitHypotheses: true, + proofReason: 'The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence.', + }; + }); + const failedChecks = checks.filter((check) => ( + !check.productPlusOneConstantMatchesCertificate || !check.squarefreeCertificateVerified + )); + const proofFamilies = [ + { + familyId: `${atom.atomId}.edge_constant_squarefree_family`, + status: verifiedLiteralCertificate && failedChecks.length === 0 + ? 'congruence_persistence_family_verified' + : 'congruence_persistence_family_needs_recheck', + proofKind: 'constant_pair_squarefree_invariant', + edgeAtomCount: checks.length, + verifiedEdgeAtomCount: checks.length - failedChecks.length, + failedEdgeAtomCount: failedChecks.length, + splitKey: atom.splitKey, + splitModulus: Number(atom.prime) * Number(atom.prime) * 25, + statement: 'For each exported literal cross pair (l,r), l and r are constants in the packet, so l*r+1 is the same integer for every row satisfying the split hypotheses.', + proofSteps: [ + 'Recompute c = l*r + 1 from the exported literal pair.', + 'Check c matches the squarefree certificate attached to the edge atom.', + 'Because c has no N or outsider variable, the edge obstruction persists over all rows covered by this literal packet.', + ], + proofBoundary: 'This is not yet a parameterized edge-family theorem. If later proof work replaces literal pair constants with formulas in N, this constant-family proof must be lifted or replaced.', + exampleEdgeAtoms: checks.slice(0, 8).map((check) => ({ + atomId: check.atomId, + leftValue: check.leftValue, + rightValue: check.rightValue, + productPlusOne: check.productPlusOne, + })), + }, + ]; + + return { + schema: 'erdos.p848_edge_congruence_persistence/1', + persistenceId: `${atom.atomId}.edge_congruence_persistence`, + status: verifiedLiteralCertificate && failedChecks.length === 0 + ? 'literal_constant_edge_persistence_verified' + : 'literal_constant_edge_persistence_needs_recheck', + proofKind: 'constant_pair_squarefree_invariant', + splitKey: atom.splitKey, + splitModulus: Number(atom.prime) * Number(atom.prime) * 25, + witnessRowCount: Array.isArray(witnessRows) ? witnessRows.length : 0, + edgeAtomCount: checks.length, + verifiedEdgeAtomCount: checks.length - failedChecks.length, + failedEdgeAtomCount: failedChecks.length, + dependsOnSampledN: false, + dependsOnWitnessOutsider: false, + proofFamilies, + checks, + failedChecks, + proofBoundary: 'This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions.', + nextTheoremAction: 'After this A5 literal persistence pass, promote matching disjointness and the K-envelope, or lift the edge proof if vertex formulas become parameterized.', + }; +} + +function buildP848MatchingKEnvelopeCertificate(atom, matchingDisjointness, kEnvelope) { + const commonCoreCount = Number(kEnvelope?.commonMatchingPairCount); + const maxRequiredMatchingLowerBound = Number(kEnvelope?.maxRequiredMatchingLowerBound); + const boundedSlackAgainstMaxK = Number(kEnvelope?.boundedSlackAgainstMaxK); + const matchingVerified = matchingDisjointness?.status === 'bounded_disjointness_certified' + && Number(matchingDisjointness.leftVertexCount) === Number(matchingDisjointness.pairCount) + && Number(matchingDisjointness.rightVertexCount) === Number(matchingDisjointness.pairCount) + && (matchingDisjointness.reusedLeftValues ?? []).length === 0 + && (matchingDisjointness.reusedRightValues ?? []).length === 0; + const kEnvelopeVerified = kEnvelope?.status === 'bounded_core_meets_sampled_K_envelope' + && Number.isFinite(commonCoreCount) + && Number.isFinite(maxRequiredMatchingLowerBound) + && Number.isFinite(boundedSlackAgainstMaxK) + && commonCoreCount >= maxRequiredMatchingLowerBound + && boundedSlackAgainstMaxK >= 0; + + return { + schema: 'erdos.p848_matching_k_envelope_certificate/1', + certificateId: `${atom.atomId}.matching_k_envelope_certificate`, + status: matchingVerified && kEnvelopeVerified + ? 'literal_matching_sampled_k_envelope_verified' + : 'literal_matching_sampled_k_envelope_needs_recheck', + proofKind: 'literal_disjoint_matching_plus_sampled_k_envelope', + matchingProof: { + status: matchingVerified + ? 'literal_matching_disjointness_verified' + : 'literal_matching_disjointness_needs_recheck', + pairCount: matchingDisjointness?.pairCount ?? null, + leftVertexCount: matchingDisjointness?.leftVertexCount ?? null, + rightVertexCount: matchingDisjointness?.rightVertexCount ?? null, + reusedLeftValues: matchingDisjointness?.reusedLeftValues ?? [], + reusedRightValues: matchingDisjointness?.reusedRightValues ?? [], + proofSteps: [ + 'Count the exported literal left vertices.', + 'Count the exported literal right vertices.', + 'Verify no left value and no right value is reused across the exported pair list.', + ], + proofBoundary: 'This proves disjointness for the exported literal pair list. If later work parameterizes vertices, disjointness must be rechecked for the parameterized formulas.', + }, + kEnvelopeProof: { + status: kEnvelopeVerified + ? 'sampled_k_envelope_dominated_by_literal_core' + : 'sampled_k_envelope_needs_recheck', + requiredMatchingLowerBoundRange: kEnvelope?.requiredMatchingLowerBoundRange ?? null, + commonMatchingPairCount: kEnvelope?.commonMatchingPairCount ?? null, + maxRequiredMatchingLowerBound: kEnvelope?.maxRequiredMatchingLowerBound ?? null, + boundedSlackAgainstMaxK: kEnvelope?.boundedSlackAgainstMaxK ?? null, + inequality: Number.isFinite(commonCoreCount) && Number.isFinite(maxRequiredMatchingLowerBound) + ? `${commonCoreCount} >= ${maxRequiredMatchingLowerBound}` + : null, + proofSteps: [ + 'Use the exported common-core pair count as the literal matching size.', + 'Compare it against the maximum required matching lower bound recorded by the packet.', + 'Record the slack and keep the all-N K-formula handoff explicit.', + ], + proofBoundary: 'This certifies the K-envelope recorded by the current split packet. It is not by itself a universal K(N,x) formula proof for every future row.', + }, + allLowerLiteralAtomsReady: matchingVerified && kEnvelopeVerified, + proofBoundary: 'A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim.', + nextTheoremAction: 'Assemble this with the verified vertex-successor and edge-persistence layers into a split-discharge readiness certificate, or emit the first missing lower atom.', + }; +} + +function buildP848SplitDischargeReadiness(packet, successorPackets) { + const relevantSuccessors = (successorPackets ?? []) + .filter((successor) => successor.parentAtomId === packet.atomId); + const vertexConditionCount = Number(packet.vertexPresenceRefinement?.conditionCount ?? 0); + const verifiedVertexSuccessorCount = relevantSuccessors + .filter((successor) => successor.symbolicVertexFamilyLemma?.status === 'symbolic_vertex_family_lemma_verified').length; + const allVertexSuccessorsVerified = vertexConditionCount > 0 + && verifiedVertexSuccessorCount === vertexConditionCount; + const lowerLayerChecks = [ + { + layerId: 'A3_vertex_presence_successors', + status: allVertexSuccessorsVerified + ? 'verified' + : vertexConditionCount === 0 + ? 'not_required' + : 'blocked', + evidence: `${verifiedVertexSuccessorCount}/${vertexConditionCount} successor vertex-family lemmas verified`, + }, + { + layerId: 'A4_edge_obstruction_certificate', + status: packet.edgeObstructionCertificate?.status === 'literal_edge_obstruction_certificate_verified' + ? 'verified' + : 'blocked', + evidence: packet.edgeObstructionCertificate?.status ?? null, + }, + { + layerId: 'A5_edge_congruence_persistence', + status: packet.edgeCongruencePersistence?.status === 'literal_constant_edge_persistence_verified' + ? 'verified' + : 'blocked', + evidence: packet.edgeCongruencePersistence?.status ?? null, + }, + { + layerId: 'A6_matching_disjointness', + status: packet.matchingKEnvelopeCertificate?.matchingProof?.status === 'literal_matching_disjointness_verified' + ? 'verified' + : 'blocked', + evidence: packet.matchingKEnvelopeCertificate?.matchingProof?.status ?? null, + }, + { + layerId: 'A7_sampled_k_envelope', + status: packet.matchingKEnvelopeCertificate?.kEnvelopeProof?.status === 'sampled_k_envelope_dominated_by_literal_core' + ? 'verified_sampled_envelope' + : 'blocked', + evidence: packet.matchingKEnvelopeCertificate?.kEnvelopeProof?.inequality ?? null, + }, + ]; + const blockingChecks = lowerLayerChecks.filter((check) => check.status === 'blocked'); + const readyForSplitLemmaCandidate = blockingChecks.length === 0; + + return { + schema: 'erdos.p848_split_discharge_readiness/1', + readinessId: `${packet.atomId}.split_discharge_readiness`, + status: readyForSplitLemmaCandidate + ? 'split_discharge_readiness_candidate' + : 'split_discharge_readiness_blocked', + proofKind: 'lower_atom_assembly_with_explicit_all_n_handoff', + atomId: packet.atomId, + splitKey: packet.splitKey, + parentObligationId: packet.parentObligationId, + targetObligationId: packet.targetObligationId, + lowerLayerChecks, + blockingChecks, + theoremCandidate: { + status: readyForSplitLemmaCandidate + ? 'candidate_with_open_all_n_handoff_gaps' + : 'blocked_by_lower_atom', + statement: `For split ${packet.splitKey}, the exported literal core supplies a disjoint matching of size ${packet.matchingCore?.commonMatchingPairCount ?? '(unknown)'} against the packet K-envelope ${JSON.stringify(packet.kEnvelope?.requiredMatchingLowerBoundRange ?? null)}.`, + lowerAtomSummary: { + vertexSuccessorConditionCount: vertexConditionCount, + verifiedVertexSuccessorCount, + edgePersistenceStatus: packet.edgeCongruencePersistence?.status ?? null, + matchingKEnvelopeStatus: packet.matchingKEnvelopeCertificate?.status ?? null, + }, + }, + openAllNHandoffGaps: [ + { + gapId: 'row_universe_split_coverage', + status: 'open', + note: 'Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile.', + }, + { + gapId: 'universal_k_formula_lift', + status: 'open', + note: 'Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane.', + }, + { + gapId: 'literal_to_parameterized_vertex_guard', + status: 'open_if_vertices_move', + note: 'If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families.', + }, + ], + proofBoundary: 'This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes.', + nextTheoremAction: readyForSplitLemmaCandidate + ? 'Attack the next p13 split profile or begin the row-universe/symbolic-K handoff once every p13 split has this readiness certificate.' + : 'Discharge the first blocked lower atom before promoting this split.', + }; +} + +function buildP848SplitAtomPacket(problem, plan, atom) { + const paths = getP848SplitAtomPacketPaths(problem, atom.atomId); + const commonMatchingPairs = Array.isArray(atom.commonMatchingPairs) ? atom.commonMatchingPairs : []; + const witnessRows = getP848SplitAtomWitnessRows(problem, atom); + const splitModulus = Number(atom.prime) * Number(atom.prime) * 25; + const uniqueLeftValues = [...new Set(commonMatchingPairs.map((pair) => pair.leftValue))].sort((left, right) => left - right); + const uniqueRightValues = [...new Set(commonMatchingPairs.map((pair) => pair.rightValue))].sort((left, right) => left - right); + const maxRequiredK = Array.isArray(atom.requiredMatchingLowerBoundRange) + ? Number(atom.requiredMatchingLowerBoundRange[1]) + : null; + const commonPairCount = Number(atom.commonMatchingPairCount ?? commonMatchingPairs.length); + const kEnvelopeSlack = Number.isFinite(maxRequiredK) && Number.isFinite(commonPairCount) + ? commonPairCount - maxRequiredK + : null; + const vertexResidues = (value) => ({ + value, + mod25: positiveModulo(value, 25), + modP: positiveModulo(value, atom.prime), + modP2: positiveModulo(value, atom.prime * atom.prime), + }); + const vertexPresenceAtoms = [ + ...uniqueLeftValues.map((value, index) => { + const presenceCheck = buildP848VertexPresenceCheck(value, witnessRows, splitModulus); + return { + atomId: `${atom.atomId}.V${index + 1}.left_${value}`, + side: 'side7', + value, + residues: vertexResidues(value), + status: presenceCheck.status, + presenceCheck, + goal: `Prove left core vertex ${value} is present in the side7 compatible set for every row in split ${atom.splitKey}.`, + }; + }), + ...uniqueRightValues.map((value, index) => { + const presenceCheck = buildP848VertexPresenceCheck(value, witnessRows, splitModulus); + return { + atomId: `${atom.atomId}.V${uniqueLeftValues.length + index + 1}.right_${value}`, + side: 'side18', + value, + residues: vertexResidues(value), + status: presenceCheck.status, + presenceCheck, + goal: `Prove right core vertex ${value} is present in the side18 compatible set for every row in split ${atom.splitKey}.`, + }; + }), + ]; + const stableVertexPresenceAtomCount = vertexPresenceAtoms + .filter((vertex) => vertex.presenceCheck?.allWitnessRowsHaveStableSplitWitness).length; + const unstableVertexPresenceAtoms = vertexPresenceAtoms + .filter((vertex) => vertex.presenceCheck?.allWitnessRowsCompatible && !vertex.presenceCheck?.allWitnessRowsHaveStableSplitWitness); + const failedVertexPresenceAtoms = vertexPresenceAtoms + .filter((vertex) => vertex.presenceCheck?.allWitnessRowsCompatible === false); + const vertexPresenceRefinement = buildP848VertexPresenceRefinement(atom, witnessRows, splitModulus, { + stableVertexPresenceAtomCount, + unstableVertexPresenceAtoms, + failedVertexPresenceAtoms, + }); + const seenLeft = new Set(); + const seenRight = new Set(); + const reusedLeftValues = []; + const reusedRightValues = []; + for (const pair of commonMatchingPairs) { + if (seenLeft.has(pair.leftValue) && !reusedLeftValues.includes(pair.leftValue)) { + reusedLeftValues.push(pair.leftValue); + } + if (seenRight.has(pair.rightValue) && !reusedRightValues.includes(pair.rightValue)) { + reusedRightValues.push(pair.rightValue); + } + seenLeft.add(pair.leftValue); + seenRight.add(pair.rightValue); + } + + const edgeObstructionAtoms = commonMatchingPairs.map((pair, index) => { + const squarefreeCheck = buildP848SquarefreeCheck(Number(pair.leftValue) * Number(pair.rightValue) + 1); + return { + atomId: `${atom.atomId}.E${index + 1}.left_${pair.leftValue}_right_${pair.rightValue}`, + pairIndex: index, + pair, + status: squarefreeCheck.isSquarefree + ? 'bounded_missing_cross_edge_certified_by_squarefree_product_plus_one' + : 'needs_missing_cross_edge_recheck_non_squarefree_product_plus_one', + squarefreeCheck, + goal: `Normalize why (${pair.leftValue}, ${pair.rightValue}) remains a missing cross edge throughout split ${atom.splitKey}.`, + }; + }); + + const allEdgeObstructionsSquarefree = edgeObstructionAtoms.every((edge) => edge.squarefreeCheck.isSquarefree); + const edgeObstructionCertificate = buildP848EdgeObstructionCertificate(atom, edgeObstructionAtoms); + const edgeCongruencePersistence = buildP848EdgeCongruencePersistence( + atom, + edgeObstructionAtoms, + edgeObstructionCertificate, + witnessRows, + ); + const matchingDisjointness = { + status: reusedLeftValues.length === 0 && reusedRightValues.length === 0 ? 'bounded_disjointness_certified' : 'failed_reused_vertex', + leftVertexCount: uniqueLeftValues.length, + rightVertexCount: uniqueRightValues.length, + pairCount: commonMatchingPairs.length, + reusedLeftValues, + reusedRightValues, + completionRule: 'A symbolic packet may promote only if the parameterized left and right vertex families remain pairwise disjoint.', + }; + const kEnvelope = { + requiredMatchingLowerBoundRange: atom.requiredMatchingLowerBoundRange, + commonMatchingPairCount: commonPairCount, + maxRequiredMatchingLowerBound: maxRequiredK, + minMatchingSlack: atom.minMatchingSlack, + boundedSlackAgainstMaxK: kEnvelopeSlack, + status: Number.isFinite(kEnvelopeSlack) && kEnvelopeSlack >= 0 + ? 'bounded_core_meets_sampled_K_envelope' + : 'blocked_core_below_sampled_K_envelope', + }; + const matchingKEnvelopeCertificate = buildP848MatchingKEnvelopeCertificate( + atom, + matchingDisjointness, + kEnvelope, + ); + + return { + schema: 'erdos.p848_split_atom_packet/1', + generatedAt: new Date().toISOString(), + problemId: '848', + packetId: paths?.packetId ?? `p848_split_atom_packet_${sanitizeP848PacketFileStem(atom.atomId)}`, + atomId: atom.atomId, + sourcePlanId: plan.planId, + parentObligationId: atom.parentObligationId, + targetObligationId: plan.scope?.targetObligationId ?? null, + prime: atom.prime, + splitKey: atom.splitKey, + priority: atom.priority, + status: 'ready_for_symbolic_persistence_work', + sourceArtifacts: { + taskList: 'TASK_LIST.json', + formalizationWork: 'FORMALIZATION_WORK.json', + matchingPatternMiner: atom.prime === 17 ? 'MATCHING_PATTERN_MINER_P17.json' : 'MATCHING_PATTERN_MINER.json', + }, + inputs: { + witnessCount: atom.witnessCount, + nRange: atom.nRange, + boundedTarget: atom.boundedTarget ?? null, + goal: atom.goal, + falsifierBoundary: atom.falsifierBoundary, + witnessRows, + splitModulus, + }, + kEnvelope, + matchingCore: { + commonMatchingPairExportComplete: atom.commonMatchingPairExportComplete, + commonMatchingPairCount: commonPairCount, + commonMatchingPairs, + }, + vertexPresenceAtoms, + vertexPresenceSummary: { + splitModulus, + witnessRowCount: witnessRows.length, + vertexPresenceAtomCount: vertexPresenceAtoms.length, + stableUnderCurrentSplitModulusCount: stableVertexPresenceAtomCount, + needsSharperSplitOrParametricWitnessCount: unstableVertexPresenceAtoms.length, + failedVertexPresenceAtomCount: failedVertexPresenceAtoms.length, + refinementStatus: vertexPresenceRefinement.status, + refinementConditionCount: vertexPresenceRefinement.conditionCount, + dominantRefinementConditions: vertexPresenceRefinement.dominantConditions, + firstUnstableAtoms: unstableVertexPresenceAtoms.slice(0, 8).map((vertex) => ({ + atomId: vertex.atomId, + side: vertex.side, + value: vertex.value, + firstSquareDivisorWitness: vertex.presenceCheck?.witnessChecks?.[0]?.firstSquareDivisorWitness ?? null, + })), + }, + vertexPresenceRefinement, + edgeObstructionAtoms, + edgeObstructionCertificate, + edgeCongruencePersistence, + matchingDisjointness, + matchingKEnvelopeCertificate, + summary: { + vertexPresenceAtomCount: vertexPresenceAtoms.length, + edgeObstructionAtomCount: edgeObstructionAtoms.length, + stableVertexPresenceAtomCount, + unstableVertexPresenceAtomCount: unstableVertexPresenceAtoms.length, + failedVertexPresenceAtomCount: failedVertexPresenceAtoms.length, + allEdgeObstructionsSquarefree, + edgeObstructionCertificateStatus: edgeObstructionCertificate.status, + edgeCongruencePersistenceStatus: edgeCongruencePersistence.status, + matchingDisjointnessStatus: matchingDisjointness.status, + matchingKEnvelopeCertificateStatus: matchingKEnvelopeCertificate.status, + readyForFirstTheoremPass: atom.commonMatchingPairExportComplete === true + && matchingDisjointness.status === 'bounded_disjointness_certified' + && Number.isFinite(kEnvelopeSlack) + && kEnvelopeSlack >= 0, + }, + nextTheoremActions: [ + 'Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N.', + unstableVertexPresenceAtoms.length > 0 + ? 'The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families.' + : 'The current split modulus stabilizes the bounded vertex compatibility witnesses; attempt symbolic persistence before adding a sharper split.', + 'Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof.', + 'Attack the packet until it either becomes a split lemma or emits a sharper sub-split key.', + ], + }; +} + +function buildP848SplitAtomSuccessorPacket(problem, parentPacket, condition, rank) { + const paths = getP848SplitAtomSuccessorPacketPaths(problem, parentPacket.atomId, condition.conditionId); + const affectedAtomIdSet = new Set(condition.atomIds ?? []); + const vertexResidueModSquare = gcdInt(condition.requiredOutsiderResidueModSquare, condition.square) === 1 + ? positiveModulo(-Number(modularInverseBigInt(condition.requiredOutsiderResidueModSquare, condition.square)), condition.square) + : null; + const affectedVertexPresenceAtoms = (parentPacket.vertexPresenceAtoms ?? []) + .filter((vertex) => affectedAtomIdSet.has(vertex.atomId)) + .map((vertex) => { + const relevantWitnessChecks = (vertex.presenceCheck?.witnessChecks ?? []) + .filter((check) => { + const squareWitness = check.firstSquareDivisorWitness; + return Number(squareWitness?.square) === Number(condition.square) + && positiveModulo(check.outsider, condition.square) === condition.requiredOutsiderResidueModSquare; + }); + const successorChecks = relevantWitnessChecks.map((check) => ({ + N: check.N, + outsider: check.outsider, + productPlusOne: check.productPlusOne, + firstSquareDivisorWitness: check.firstSquareDivisorWitness, + requiredOutsiderResidueModSquare: condition.requiredOutsiderResidueModSquare, + witnessOutsiderResidueModSquare: positiveModulo(check.outsider, condition.square), + witnessSatisfiesSuccessorResidue: positiveModulo(check.outsider, condition.square) + === condition.requiredOutsiderResidueModSquare, + stableUnderSuccessorSplitModulus: + (Number(condition.currentSplitCompatibility.combinedSplitModulus) * Number(vertex.value)) + % Number(condition.square) === 0, + })); + + return { + atomId: vertex.atomId, + side: vertex.side, + value: vertex.value, + residues: vertex.residues, + residueModSquare: positiveModulo(vertex.value, condition.square), + successorChecks, + status: successorChecks.length > 0 + && successorChecks.every((check) => check.witnessSatisfiesSuccessorResidue && check.stableUnderSuccessorSplitModulus) + ? 'bounded_presence_stabilized_by_successor_square_residue' + : 'needs_successor_presence_recheck', + }; + }); + const stabilizedAtomCount = affectedVertexPresenceAtoms + .filter((vertex) => vertex.status === 'bounded_presence_stabilized_by_successor_square_residue').length; + const failedAtomCount = affectedVertexPresenceAtoms.length - stabilizedAtomCount; + const symbolicFamilyChecks = affectedVertexPresenceAtoms.map((vertex) => ({ + atomId: vertex.atomId, + value: vertex.value, + residueModSquare: vertex.residueModSquare, + expectedVertexResidueModSquare: vertexResidueModSquare, + vertexMatchesResidueFamily: vertexResidueModSquare !== null && vertex.residueModSquare === vertexResidueModSquare, + productPlusOneResidueModSquare: vertexResidueModSquare === null + ? null + : positiveModulo( + (condition.requiredOutsiderResidueModSquare * vertexResidueModSquare) + 1, + condition.square, + ), + })); + const allAtomsMatchSymbolicFamily = symbolicFamilyChecks.length > 0 + && symbolicFamilyChecks.every((check) => ( + check.vertexMatchesResidueFamily && check.productPlusOneResidueModSquare === 0 + )); + const symbolicVertexFamilyLemma = { + lemmaId: `${condition.conditionId}_vertex_family`, + status: allAtomsMatchSymbolicFamily + ? 'symbolic_vertex_family_lemma_verified' + : vertexResidueModSquare === null + ? 'blocked_non_unit_outsider_residue' + : 'needs_symbolic_vertex_family_recheck', + statement: vertexResidueModSquare === null + ? `The outsider residue ${condition.requiredOutsiderResidueModSquare} is not a unit modulo ${condition.square}; use a non-unit divisibility split instead of inverse-residue normalization.` + : `If outsider ≡ ${condition.requiredOutsiderResidueModSquare} (mod ${condition.square}) and vertex ≡ ${vertexResidueModSquare} (mod ${condition.square}), then outsider * vertex + 1 ≡ 0 (mod ${condition.square}).`, + outsiderResidueModSquare: condition.requiredOutsiderResidueModSquare, + vertexResidueModSquare, + square: condition.square, + affectedAtomCount: affectedVertexPresenceAtoms.length, + verifiedAtomCount: symbolicFamilyChecks.filter((check) => ( + check.vertexMatchesResidueFamily && check.productPlusOneResidueModSquare === 0 + )).length, + failedAtomCount: symbolicFamilyChecks.filter((check) => ( + !check.vertexMatchesResidueFamily || check.productPlusOneResidueModSquare !== 0 + )).length, + checks: symbolicFamilyChecks, + proofBoundary: 'This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas.', + }; + + return { + schema: 'erdos.p848_split_atom_successor_packet/1', + generatedAt: new Date().toISOString(), + problemId: '848', + packetId: paths?.packetId ?? `p848_split_atom_successor_packet_${sanitizeP848PacketFileStem(condition.successorAtomId)}`, + parentPacketId: parentPacket.packetId, + parentAtomId: parentPacket.atomId, + successorAtomId: condition.successorAtomId, + successorRank: rank, + conditionId: condition.conditionId, + priority: rank === 1 ? 'highest_refinement_successor' : 'dominant_refinement_successor', + status: failedAtomCount === 0 + ? 'candidate_successor_obligation_verified' + : 'candidate_successor_obligation_needs_recheck', + splitRefinement: { + parentSplitKey: parentPacket.splitKey, + successorSplitKey: condition.successorSplitKey, + parentSplitModulus: condition.currentSplitCompatibility.currentSplitModulus, + successorSplitModulus: condition.currentSplitCompatibility.combinedSplitModulus, + square: condition.square, + divisor: condition.divisor, + requiredOutsiderResidueModSquare: condition.requiredOutsiderResidueModSquare, + compatibleWithCurrentSplit: condition.currentSplitCompatibility.compatibleWithCurrentSplit, + }, + symbolicVertexFamilyLemma, + theoremObligation: { + kind: 'square_residue_vertex_presence_subobligation', + parentObligationId: parentPacket.parentObligationId, + targetObligationId: parentPacket.targetObligationId, + statement: `Under ${condition.successorSplitKey}, stabilize the ${condition.atomCount} literal vertex-presence atoms whose first square witness is ${condition.square}.`, + proofBoundary: 'This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too.', + }, + affectedVertexPresenceAtoms, + checks: { + affectedAtomCount: affectedVertexPresenceAtoms.length, + stabilizedAtomCount, + failedAtomCount, + allAffectedAtomsPresent: affectedVertexPresenceAtoms.length === condition.atomCount, + allAffectedAtomsStabilized: failedAtomCount === 0, + witnessRowCount: condition.witnessRowCount, + witnessRows: condition.witnessRows, + }, + nextTheoremActions: [ + 'Promote this square-residue successor into a symbolic vertex-family lemma.', + 'After this condition is proved, attack the next sibling square-residue successor condition.', + 'Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled.', + ], + }; +} + +function buildP848SplitAtomSuccessorPackets(problem, packets) { + const parentPackets = packets.filter((packet) => ( + packet.priority === 'highest_singleton_profile' + || (Number(packet.prime) === 13 && packet.priority === 'high_p13_active_lane') + )); + const successors = []; + for (const parentPacket of parentPackets) { + const conditions = parentPacket.vertexPresenceRefinement?.conditions ?? []; + for (const [index, condition] of conditions.entries()) { + successors.push(buildP848SplitAtomSuccessorPacket(problem, parentPacket, condition, index + 1)); + } + } + return successors; +} + +function renderP848SplitAtomPacketMarkdown(packet) { + const lines = [ + `# ${packet.atomId}`, + '', + 'This is a theorem-facing split atom packet for Problem 848. It is intentionally atomic: one split profile, one common matching core, one K-envelope, and deterministic sub-atoms for the next proof pass.', + '', + '## Summary', + '', + `- Packet id: \`${packet.packetId}\``, + `- Parent obligation: \`${packet.parentObligationId}\``, + `- Target obligation: \`${packet.targetObligationId ?? '(none)'}\``, + `- Prime lane: \`${packet.prime}\``, + `- Split key: \`${packet.splitKey}\``, + `- Priority: \`${packet.priority}\``, + `- Status: \`${packet.status}\``, + `- Witnesses: \`${packet.inputs.witnessCount}\` over \`${packet.inputs.nRange ?? '(unknown)'}\``, + `- Common core size: \`${packet.matchingCore.commonMatchingPairCount}\``, + `- K-envelope: \`${JSON.stringify(packet.kEnvelope.requiredMatchingLowerBoundRange)}\`, slack against max K \`${packet.kEnvelope.boundedSlackAgainstMaxK ?? '(unknown)'}\``, + `- Vertex atoms: \`${packet.summary.vertexPresenceAtomCount}\``, + `- Vertex atoms stable under current split modulus: \`${packet.summary.stableVertexPresenceAtomCount}\``, + `- Vertex atoms needing sharper split or parameterization: \`${packet.summary.unstableVertexPresenceAtomCount}\``, + `- Edge atoms: \`${packet.summary.edgeObstructionAtomCount}\``, + `- Edge certificate: \`${packet.summary.edgeObstructionCertificateStatus ?? '(none)'}\``, + `- Edge congruence persistence: \`${packet.summary.edgeCongruencePersistenceStatus ?? '(none)'}\``, + `- Disjointness: \`${packet.matchingDisjointness.status}\``, + `- Matching/K certificate: \`${packet.summary.matchingKEnvelopeCertificateStatus ?? '(none)'}\``, + '', + '## Goal', + '', + packet.inputs.goal ?? '(none)', + '', + '## Falsifier Boundary', + '', + packet.inputs.falsifierBoundary ?? '(none)', + '', + '## Next Theorem Actions', + '', + ]; + for (const action of packet.nextTheoremActions ?? []) { + lines.push(`- ${action}`); + } + lines.push('', '## K Envelope', ''); + lines.push(`- Status: \`${packet.kEnvelope.status}\``); + lines.push(`- Common core count: \`${packet.kEnvelope.commonMatchingPairCount}\``); + lines.push(`- Max required K: \`${packet.kEnvelope.maxRequiredMatchingLowerBound ?? '(unknown)'}\``); + lines.push(`- Min matching slack: \`${packet.kEnvelope.minMatchingSlack ?? '(unknown)'}\``); + lines.push('', '## Matching And K-Envelope Certificate', ''); + lines.push(`- Status: \`${packet.matchingKEnvelopeCertificate?.status ?? '(none)'}\``); + lines.push(`- Proof kind: \`${packet.matchingKEnvelopeCertificate?.proofKind ?? '(none)'}\``); + lines.push(`- Matching proof: \`${packet.matchingKEnvelopeCertificate?.matchingProof?.status ?? '(none)'}\``); + lines.push(`- K proof: \`${packet.matchingKEnvelopeCertificate?.kEnvelopeProof?.status ?? '(none)'}\``); + lines.push(`- K inequality: \`${packet.matchingKEnvelopeCertificate?.kEnvelopeProof?.inequality ?? '(none)'}\``); + lines.push(`- Proof boundary: ${packet.matchingKEnvelopeCertificate?.proofBoundary ?? '(none)'}`); + lines.push('', '## Split Discharge Readiness', ''); + lines.push(`- Status: \`${packet.splitDischargeReadiness?.status ?? '(none)'}\``); + lines.push(`- Proof kind: \`${packet.splitDischargeReadiness?.proofKind ?? '(none)'}\``); + lines.push(`- Theorem candidate: \`${packet.splitDischargeReadiness?.theoremCandidate?.status ?? '(none)'}\``); + lines.push(`- Blocking lower checks: \`${packet.splitDischargeReadiness?.blockingChecks?.length ?? 0}\``); + lines.push(`- Open all-N handoff gaps: \`${packet.splitDischargeReadiness?.openAllNHandoffGaps?.length ?? 0}\``); + lines.push(`- Proof boundary: ${packet.splitDischargeReadiness?.proofBoundary ?? '(none)'}`); + for (const gap of packet.splitDischargeReadiness?.openAllNHandoffGaps ?? []) { + lines.push(`- Handoff gap \`${gap.gapId}\` [${gap.status}]: ${gap.note}`); + } + lines.push('', '## Vertex Presence Stability', ''); + lines.push(`- Split modulus: \`${packet.vertexPresenceSummary.splitModulus}\``); + lines.push(`- Witness rows: \`${packet.vertexPresenceSummary.witnessRowCount}\``); + lines.push(`- Stable under current split modulus: \`${packet.vertexPresenceSummary.stableUnderCurrentSplitModulusCount}\``); + lines.push(`- Needs sharper split or parametric witness: \`${packet.vertexPresenceSummary.needsSharperSplitOrParametricWitnessCount}\``); + for (const vertex of packet.vertexPresenceSummary.firstUnstableAtoms ?? []) { + lines.push(`- First unstable vertex atom \`${vertex.atomId}\`: side ${vertex.side}, value ${vertex.value}, first square witness ${JSON.stringify(vertex.firstSquareDivisorWitness)}`); + } + lines.push('', '## Vertex Presence Refinement', ''); + lines.push(`- Status: \`${packet.vertexPresenceRefinement?.status ?? '(none)'}\``); + lines.push(`- Deterministic move: \`${packet.vertexPresenceRefinement?.deterministicMove ?? '(none)'}\``); + lines.push(`- Refinement condition count: \`${packet.vertexPresenceRefinement?.conditionCount ?? 0}\``); + lines.push(`- Covered unstable atoms: \`${packet.vertexPresenceRefinement?.coveredUnstableAtomCount ?? 0}\``); + lines.push(`- Uncovered unstable atoms: \`${packet.vertexPresenceRefinement?.uncoveredUnstableAtomCount ?? 0}\``); + lines.push(`- Proof boundary: ${packet.vertexPresenceRefinement?.proofBoundary ?? '(none)'}`); + for (const condition of packet.vertexPresenceRefinement?.conditions ?? []) { + lines.push(`- Condition \`${condition.conditionId}\`: out mod ${condition.square} = ${condition.requiredOutsiderResidueModSquare}, atoms=${condition.atomCount}, combined modulus=${condition.currentSplitCompatibility?.combinedSplitModulus ?? '(unknown)'}, successor=\`${condition.successorSplitKey}\``); + } + lines.push('', '## Edge Obstruction Certificate', ''); + lines.push(`- Status: \`${packet.edgeObstructionCertificate?.status ?? '(none)'}\``); + lines.push(`- Proof kind: \`${packet.edgeObstructionCertificate?.proofKind ?? '(none)'}\``); + lines.push(`- Edge atoms: \`${packet.edgeObstructionCertificate?.edgeAtomCount ?? 0}\``); + lines.push(`- Squarefree edge atoms: \`${packet.edgeObstructionCertificate?.squarefreeEdgeAtomCount ?? 0}\``); + lines.push(`- Non-squarefree edge atoms: \`${packet.edgeObstructionCertificate?.nonSquarefreeEdgeAtomCount ?? 0}\``); + lines.push(`- Product-plus-one range: \`${packet.edgeObstructionCertificate?.productPlusOneRange ? JSON.stringify(packet.edgeObstructionCertificate.productPlusOneRange) : '(none)'}\``); + lines.push(`- Mod 25 classes: \`${packet.edgeObstructionCertificate?.residueSummary?.mod25ClassCount ?? 0}\``); + lines.push(`- Prime-residue classes: \`${packet.edgeObstructionCertificate?.residueSummary?.primeResidueClassCount ?? 0}\``); + lines.push(`- Prime-square fingerprints: \`${packet.edgeObstructionCertificate?.residueSummary?.primeSquareFingerprintCount ?? 0}\``); + lines.push(`- Proof boundary: ${packet.edgeObstructionCertificate?.proofBoundary ?? '(none)'}`); + for (const group of packet.edgeObstructionCertificate?.mod25Classes ?? []) { + lines.push(`- Mod25 class \`${group.groupKey}\`: edges=${group.edgeCount}`); + } + for (const group of (packet.edgeObstructionCertificate?.primeResidueClasses ?? []).slice(0, 13)) { + lines.push(`- Prime-residue class \`${group.groupKey}\`: edges=${group.edgeCount}`); + } + lines.push('', '## Edge Congruence Persistence', ''); + lines.push(`- Status: \`${packet.edgeCongruencePersistence?.status ?? '(none)'}\``); + lines.push(`- Proof kind: \`${packet.edgeCongruencePersistence?.proofKind ?? '(none)'}\``); + lines.push(`- Edge atoms: \`${packet.edgeCongruencePersistence?.edgeAtomCount ?? 0}\``); + lines.push(`- Verified edge atoms: \`${packet.edgeCongruencePersistence?.verifiedEdgeAtomCount ?? 0}\``); + lines.push(`- Failed edge atoms: \`${packet.edgeCongruencePersistence?.failedEdgeAtomCount ?? 0}\``); + lines.push(`- Depends on sampled N: \`${packet.edgeCongruencePersistence?.dependsOnSampledN ? 'yes' : 'no'}\``); + lines.push(`- Depends on witness outsider: \`${packet.edgeCongruencePersistence?.dependsOnWitnessOutsider ? 'yes' : 'no'}\``); + lines.push(`- Proof boundary: ${packet.edgeCongruencePersistence?.proofBoundary ?? '(none)'}`); + for (const family of packet.edgeCongruencePersistence?.proofFamilies ?? []) { + lines.push(`- Family \`${family.familyId}\`: status=\`${family.status}\`, edges=${family.edgeAtomCount}, proof=${family.proofKind}`); + } + lines.push('', '## Matching Core', ''); + for (const pair of packet.matchingCore.commonMatchingPairs ?? []) { + lines.push(`- Pair (${pair.leftValue}, ${pair.rightValue}); residues mod25 ${pair.leftMod25}:${pair.rightMod25}, mod p ${pair.leftModP}:${pair.rightModP}, mod p^2 ${pair.leftModP2}:${pair.rightModP2}; product+1 mod p^2 ${pair.productPlusOneModP2}`); + } + return `${lines.join('\n')}\n`; +} + +function renderP848SplitAtomSuccessorPacketMarkdown(packet) { + const lines = [ + `# ${packet.successorAtomId}`, + '', + 'This is a focused successor packet emitted from a Problem 848 split atom refinement condition.', + '', + '## Summary', + '', + `- Packet id: \`${packet.packetId}\``, + `- Parent atom: \`${packet.parentAtomId}\``, + `- Condition: \`${packet.conditionId}\``, + `- Priority: \`${packet.priority}\``, + `- Status: \`${packet.status}\``, + `- Successor split: \`${packet.splitRefinement.successorSplitKey}\``, + `- Successor modulus: \`${packet.splitRefinement.successorSplitModulus}\``, + `- Square witness: \`${packet.splitRefinement.square}\``, + `- Required outsider residue: \`${packet.splitRefinement.requiredOutsiderResidueModSquare}\``, + `- Affected atoms: \`${packet.checks.affectedAtomCount}\``, + `- Stabilized atoms: \`${packet.checks.stabilizedAtomCount}\``, + `- Failed atoms: \`${packet.checks.failedAtomCount}\``, + `- Symbolic family lemma: \`${packet.symbolicVertexFamilyLemma?.status ?? '(none)'}\``, + `- Vertex residue family: \`${packet.symbolicVertexFamilyLemma?.vertexResidueModSquare ?? '(none)'} mod ${packet.symbolicVertexFamilyLemma?.square ?? '(unknown)'}\``, + '', + '## Theorem Obligation', + '', + packet.theoremObligation.statement, + '', + `Boundary: ${packet.theoremObligation.proofBoundary}`, + '', + '## Symbolic Vertex-Family Lemma', + '', + packet.symbolicVertexFamilyLemma?.statement ?? '(none)', + '', + `Boundary: ${packet.symbolicVertexFamilyLemma?.proofBoundary ?? '(none)'}`, + '', + '## Next Theorem Actions', + '', + ]; + for (const action of packet.nextTheoremActions ?? []) { + lines.push(`- ${action}`); + } + lines.push('', '## Affected Vertex Atoms', ''); + for (const atom of packet.affectedVertexPresenceAtoms ?? []) { + lines.push(`- \`${atom.atomId}\`: side=${atom.side}, value=${atom.value}, status=\`${atom.status}\``); + } + return `${lines.join('\n')}\n`; +} + +function buildP848SideCountFloorAtomPackets(problem, plan) { + const lift = plan?.slackDominanceSymbolicLift ?? null; + if (lift?.status !== 'bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed') { + return []; + } + const strata = Array.isArray(lift.formulaStrata) ? lift.formulaStrata : []; + const finiteFloors = strata + .map((stratum) => Number(stratum.minSideCountSlackFormula)) + .filter(Number.isFinite); + if (finiteFloors.length === 0) { + return []; + } + const weakestFloor = Math.min(...finiteFloors); + const weakestStrata = strata + .filter((stratum) => Number(stratum.minSideCountSlackFormula) === weakestFloor) + .sort((left, right) => ( + right.rowCount - left.rowCount + || left.splitKey.localeCompare(right.splitKey) + )); + + return weakestStrata.map((stratum, index) => { + const atomId = `D2_p13_side_count_floor_${sanitizeP848PacketFileStem(stratum.splitKey)}`; + const paths = getP848SideCountFloorPacketPaths(problem, atomId); + const targetFloor = Number(lift.targetNonTightSlackLowerBound); + const observedFloor = Number(stratum.minSideCountSlackFormula); + const largerSideLabel = stratum.largerSideLabel ?? (String(stratum.splitKey).includes('smaller=side7') ? 'side18' : 'side7'); + const structuralMarginAtomId = `D2_p13_structural_margin_${sanitizeP848PacketFileStem(stratum.splitKey)}_${largerSideLabel}`; + const targetAugmentedMarginConstant = Number.isFinite(targetFloor) ? targetFloor + 1 : null; + const dMaxBudget = Number.isFinite(Number(stratum.maxDMax)) ? Number(stratum.maxDMax) : null; + const residualDynamicMarginConstant = dMaxBudget !== null && targetAugmentedMarginConstant !== null + ? dMaxBudget + targetAugmentedMarginConstant + : null; + const dMaxSubatomId = `D2_p13_dmax_bound_${sanitizeP848PacketFileStem(stratum.splitKey)}`; + const dMaxBoundProbe = readP848DMaxBoundProbe(problem, dMaxSubatomId); + const dMaxGrowthSubatomId = dMaxBoundProbe?.successorAtomId + ?? `D2_p13_dmax_growth_${sanitizeP848PacketFileStem(stratum.splitKey)}`; + const dMaxGrowthProfile = readP848DMaxGrowthProfile(problem, dMaxGrowthSubatomId); + const dMaxGrowthFirstSubatomId = dMaxGrowthProfile?.firstOpenSubatom?.atomId ?? null; + const dMaxQ2ProgressionProof = readP848DMaxQProgressionProof(problem, dMaxGrowthFirstSubatomId); + const dMaxGrowthFirstSubatom = dMaxGrowthProfile?.firstOpenSubatom + ? { + atomId: dMaxGrowthProfile.firstOpenSubatom.atomId, + status: dMaxQ2ProgressionProof?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxGrowthProfile.firstOpenSubatom.status ?? 'needed', + term: 'dMax q=2 progression contribution', + dependsOn: [dMaxGrowthSubatomId], + profileId: dMaxGrowthProfile.profileId, + profileJsonPath: dMaxGrowthProfile.jsonPath, + statement: dMaxGrowthProfile.firstOpenSubatom.statement, + completionRule: dMaxGrowthProfile.firstOpenSubatom.completionRule ?? null, + proofArtifact: dMaxQ2ProgressionProof + ? { + proofId: dMaxQ2ProgressionProof.proofId, + jsonPath: dMaxQ2ProgressionProof.jsonPath, + status: dMaxQ2ProgressionProof.status, + q: dMaxQ2ProgressionProof.q, + proofKind: dMaxQ2ProgressionProof.proofKind, + nextSubatomId: dMaxQ2ProgressionProof.nextSubatom?.atomId ?? null, + } + : null, + proofBoundary: 'This is the first floor-function subatom emitted from the bounded dMax growth profile.', + } + : null; + const dMaxQ3ProgressionSubatom = dMaxQ2ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ2ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ2ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ2ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=3 progression contribution', + dependsOn: [dMaxGrowthFirstSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ2ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ2ProgressionProof.jsonPath, + statement: dMaxQ2ProgressionProof.nextSubatom.statement + ?? `Prove the q=3 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ2ProgressionProof.nextSubatom.completionRule + ?? 'The q=3 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ2ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=2 CRT upper-bound component.', + } + : null; + const dMaxQ3ProgressionProof = dMaxQ3ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ3ProgressionSubatom.atomId) + : null; + const dMaxQ5ProgressionSubatom = dMaxQ3ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ3ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ3ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ3ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=5 progression contribution', + dependsOn: [dMaxQ3ProgressionSubatom?.atomId ?? dMaxGrowthFirstSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ3ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ3ProgressionProof.jsonPath, + statement: dMaxQ3ProgressionProof.nextSubatom.statement + ?? `Prove the q=5 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ3ProgressionProof.nextSubatom.completionRule + ?? 'The q=5 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ3ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=3 CRT upper-bound component.', + } + : null; + const dMaxQ5ProgressionProof = dMaxQ5ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ5ProgressionSubatom.atomId) + : null; + const dMaxQ7ProgressionSubatom = dMaxQ5ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ5ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ5ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ5ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=7 progression contribution', + dependsOn: [dMaxQ5ProgressionSubatom?.atomId ?? dMaxQ3ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ5ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ5ProgressionProof.jsonPath, + statement: dMaxQ5ProgressionProof.nextSubatom.statement + ?? `Prove the q=7 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ5ProgressionProof.nextSubatom.completionRule + ?? 'The q=7 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ5ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=5 CRT upper-bound component.', + } + : null; + const dMaxQ7ProgressionProof = dMaxQ7ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ7ProgressionSubatom.atomId) + : null; + const dMaxQ11ProgressionSubatom = dMaxQ7ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ7ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ7ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ7ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=11 progression contribution', + dependsOn: [dMaxQ7ProgressionSubatom?.atomId ?? dMaxQ5ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ7ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ7ProgressionProof.jsonPath, + statement: dMaxQ7ProgressionProof.nextSubatom.statement + ?? `Prove the q=11 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ7ProgressionProof.nextSubatom.completionRule + ?? 'The q=11 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ7ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=7 CRT upper-bound component.', + } + : null; + const dMaxQ11ProgressionProof = dMaxQ11ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ11ProgressionSubatom.atomId) + : null; + const dMaxQ19ProgressionSubatom = dMaxQ11ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ11ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ11ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ11ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=19 progression contribution', + dependsOn: [dMaxQ11ProgressionSubatom?.atomId ?? dMaxQ7ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ11ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ11ProgressionProof.jsonPath, + statement: dMaxQ11ProgressionProof.nextSubatom.statement + ?? `Prove the q=19 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ11ProgressionProof.nextSubatom.completionRule + ?? 'The q=19 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ11ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=11 CRT upper-bound component.', + } + : null; + const dMaxQ19ProgressionProof = dMaxQ19ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ19ProgressionSubatom.atomId) + : null; + const dMaxQ23ProgressionSubatom = dMaxQ19ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ19ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ19ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ19ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=23 progression contribution', + dependsOn: [dMaxQ19ProgressionSubatom?.atomId ?? dMaxQ11ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ19ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ19ProgressionProof.jsonPath, + statement: dMaxQ19ProgressionProof.nextSubatom.statement + ?? `Prove the q=23 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ19ProgressionProof.nextSubatom.completionRule + ?? 'The q=23 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ19ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=19 CRT upper-bound component.', + } + : null; + const dMaxQ23ProgressionProof = dMaxQ23ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ23ProgressionSubatom.atomId) + : null; + const dMaxQ31ProgressionSubatom = dMaxQ23ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ23ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ23ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ23ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=31 progression contribution', + dependsOn: [dMaxQ23ProgressionSubatom?.atomId ?? dMaxQ19ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ23ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ23ProgressionProof.jsonPath, + statement: dMaxQ23ProgressionProof.nextSubatom.statement + ?? `Prove the q=31 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ23ProgressionProof.nextSubatom.completionRule + ?? 'The q=31 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ23ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=23 CRT upper-bound component.', + } + : null; + const dMaxQ31ProgressionProof = dMaxQ31ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ31ProgressionSubatom.atomId) + : null; + const dMaxQ251ProgressionSubatom = dMaxQ31ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ31ProgressionProof.nextSubatom.atomId, + status: readP848DMaxQProgressionProof(problem, dMaxQ31ProgressionProof.nextSubatom.atomId)?.status === 'symbolic_upper_bound_verified' + ? 'symbolic_upper_bound_verified' + : dMaxQ31ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax q=251 progression contribution', + dependsOn: [dMaxQ31ProgressionSubatom?.atomId ?? dMaxQ23ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ31ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ31ProgressionProof.jsonPath, + statement: dMaxQ31ProgressionProof.nextSubatom.statement + ?? `Prove the q=251 same-prime degree progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxQ31ProgressionProof.nextSubatom.completionRule + ?? 'The q=251 progression contribution is bounded by CRT floor functions, or emits a sharper exclusion atom.', + proofArtifact: (() => { + const proof = readP848DMaxQProgressionProof(problem, dMaxQ31ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + q: proof.q, + proofKind: proof.proofKind, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next square-divisor floor-function subatom after the verified q=31 CRT upper-bound component.', + } + : null; + const dMaxQ251ProgressionProof = dMaxQ251ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxQProgressionProof(problem, dMaxQ251ProgressionSubatom.atomId) + : null; + const dMaxTailRecombinationProof = dMaxQ251ProgressionProof?.nextSubatom?.atomId + ? readP848DMaxTailRecombinationProof(problem, dMaxQ251ProgressionProof.nextSubatom.atomId) + : null; + const dMaxTailRecombinationSubatom = dMaxQ251ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxQ251ProgressionProof.nextSubatom.atomId, + status: dMaxTailRecombinationProof?.status ?? dMaxQ251ProgressionProof.nextSubatom.status ?? 'needed', + term: 'dMax tail/recombination envelope', + dependsOn: [dMaxQ251ProgressionSubatom?.atomId ?? dMaxQ31ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxQ251ProgressionProof.proofId, + predecessorProofJsonPath: dMaxQ251ProgressionProof.jsonPath, + verifiedComponentQs: dMaxTailRecombinationProof?.verifiedComponentQs ?? [2, 3, 5, 7, 11, 19, 23, 31, 251], + statement: dMaxQ251ProgressionProof.nextSubatom.statement + ?? `Recombine verified q-components with a symbolic tail bound for ${stratum.splitKey}.`, + completionRule: dMaxQ251ProgressionProof.nextSubatom.completionRule + ?? 'The verified q-components plus a symbolic tail estimate imply the required dMax growth envelope, or emit the first unresolved tail range.', + proofArtifact: dMaxTailRecombinationProof + ? { + proofId: dMaxTailRecombinationProof.proofId, + jsonPath: dMaxTailRecombinationProof.jsonPath, + status: dMaxTailRecombinationProof.status, + proofKind: dMaxTailRecombinationProof.proofKind, + q13Status: dMaxTailRecombinationProof.q13ResidueExclusion?.status ?? null, + nextSubatomId: dMaxTailRecombinationProof.nextSubatom?.atomId ?? null, + } + : null, + proofBoundary: 'This is the first non-singleton dMax growth atom after all observed q-progression components in the bounded profile have proof artifacts.', + } + : null; + const dMaxTailQ17ProgressionSubatom = dMaxTailRecombinationProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailRecombinationProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailRecombinationProof.nextSubatom.atomId)?.status + ?? dMaxTailRecombinationProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=17 progression contribution', + dependsOn: [dMaxTailRecombinationSubatom?.atomId ?? dMaxQ251ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailRecombinationProof.proofId, + predecessorProofJsonPath: dMaxTailRecombinationProof.jsonPath, + q: dMaxTailRecombinationProof.nextSubatom.q ?? 17, + statement: dMaxTailRecombinationProof.nextSubatom.statement + ?? `Prove the q=17 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailRecombinationProof.nextSubatom.completionRule + ?? 'The q=17 tail progression contribution is bounded by CRT floor functions, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailRecombinationProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the first unresolved tail-prime subatom after the target-prime q=13 square divisor is excluded by the split residue.', + } + : null; + const dMaxTailQ17ProgressionProof = dMaxTailQ17ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ17ProgressionSubatom.atomId) + : null; + const dMaxTailQ19PlusProgressionSubatom = dMaxTailQ17ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ17ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ17ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ17ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=19 plus-side progression contribution', + dependsOn: [dMaxTailQ17ProgressionSubatom?.atomId ?? dMaxTailRecombinationSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ17ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ17ProgressionProof.jsonPath, + q: dMaxTailQ17ProgressionProof.nextSubatom.q ?? 19, + side: dMaxTailQ17ProgressionProof.nextSubatom.side ?? 'plus', + statement: dMaxTailQ17ProgressionProof.nextSubatom.statement + ?? `Prove the plus-side q=19 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailQ17ProgressionProof.nextSubatom.completionRule + ?? 'The plus-side q=19 tail progression contribution is bounded by a CRT floor function, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ17ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + side: proof.side ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This side-specific tail atom is required because the observed q=19 component proof covered only the minus witness.', + } + : null; + const dMaxTailQ19PlusProgressionProof = dMaxTailQ19PlusProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ19PlusProgressionSubatom.atomId) + : null; + const dMaxTailQ11MinusProgressionSubatom = dMaxTailQ19PlusProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ19PlusProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ19PlusProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ19PlusProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=11 minus-side progression contribution', + dependsOn: [dMaxTailQ19PlusProgressionSubatom?.atomId ?? dMaxTailQ17ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ19PlusProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ19PlusProgressionProof.jsonPath, + q: dMaxTailQ19PlusProgressionProof.nextSubatom.q ?? 11, + side: dMaxTailQ19PlusProgressionProof.nextSubatom.side ?? 'minus', + statement: dMaxTailQ19PlusProgressionProof.nextSubatom.statement + ?? `Prove the minus-side q=11 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailQ19PlusProgressionProof.nextSubatom.completionRule + ?? 'The minus-side q=11 tail progression contribution is bounded by a CRT floor function, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ19PlusProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + side: proof.side ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This backfill atom is required because the observed q=11 component proof covered only the plus witness.', + } + : null; + const dMaxTailQ11MinusProgressionProof = dMaxTailQ11MinusProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ11MinusProgressionSubatom.atomId) + : null; + const dMaxTailQ23PlusProgressionSubatom = dMaxTailQ11MinusProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ11MinusProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ11MinusProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ11MinusProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=23 plus-side progression contribution', + dependsOn: [dMaxTailQ11MinusProgressionSubatom?.atomId ?? dMaxTailQ19PlusProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ11MinusProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ11MinusProgressionProof.jsonPath, + q: dMaxTailQ11MinusProgressionProof.nextSubatom.q ?? 23, + side: dMaxTailQ11MinusProgressionProof.nextSubatom.side ?? 'plus', + statement: dMaxTailQ11MinusProgressionProof.nextSubatom.statement + ?? `Prove the plus-side q=23 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailQ11MinusProgressionProof.nextSubatom.completionRule + ?? 'The plus-side q=23 tail progression contribution is bounded by a CRT floor function, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ11MinusProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + side: proof.side ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This side-specific tail atom is required because the observed q=23 component proof covered only the minus witness.', + } + : null; + const dMaxTailQ23PlusProgressionProof = dMaxTailQ23PlusProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ23PlusProgressionSubatom.atomId) + : null; + const dMaxTailQ31MinusProgressionSubatom = dMaxTailQ23PlusProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ23PlusProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ23PlusProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ23PlusProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=31 minus-side progression contribution', + dependsOn: [dMaxTailQ23PlusProgressionSubatom?.atomId ?? dMaxTailQ11MinusProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ23PlusProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ23PlusProgressionProof.jsonPath, + q: dMaxTailQ23PlusProgressionProof.nextSubatom.q ?? 31, + side: dMaxTailQ23PlusProgressionProof.nextSubatom.side ?? 'minus', + statement: dMaxTailQ23PlusProgressionProof.nextSubatom.statement + ?? `Prove the minus-side q=31 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailQ23PlusProgressionProof.nextSubatom.completionRule + ?? 'The minus-side q=31 tail progression contribution is bounded by a CRT floor function, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ23PlusProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + side: proof.side ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This side-specific tail atom is required because the observed q=31 component proof covered only the plus witness.', + } + : null; + const dMaxTailQ31MinusProgressionProof = dMaxTailQ31MinusProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ31MinusProgressionSubatom.atomId) + : null; + const dMaxTailQ251MinusProgressionSubatom = dMaxTailQ31MinusProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ31MinusProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ31MinusProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ31MinusProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=251 minus-side progression contribution', + dependsOn: [dMaxTailQ31MinusProgressionSubatom?.atomId ?? dMaxTailQ23PlusProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ31MinusProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ31MinusProgressionProof.jsonPath, + q: dMaxTailQ31MinusProgressionProof.nextSubatom.q ?? 251, + side: dMaxTailQ31MinusProgressionProof.nextSubatom.side ?? 'minus', + statement: dMaxTailQ31MinusProgressionProof.nextSubatom.statement + ?? `Prove the minus-side q=251 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailQ31MinusProgressionProof.nextSubatom.completionRule + ?? 'The minus-side q=251 tail progression contribution is bounded by a CRT floor function, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ31MinusProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + side: proof.side ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This side-specific tail atom is required because the observed q=251 component proof covered only the plus witness.', + } + : null; + const dMaxTailQ251MinusProgressionProof = dMaxTailQ251MinusProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ251MinusProgressionSubatom.atomId) + : null; + const dMaxTailQ29ProgressionSubatom = dMaxTailQ251MinusProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ251MinusProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ251MinusProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ251MinusProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=29 progression contribution', + dependsOn: [dMaxTailQ251MinusProgressionSubatom?.atomId ?? dMaxTailQ31MinusProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ251MinusProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ251MinusProgressionProof.jsonPath, + q: dMaxTailQ251MinusProgressionProof.nextSubatom.q ?? 29, + statement: dMaxTailQ251MinusProgressionProof.nextSubatom.statement + ?? `Prove the q=29 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ251MinusProgressionProof.nextSubatom.completionRule + ?? 'The q=29 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ251MinusProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the first remaining non-observed tail-prime subatom after observed q-components and their side complements are certified.', + } + : null; + const dMaxTailQ29ProgressionProof = dMaxTailQ29ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ29ProgressionSubatom.atomId) + : null; + const dMaxTailQ37ProgressionSubatom = dMaxTailQ29ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ29ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ29ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ29ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=37 progression contribution', + dependsOn: [dMaxTailQ29ProgressionSubatom?.atomId ?? dMaxTailQ251MinusProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ29ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ29ProgressionProof.jsonPath, + q: dMaxTailQ29ProgressionProof.nextSubatom.q ?? 37, + statement: dMaxTailQ29ProgressionProof.nextSubatom.statement + ?? `Prove the q=37 same-prime degree tail atom for ${stratum.splitKey}, including the plus-side witness-divisibility exclusion.`, + completionRule: dMaxTailQ29ProgressionProof.nextSubatom.completionRule + ?? 'The q=37 tail contribution is bounded by CRT floor functions/exclusions, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ29ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This residual tail-prime atom is special because q=37 divides the plus witness 1591, excluding that side before the minus-side CRT floor bound.', + } + : null; + const dMaxTailQ37ProgressionProof = dMaxTailQ37ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ37ProgressionSubatom.atomId) + : null; + const dMaxTailQ41ProgressionSubatom = dMaxTailQ37ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ37ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ37ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ37ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=41 progression contribution', + dependsOn: [dMaxTailQ37ProgressionSubatom?.atomId ?? dMaxTailQ29ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ37ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ37ProgressionProof.jsonPath, + q: dMaxTailQ37ProgressionProof.nextSubatom.q ?? 41, + statement: dMaxTailQ37ProgressionProof.nextSubatom.statement + ?? `Prove the q=41 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ37ProgressionProof.nextSubatom.completionRule + ?? 'The q=41 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ37ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=37 witness-divisibility exclusion plus minus-side floor bound.', + } + : null; + const dMaxTailQ41ProgressionProof = dMaxTailQ41ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ41ProgressionSubatom.atomId) + : null; + const dMaxTailQ43ProgressionSubatom = dMaxTailQ41ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ41ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ41ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ41ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=43 progression contribution', + dependsOn: [dMaxTailQ41ProgressionSubatom?.atomId ?? dMaxTailQ37ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ41ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ41ProgressionProof.jsonPath, + q: dMaxTailQ41ProgressionProof.nextSubatom.q ?? 43, + statement: dMaxTailQ41ProgressionProof.nextSubatom.statement + ?? `Prove the q=43 same-prime degree tail atom for ${stratum.splitKey}, including the plus-side witness-divisibility exclusion.`, + completionRule: dMaxTailQ41ProgressionProof.nextSubatom.completionRule + ?? 'The q=43 tail contribution is bounded by CRT floor functions/exclusions, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ41ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This residual tail-prime atom is special because q=43 divides the plus witness 1591, excluding that side before the minus-side CRT floor bound.', + } + : null; + const dMaxTailQ43ProgressionProof = dMaxTailQ43ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ43ProgressionSubatom.atomId) + : null; + const dMaxTailQ47ProgressionSubatom = dMaxTailQ43ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ43ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ43ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ43ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=47 progression contribution', + dependsOn: [dMaxTailQ43ProgressionSubatom?.atomId ?? dMaxTailQ41ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ43ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ43ProgressionProof.jsonPath, + q: dMaxTailQ43ProgressionProof.nextSubatom.q ?? 47, + statement: dMaxTailQ43ProgressionProof.nextSubatom.statement + ?? `Prove the q=47 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ43ProgressionProof.nextSubatom.completionRule + ?? 'The q=47 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ43ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=43 witness-divisibility exclusion plus minus-side floor bound.', + } + : null; + const dMaxTailQ47ProgressionProof = dMaxTailQ47ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ47ProgressionSubatom.atomId) + : null; + const dMaxTailQ53ProgressionSubatom = dMaxTailQ47ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ47ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ47ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ47ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=53 progression contribution', + dependsOn: [dMaxTailQ47ProgressionSubatom?.atomId ?? dMaxTailQ43ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ47ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ47ProgressionProof.jsonPath, + q: dMaxTailQ47ProgressionProof.nextSubatom.q ?? 53, + statement: dMaxTailQ47ProgressionProof.nextSubatom.statement + ?? `Prove the q=53 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ47ProgressionProof.nextSubatom.completionRule + ?? 'The q=53 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ47ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=47 two-sided floor-bound component.', + } + : null; + const dMaxTailQ53ProgressionProof = dMaxTailQ53ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ53ProgressionSubatom.atomId) + : null; + const dMaxTailQ59ProgressionSubatom = dMaxTailQ53ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ53ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ53ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ53ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=59 progression contribution', + dependsOn: [dMaxTailQ53ProgressionSubatom?.atomId ?? dMaxTailQ47ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ53ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ53ProgressionProof.jsonPath, + q: dMaxTailQ53ProgressionProof.nextSubatom.q ?? 59, + statement: dMaxTailQ53ProgressionProof.nextSubatom.statement + ?? `Prove the q=59 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ53ProgressionProof.nextSubatom.completionRule + ?? 'The q=59 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ53ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=53 two-sided floor-bound component.', + } + : null; + const dMaxTailQ59ProgressionProof = dMaxTailQ59ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ59ProgressionSubatom.atomId) + : null; + const dMaxTailQ61ProgressionSubatom = dMaxTailQ59ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ59ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ59ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ59ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=61 progression contribution', + dependsOn: [dMaxTailQ59ProgressionSubatom?.atomId ?? dMaxTailQ53ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ59ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ59ProgressionProof.jsonPath, + q: dMaxTailQ59ProgressionProof.nextSubatom.q ?? 61, + statement: dMaxTailQ59ProgressionProof.nextSubatom.statement + ?? `Prove the q=61 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ59ProgressionProof.nextSubatom.completionRule + ?? 'The q=61 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ59ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=59 two-sided floor-bound component.', + } + : null; + const dMaxTailQ61ProgressionProof = dMaxTailQ61ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ61ProgressionSubatom.atomId) + : null; + const dMaxTailQ67ProgressionSubatom = dMaxTailQ61ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ61ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ61ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ61ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=67 progression contribution', + dependsOn: [dMaxTailQ61ProgressionSubatom?.atomId ?? dMaxTailQ59ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ61ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ61ProgressionProof.jsonPath, + q: dMaxTailQ61ProgressionProof.nextSubatom.q ?? 67, + statement: dMaxTailQ61ProgressionProof.nextSubatom.statement + ?? `Prove the q=67 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ61ProgressionProof.nextSubatom.completionRule + ?? 'The q=67 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ61ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=61 two-sided floor-bound component.', + } + : null; + const dMaxTailQ67ProgressionProof = dMaxTailQ67ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ67ProgressionSubatom.atomId) + : null; + const dMaxTailQ71ProgressionSubatom = dMaxTailQ67ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ67ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ67ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ67ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=71 progression contribution', + dependsOn: [dMaxTailQ67ProgressionSubatom?.atomId ?? dMaxTailQ61ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ67ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ67ProgressionProof.jsonPath, + q: dMaxTailQ67ProgressionProof.nextSubatom.q ?? 71, + statement: dMaxTailQ67ProgressionProof.nextSubatom.statement + ?? `Prove the q=71 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ67ProgressionProof.nextSubatom.completionRule + ?? 'The q=71 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ67ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=67 two-sided floor-bound component.', + } + : null; + const dMaxTailQ71ProgressionProof = dMaxTailQ71ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ71ProgressionSubatom.atomId) + : null; + const dMaxTailQ73ProgressionSubatom = dMaxTailQ71ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ71ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ71ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ71ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=73 progression contribution', + dependsOn: [dMaxTailQ71ProgressionSubatom?.atomId ?? dMaxTailQ67ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ71ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ71ProgressionProof.jsonPath, + q: dMaxTailQ71ProgressionProof.nextSubatom.q ?? 73, + statement: dMaxTailQ71ProgressionProof.nextSubatom.statement + ?? `Prove the q=73 same-prime degree tail atom for ${stratum.splitKey}, including the minus-side witness-divisibility exclusion.`, + completionRule: dMaxTailQ71ProgressionProof.nextSubatom.completionRule + ?? 'The q=73 tail contribution is bounded by the plus-side CRT floor function and minus-side exclusion, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ71ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This residual tail-prime atom is special because q=73 divides the minus witness 9563, excluding that side before the plus-side CRT floor bound.', + } + : null; + const dMaxTailQ73ProgressionProof = dMaxTailQ73ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ73ProgressionSubatom.atomId) + : null; + const dMaxTailQ79ProgressionSubatom = dMaxTailQ73ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ73ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ73ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ73ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=79 progression contribution', + dependsOn: [dMaxTailQ73ProgressionSubatom?.atomId ?? dMaxTailQ71ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ73ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ73ProgressionProof.jsonPath, + q: dMaxTailQ73ProgressionProof.nextSubatom.q ?? 79, + statement: dMaxTailQ73ProgressionProof.nextSubatom.statement + ?? `Prove the q=79 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ73ProgressionProof.nextSubatom.completionRule + ?? 'The q=79 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ73ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=73 plus-side floor-bound and minus-side exclusion component.', + } + : null; + const dMaxTailQ79ProgressionProof = dMaxTailQ79ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ79ProgressionSubatom.atomId) + : null; + const dMaxTailQ83ProgressionSubatom = dMaxTailQ79ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ79ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ79ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ79ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=83 progression contribution', + dependsOn: [dMaxTailQ79ProgressionSubatom?.atomId ?? dMaxTailQ73ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ79ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ79ProgressionProof.jsonPath, + q: dMaxTailQ79ProgressionProof.nextSubatom.q ?? 83, + statement: dMaxTailQ79ProgressionProof.nextSubatom.statement + ?? `Prove the q=83 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ79ProgressionProof.nextSubatom.completionRule + ?? 'The q=83 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ79ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=79 two-sided floor-bound component.', + } + : null; + const dMaxTailQ83ProgressionProof = dMaxTailQ83ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ83ProgressionSubatom.atomId) + : null; + const dMaxTailQ89ProgressionSubatom = dMaxTailQ83ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ83ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ83ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ83ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=89 progression contribution', + dependsOn: [dMaxTailQ83ProgressionSubatom?.atomId ?? dMaxTailQ79ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ83ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ83ProgressionProof.jsonPath, + q: dMaxTailQ83ProgressionProof.nextSubatom.q ?? 89, + statement: dMaxTailQ83ProgressionProof.nextSubatom.statement + ?? `Prove the q=89 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ83ProgressionProof.nextSubatom.completionRule + ?? 'The q=89 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ83ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=83 two-sided floor-bound component.', + } + : null; + const dMaxTailQ89ProgressionProof = dMaxTailQ89ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ89ProgressionSubatom.atomId) + : null; + const dMaxTailQ97ProgressionSubatom = dMaxTailQ89ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ89ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ89ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ89ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=97 progression contribution', + dependsOn: [dMaxTailQ89ProgressionSubatom?.atomId ?? dMaxTailQ83ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ89ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ89ProgressionProof.jsonPath, + q: dMaxTailQ89ProgressionProof.nextSubatom.q ?? 97, + statement: dMaxTailQ89ProgressionProof.nextSubatom.statement + ?? `Prove the q=97 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ89ProgressionProof.nextSubatom.completionRule + ?? 'The q=97 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ89ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=89 two-sided floor-bound component.', + } + : null; + const dMaxTailQ97ProgressionProof = dMaxTailQ97ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ97ProgressionSubatom.atomId) + : null; + const dMaxTailQ101ProgressionSubatom = dMaxTailQ97ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ97ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ97ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ97ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=101 progression contribution', + dependsOn: [dMaxTailQ97ProgressionSubatom?.atomId ?? dMaxTailQ89ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ97ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ97ProgressionProof.jsonPath, + q: dMaxTailQ97ProgressionProof.nextSubatom.q ?? 101, + statement: dMaxTailQ97ProgressionProof.nextSubatom.statement + ?? `Prove the q=101 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ97ProgressionProof.nextSubatom.completionRule + ?? 'The q=101 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ97ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=97 two-sided floor-bound component.', + } + : null; + const dMaxTailQ101ProgressionProof = dMaxTailQ101ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ101ProgressionSubatom.atomId) + : null; + const dMaxTailQ103ProgressionSubatom = dMaxTailQ101ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ101ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ101ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ101ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=103 progression contribution', + dependsOn: [dMaxTailQ101ProgressionSubatom?.atomId ?? dMaxTailQ97ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ101ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ101ProgressionProof.jsonPath, + q: dMaxTailQ101ProgressionProof.nextSubatom.q ?? 103, + statement: dMaxTailQ101ProgressionProof.nextSubatom.statement + ?? `Prove the q=103 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ101ProgressionProof.nextSubatom.completionRule + ?? 'The q=103 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ101ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=101 two-sided floor-bound component.', + } + : null; + const dMaxTailQ103ProgressionProof = dMaxTailQ103ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ103ProgressionSubatom.atomId) + : null; + const dMaxTailQ107ProgressionSubatom = dMaxTailQ103ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ103ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ103ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ103ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=107 progression contribution', + dependsOn: [dMaxTailQ103ProgressionSubatom?.atomId ?? dMaxTailQ101ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ103ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ103ProgressionProof.jsonPath, + q: dMaxTailQ103ProgressionProof.nextSubatom.q ?? 107, + statement: dMaxTailQ103ProgressionProof.nextSubatom.statement + ?? `Prove the q=107 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ103ProgressionProof.nextSubatom.completionRule + ?? 'The q=107 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ103ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=103 two-sided floor-bound component.', + } + : null; + const dMaxTailQ107ProgressionProof = dMaxTailQ107ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ107ProgressionSubatom.atomId) + : null; + const dMaxTailQ109ProgressionSubatom = dMaxTailQ107ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ107ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ107ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ107ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=109 progression contribution', + dependsOn: [dMaxTailQ107ProgressionSubatom?.atomId ?? dMaxTailQ103ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ107ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ107ProgressionProof.jsonPath, + q: dMaxTailQ107ProgressionProof.nextSubatom.q ?? 109, + statement: dMaxTailQ107ProgressionProof.nextSubatom.statement + ?? `Prove the q=109 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ107ProgressionProof.nextSubatom.completionRule + ?? 'The q=109 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ107ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=107 two-sided floor-bound component.', + } + : null; + const dMaxTailQ109ProgressionProof = dMaxTailQ109ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ109ProgressionSubatom.atomId) + : null; + const dMaxTailQ113ProgressionSubatom = dMaxTailQ109ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ109ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ109ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ109ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=113 progression contribution', + dependsOn: [dMaxTailQ109ProgressionSubatom?.atomId ?? dMaxTailQ107ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ109ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ109ProgressionProof.jsonPath, + q: dMaxTailQ109ProgressionProof.nextSubatom.q ?? 113, + statement: dMaxTailQ109ProgressionProof.nextSubatom.statement + ?? `Prove the q=113 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ109ProgressionProof.nextSubatom.completionRule + ?? 'The q=113 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ109ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=109 two-sided floor-bound component.', + } + : null; + const dMaxTailQ113ProgressionProof = dMaxTailQ113ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ113ProgressionSubatom.atomId) + : null; + const dMaxTailQ127ProgressionSubatom = dMaxTailQ113ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ113ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ113ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ113ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=127 progression contribution', + dependsOn: [dMaxTailQ113ProgressionSubatom?.atomId ?? dMaxTailQ109ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ113ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ113ProgressionProof.jsonPath, + q: dMaxTailQ113ProgressionProof.nextSubatom.q ?? 127, + statement: dMaxTailQ113ProgressionProof.nextSubatom.statement + ?? `Prove the q=127 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ113ProgressionProof.nextSubatom.completionRule + ?? 'The q=127 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ113ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=113 two-sided floor-bound component.', + } + : null; + const dMaxTailQ127ProgressionProof = dMaxTailQ127ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ127ProgressionSubatom.atomId) + : null; + const dMaxTailQ131ProgressionSubatom = dMaxTailQ127ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ127ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ127ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ127ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=131 progression contribution', + dependsOn: [dMaxTailQ127ProgressionSubatom?.atomId ?? dMaxTailQ113ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ127ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ127ProgressionProof.jsonPath, + q: dMaxTailQ127ProgressionProof.nextSubatom.q ?? 131, + statement: dMaxTailQ127ProgressionProof.nextSubatom.statement + ?? `Prove the q=131 same-prime degree tail progression upper bound for ${stratum.splitKey}.`, + completionRule: dMaxTailQ127ProgressionProof.nextSubatom.completionRule + ?? 'The q=131 tail progression contribution is bounded by a plus-side CRT floor function and minus-side witness-divisibility exclusion, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ127ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=127 two-sided floor-bound component.', + } + : null; + const dMaxTailQ131ProgressionProof = dMaxTailQ131ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ131ProgressionSubatom.atomId) + : null; + const dMaxTailQ137ProgressionSubatom = dMaxTailQ131ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ131ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ131ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ131ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=137 progression contribution', + dependsOn: [dMaxTailQ131ProgressionSubatom?.atomId ?? dMaxTailQ127ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ131ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ131ProgressionProof.jsonPath, + q: dMaxTailQ131ProgressionProof.nextSubatom.q ?? 137, + statement: dMaxTailQ131ProgressionProof.nextSubatom.statement + ?? `Prove the q=137 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ131ProgressionProof.nextSubatom.completionRule + ?? 'The q=137 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ131ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=131 CRT/exclusion component.', + } + : null; + const dMaxTailQ137ProgressionProof = dMaxTailQ137ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ137ProgressionSubatom.atomId) + : null; + const dMaxTailQ139ProgressionSubatom = dMaxTailQ137ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ137ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ137ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ137ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=139 progression contribution', + dependsOn: [dMaxTailQ137ProgressionSubatom?.atomId ?? dMaxTailQ131ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ137ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ137ProgressionProof.jsonPath, + q: dMaxTailQ137ProgressionProof.nextSubatom.q ?? 139, + statement: dMaxTailQ137ProgressionProof.nextSubatom.statement + ?? `Prove the q=139 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ137ProgressionProof.nextSubatom.completionRule + ?? 'The q=139 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ137ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=137 two-sided floor-bound component.', + } + : null; + const dMaxTailQ139ProgressionProof = dMaxTailQ139ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ139ProgressionSubatom.atomId) + : null; + const dMaxTailQ149ProgressionSubatom = dMaxTailQ139ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ139ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ139ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ139ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=149 progression contribution', + dependsOn: [dMaxTailQ139ProgressionSubatom?.atomId ?? dMaxTailQ137ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ139ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ139ProgressionProof.jsonPath, + q: dMaxTailQ139ProgressionProof.nextSubatom.q ?? 149, + statement: dMaxTailQ139ProgressionProof.nextSubatom.statement + ?? `Prove the q=149 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ139ProgressionProof.nextSubatom.completionRule + ?? 'The q=149 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ139ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=139 two-sided floor-bound component.', + } + : null; + const dMaxTailQ149ProgressionProof = dMaxTailQ149ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ149ProgressionSubatom.atomId) + : null; + const dMaxTailQ151ProgressionSubatom = dMaxTailQ149ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ149ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ149ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ149ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=151 progression contribution', + dependsOn: [dMaxTailQ149ProgressionSubatom?.atomId ?? dMaxTailQ139ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ149ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ149ProgressionProof.jsonPath, + q: dMaxTailQ149ProgressionProof.nextSubatom.q ?? 151, + statement: dMaxTailQ149ProgressionProof.nextSubatom.statement + ?? `Prove the q=151 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ149ProgressionProof.nextSubatom.completionRule + ?? 'The q=151 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ149ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=149 two-sided floor-bound component.', + } + : null; + const dMaxTailQ151ProgressionProof = dMaxTailQ151ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ151ProgressionSubatom.atomId) + : null; + const dMaxTailQ157ProgressionSubatom = dMaxTailQ151ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ151ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ151ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ151ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=157 progression contribution', + dependsOn: [dMaxTailQ151ProgressionSubatom?.atomId ?? dMaxTailQ149ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ151ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ151ProgressionProof.jsonPath, + q: dMaxTailQ151ProgressionProof.nextSubatom.q ?? 157, + statement: dMaxTailQ151ProgressionProof.nextSubatom.statement + ?? `Prove the q=157 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ151ProgressionProof.nextSubatom.completionRule + ?? 'The q=157 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ151ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=151 two-sided floor-bound component.', + } + : null; + const dMaxTailQ157ProgressionProof = dMaxTailQ157ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ157ProgressionSubatom.atomId) + : null; + const dMaxTailQ163ProgressionSubatom = dMaxTailQ157ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ157ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ157ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ157ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=163 progression contribution', + dependsOn: [dMaxTailQ157ProgressionSubatom?.atomId ?? dMaxTailQ151ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ157ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ157ProgressionProof.jsonPath, + q: dMaxTailQ157ProgressionProof.nextSubatom.q ?? 163, + statement: dMaxTailQ157ProgressionProof.nextSubatom.statement + ?? `Prove the q=163 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ157ProgressionProof.nextSubatom.completionRule + ?? 'The q=163 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ157ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=157 two-sided floor-bound component.', + } + : null; + const dMaxTailQ163ProgressionProof = dMaxTailQ163ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ163ProgressionSubatom.atomId) + : null; + const dMaxTailQ167ProgressionSubatom = dMaxTailQ163ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ163ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ163ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ163ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=167 progression contribution', + dependsOn: [dMaxTailQ163ProgressionSubatom?.atomId ?? dMaxTailQ157ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ163ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ163ProgressionProof.jsonPath, + q: dMaxTailQ163ProgressionProof.nextSubatom.q ?? 167, + statement: dMaxTailQ163ProgressionProof.nextSubatom.statement + ?? `Prove the q=167 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ163ProgressionProof.nextSubatom.completionRule + ?? 'The q=167 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ163ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=163 two-sided floor-bound component.', + } + : null; + const dMaxTailQ167ProgressionProof = dMaxTailQ167ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ167ProgressionSubatom.atomId) + : null; + const dMaxTailQ173ProgressionSubatom = dMaxTailQ167ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ167ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ167ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ167ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=173 progression contribution', + dependsOn: [dMaxTailQ167ProgressionSubatom?.atomId ?? dMaxTailQ163ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ167ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ167ProgressionProof.jsonPath, + q: dMaxTailQ167ProgressionProof.nextSubatom.q ?? 173, + statement: dMaxTailQ167ProgressionProof.nextSubatom.statement + ?? `Prove the q=173 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ167ProgressionProof.nextSubatom.completionRule + ?? 'The q=173 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ167ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=167 two-sided floor-bound component.', + } + : null; + const dMaxTailQ173ProgressionProof = dMaxTailQ173ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ173ProgressionSubatom.atomId) + : null; + const dMaxTailQ179ProgressionSubatom = dMaxTailQ173ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ173ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ173ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ173ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=179 progression contribution', + dependsOn: [dMaxTailQ173ProgressionSubatom?.atomId ?? dMaxTailQ167ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ173ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ173ProgressionProof.jsonPath, + q: dMaxTailQ173ProgressionProof.nextSubatom.q ?? 179, + statement: dMaxTailQ173ProgressionProof.nextSubatom.statement + ?? `Prove the q=179 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ173ProgressionProof.nextSubatom.completionRule + ?? 'The q=179 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ173ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=173 two-sided floor-bound component.', + } + : null; + const dMaxTailQ179ProgressionProof = dMaxTailQ179ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ179ProgressionSubatom.atomId) + : null; + const dMaxTailQ181ProgressionSubatom = dMaxTailQ179ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ179ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ179ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ179ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=181 progression contribution', + dependsOn: [dMaxTailQ179ProgressionSubatom?.atomId ?? dMaxTailQ173ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ179ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ179ProgressionProof.jsonPath, + q: dMaxTailQ179ProgressionProof.nextSubatom.q ?? 181, + statement: dMaxTailQ179ProgressionProof.nextSubatom.statement + ?? `Prove the q=181 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ179ProgressionProof.nextSubatom.completionRule + ?? 'The q=181 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ179ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=179 two-sided floor-bound component.', + } + : null; + const dMaxTailQ181ProgressionProof = dMaxTailQ181ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ181ProgressionSubatom.atomId) + : null; + const dMaxTailQ191ProgressionSubatom = dMaxTailQ181ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ181ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ181ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ181ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=191 progression contribution', + dependsOn: [dMaxTailQ181ProgressionSubatom?.atomId ?? dMaxTailQ179ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ181ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ181ProgressionProof.jsonPath, + q: dMaxTailQ181ProgressionProof.nextSubatom.q ?? 191, + statement: dMaxTailQ181ProgressionProof.nextSubatom.statement + ?? `Prove the q=191 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ181ProgressionProof.nextSubatom.completionRule + ?? 'The q=191 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ181ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=181 two-sided floor-bound component.', + } + : null; + const dMaxTailQ191ProgressionProof = dMaxTailQ191ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ191ProgressionSubatom.atomId) + : null; + const dMaxTailQ193ProgressionSubatom = dMaxTailQ191ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ191ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ191ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ191ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=193 progression contribution', + dependsOn: [dMaxTailQ191ProgressionSubatom?.atomId ?? dMaxTailQ181ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ191ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ191ProgressionProof.jsonPath, + q: dMaxTailQ191ProgressionProof.nextSubatom.q ?? 193, + statement: dMaxTailQ191ProgressionProof.nextSubatom.statement + ?? `Prove the q=193 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ191ProgressionProof.nextSubatom.completionRule + ?? 'The q=193 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ191ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=191 two-sided floor-bound component.', + } + : null; + const dMaxTailQ193ProgressionProof = dMaxTailQ193ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ193ProgressionSubatom.atomId) + : null; + const dMaxTailQ197ProgressionSubatom = dMaxTailQ193ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ193ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ193ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ193ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=197 progression contribution', + dependsOn: [dMaxTailQ193ProgressionSubatom?.atomId ?? dMaxTailQ191ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ193ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ193ProgressionProof.jsonPath, + q: dMaxTailQ193ProgressionProof.nextSubatom.q ?? 197, + statement: dMaxTailQ193ProgressionProof.nextSubatom.statement + ?? `Prove the q=197 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ193ProgressionProof.nextSubatom.completionRule + ?? 'The q=197 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ193ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=193 two-sided floor-bound component.', + } + : null; + const dMaxTailQ197ProgressionProof = dMaxTailQ197ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ197ProgressionSubatom.atomId) + : null; + const dMaxTailQ199ProgressionSubatom = dMaxTailQ197ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ197ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ197ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ197ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=199 progression contribution', + dependsOn: [dMaxTailQ197ProgressionSubatom?.atomId ?? dMaxTailQ193ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ197ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ197ProgressionProof.jsonPath, + q: dMaxTailQ197ProgressionProof.nextSubatom.q ?? 199, + statement: dMaxTailQ197ProgressionProof.nextSubatom.statement + ?? `Prove the q=199 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ197ProgressionProof.nextSubatom.completionRule + ?? 'The q=199 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ197ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=197 two-sided floor-bound component.', + } + : null; + const dMaxTailQ199ProgressionProof = dMaxTailQ199ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ199ProgressionSubatom.atomId) + : null; + const dMaxTailQ211ProgressionSubatom = dMaxTailQ199ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ199ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ199ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ199ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=211 progression contribution', + dependsOn: [dMaxTailQ199ProgressionSubatom?.atomId ?? dMaxTailQ197ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ199ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ199ProgressionProof.jsonPath, + q: dMaxTailQ199ProgressionProof.nextSubatom.q ?? 211, + statement: dMaxTailQ199ProgressionProof.nextSubatom.statement + ?? `Prove the q=211 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ199ProgressionProof.nextSubatom.completionRule + ?? 'The q=211 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ199ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=199 two-sided floor-bound component.', + } + : null; + const dMaxTailQ211ProgressionProof = dMaxTailQ211ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ211ProgressionSubatom.atomId) + : null; + const dMaxTailQ223ProgressionSubatom = dMaxTailQ211ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ211ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ211ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ211ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=223 progression contribution', + dependsOn: [dMaxTailQ211ProgressionSubatom?.atomId ?? dMaxTailQ199ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ211ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ211ProgressionProof.jsonPath, + q: dMaxTailQ211ProgressionProof.nextSubatom.q ?? 223, + statement: dMaxTailQ211ProgressionProof.nextSubatom.statement + ?? `Prove the q=223 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ211ProgressionProof.nextSubatom.completionRule + ?? 'The q=223 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ211ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=211 two-sided floor-bound component.', + } + : null; + const dMaxTailQ223ProgressionProof = dMaxTailQ223ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ223ProgressionSubatom.atomId) + : null; + const dMaxTailQ227ProgressionSubatom = dMaxTailQ223ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ223ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ223ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ223ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=227 progression contribution', + dependsOn: [dMaxTailQ223ProgressionSubatom?.atomId ?? dMaxTailQ211ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ223ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ223ProgressionProof.jsonPath, + q: dMaxTailQ223ProgressionProof.nextSubatom.q ?? 227, + statement: dMaxTailQ223ProgressionProof.nextSubatom.statement + ?? `Prove the q=227 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ223ProgressionProof.nextSubatom.completionRule + ?? 'The q=227 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ223ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=223 two-sided floor-bound component.', + } + : null; + const dMaxTailQ227ProgressionProof = dMaxTailQ227ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ227ProgressionSubatom.atomId) + : null; + const dMaxTailQ229ProgressionSubatom = dMaxTailQ227ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ227ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ227ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ227ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=229 progression contribution', + dependsOn: [dMaxTailQ227ProgressionSubatom?.atomId ?? dMaxTailQ223ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ227ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ227ProgressionProof.jsonPath, + q: dMaxTailQ227ProgressionProof.nextSubatom.q ?? 229, + statement: dMaxTailQ227ProgressionProof.nextSubatom.statement + ?? `Prove the q=229 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ227ProgressionProof.nextSubatom.completionRule + ?? 'The q=229 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ227ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=227 two-sided floor-bound component.', + } + : null; + const dMaxTailQ229ProgressionProof = dMaxTailQ229ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ229ProgressionSubatom.atomId) + : null; + const dMaxTailQ233ProgressionSubatom = dMaxTailQ229ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ229ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ229ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ229ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=233 progression contribution', + dependsOn: [dMaxTailQ229ProgressionSubatom?.atomId ?? dMaxTailQ227ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ229ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ229ProgressionProof.jsonPath, + q: dMaxTailQ229ProgressionProof.nextSubatom.q ?? 233, + statement: dMaxTailQ229ProgressionProof.nextSubatom.statement + ?? `Prove the q=233 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ229ProgressionProof.nextSubatom.completionRule + ?? 'The q=233 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ229ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=229 two-sided floor-bound component.', + } + : null; + const dMaxTailQ233ProgressionProof = dMaxTailQ233ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ233ProgressionSubatom.atomId) + : null; + const dMaxTailQ239ProgressionSubatom = dMaxTailQ233ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ233ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ233ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ233ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=239 progression contribution', + dependsOn: [dMaxTailQ233ProgressionSubatom?.atomId ?? dMaxTailQ229ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ233ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ233ProgressionProof.jsonPath, + q: dMaxTailQ233ProgressionProof.nextSubatom.q ?? 239, + statement: dMaxTailQ233ProgressionProof.nextSubatom.statement + ?? `Prove the q=239 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ233ProgressionProof.nextSubatom.completionRule + ?? 'The q=239 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ233ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=233 two-sided floor-bound component.', + } + : null; + const dMaxTailQ239ProgressionProof = dMaxTailQ239ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ239ProgressionSubatom.atomId) + : null; + const dMaxTailQ241ProgressionSubatom = dMaxTailQ239ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ239ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ239ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ239ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=241 progression contribution', + dependsOn: [dMaxTailQ239ProgressionSubatom?.atomId ?? dMaxTailQ233ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ239ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ239ProgressionProof.jsonPath, + q: dMaxTailQ239ProgressionProof.nextSubatom.q ?? 241, + statement: dMaxTailQ239ProgressionProof.nextSubatom.statement + ?? `Prove the q=241 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ239ProgressionProof.nextSubatom.completionRule + ?? 'The q=241 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ239ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=239 two-sided floor-bound component.', + } + : null; + const dMaxTailQ241ProgressionProof = dMaxTailQ241ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ241ProgressionSubatom.atomId) + : null; + const dMaxTailQ257ProgressionSubatom = dMaxTailQ241ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ241ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ241ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ241ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=257 progression contribution', + dependsOn: [dMaxTailQ241ProgressionSubatom?.atomId ?? dMaxTailQ239ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ241ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ241ProgressionProof.jsonPath, + q: dMaxTailQ241ProgressionProof.nextSubatom.q ?? 257, + statement: dMaxTailQ241ProgressionProof.nextSubatom.statement + ?? `Prove the q=257 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ241ProgressionProof.nextSubatom.completionRule + ?? 'The q=257 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ241ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=241 two-sided floor-bound component; q=251 was already covered by the observed q251 packet and its minus-side complement.', + } + : null; + const dMaxTailQ257ProgressionProof = dMaxTailQ257ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ257ProgressionSubatom.atomId) + : null; + const dMaxTailQ263ProgressionSubatom = dMaxTailQ257ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ257ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ257ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ257ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=263 progression contribution', + dependsOn: [dMaxTailQ257ProgressionSubatom?.atomId ?? dMaxTailQ241ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ257ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ257ProgressionProof.jsonPath, + q: dMaxTailQ257ProgressionProof.nextSubatom.q ?? 263, + statement: dMaxTailQ257ProgressionProof.nextSubatom.statement + ?? `Prove the q=263 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ257ProgressionProof.nextSubatom.completionRule + ?? 'The q=263 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ257ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=257 two-sided floor-bound component.', + } + : null; + const dMaxTailQ263ProgressionProof = dMaxTailQ263ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ263ProgressionSubatom.atomId) + : null; + const dMaxTailQ269ProgressionSubatom = dMaxTailQ263ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ263ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ263ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ263ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=269 progression contribution', + dependsOn: [dMaxTailQ263ProgressionSubatom?.atomId ?? dMaxTailQ257ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ263ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ263ProgressionProof.jsonPath, + q: dMaxTailQ263ProgressionProof.nextSubatom.q ?? 269, + statement: dMaxTailQ263ProgressionProof.nextSubatom.statement + ?? `Prove the q=269 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ263ProgressionProof.nextSubatom.completionRule + ?? 'The q=269 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ263ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=263 two-sided floor-bound component.', + } + : null; + const dMaxTailQ269ProgressionProof = dMaxTailQ269ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ269ProgressionSubatom.atomId) + : null; + const dMaxTailQ271ProgressionSubatom = dMaxTailQ269ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ269ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ269ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ269ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=271 progression contribution', + dependsOn: [dMaxTailQ269ProgressionSubatom?.atomId ?? dMaxTailQ263ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ269ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ269ProgressionProof.jsonPath, + q: dMaxTailQ269ProgressionProof.nextSubatom.q ?? 271, + statement: dMaxTailQ269ProgressionProof.nextSubatom.statement + ?? `Prove the q=271 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ269ProgressionProof.nextSubatom.completionRule + ?? 'The q=271 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ269ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=269 two-sided floor-bound component.', + } + : null; + const dMaxTailQ271ProgressionProof = dMaxTailQ271ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ271ProgressionSubatom.atomId) + : null; + const dMaxTailQ277ProgressionSubatom = dMaxTailQ271ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ271ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ271ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ271ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=277 progression contribution', + dependsOn: [dMaxTailQ271ProgressionSubatom?.atomId ?? dMaxTailQ269ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ271ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ271ProgressionProof.jsonPath, + q: dMaxTailQ271ProgressionProof.nextSubatom.q ?? 277, + statement: dMaxTailQ271ProgressionProof.nextSubatom.statement + ?? `Prove the q=277 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ271ProgressionProof.nextSubatom.completionRule + ?? 'The q=277 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ271ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=271 two-sided floor-bound component.', + } + : null; + const dMaxTailQ277ProgressionProof = dMaxTailQ277ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ277ProgressionSubatom.atomId) + : null; + const dMaxTailQ281ProgressionSubatom = dMaxTailQ277ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ277ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ277ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ277ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=281 progression contribution', + dependsOn: [dMaxTailQ277ProgressionSubatom?.atomId ?? dMaxTailQ271ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ277ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ277ProgressionProof.jsonPath, + q: dMaxTailQ277ProgressionProof.nextSubatom.q ?? 281, + statement: dMaxTailQ277ProgressionProof.nextSubatom.statement + ?? `Prove the q=281 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ277ProgressionProof.nextSubatom.completionRule + ?? 'The q=281 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ277ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=277 two-sided floor-bound component.', + } + : null; + const dMaxTailQ281ProgressionProof = dMaxTailQ281ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ281ProgressionSubatom.atomId) + : null; + const dMaxTailQ283ProgressionSubatom = dMaxTailQ281ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ281ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ281ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ281ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=283 progression contribution', + dependsOn: [dMaxTailQ281ProgressionSubatom?.atomId ?? dMaxTailQ277ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ281ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ281ProgressionProof.jsonPath, + q: dMaxTailQ281ProgressionProof.nextSubatom.q ?? 283, + statement: dMaxTailQ281ProgressionProof.nextSubatom.statement + ?? `Prove the q=283 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ281ProgressionProof.nextSubatom.completionRule + ?? 'The q=283 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ281ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=281 two-sided floor-bound component.', + } + : null; + const dMaxTailQ283ProgressionProof = dMaxTailQ283ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ283ProgressionSubatom.atomId) + : null; + const dMaxTailQ293ProgressionSubatom = dMaxTailQ283ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ283ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ283ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ283ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=293 progression contribution', + dependsOn: [dMaxTailQ283ProgressionSubatom?.atomId ?? dMaxTailQ281ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ283ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ283ProgressionProof.jsonPath, + q: dMaxTailQ283ProgressionProof.nextSubatom.q ?? 293, + statement: dMaxTailQ283ProgressionProof.nextSubatom.statement + ?? `Prove the q=293 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ283ProgressionProof.nextSubatom.completionRule + ?? 'The q=293 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ283ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=283 two-sided floor-bound component.', + } + : null; + const dMaxTailQ293ProgressionProof = dMaxTailQ293ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ293ProgressionSubatom.atomId) + : null; + const dMaxTailQ307ProgressionSubatom = dMaxTailQ293ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ293ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ293ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ293ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=307 progression contribution', + dependsOn: [dMaxTailQ293ProgressionSubatom?.atomId ?? dMaxTailQ283ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ293ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ293ProgressionProof.jsonPath, + q: dMaxTailQ293ProgressionProof.nextSubatom.q ?? 307, + statement: dMaxTailQ293ProgressionProof.nextSubatom.statement + ?? `Prove the q=307 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ293ProgressionProof.nextSubatom.completionRule + ?? 'The q=307 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ293ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=293 two-sided floor-bound component.', + } + : null; + const dMaxTailQ307ProgressionProof = dMaxTailQ307ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ307ProgressionSubatom.atomId) + : null; + const dMaxTailQ311ProgressionSubatom = dMaxTailQ307ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ307ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ307ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ307ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=311 progression contribution', + dependsOn: [dMaxTailQ307ProgressionSubatom?.atomId ?? dMaxTailQ293ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ307ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ307ProgressionProof.jsonPath, + q: dMaxTailQ307ProgressionProof.nextSubatom.q ?? 311, + statement: dMaxTailQ307ProgressionProof.nextSubatom.statement + ?? `Prove the q=311 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ307ProgressionProof.nextSubatom.completionRule + ?? 'The q=311 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ307ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=307 two-sided floor-bound component.', + } + : null; + const dMaxTailQ311ProgressionProof = dMaxTailQ311ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ311ProgressionSubatom.atomId) + : null; + const dMaxTailQ313ProgressionSubatom = dMaxTailQ311ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ311ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ311ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ311ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=313 progression contribution', + dependsOn: [dMaxTailQ311ProgressionSubatom?.atomId ?? dMaxTailQ307ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ311ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ311ProgressionProof.jsonPath, + q: dMaxTailQ311ProgressionProof.nextSubatom.q ?? 313, + statement: dMaxTailQ311ProgressionProof.nextSubatom.statement + ?? `Prove the q=313 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ311ProgressionProof.nextSubatom.completionRule + ?? 'The q=313 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ311ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=311 two-sided floor-bound component.', + } + : null; + const dMaxTailQ313ProgressionProof = dMaxTailQ313ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ313ProgressionSubatom.atomId) + : null; + const dMaxTailQ317ProgressionSubatom = dMaxTailQ313ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ313ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ313ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ313ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=317 progression contribution', + dependsOn: [dMaxTailQ313ProgressionSubatom?.atomId ?? dMaxTailQ311ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ313ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ313ProgressionProof.jsonPath, + q: dMaxTailQ313ProgressionProof.nextSubatom.q ?? 317, + statement: dMaxTailQ313ProgressionProof.nextSubatom.statement + ?? `Prove the q=317 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ313ProgressionProof.nextSubatom.completionRule + ?? 'The q=317 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ313ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=313 two-sided floor-bound component.', + } + : null; + const dMaxTailQ317ProgressionProof = dMaxTailQ317ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ317ProgressionSubatom.atomId) + : null; + const dMaxTailQ331ProgressionSubatom = dMaxTailQ317ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ317ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ317ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ317ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=331 progression contribution', + dependsOn: [dMaxTailQ317ProgressionSubatom?.atomId ?? dMaxTailQ313ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ317ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ317ProgressionProof.jsonPath, + q: dMaxTailQ317ProgressionProof.nextSubatom.q ?? 331, + statement: dMaxTailQ317ProgressionProof.nextSubatom.statement + ?? `Prove the q=331 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ317ProgressionProof.nextSubatom.completionRule + ?? 'The q=331 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ317ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=317 two-sided floor-bound component.', + } + : null; + const dMaxTailQ331ProgressionProof = dMaxTailQ331ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ331ProgressionSubatom.atomId) + : null; + const dMaxTailQ337ProgressionSubatom = dMaxTailQ331ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ331ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ331ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ331ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=337 progression contribution', + dependsOn: [dMaxTailQ331ProgressionSubatom?.atomId ?? dMaxTailQ317ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ331ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ331ProgressionProof.jsonPath, + q: dMaxTailQ331ProgressionProof.nextSubatom.q ?? 337, + statement: dMaxTailQ331ProgressionProof.nextSubatom.statement + ?? `Prove the q=337 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ331ProgressionProof.nextSubatom.completionRule + ?? 'The q=337 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ331ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=331 two-sided floor-bound component.', + } + : null; + const dMaxTailQ337ProgressionProof = dMaxTailQ337ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ337ProgressionSubatom.atomId) + : null; + const dMaxTailQ347ProgressionSubatom = dMaxTailQ337ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ337ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ337ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ337ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=347 progression contribution', + dependsOn: [dMaxTailQ337ProgressionSubatom?.atomId ?? dMaxTailQ331ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ337ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ337ProgressionProof.jsonPath, + q: dMaxTailQ337ProgressionProof.nextSubatom.q ?? 347, + statement: dMaxTailQ337ProgressionProof.nextSubatom.statement + ?? `Prove the q=347 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ337ProgressionProof.nextSubatom.completionRule + ?? 'The q=347 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ337ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=337 two-sided floor-bound component.', + } + : null; + const dMaxTailQ347ProgressionProof = dMaxTailQ347ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ347ProgressionSubatom.atomId) + : null; + const dMaxTailQ349ProgressionSubatom = dMaxTailQ347ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ347ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ347ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ347ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=349 progression contribution', + dependsOn: [dMaxTailQ347ProgressionSubatom?.atomId ?? dMaxTailQ337ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ347ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ347ProgressionProof.jsonPath, + q: dMaxTailQ347ProgressionProof.nextSubatom.q ?? 349, + statement: dMaxTailQ347ProgressionProof.nextSubatom.statement + ?? `Prove the q=349 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ347ProgressionProof.nextSubatom.completionRule + ?? 'The q=349 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ347ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=347 two-sided floor-bound component.', + } + : null; + const dMaxTailQ349ProgressionProof = dMaxTailQ349ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ349ProgressionSubatom.atomId) + : null; + const dMaxTailQ353ProgressionSubatom = dMaxTailQ349ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ349ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ349ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ349ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=353 progression contribution', + dependsOn: [dMaxTailQ349ProgressionSubatom?.atomId ?? dMaxTailQ347ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ349ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ349ProgressionProof.jsonPath, + q: dMaxTailQ349ProgressionProof.nextSubatom.q ?? 353, + statement: dMaxTailQ349ProgressionProof.nextSubatom.statement + ?? `Prove the q=353 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ349ProgressionProof.nextSubatom.completionRule + ?? 'The q=353 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ349ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=349 two-sided floor-bound component.', + } + : null; + const dMaxTailQ353ProgressionProof = dMaxTailQ353ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ353ProgressionSubatom.atomId) + : null; + const dMaxTailQ359ProgressionSubatom = dMaxTailQ353ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ353ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ353ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ353ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=359 progression contribution', + dependsOn: [dMaxTailQ353ProgressionSubatom?.atomId ?? dMaxTailQ349ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ353ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ353ProgressionProof.jsonPath, + q: dMaxTailQ353ProgressionProof.nextSubatom.q ?? 359, + statement: dMaxTailQ353ProgressionProof.nextSubatom.statement + ?? `Prove the q=359 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ353ProgressionProof.nextSubatom.completionRule + ?? 'The q=359 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ353ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=353 two-sided floor-bound component.', + } + : null; + const dMaxTailQ359ProgressionProof = dMaxTailQ359ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ359ProgressionSubatom.atomId) + : null; + const dMaxTailQ367ProgressionSubatom = dMaxTailQ359ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ359ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ359ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ359ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=367 progression contribution', + dependsOn: [dMaxTailQ359ProgressionSubatom?.atomId ?? dMaxTailQ353ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ359ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ359ProgressionProof.jsonPath, + q: dMaxTailQ359ProgressionProof.nextSubatom.q ?? 367, + statement: dMaxTailQ359ProgressionProof.nextSubatom.statement + ?? `Prove the q=367 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ359ProgressionProof.nextSubatom.completionRule + ?? 'The q=367 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ359ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=359 two-sided floor-bound component.', + } + : null; + const dMaxTailQ367ProgressionProof = dMaxTailQ367ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ367ProgressionSubatom.atomId) + : null; + const dMaxTailQ373ProgressionSubatom = dMaxTailQ367ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ367ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ367ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ367ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=373 progression contribution', + dependsOn: [dMaxTailQ367ProgressionSubatom?.atomId ?? dMaxTailQ359ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ367ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ367ProgressionProof.jsonPath, + q: dMaxTailQ367ProgressionProof.nextSubatom.q ?? 373, + statement: dMaxTailQ367ProgressionProof.nextSubatom.statement + ?? `Prove the q=373 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ367ProgressionProof.nextSubatom.completionRule + ?? 'The q=373 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ367ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=367 two-sided floor-bound component.', + } + : null; + const dMaxTailQ373ProgressionProof = dMaxTailQ373ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ373ProgressionSubatom.atomId) + : null; + const dMaxTailQ379ProgressionSubatom = dMaxTailQ373ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ373ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ373ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ373ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=379 progression contribution', + dependsOn: [dMaxTailQ373ProgressionSubatom?.atomId ?? dMaxTailQ367ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ373ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ373ProgressionProof.jsonPath, + q: dMaxTailQ373ProgressionProof.nextSubatom.q ?? 379, + statement: dMaxTailQ373ProgressionProof.nextSubatom.statement + ?? `Prove the q=379 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ373ProgressionProof.nextSubatom.completionRule + ?? 'The q=379 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ373ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=373 two-sided floor-bound component.', + } + : null; + const dMaxTailQ379ProgressionProof = dMaxTailQ379ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ379ProgressionSubatom.atomId) + : null; + const dMaxTailQ383ProgressionSubatom = dMaxTailQ379ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ379ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ379ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ379ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=383 progression contribution', + dependsOn: [dMaxTailQ379ProgressionSubatom?.atomId ?? dMaxTailQ373ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ379ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ379ProgressionProof.jsonPath, + q: dMaxTailQ379ProgressionProof.nextSubatom.q ?? 383, + statement: dMaxTailQ379ProgressionProof.nextSubatom.statement + ?? `Prove the q=383 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ379ProgressionProof.nextSubatom.completionRule + ?? 'The q=383 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ379ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=379 two-sided floor-bound component.', + } + : null; + const dMaxTailQ383ProgressionProof = dMaxTailQ383ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ383ProgressionSubatom.atomId) + : null; + const dMaxTailQ389ProgressionSubatom = dMaxTailQ383ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ383ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ383ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ383ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=389 progression contribution', + dependsOn: [dMaxTailQ383ProgressionSubatom?.atomId ?? dMaxTailQ379ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ383ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ383ProgressionProof.jsonPath, + q: dMaxTailQ383ProgressionProof.nextSubatom.q ?? 389, + statement: dMaxTailQ383ProgressionProof.nextSubatom.statement + ?? `Prove the q=389 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ383ProgressionProof.nextSubatom.completionRule + ?? 'The q=389 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ383ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=383 two-sided floor-bound component.', + } + : null; + const dMaxTailQ389ProgressionProof = dMaxTailQ389ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ389ProgressionSubatom.atomId) + : null; + const dMaxTailQ397ProgressionSubatom = dMaxTailQ389ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ389ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ389ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ389ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=397 progression contribution', + dependsOn: [dMaxTailQ389ProgressionSubatom?.atomId ?? dMaxTailQ383ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ389ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ389ProgressionProof.jsonPath, + q: dMaxTailQ389ProgressionProof.nextSubatom.q ?? 397, + statement: dMaxTailQ389ProgressionProof.nextSubatom.statement + ?? `Prove the q=397 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ389ProgressionProof.nextSubatom.completionRule + ?? 'The q=397 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ389ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=389 two-sided floor-bound component.', + } + : null; + const dMaxTailQ397ProgressionProof = dMaxTailQ397ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ397ProgressionSubatom.atomId) + : null; + const dMaxTailQ401ProgressionSubatom = dMaxTailQ397ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ397ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ397ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ397ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=401 progression contribution', + dependsOn: [dMaxTailQ397ProgressionSubatom?.atomId ?? dMaxTailQ389ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ397ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ397ProgressionProof.jsonPath, + q: dMaxTailQ397ProgressionProof.nextSubatom.q ?? 401, + statement: dMaxTailQ397ProgressionProof.nextSubatom.statement + ?? `Prove the q=401 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ397ProgressionProof.nextSubatom.completionRule + ?? 'The q=401 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ397ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=397 two-sided floor-bound component.', + } + : null; + const dMaxTailQ401ProgressionProof = dMaxTailQ401ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ401ProgressionSubatom.atomId) + : null; + const dMaxTailQ409ProgressionSubatom = dMaxTailQ401ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ401ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ401ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ401ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=409 progression contribution', + dependsOn: [dMaxTailQ401ProgressionSubatom?.atomId ?? dMaxTailQ397ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ401ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ401ProgressionProof.jsonPath, + q: dMaxTailQ401ProgressionProof.nextSubatom.q ?? 409, + statement: dMaxTailQ401ProgressionProof.nextSubatom.statement + ?? `Prove the q=409 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ401ProgressionProof.nextSubatom.completionRule + ?? 'The q=409 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ401ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=401 two-sided floor-bound component.', + } + : null; + const dMaxTailQ409ProgressionProof = dMaxTailQ409ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ409ProgressionSubatom.atomId) + : null; + const dMaxTailQ419ProgressionSubatom = dMaxTailQ409ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ409ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ409ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ409ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=419 progression contribution', + dependsOn: [dMaxTailQ409ProgressionSubatom?.atomId ?? dMaxTailQ401ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ409ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ409ProgressionProof.jsonPath, + q: dMaxTailQ409ProgressionProof.nextSubatom.q ?? 419, + statement: dMaxTailQ409ProgressionProof.nextSubatom.statement + ?? `Prove the q=419 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ409ProgressionProof.nextSubatom.completionRule + ?? 'The q=419 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ409ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=409 two-sided floor-bound component.', + } + : null; + const dMaxTailQ419ProgressionProof = dMaxTailQ419ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ419ProgressionSubatom.atomId) + : null; + const dMaxTailQ421ProgressionSubatom = dMaxTailQ419ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ419ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ419ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ419ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=421 progression contribution', + dependsOn: [dMaxTailQ419ProgressionSubatom?.atomId ?? dMaxTailQ409ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ419ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ419ProgressionProof.jsonPath, + q: dMaxTailQ419ProgressionProof.nextSubatom.q ?? 421, + statement: dMaxTailQ419ProgressionProof.nextSubatom.statement + ?? `Prove the q=421 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ419ProgressionProof.nextSubatom.completionRule + ?? 'The q=421 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ419ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=419 two-sided floor-bound component.', + } + : null; + const dMaxTailQ421ProgressionProof = dMaxTailQ421ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ421ProgressionSubatom.atomId) + : null; + const dMaxTailQ431ProgressionSubatom = dMaxTailQ421ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ421ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ421ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ421ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=431 progression contribution', + dependsOn: [dMaxTailQ421ProgressionSubatom?.atomId ?? dMaxTailQ419ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ421ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ421ProgressionProof.jsonPath, + q: dMaxTailQ421ProgressionProof.nextSubatom.q ?? 431, + statement: dMaxTailQ421ProgressionProof.nextSubatom.statement + ?? `Prove the q=431 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ421ProgressionProof.nextSubatom.completionRule + ?? 'The q=431 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ421ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=421 two-sided floor-bound component.', + } + : null; + const dMaxTailQ431ProgressionProof = dMaxTailQ431ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ431ProgressionSubatom.atomId) + : null; + const dMaxTailQ433ProgressionSubatom = dMaxTailQ431ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ431ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ431ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ431ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=433 progression contribution', + dependsOn: [dMaxTailQ431ProgressionSubatom?.atomId ?? dMaxTailQ421ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ431ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ431ProgressionProof.jsonPath, + q: dMaxTailQ431ProgressionProof.nextSubatom.q ?? 433, + statement: dMaxTailQ431ProgressionProof.nextSubatom.statement + ?? `Prove the q=433 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ431ProgressionProof.nextSubatom.completionRule + ?? 'The q=433 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ431ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=431 two-sided floor-bound component.', + } + : null; + const dMaxTailQ433ProgressionProof = dMaxTailQ433ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ433ProgressionSubatom.atomId) + : null; + const dMaxTailQ439ProgressionSubatom = dMaxTailQ433ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ433ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ433ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ433ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=439 progression contribution', + dependsOn: [dMaxTailQ433ProgressionSubatom?.atomId ?? dMaxTailQ431ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ433ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ433ProgressionProof.jsonPath, + q: dMaxTailQ433ProgressionProof.nextSubatom.q ?? 439, + statement: dMaxTailQ433ProgressionProof.nextSubatom.statement + ?? `Prove the q=439 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ433ProgressionProof.nextSubatom.completionRule + ?? 'The q=439 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ433ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=433 two-sided floor-bound component.', + } + : null; + const dMaxTailQ439ProgressionProof = dMaxTailQ439ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ439ProgressionSubatom.atomId) + : null; + const dMaxTailQ443ProgressionSubatom = dMaxTailQ439ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ439ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ439ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ439ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=443 progression contribution', + dependsOn: [dMaxTailQ439ProgressionSubatom?.atomId ?? dMaxTailQ433ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ439ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ439ProgressionProof.jsonPath, + q: dMaxTailQ439ProgressionProof.nextSubatom.q ?? 443, + statement: dMaxTailQ439ProgressionProof.nextSubatom.statement + ?? `Prove the q=443 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ439ProgressionProof.nextSubatom.completionRule + ?? 'The q=443 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ439ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=439 two-sided floor-bound component.', + } + : null; + const dMaxTailQ443ProgressionProof = dMaxTailQ443ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ443ProgressionSubatom.atomId) + : null; + const dMaxTailQ449ProgressionSubatom = dMaxTailQ443ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ443ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ443ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ443ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=449 progression contribution', + dependsOn: [dMaxTailQ443ProgressionSubatom?.atomId ?? dMaxTailQ439ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ443ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ443ProgressionProof.jsonPath, + q: dMaxTailQ443ProgressionProof.nextSubatom.q ?? 449, + statement: dMaxTailQ443ProgressionProof.nextSubatom.statement + ?? `Prove the q=449 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ443ProgressionProof.nextSubatom.completionRule + ?? 'The q=449 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ443ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=443 two-sided floor-bound component.', + } + : null; + const dMaxTailQ449ProgressionProof = dMaxTailQ449ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ449ProgressionSubatom.atomId) + : null; + const dMaxTailQ457ProgressionSubatom = dMaxTailQ449ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ449ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ449ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ449ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=457 progression contribution', + dependsOn: [dMaxTailQ449ProgressionSubatom?.atomId ?? dMaxTailQ443ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ449ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ449ProgressionProof.jsonPath, + q: dMaxTailQ449ProgressionProof.nextSubatom.q ?? 457, + statement: dMaxTailQ449ProgressionProof.nextSubatom.statement + ?? `Prove the q=457 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ449ProgressionProof.nextSubatom.completionRule + ?? 'The q=457 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ449ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=449 two-sided floor-bound component.', + } + : null; + const dMaxTailQ457ProgressionProof = dMaxTailQ457ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ457ProgressionSubatom.atomId) + : null; + const dMaxTailQ461ProgressionSubatom = dMaxTailQ457ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ457ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ457ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ457ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=461 progression contribution', + dependsOn: [dMaxTailQ457ProgressionSubatom?.atomId ?? dMaxTailQ449ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ457ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ457ProgressionProof.jsonPath, + q: dMaxTailQ457ProgressionProof.nextSubatom.q ?? 461, + statement: dMaxTailQ457ProgressionProof.nextSubatom.statement + ?? `Prove the q=461 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ457ProgressionProof.nextSubatom.completionRule + ?? 'The q=461 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ457ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=457 two-sided floor-bound component.', + } + : null; + const dMaxTailQ461ProgressionProof = dMaxTailQ461ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ461ProgressionSubatom.atomId) + : null; + const dMaxTailQ463ProgressionSubatom = dMaxTailQ461ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ461ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ461ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ461ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=463 progression contribution', + dependsOn: [dMaxTailQ461ProgressionSubatom?.atomId ?? dMaxTailQ457ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ461ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ461ProgressionProof.jsonPath, + q: dMaxTailQ461ProgressionProof.nextSubatom.q ?? 463, + statement: dMaxTailQ461ProgressionProof.nextSubatom.statement + ?? `Prove the q=463 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ461ProgressionProof.nextSubatom.completionRule + ?? 'The q=463 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ461ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=461 two-sided floor-bound component.', + } + : null; + const dMaxTailQ463ProgressionProof = dMaxTailQ463ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ463ProgressionSubatom.atomId) + : null; + const dMaxTailQ467ProgressionSubatom = dMaxTailQ463ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ463ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ463ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ463ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=467 progression contribution', + dependsOn: [dMaxTailQ463ProgressionSubatom?.atomId ?? dMaxTailQ461ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ463ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ463ProgressionProof.jsonPath, + q: dMaxTailQ463ProgressionProof.nextSubatom.q ?? 467, + statement: dMaxTailQ463ProgressionProof.nextSubatom.statement + ?? `Prove the q=467 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ463ProgressionProof.nextSubatom.completionRule + ?? 'The q=467 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ463ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=463 two-sided floor-bound component.', + } + : null; + const dMaxTailQ467ProgressionProof = dMaxTailQ467ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ467ProgressionSubatom.atomId) + : null; + const dMaxTailQ479ProgressionSubatom = dMaxTailQ467ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ467ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ467ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ467ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=479 progression contribution', + dependsOn: [dMaxTailQ467ProgressionSubatom?.atomId ?? dMaxTailQ463ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ467ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ467ProgressionProof.jsonPath, + q: dMaxTailQ467ProgressionProof.nextSubatom.q ?? 479, + statement: dMaxTailQ467ProgressionProof.nextSubatom.statement + ?? `Prove the q=479 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ467ProgressionProof.nextSubatom.completionRule + ?? 'The q=479 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ467ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=467 two-sided floor-bound component.', + } + : null; + const dMaxTailQ479ProgressionProof = dMaxTailQ479ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ479ProgressionSubatom.atomId) + : null; + const dMaxTailQ487ProgressionSubatom = dMaxTailQ479ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ479ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ479ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ479ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=487 progression contribution', + dependsOn: [dMaxTailQ479ProgressionSubatom?.atomId ?? dMaxTailQ467ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ479ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ479ProgressionProof.jsonPath, + q: dMaxTailQ479ProgressionProof.nextSubatom.q ?? 487, + statement: dMaxTailQ479ProgressionProof.nextSubatom.statement + ?? `Prove the q=487 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ479ProgressionProof.nextSubatom.completionRule + ?? 'The q=487 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ479ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=479 two-sided floor-bound component.', + } + : null; + const dMaxTailQ487ProgressionProof = dMaxTailQ487ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ487ProgressionSubatom.atomId) + : null; + const dMaxTailQ491ProgressionSubatom = dMaxTailQ487ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ487ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ487ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ487ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=491 progression contribution', + dependsOn: [dMaxTailQ487ProgressionSubatom?.atomId ?? dMaxTailQ479ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ487ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ487ProgressionProof.jsonPath, + q: dMaxTailQ487ProgressionProof.nextSubatom.q ?? 491, + statement: dMaxTailQ487ProgressionProof.nextSubatom.statement + ?? `Prove the q=491 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ487ProgressionProof.nextSubatom.completionRule + ?? 'The q=491 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ487ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=487 two-sided floor-bound component.', + } + : null; + const dMaxTailQ491ProgressionProof = dMaxTailQ491ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ491ProgressionSubatom.atomId) + : null; + const dMaxTailQ499ProgressionSubatom = dMaxTailQ491ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ491ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ491ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ491ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=499 progression contribution', + dependsOn: [dMaxTailQ491ProgressionSubatom?.atomId ?? dMaxTailQ487ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ491ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ491ProgressionProof.jsonPath, + q: dMaxTailQ491ProgressionProof.nextSubatom.q ?? 499, + statement: dMaxTailQ491ProgressionProof.nextSubatom.statement + ?? `Prove the q=499 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ491ProgressionProof.nextSubatom.completionRule + ?? 'The q=499 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ491ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=491 two-sided floor-bound component.', + } + : null; + const dMaxTailQ499ProgressionProof = dMaxTailQ499ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ499ProgressionSubatom.atomId) + : null; + const dMaxTailQ503ProgressionSubatom = dMaxTailQ499ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ499ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ499ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ499ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=503 progression contribution', + dependsOn: [dMaxTailQ499ProgressionSubatom?.atomId ?? dMaxTailQ491ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ499ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ499ProgressionProof.jsonPath, + q: dMaxTailQ499ProgressionProof.nextSubatom.q ?? 503, + statement: dMaxTailQ499ProgressionProof.nextSubatom.statement + ?? `Prove the q=503 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ499ProgressionProof.nextSubatom.completionRule + ?? 'The q=503 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ499ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=499 two-sided floor-bound component.', + } + : null; + const dMaxTailQ503ProgressionProof = dMaxTailQ503ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ503ProgressionSubatom.atomId) + : null; + const dMaxTailQ509ProgressionSubatom = dMaxTailQ503ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ503ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ503ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ503ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=509 progression contribution', + dependsOn: [dMaxTailQ503ProgressionSubatom?.atomId ?? dMaxTailQ499ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ503ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ503ProgressionProof.jsonPath, + q: dMaxTailQ503ProgressionProof.nextSubatom.q ?? 509, + statement: dMaxTailQ503ProgressionProof.nextSubatom.statement + ?? `Prove the q=509 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ503ProgressionProof.nextSubatom.completionRule + ?? 'The q=509 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ503ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=503 two-sided floor-bound component.', + } + : null; + const dMaxTailQ509ProgressionProof = dMaxTailQ509ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ509ProgressionSubatom.atomId) + : null; + const dMaxTailQ521ProgressionSubatom = dMaxTailQ509ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ509ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ509ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ509ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=521 progression contribution', + dependsOn: [dMaxTailQ509ProgressionSubatom?.atomId ?? dMaxTailQ503ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ509ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ509ProgressionProof.jsonPath, + q: dMaxTailQ509ProgressionProof.nextSubatom.q ?? 521, + statement: dMaxTailQ509ProgressionProof.nextSubatom.statement + ?? `Prove the q=521 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ509ProgressionProof.nextSubatom.completionRule + ?? 'The q=521 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ509ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=509 two-sided floor-bound component.', + } + : null; + const dMaxTailQ521ProgressionProof = dMaxTailQ521ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ521ProgressionSubatom.atomId) + : null; + const dMaxTailQ523ProgressionSubatom = dMaxTailQ521ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ521ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ521ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ521ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=523 progression contribution', + dependsOn: [dMaxTailQ521ProgressionSubatom?.atomId ?? dMaxTailQ509ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ521ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ521ProgressionProof.jsonPath, + q: dMaxTailQ521ProgressionProof.nextSubatom.q ?? 523, + statement: dMaxTailQ521ProgressionProof.nextSubatom.statement + ?? `Prove the q=523 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ521ProgressionProof.nextSubatom.completionRule + ?? 'The q=523 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ521ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=521 two-sided floor-bound component.', + } + : null; + const dMaxTailQ523ProgressionProof = dMaxTailQ523ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ523ProgressionSubatom.atomId) + : null; + const dMaxTailQ541ProgressionSubatom = dMaxTailQ523ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ523ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ523ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ523ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=541 progression contribution', + dependsOn: [dMaxTailQ523ProgressionSubatom?.atomId ?? dMaxTailQ521ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ523ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ523ProgressionProof.jsonPath, + q: dMaxTailQ523ProgressionProof.nextSubatom.q ?? 541, + statement: dMaxTailQ523ProgressionProof.nextSubatom.statement + ?? `Prove the q=541 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ523ProgressionProof.nextSubatom.completionRule + ?? 'The q=541 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ523ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=523 two-sided floor-bound component.', + } + : null; + const dMaxTailQ541ProgressionProof = dMaxTailQ541ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ541ProgressionSubatom.atomId) + : null; + const dMaxTailQ547ProgressionSubatom = dMaxTailQ541ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ541ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ541ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ541ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=547 progression contribution', + dependsOn: [dMaxTailQ541ProgressionSubatom?.atomId ?? dMaxTailQ523ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ541ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ541ProgressionProof.jsonPath, + q: dMaxTailQ541ProgressionProof.nextSubatom.q ?? 547, + statement: dMaxTailQ541ProgressionProof.nextSubatom.statement + ?? `Prove the q=547 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ541ProgressionProof.nextSubatom.completionRule + ?? 'The q=547 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ541ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=541 two-sided floor-bound component.', + } + : null; + const dMaxTailQ547ProgressionProof = dMaxTailQ547ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ547ProgressionSubatom.atomId) + : null; + const dMaxTailQ557ProgressionSubatom = dMaxTailQ547ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ547ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ547ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ547ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=557 progression contribution', + dependsOn: [dMaxTailQ547ProgressionSubatom?.atomId ?? dMaxTailQ541ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ547ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ547ProgressionProof.jsonPath, + q: dMaxTailQ547ProgressionProof.nextSubatom.q ?? 557, + statement: dMaxTailQ547ProgressionProof.nextSubatom.statement + ?? `Prove the q=557 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ547ProgressionProof.nextSubatom.completionRule + ?? 'The q=557 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ547ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=547 two-sided floor-bound component.', + } + : null; + const dMaxTailQ557ProgressionProof = dMaxTailQ557ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ557ProgressionSubatom.atomId) + : null; + const dMaxTailQ563ProgressionSubatom = dMaxTailQ557ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ557ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ557ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ557ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=563 progression contribution', + dependsOn: [dMaxTailQ557ProgressionSubatom?.atomId ?? dMaxTailQ547ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ557ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ557ProgressionProof.jsonPath, + q: dMaxTailQ557ProgressionProof.nextSubatom.q ?? 563, + statement: dMaxTailQ557ProgressionProof.nextSubatom.statement + ?? `Prove the q=563 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ557ProgressionProof.nextSubatom.completionRule + ?? 'The q=563 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ557ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=557 two-sided floor-bound component.', + } + : null; + const dMaxTailQ563ProgressionProof = dMaxTailQ563ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ563ProgressionSubatom.atomId) + : null; + const dMaxTailQ569ProgressionSubatom = dMaxTailQ563ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ563ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ563ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ563ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=569 progression contribution', + dependsOn: [dMaxTailQ563ProgressionSubatom?.atomId ?? dMaxTailQ557ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ563ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ563ProgressionProof.jsonPath, + q: dMaxTailQ563ProgressionProof.nextSubatom.q ?? 569, + statement: dMaxTailQ563ProgressionProof.nextSubatom.statement + ?? `Prove the q=569 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ563ProgressionProof.nextSubatom.completionRule + ?? 'The q=569 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ563ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=563 two-sided floor-bound component.', + } + : null; + const dMaxTailQ569ProgressionProof = dMaxTailQ569ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ569ProgressionSubatom.atomId) + : null; + const dMaxTailQ571ProgressionSubatom = dMaxTailQ569ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ569ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ569ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ569ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=571 progression contribution', + dependsOn: [dMaxTailQ569ProgressionSubatom?.atomId ?? dMaxTailQ563ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ569ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ569ProgressionProof.jsonPath, + q: dMaxTailQ569ProgressionProof.nextSubatom.q ?? 571, + statement: dMaxTailQ569ProgressionProof.nextSubatom.statement + ?? `Prove the q=571 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ569ProgressionProof.nextSubatom.completionRule + ?? 'The q=571 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ569ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=569 two-sided floor-bound component.', + } + : null; + const dMaxTailQ571ProgressionProof = dMaxTailQ571ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ571ProgressionSubatom.atomId) + : null; + const dMaxTailQ577ProgressionSubatom = dMaxTailQ571ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ571ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ571ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ571ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=577 progression contribution', + dependsOn: [dMaxTailQ571ProgressionSubatom?.atomId ?? dMaxTailQ569ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ571ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ571ProgressionProof.jsonPath, + q: dMaxTailQ571ProgressionProof.nextSubatom.q ?? 577, + statement: dMaxTailQ571ProgressionProof.nextSubatom.statement + ?? `Prove the q=577 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ571ProgressionProof.nextSubatom.completionRule + ?? 'The q=577 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ571ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=571 two-sided floor-bound component.', + } + : null; + const dMaxTailQ577ProgressionProof = dMaxTailQ577ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ577ProgressionSubatom.atomId) + : null; + const dMaxTailQ587ProgressionSubatom = dMaxTailQ577ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ577ProgressionProof.nextSubatom.atomId, + status: readP848DMaxTailRecombinationProof(problem, dMaxTailQ577ProgressionProof.nextSubatom.atomId)?.status + ?? dMaxTailQ577ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q=587 progression contribution', + dependsOn: [dMaxTailQ577ProgressionSubatom?.atomId ?? dMaxTailQ571ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ577ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ577ProgressionProof.jsonPath, + q: dMaxTailQ577ProgressionProof.nextSubatom.q ?? 587, + statement: dMaxTailQ577ProgressionProof.nextSubatom.statement + ?? `Prove the q=587 same-prime degree tail progression upper bound for both witness sides in ${stratum.splitKey}.`, + completionRule: dMaxTailQ577ProgressionProof.nextSubatom.completionRule + ?? 'The q=587 tail progression contribution is bounded by CRT floor functions for both witnesses, or emits the next unresolved tail atom.', + proofArtifact: (() => { + const proof = readP848DMaxTailRecombinationProof(problem, dMaxTailQ577ProgressionProof.nextSubatom.atomId); + return proof + ? { + proofId: proof.proofId, + jsonPath: proof.jsonPath, + status: proof.status, + proofKind: proof.proofKind, + q: proof.q ?? null, + nextSubatomId: proof.nextSubatom?.atomId ?? null, + } + : null; + })(), + proofBoundary: 'This is the next residual tail-prime subatom after the q=577 two-sided floor-bound component.', + } + : null; + const dMaxTailQ587ProgressionProof = dMaxTailQ587ProgressionSubatom?.proofArtifact?.status === 'symbolic_upper_bound_verified' + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ587ProgressionSubatom.atomId) + : null; + const dMaxTailQGe587ParametricZeroFloorProof = dMaxTailQ587ProgressionProof?.nextSubatom?.atomId + ? readP848DMaxTailRecombinationProof(problem, dMaxTailQ587ProgressionProof.nextSubatom.atomId) + : null; + const dMaxTailQGe587ParametricZeroFloorSubatom = dMaxTailQ587ProgressionProof?.nextSubatom?.atomId + ? { + atomId: dMaxTailQ587ProgressionProof.nextSubatom.atomId, + status: dMaxTailQGe587ParametricZeroFloorProof?.status + ?? dMaxTailQ587ProgressionProof.nextSubatom.status + ?? 'needed', + term: 'dMax tail q>=587 parametric zero-floor lift', + dependsOn: [dMaxTailQ587ProgressionSubatom?.atomId ?? dMaxTailQ577ProgressionSubatom?.atomId ?? dMaxGrowthSubatomId], + predecessorProofId: dMaxTailQ587ProgressionProof.proofId, + predecessorProofJsonPath: dMaxTailQ587ProgressionProof.jsonPath, + qRange: dMaxTailQ587ProgressionProof.nextSubatom.qRange ?? 'q>=587', + statement: dMaxTailQ587ProgressionProof.nextSubatom.statement + ?? `Lift the q>=587 tail-prime zero-floor profile into a parametric tail lemma for ${stratum.splitKey}.`, + completionRule: dMaxTailQ587ProgressionProof.nextSubatom.completionRule + ?? 'Either prove the q>=587 aggregate tail lemma or emit the first named exceptional prime/range that prevents it.', + boundedRangeProfile: dMaxTailQ587ProgressionProof.remainingTailRangeProfile + ? { + status: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.status, + profileRange: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.profileRange, + startPrime: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.startPrime, + plusWitnessProductCutoff: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.plusWitnessProductCutoff, + minusWitnessProductCutoff: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.minusWitnessProductCutoff, + scannedWitnessSideRowCount: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.scannedWitnessSideRowCount, + nonzeroRawFloorCount: dMaxTailQ587ProgressionProof.remainingTailRangeProfile.nonzeroRawFloorCount, + } + : null, + proofArtifact: dMaxTailQGe587ParametricZeroFloorProof + ? { + proofId: dMaxTailQGe587ParametricZeroFloorProof.proofId, + jsonPath: dMaxTailQGe587ParametricZeroFloorProof.jsonPath, + status: dMaxTailQGe587ParametricZeroFloorProof.status, + proofKind: dMaxTailQGe587ParametricZeroFloorProof.proofKind, + qRange: dMaxTailQGe587ParametricZeroFloorProof.qRange?.statement + ?? dMaxTailQGe587ParametricZeroFloorProof.qRange + ?? null, + nextSubatomId: dMaxTailQGe587ParametricZeroFloorProof.nextSubatom?.atomId ?? null, + } + : null, + proofBoundary: 'This aggregate handoff is bounded-profile evidence only; it must be lifted before any all-N dMax tail or side-count-floor claim.', + } + : null; + const dMaxTailQGe587ParametricZeroFloorVerified = [ + 'bounded_parametric_zero_floor_verified', + 'symbolic_upper_bound_verified', + ].includes(dMaxTailQGe587ParametricZeroFloorSubatom?.proofArtifact?.status); + const dynamicMarginSubatomId = `D2_p13_dynamic_margin_${sanitizeP848PacketFileStem(stratum.splitKey)}_${largerSideLabel}`; + const structuralMarginVerified = Number.isFinite(Number(stratum.minStructuralMargin)) + && Number(stratum.minStructuralMargin) >= 0; + const dynamicMarginProof = readP848DynamicMarginProof(problem, dynamicMarginSubatomId); + const dynamicMarginSymbolicLiftProof = dynamicMarginProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedSuccessorProof = dynamicMarginSymbolicLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginSymbolicLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedSymbolicLiftProof = dynamicMarginExactMixedSuccessorProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedSuccessorProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionProof = dynamicMarginExactMixedSymbolicLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionParametricLiftProof = dynamicMarginExactMixedMatchingInjectionProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionFiniteMenuProof = dynamicMarginExactMixedMatchingInjectionParametricLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof = dynamicMarginExactMixedMatchingInjectionFiniteMenuProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof = dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof = dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof = dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof = dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.atomId) + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof?.nextSubatom?.atomId + ? readP848DynamicMarginProof(problem, dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.atomId) + : null; + const dMaxSubatom = { + atomId: dMaxSubatomId, + status: dMaxBoundProbe?.status === 'bounded_counterexample_to_constant_dmax_bound' + ? 'bounded_constant_bound_falsified_successor_atom_needed' + : 'needed', + term: 'dMax', + targetBound: dMaxBudget, + boundedRange: { + min: stratum.minDMax, + max: stratum.maxDMax, + }, + statement: dMaxBudget === null + ? `Prove a symbolic dMax bound for ${stratum.splitKey}.` + : `For every future p=13 threat row with ${stratum.splitKey}, prove dMax <= ${dMaxBudget}.`, + probeArtifact: dMaxBoundProbe + ? { + probeId: dMaxBoundProbe.probeId, + jsonPath: dMaxBoundProbe.jsonPath, + status: dMaxBoundProbe.status, + probeRange: dMaxBoundProbe.probeRange, + targetRowCount: dMaxBoundProbe.targetRowCount, + firstCounterexample: dMaxBoundProbe.firstCounterexample ?? null, + maxObservedDMax: dMaxBoundProbe.maxObservedDMax ?? null, + successorAtomId: dMaxBoundProbe.successorAtomId ?? dMaxGrowthSubatomId, + } + : null, + successorAtomId: dMaxBoundProbe?.successorAtomId ?? null, + proofBoundary: dMaxBoundProbe?.proofBoundary + ?? 'This isolates the maximum same-prime cross-degree term from the structural margin. The bounded constant value is not an all-N proof.', + }; + const dMaxGrowthSubatom = dMaxBoundProbe + ? { + atomId: dMaxGrowthSubatomId, + status: dMaxGrowthProfile ? 'bounded_growth_profile_emitted_subatom_needed' : 'needed', + term: 'dMax growth envelope', + dependsOn: [dMaxSubatomId], + replacesFalseAtomId: dMaxSubatomId, + targetBound: dMaxBudget, + firstCounterexample: dMaxBoundProbe.firstCounterexample ?? null, + maxObservedDMax: dMaxBoundProbe.maxObservedDMax ?? null, + growthProfile: dMaxGrowthProfile + ? { + profileId: dMaxGrowthProfile.profileId, + jsonPath: dMaxGrowthProfile.jsonPath, + status: dMaxGrowthProfile.status, + probeRange: dMaxGrowthProfile.probeRange, + firstOpenSubatomId: dMaxGrowthProfile.firstOpenSubatomId ?? dMaxGrowthFirstSubatom?.atomId ?? null, + growthWitnessCount: Array.isArray(dMaxGrowthProfile.growthWitnesses) + ? dMaxGrowthProfile.growthWitnesses.length + : null, + } + : null, + statement: `Replace the false constant dMax <= ${dMaxBudget ?? '(bounded value)'} with a symbolic same-prime degree-growth envelope for ${stratum.splitKey}.`, + proofBoundary: 'This successor atom is required because the extended local probe found the same split with dMax above the original bounded constant.', + } + : null; + const dynamicMarginSubatom = { + atomId: dynamicMarginSubatomId, + status: dynamicMarginProof?.status + ?? (dMaxTailQGe587ParametricZeroFloorVerified + ? 'needed_after_dmax_tail_range_lift' + : dMaxBoundProbe ? 'blocked_by_dmax_growth_envelope' : 'needed_after_dmax_bound'), + term: `${largerSideLabel}Count + vMax + rGreater`, + dependsOn: [dMaxGrowthSubatom?.atomId ?? dMaxSubatomId], + residualDynamicMarginConstant, + inequality: residualDynamicMarginConstant === null + ? null + : `${largerSideLabel}Count + vMax + rGreater + ${residualDynamicMarginConstant} <= candidateSize`, + boundedMarginRange: { + min: stratum.minStructuralMargin, + max: stratum.maxStructuralMargin, + }, + statement: dMaxBoundProbe + ? `After the dMax growth envelope is proved for ${stratum.splitKey}, recompute the residual dynamic margin; the bounded-budget constant ${residualDynamicMarginConstant ?? '(unknown)'} is not valid as an all-N handoff.` + : residualDynamicMarginConstant === null + ? `After dMax is bounded, prove the residual dynamic margin for ${stratum.splitKey}.` + : `Assuming dMax <= ${dMaxBudget}, prove ${largerSideLabel}Count + vMax + rGreater + ${residualDynamicMarginConstant} <= candidateSize for ${stratum.splitKey}.`, + proofArtifact: dynamicMarginProof + ? { + proofId: dynamicMarginProof.proofId, + jsonPath: dynamicMarginProof.jsonPath, + status: dynamicMarginProof.status, + proofKind: dynamicMarginProof.proofKind, + nextSubatomId: dynamicMarginProof.nextSubatom?.atomId ?? null, + residualDynamicMarginRange: dynamicMarginProof.boundedProfile?.residualDynamicMarginRange ?? null, + } + : null, + proofBoundary: dMaxBoundProbe + ? 'The residual dynamic margin must be re-derived after a symbolic dMax growth envelope replaces the false constant bound.' + : 'This is the coupled moving-count margin left after budgeting dMax. It still needs a symbolic inequality for compatibility counts, p13 root counts, higher-root events, and the base candidate side.', + }; + const dynamicMarginSymbolicLiftSubatom = dynamicMarginProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginProof.nextSubatom.atomId, + status: dynamicMarginSymbolicLiftProof?.status ?? dynamicMarginProof.nextSubatom.status ?? 'needed', + term: `${largerSideLabel} residual dynamic margin symbolic lift`, + dependsOn: [dynamicMarginSubatomId], + predecessorProofId: dynamicMarginProof.proofId, + predecessorProofJsonPath: dynamicMarginProof.jsonPath, + targetInequality: dynamicMarginProof.algebraicReduction?.symbolicLiftTarget ?? null, + statement: dynamicMarginProof.nextSubatom.statement + ?? `Lift the residual dynamic-margin replay for ${stratum.splitKey} into a symbolic side-count threshold lemma.`, + completionRule: dynamicMarginProof.nextSubatom.completionRule + ?? 'The residual dynamic margin is proved symbolically, or the first exact obstruction becomes a sharper successor atom.', + proofArtifact: dynamicMarginSymbolicLiftProof + ? { + proofId: dynamicMarginSymbolicLiftProof.proofId, + jsonPath: dynamicMarginSymbolicLiftProof.jsonPath, + status: dynamicMarginSymbolicLiftProof.status, + proofKind: dynamicMarginSymbolicLiftProof.proofKind, + targetInequality: dynamicMarginSymbolicLiftProof.targetInequality ?? null, + firstObstruction: dynamicMarginSymbolicLiftProof.firstObstruction + ? { + N: dynamicMarginSymbolicLiftProof.firstObstruction.N, + outsider: dynamicMarginSymbolicLiftProof.firstObstruction.outsider, + targetLeftSide: dynamicMarginSymbolicLiftProof.firstObstruction.targetLeftSide, + targetDeficit: dynamicMarginSymbolicLiftProof.firstObstruction.targetDeficit, + } + : null, + nextSubatomId: dynamicMarginSymbolicLiftProof.nextSubatom?.atomId ?? null, + } + : null, + proofBoundary: dynamicMarginSymbolicLiftProof?.proofBoundary + ?? 'This is the theorem-facing symbolic lift left after the bounded residual dynamic-margin replay; do not promote the bounded replay itself as an all-N proof.', + } + : null; + const dynamicMarginSymbolicLiftSuccessorSubatom = dynamicMarginSymbolicLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginSymbolicLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedSuccessorProof?.status ?? dynamicMarginSymbolicLiftProof.nextSubatom.status ?? 'needed', + term: dynamicMarginSymbolicLiftProof.nextSubatom.term ?? `${largerSideLabel} exact mixed-margin successor`, + dependsOn: [dynamicMarginProof.nextSubatom.atomId], + predecessorProofId: dynamicMarginSymbolicLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginSymbolicLiftProof.jsonPath, + replacesFalseAtomId: dynamicMarginProof.nextSubatom.atomId, + targetInequality: dynamicMarginExactMixedSuccessorProof?.targetInequality + ?? dynamicMarginSymbolicLiftProof.nextSubatom.targetInequality + ?? null, + firstObstruction: dynamicMarginSymbolicLiftProof.firstObstruction ?? null, + statement: dynamicMarginSymbolicLiftProof.nextSubatom.statement + ?? `Replace the false ${largerSideLabel} threshold lift for ${stratum.splitKey} with an exact mixed-margin successor atom.`, + completionRule: dynamicMarginSymbolicLiftProof.nextSubatom.completionRule + ?? 'The exact mixed-margin successor is proved symbolically, or the first sharper residue/root-universe obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedSuccessorProof + ? { + proofId: dynamicMarginExactMixedSuccessorProof.proofId, + jsonPath: dynamicMarginExactMixedSuccessorProof.jsonPath, + status: dynamicMarginExactMixedSuccessorProof.status, + proofKind: dynamicMarginExactMixedSuccessorProof.proofKind, + boundedRowCount: dynamicMarginExactMixedSuccessorProof.boundedProfile?.rowCount ?? null, + exactMixedMarginRange: dynamicMarginExactMixedSuccessorProof.boundedProfile?.exactMixedMarginRange ?? null, + allRowsSaturateSmallerSide: dynamicMarginExactMixedSuccessorProof.boundedProfile?.allRowsSaturateSmallerSide ?? null, + nextSubatomId: dynamicMarginExactMixedSuccessorProof.nextSubatom?.atomId ?? null, + } + : null, + proofBoundary: dynamicMarginExactMixedSuccessorProof?.proofBoundary + ?? dynamicMarginSymbolicLiftProof.nextSubatom.proofBoundary + ?? 'This successor exists because the proposed side-count threshold lift is falsified by a bounded future-row/root-universe obstruction.', + } + : null; + const dynamicMarginExactMixedSymbolicLiftSubatom = dynamicMarginExactMixedSuccessorProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedSuccessorProof.nextSubatom.atomId, + status: dynamicMarginExactMixedSymbolicLiftProof?.status + ?? dynamicMarginExactMixedSuccessorProof.nextSubatom.status + ?? 'needed', + term: `${largerSideLabel} exact mixed-margin symbolic lift`, + dependsOn: [dynamicMarginSymbolicLiftSuccessorSubatom?.atomId ?? dynamicMarginProof.nextSubatom.atomId], + predecessorProofId: dynamicMarginExactMixedSuccessorProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedSuccessorProof.jsonPath, + targetInequality: dynamicMarginExactMixedSuccessorProof.targetInequality ?? null, + statement: dynamicMarginExactMixedSuccessorProof.nextSubatom.statement + ?? `Lift the exact mixed-margin successor for ${stratum.splitKey} into a symbolic matching-saturation and margin lemma.`, + completionRule: dynamicMarginExactMixedSuccessorProof.nextSubatom.completionRule + ?? 'The exact mixed-margin successor is proved symbolically, or the first sharper residue/root-universe obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedSymbolicLiftProof + ? { + proofId: dynamicMarginExactMixedSymbolicLiftProof.proofId, + jsonPath: dynamicMarginExactMixedSymbolicLiftProof.jsonPath, + status: dynamicMarginExactMixedSymbolicLiftProof.status, + proofKind: dynamicMarginExactMixedSymbolicLiftProof.proofKind, + nextSubatomId: dynamicMarginExactMixedSymbolicLiftProof.nextSubatom?.atomId ?? null, + } + : null, + proofBoundary: dynamicMarginExactMixedSuccessorProof.nextSubatom.proofBoundary + ?? 'This symbolic lift is required because the exact mixed-margin successor is only bounded-profile evidence so far.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSubatom = dynamicMarginExactMixedSymbolicLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionProof?.status + ?? dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching injection`, + dependsOn: [dynamicMarginExactMixedSymbolicLiftSubatom?.atomId ?? dynamicMarginSymbolicLiftSuccessorSubatom?.atomId ?? dynamicMarginProof.nextSubatom.atomId], + predecessorProofId: dynamicMarginExactMixedSymbolicLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedSymbolicLiftProof.jsonPath, + targetInequality: dynamicMarginExactMixedSymbolicLiftProof.symbolicReduction?.matchingSaturationSublemma?.statement + ?? dynamicMarginExactMixedSymbolicLiftProof.targetInequality + ?? null, + statement: dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.statement + ?? `Prove the missing-cross matching injection for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.completionRule + ?? 'The matching injection saturates the smaller side, or the first residue/root-universe obstruction is emitted.', + nextAfterDischarge: dynamicMarginExactMixedSymbolicLiftProof.nextSubatom.nextAfterDischarge ?? null, + proofArtifact: dynamicMarginExactMixedMatchingInjectionProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionProof.proofKind, + sourceRowCount: dynamicMarginExactMixedMatchingInjectionProof.boundedPrefixProfile?.sourceRowCount ?? null, + stableCorePairCount: dynamicMarginExactMixedMatchingInjectionProof.boundedPrefixProfile?.stableCorePairCount ?? null, + extensionPairCount: dynamicMarginExactMixedMatchingInjectionProof.boundedPrefixProfile?.extensionPairCount ?? null, + extendedEventMaxN: dynamicMarginExactMixedMatchingInjectionProof.extendedEventProbe?.maxN ?? null, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedSymbolicLiftProof.proofId, + jsonPath: dynamicMarginExactMixedSymbolicLiftProof.jsonPath, + status: dynamicMarginExactMixedSymbolicLiftProof.status, + proofKind: dynamicMarginExactMixedSymbolicLiftProof.proofKind, + remainingSubatomIds: Array.isArray(dynamicMarginExactMixedSymbolicLiftProof.remainingSubatoms) + ? dynamicMarginExactMixedSymbolicLiftProof.remainingSubatoms.map((subatom) => subatom.atomId).filter(Boolean) + : [], + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionProof?.proofBoundary + ?? dynamicMarginExactMixedSymbolicLiftProof.proofBoundary + ?? 'This is the first symbolic sublemma needed by the exact mixed-margin lift; bounded matching evidence alone is not enough.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom = dynamicMarginExactMixedMatchingInjectionProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionParametricLiftProof?.status + ?? dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection parametric lift`, + dependsOn: [dynamicMarginExactMixedMatchingInjectionSubatom?.atomId ?? dynamicMarginExactMixedSymbolicLiftSubatom?.atomId], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionProof.jsonPath, + targetInequality: dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.targetInequality + ?? dynamicMarginExactMixedMatchingInjectionProof.targetInjection + ?? null, + statement: dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.statement + ?? `Turn the bounded matching-injection profile for ${stratum.splitKey} into a parametric prefix-extension proof.`, + completionRule: dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.completionRule + ?? 'The parametric injection lift saturates the smaller side, or the first future event-row obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionParametricLiftProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionProof.proofKind, + sourceRowCount: dynamicMarginExactMixedMatchingInjectionProof.boundedPrefixProfile?.sourceRowCount ?? null, + extendedEventMaxN: dynamicMarginExactMixedMatchingInjectionProof.extendedEventProbe?.maxN ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionParametricLiftProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionProof.nextSubatom.proofBoundary + ?? 'This parametric lift is required because the matching-injection profile is bounded evidence only.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom = dynamicMarginExactMixedMatchingInjectionParametricLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof?.status + ?? dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection augmenting menu`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSubatom?.atomId + ?? dynamicMarginExactMixedSymbolicLiftSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.jsonPath, + targetInequality: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.targetInjection + ?? dynamicMarginExactMixedMatchingInjectionProof?.targetInjection + ?? null, + statement: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.statement + ?? `Prove the finite augmenting-path menu for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.completionRule + ?? 'The finite augmenting menu saturates the smaller side, or the first future event-row obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.proofKind, + boundedEventMaxN: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.boundedEventScan?.maxN ?? null, + directInsertionCount: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.onlineAugmentingPathProfile?.directInsertionCount ?? null, + replacementPathCount: dynamicMarginExactMixedMatchingInjectionParametricLiftProof.onlineAugmentingPathProfile?.replacementPathCount ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionParametricLiftProof.nextSubatom.proofBoundary + ?? 'This finite-menu target is required because the online augmentation profile is bounded evidence only.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorSubatom = dynamicMarginExactMixedMatchingInjectionFiniteMenuProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof?.status + ?? dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection direct-delta successor`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.jsonPath, + targetEdge: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.targetEdge + ?? dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.successorDirectEdgeWitness + ?? null, + firstFailure: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.boundedReplayAgainstMenu?.firstFailure ?? null, + statement: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.statement + ?? `Prove the direct-delta successor branch for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.completionRule + ?? 'The direct-delta successor branch is proved symbolically, or the first future event-row obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.proofKind, + firstFailureLeft: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.boundedReplayAgainstMenu?.firstFailure?.left ?? null, + successorDelta: dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.successorDirectEdgeWitness?.delta ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionFiniteMenuProof.nextSubatom.proofBoundary + ?? 'This direct-delta successor exists because the mined finite augmenting menu was falsified by a bounded future event row.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorSubatom = dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof?.status + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection direct-delta -39 successor`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.jsonPath, + targetEdge: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.targetEdge + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.successorDirectEdgeWitness + ?? null, + firstFailure: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.boundedReplayAgainstEnlargedMenu?.firstFailure ?? null, + statement: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.statement + ?? `Prove the direct-delta -39 successor branch for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.completionRule + ?? 'The direct-delta -39 successor branch is proved symbolically, or the first future event-row obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.proofKind, + firstFailureLeft: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.boundedReplayAgainstEnlargedMenu?.firstFailure?.left ?? null, + successorDelta: dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.successorDirectEdgeWitness?.delta ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorProof.nextSubatom.proofBoundary + ?? 'This direct-delta -39 successor exists because the enlarged delta -1089 menu was falsified by a bounded future event row.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftSubatom = dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof?.status + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection residue-parametric delta-selection lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.jsonPath, + seedFailures: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.seedFailures + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.staircaseEvidence?.boundedDirectDeltaRepairs?.map((repair) => repair.failureN) + ?? null, + seedDeltas: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.seedDeltas + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.staircaseEvidence?.boundedDirectDeltaRepairs?.map((repair) => repair.repairDelta) + ?? null, + statement: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.statement + ?? `Prove a residue-parametric delta-selection lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.completionRule + ?? 'A residue-parametric delta-selection theorem replaces the direct-delta staircase, or the first uncovered event row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.proofKind, + firstFailureLeft: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.boundedReplayAgainstEnlargedMenu?.firstFailure?.left ?? null, + generalizationSeedDelta: dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.successorDirectEdgeWitness?.delta ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorProof.nextSubatom.proofBoundary + ?? 'This generalization target exists because repeated bounded direct-delta repairs indicate a growing staircase rather than a finite singleton branch.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftSubatom = dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof?.status + ?? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection residue direct-selector lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.jsonPath, + seedFailures: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.seedFailures + ?? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.seedDirectRepairs?.map((repair) => repair.left) + ?? null, + seedDeltas: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.seedDeltas + ?? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.seedDirectRepairs?.map((repair) => repair.delta) + ?? null, + downstreamSublemmas: Array.isArray(dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.reduction?.sublemmas) + ? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.reduction.sublemmas + .map((sublemma) => sublemma.sublemmaId) + .filter(Boolean) + : [], + statement: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.statement + ?? `Prove a residue direct-selector lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.completionRule + ?? 'A residue selector produces a side18-compatible endpoint for every future event row, or the first uncovered row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.proofKind, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftProof.nextSubatom.proofBoundary + ?? 'This is the first symbolic sublemma of the residue-parametric delta-selection lift; it does not by itself prove the all-N matching injection.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftSubatom = dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof?.status + ?? dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.jsonPath, + selectorRule: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.selectorRule?.name ?? null, + selectedDeltas: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.selectorRule?.formula?.deltaSet ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.statement + ?? `Prove selected cross-squarefreeness for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.completionRule + ?? 'The selected endpoint is a missing-cross edge for every future event row, or the first square-divisor obstruction is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.proofKind, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftProof.nextSubatom.proofBoundary + ?? 'This sublemma proves the selected endpoints are missing-cross edges; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception menu`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.jsonPath, + seedException: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.seedException + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.firstSquareDivisorException + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.statement + ?? `Prove selected cross-squarefree exception menu for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.completionRule + ?? 'A replacement menu handles selected-endpoint square-divisor exceptions, or the first uncovered row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.proofKind, + firstFailureLeft: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.firstSquareDivisorException?.left ?? null, + repairDelta: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.localRepairProbe?.firstValidRepair?.delta ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftProof.nextSubatom.proofBoundary + ?? 'This exception menu is needed because the fixed selected endpoint is not always cross-squarefree.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception finite-window lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.jsonPath, + finiteWindowMenuDeltas: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.finiteWindowMenu?.deltaSet ?? [], + boundedExceptionProfile: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile + ? { + maxN: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile.maxN ?? null, + selectedCrossExceptions: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile.selectedCrossExceptions ?? null, + coveredByFiniteWindowMenu: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile.coveredByFiniteWindowMenu ?? null, + firstUncoveredReplacementRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile.firstUncoveredReplacementRow ?? null, + } + : null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception finite-window lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.completionRule + ?? 'A finite-window replacement selector handles every selected-cross exception, or the first uncovered row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.proofKind, + boundedMaxN: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile?.maxN ?? null, + firstUncoveredReplacementRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.boundedExceptionProfile?.firstUncoveredReplacementRow ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuProof.nextSubatom.proofBoundary + ?? 'This finite-window lift is still an exception-menu sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception right-compatibility escape lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.jsonPath, + seedUncoveredRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.seedUncoveredRow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.firstUncoveredRow?.left + ?? null, + seedEscapeDeltas: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.seedEscapeDeltas + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.finiteWindowMenu?.firstEscapeDeltas + ?? [], + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception right-compatibility escape lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.completionRule + ?? 'A right-compatibility escape selector handles finite-window misses, or the first row with no bounded repair is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.proofKind, + firstUncoveredRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.firstUncoveredRow?.left ?? null, + firstEscapeDeltas: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.finiteWindowMenu?.firstEscapeDeltas ?? [], + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftProof.nextSubatom.proofBoundary + ?? 'This escape lift is still an exception-menu sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception small-prime CRT escape selector lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.seedPrimeSet + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.smallPrimeEscapeProfile?.primeSet + ?? [], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.smallPrimeEscapeProfile?.escapeWindow + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception small-prime CRT escape selector for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.completionRule + ?? 'A symbolic small-prime CRT selector handles right-compatible escape repairs, or the first finite-window miss outside that selector is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.proofKind, + boundedMaxN: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.smallPrimeEscapeProfile?.maxN ?? null, + finiteWindowMisses: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.smallPrimeEscapeProfile?.finiteWindowMisses ?? null, + escapeCovered: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.smallPrimeEscapeProfile?.escapeCovered ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeProof.nextSubatom.proofBoundary + ?? 'This small-prime selector is still an exception-menu sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception p=7 endpoint fallback lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.jsonPath, + seedEndpointPrime: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.seedEndpointPrime + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.symbolicEndpointLemma?.prime + ?? null, + seedDeltaFormula: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.seedDeltaFormula + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.symbolicEndpointLemma?.deltaFormula + ?? null, + seedCrossBadCount: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.seedCrossBadCount + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.boundedFallbackProfile?.p7EndpointCrossBad + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception p=7 endpoint fallback selector for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.completionRule + ?? 'A symbolic cross-squarefree fallback selector handles p=7 endpoint cross-bad rows, or the first finite-window miss outside that fallback rule is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.proofKind, + p7EndpointCrossBad: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.boundedFallbackProfile?.p7EndpointCrossBad ?? null, + smallPrimeFallbackCovered: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.boundedFallbackProfile?.smallPrimeFallbackCovered ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorProof.nextSubatom.proofBoundary + ?? 'The p=7 endpoint proves right-compatibility symbolically; selected cross-squarefreeness and collision-free matching remain separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception period-shifted endpoint menu lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.seedPrimeSet + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.periodShiftedEndpointMenu?.primeSet + ?? [], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.boundedFallbackProfile?.escapeWindow + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception period-shifted endpoint menu lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.completionRule + ?? 'A symbolic finite endpoint-menu lift covers all p=7 endpoint cross-bad rows, or the first row outside the menu is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.proofKind, + p7EndpointCrossBad: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.boundedFallbackProfile?.p7EndpointCrossBad ?? null, + periodShiftedEndpointCovered: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.boundedFallbackProfile?.periodShiftedEndpointCovered ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackProof.nextSubatom.proofBoundary + ?? 'The period-shifted endpoint menu remains a cross-squarefree selector sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception period-shifted endpoint-menu squarefree sieve lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.seedPrimeSet + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.boundedReplay?.allowedRightPrimeSet + ?? [], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.boundedReplay?.escapeWindow + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception period-shifted endpoint-menu squarefree sieve lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.completionRule + ?? 'A symbolic sieve/hitting lemma proves cross-squarefree endpoint existence for the menu, or the first fully cross-blocked row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.proofKind, + boundedMaxN: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.boundedReplay?.maxN ?? null, + firstNoPeriodShiftedEndpoint: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.boundedReplay?.firstNoPeriodShiftedEndpoint ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuProof.nextSubatom.proofBoundary + ?? 'The squarefree sieve lift remains a cross-squarefree selector sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception p7 period-shift plus q17 residual lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.seedPrimeSet + ?? [7, 17], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.boundedProfile?.escapeWindow + ?? null, + residualClass: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.residualClass + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.boundedProfile?.residualClass + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception p7 period-shift plus q17 residual lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.completionRule + ?? 'A symbolic p7-shift plus q17 residual lemma proves cross-squarefree endpoint existence for the menu, or the first q17 residual cross-bad row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.proofKind, + p7PeriodShiftCovered: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.boundedProfile?.p7PeriodShiftCovered ?? null, + p7PeriodShiftResidualCount: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.boundedProfile?.p7PeriodShiftResidualCount ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveProof.nextSubatom.proofBoundary + ?? 'The p7 shift plus q17 residual lift remains a cross-squarefree selector sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception q17 residual cross-bad fallback lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.seedPrimeSet + ?? [11, 19, 23, 31], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.localFallbackSeed?.seedWindow + ?? null, + firstCrossBadSeed: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.firstCrossBadSeed + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.boundedResidualScan?.firstQ17CrossBadRow + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception q17 residual cross-bad fallback lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.completionRule + ?? 'A symbolic fallback selector covers q17 residual cross-bad rows, or the first fully fallback-blocked row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.proofKind, + firstQ17CrossBadRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.boundedResidualScan?.firstQ17CrossBadRow ?? null, + localFallbackSeedCount: Array.isArray(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.localFallbackSeed?.candidateEndpoints) + ? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.localFallbackSeed.candidateEndpoints.length + : null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualProof.nextSubatom.proofBoundary + ?? 'The q17 residual cross-bad fallback lift remains a cross-squarefree selector sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception q17 residual p13-expanded fallback menu lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.seedPrimeSet + ?? [11, 13, 19, 23, 31], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.seedMenu?.escapeWindow + ?? null, + firstRepairSeed: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.firstRepairSeed + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.localP13RepairSeed + ?? null, + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception q17 residual p13-expanded fallback menu lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.completionRule + ?? 'A symbolic expanded fallback selector covers q17 residual cross-bad rows, or the first fully expanded-menu-blocked row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.proofKind, + firstFullyFallbackBlockedRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.firstFullyFallbackBlockedRow ?? null, + localP13RepairSeed: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.localP13RepairSeed ?? null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackProof.nextSubatom.proofBoundary + ?? 'The q17 residual p13-expanded fallback menu lift remains a cross-squarefree selector sublemma; collision-free matching remains separate.', + } + : null; + const dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuSubatom = dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof?.nextSubatom?.atomId + ? { + atomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.atomId, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof?.status + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.status + ?? 'needed', + term: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.term + ?? `${largerSideLabel} exact mixed matching-injection selected cross-squarefree exception q17 residual window-relaxed fallback menu lift`, + dependsOn: [ + dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom?.atomId + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom?.atomId, + ], + predecessorProofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.proofId, + predecessorProofJsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.jsonPath, + seedPrimeSet: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.seedPrimeSet + ?? [23, 31, 37, 41, 61], + seedEscapeWindow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.seedEscapeWindow + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.expandedMenu?.escapeWindow + ?? null, + firstRepairSeeds: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.firstRepairSeeds + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.windowRelaxedRepairSeeds + ?? [], + remainingAfterDischarge: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.remainingAfterDischarge ?? [], + statement: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.statement + ?? `Prove the selected cross-squarefree exception q17 residual window-relaxed fallback menu lift for ${stratum.splitKey}.`, + completionRule: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.completionRule + ?? 'A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows, or the first fully window-relaxed blocked row is emitted.', + proofArtifact: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof + ? { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof.proofKind, + nextSubatomId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof.nextSubatom?.atomId ?? null, + } + : { + proofId: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.proofId, + jsonPath: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.jsonPath, + status: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.status, + proofKind: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.proofKind, + firstFullyExpandedMenuBlockedRow: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.firstFullyExpandedMenuBlockedRow ?? null, + windowRelaxedRepairSeedCount: Array.isArray(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.windowRelaxedRepairSeeds) + ? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.windowRelaxedRepairSeeds.length + : null, + }, + proofBoundary: dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuProof?.proofBoundary + ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuProof.nextSubatom.proofBoundary + ?? 'The q17 residual window-relaxed fallback menu lift remains a cross-squarefree selector sublemma; collision-free matching remains separate.', + } + : null; + const movingTermSubatoms = [ + dMaxSubatom, + ...(dMaxGrowthSubatom ? [dMaxGrowthSubatom] : []), + ...(dMaxGrowthFirstSubatom ? [dMaxGrowthFirstSubatom] : []), + ...(dMaxQ3ProgressionSubatom ? [dMaxQ3ProgressionSubatom] : []), + ...(dMaxQ5ProgressionSubatom ? [dMaxQ5ProgressionSubatom] : []), + ...(dMaxQ7ProgressionSubatom ? [dMaxQ7ProgressionSubatom] : []), + ...(dMaxQ11ProgressionSubatom ? [dMaxQ11ProgressionSubatom] : []), + ...(dMaxQ19ProgressionSubatom ? [dMaxQ19ProgressionSubatom] : []), + ...(dMaxQ23ProgressionSubatom ? [dMaxQ23ProgressionSubatom] : []), + ...(dMaxQ31ProgressionSubatom ? [dMaxQ31ProgressionSubatom] : []), + ...(dMaxQ251ProgressionSubatom ? [dMaxQ251ProgressionSubatom] : []), + ...(dMaxTailRecombinationSubatom ? [dMaxTailRecombinationSubatom] : []), + ...(dMaxTailQ17ProgressionSubatom ? [dMaxTailQ17ProgressionSubatom] : []), + ...(dMaxTailQ19PlusProgressionSubatom ? [dMaxTailQ19PlusProgressionSubatom] : []), + ...(dMaxTailQ11MinusProgressionSubatom ? [dMaxTailQ11MinusProgressionSubatom] : []), + ...(dMaxTailQ23PlusProgressionSubatom ? [dMaxTailQ23PlusProgressionSubatom] : []), + ...(dMaxTailQ31MinusProgressionSubatom ? [dMaxTailQ31MinusProgressionSubatom] : []), + ...(dMaxTailQ251MinusProgressionSubatom ? [dMaxTailQ251MinusProgressionSubatom] : []), + ...(dMaxTailQ29ProgressionSubatom ? [dMaxTailQ29ProgressionSubatom] : []), + ...(dMaxTailQ37ProgressionSubatom ? [dMaxTailQ37ProgressionSubatom] : []), + ...(dMaxTailQ41ProgressionSubatom ? [dMaxTailQ41ProgressionSubatom] : []), + ...(dMaxTailQ43ProgressionSubatom ? [dMaxTailQ43ProgressionSubatom] : []), + ...(dMaxTailQ47ProgressionSubatom ? [dMaxTailQ47ProgressionSubatom] : []), + ...(dMaxTailQ53ProgressionSubatom ? [dMaxTailQ53ProgressionSubatom] : []), + ...(dMaxTailQ59ProgressionSubatom ? [dMaxTailQ59ProgressionSubatom] : []), + ...(dMaxTailQ61ProgressionSubatom ? [dMaxTailQ61ProgressionSubatom] : []), + ...(dMaxTailQ67ProgressionSubatom ? [dMaxTailQ67ProgressionSubatom] : []), + ...(dMaxTailQ71ProgressionSubatom ? [dMaxTailQ71ProgressionSubatom] : []), + ...(dMaxTailQ73ProgressionSubatom ? [dMaxTailQ73ProgressionSubatom] : []), + ...(dMaxTailQ79ProgressionSubatom ? [dMaxTailQ79ProgressionSubatom] : []), + ...(dMaxTailQ83ProgressionSubatom ? [dMaxTailQ83ProgressionSubatom] : []), + ...(dMaxTailQ89ProgressionSubatom ? [dMaxTailQ89ProgressionSubatom] : []), + ...(dMaxTailQ97ProgressionSubatom ? [dMaxTailQ97ProgressionSubatom] : []), + ...(dMaxTailQ101ProgressionSubatom ? [dMaxTailQ101ProgressionSubatom] : []), + ...(dMaxTailQ103ProgressionSubatom ? [dMaxTailQ103ProgressionSubatom] : []), + ...(dMaxTailQ107ProgressionSubatom ? [dMaxTailQ107ProgressionSubatom] : []), + ...(dMaxTailQ109ProgressionSubatom ? [dMaxTailQ109ProgressionSubatom] : []), + ...(dMaxTailQ113ProgressionSubatom ? [dMaxTailQ113ProgressionSubatom] : []), + ...(dMaxTailQ127ProgressionSubatom ? [dMaxTailQ127ProgressionSubatom] : []), + ...(dMaxTailQ131ProgressionSubatom ? [dMaxTailQ131ProgressionSubatom] : []), + ...(dMaxTailQ137ProgressionSubatom ? [dMaxTailQ137ProgressionSubatom] : []), + ...(dMaxTailQ139ProgressionSubatom ? [dMaxTailQ139ProgressionSubatom] : []), + ...(dMaxTailQ149ProgressionSubatom ? [dMaxTailQ149ProgressionSubatom] : []), + ...(dMaxTailQ151ProgressionSubatom ? [dMaxTailQ151ProgressionSubatom] : []), + ...(dMaxTailQ157ProgressionSubatom ? [dMaxTailQ157ProgressionSubatom] : []), + ...(dMaxTailQ163ProgressionSubatom ? [dMaxTailQ163ProgressionSubatom] : []), + ...(dMaxTailQ167ProgressionSubatom ? [dMaxTailQ167ProgressionSubatom] : []), + ...(dMaxTailQ173ProgressionSubatom ? [dMaxTailQ173ProgressionSubatom] : []), + ...(dMaxTailQ179ProgressionSubatom ? [dMaxTailQ179ProgressionSubatom] : []), + ...(dMaxTailQ181ProgressionSubatom ? [dMaxTailQ181ProgressionSubatom] : []), + ...(dMaxTailQ191ProgressionSubatom ? [dMaxTailQ191ProgressionSubatom] : []), + ...(dMaxTailQ193ProgressionSubatom ? [dMaxTailQ193ProgressionSubatom] : []), + ...(dMaxTailQ197ProgressionSubatom ? [dMaxTailQ197ProgressionSubatom] : []), + ...(dMaxTailQ199ProgressionSubatom ? [dMaxTailQ199ProgressionSubatom] : []), + ...(dMaxTailQ211ProgressionSubatom ? [dMaxTailQ211ProgressionSubatom] : []), + ...(dMaxTailQ223ProgressionSubatom ? [dMaxTailQ223ProgressionSubatom] : []), + ...(dMaxTailQ227ProgressionSubatom ? [dMaxTailQ227ProgressionSubatom] : []), + ...(dMaxTailQ229ProgressionSubatom ? [dMaxTailQ229ProgressionSubatom] : []), + ...(dMaxTailQ233ProgressionSubatom ? [dMaxTailQ233ProgressionSubatom] : []), + ...(dMaxTailQ239ProgressionSubatom ? [dMaxTailQ239ProgressionSubatom] : []), + ...(dMaxTailQ241ProgressionSubatom ? [dMaxTailQ241ProgressionSubatom] : []), + ...(dMaxTailQ257ProgressionSubatom ? [dMaxTailQ257ProgressionSubatom] : []), + ...(dMaxTailQ263ProgressionSubatom ? [dMaxTailQ263ProgressionSubatom] : []), + ...(dMaxTailQ269ProgressionSubatom ? [dMaxTailQ269ProgressionSubatom] : []), + ...(dMaxTailQ271ProgressionSubatom ? [dMaxTailQ271ProgressionSubatom] : []), + ...(dMaxTailQ277ProgressionSubatom ? [dMaxTailQ277ProgressionSubatom] : []), + ...(dMaxTailQ281ProgressionSubatom ? [dMaxTailQ281ProgressionSubatom] : []), + ...(dMaxTailQ283ProgressionSubatom ? [dMaxTailQ283ProgressionSubatom] : []), + ...(dMaxTailQ293ProgressionSubatom ? [dMaxTailQ293ProgressionSubatom] : []), + ...(dMaxTailQ307ProgressionSubatom ? [dMaxTailQ307ProgressionSubatom] : []), + ...(dMaxTailQ311ProgressionSubatom ? [dMaxTailQ311ProgressionSubatom] : []), + ...(dMaxTailQ313ProgressionSubatom ? [dMaxTailQ313ProgressionSubatom] : []), + ...(dMaxTailQ317ProgressionSubatom ? [dMaxTailQ317ProgressionSubatom] : []), + ...(dMaxTailQ331ProgressionSubatom ? [dMaxTailQ331ProgressionSubatom] : []), + ...(dMaxTailQ337ProgressionSubatom ? [dMaxTailQ337ProgressionSubatom] : []), + ...(dMaxTailQ347ProgressionSubatom ? [dMaxTailQ347ProgressionSubatom] : []), + ...(dMaxTailQ349ProgressionSubatom ? [dMaxTailQ349ProgressionSubatom] : []), + ...(dMaxTailQ353ProgressionSubatom ? [dMaxTailQ353ProgressionSubatom] : []), + ...(dMaxTailQ359ProgressionSubatom ? [dMaxTailQ359ProgressionSubatom] : []), + ...(dMaxTailQ367ProgressionSubatom ? [dMaxTailQ367ProgressionSubatom] : []), + ...(dMaxTailQ373ProgressionSubatom ? [dMaxTailQ373ProgressionSubatom] : []), + ...(dMaxTailQ379ProgressionSubatom ? [dMaxTailQ379ProgressionSubatom] : []), + ...(dMaxTailQ383ProgressionSubatom ? [dMaxTailQ383ProgressionSubatom] : []), + ...(dMaxTailQ389ProgressionSubatom ? [dMaxTailQ389ProgressionSubatom] : []), + ...(dMaxTailQ397ProgressionSubatom ? [dMaxTailQ397ProgressionSubatom] : []), + ...(dMaxTailQ401ProgressionSubatom ? [dMaxTailQ401ProgressionSubatom] : []), + ...(dMaxTailQ409ProgressionSubatom ? [dMaxTailQ409ProgressionSubatom] : []), + ...(dMaxTailQ419ProgressionSubatom ? [dMaxTailQ419ProgressionSubatom] : []), + ...(dMaxTailQ421ProgressionSubatom ? [dMaxTailQ421ProgressionSubatom] : []), + ...(dMaxTailQ431ProgressionSubatom ? [dMaxTailQ431ProgressionSubatom] : []), + ...(dMaxTailQ433ProgressionSubatom ? [dMaxTailQ433ProgressionSubatom] : []), + ...(dMaxTailQ439ProgressionSubatom ? [dMaxTailQ439ProgressionSubatom] : []), + ...(dMaxTailQ443ProgressionSubatom ? [dMaxTailQ443ProgressionSubatom] : []), + ...(dMaxTailQ449ProgressionSubatom ? [dMaxTailQ449ProgressionSubatom] : []), + ...(dMaxTailQ457ProgressionSubatom ? [dMaxTailQ457ProgressionSubatom] : []), + ...(dMaxTailQ461ProgressionSubatom ? [dMaxTailQ461ProgressionSubatom] : []), + ...(dMaxTailQ463ProgressionSubatom ? [dMaxTailQ463ProgressionSubatom] : []), + ...(dMaxTailQ467ProgressionSubatom ? [dMaxTailQ467ProgressionSubatom] : []), + ...(dMaxTailQ479ProgressionSubatom ? [dMaxTailQ479ProgressionSubatom] : []), + ...(dMaxTailQ487ProgressionSubatom ? [dMaxTailQ487ProgressionSubatom] : []), + ...(dMaxTailQ491ProgressionSubatom ? [dMaxTailQ491ProgressionSubatom] : []), + ...(dMaxTailQ499ProgressionSubatom ? [dMaxTailQ499ProgressionSubatom] : []), + ...(dMaxTailQ503ProgressionSubatom ? [dMaxTailQ503ProgressionSubatom] : []), + ...(dMaxTailQ509ProgressionSubatom ? [dMaxTailQ509ProgressionSubatom] : []), + ...(dMaxTailQ521ProgressionSubatom ? [dMaxTailQ521ProgressionSubatom] : []), + ...(dMaxTailQ523ProgressionSubatom ? [dMaxTailQ523ProgressionSubatom] : []), + ...(dMaxTailQ541ProgressionSubatom ? [dMaxTailQ541ProgressionSubatom] : []), + ...(dMaxTailQ547ProgressionSubatom ? [dMaxTailQ547ProgressionSubatom] : []), + ...(dMaxTailQ557ProgressionSubatom ? [dMaxTailQ557ProgressionSubatom] : []), + ...(dMaxTailQ563ProgressionSubatom ? [dMaxTailQ563ProgressionSubatom] : []), + ...(dMaxTailQ569ProgressionSubatom ? [dMaxTailQ569ProgressionSubatom] : []), + ...(dMaxTailQ571ProgressionSubatom ? [dMaxTailQ571ProgressionSubatom] : []), + ...(dMaxTailQ577ProgressionSubatom ? [dMaxTailQ577ProgressionSubatom] : []), + ...(dMaxTailQ587ProgressionSubatom ? [dMaxTailQ587ProgressionSubatom] : []), + ...(dMaxTailQGe587ParametricZeroFloorSubatom ? [dMaxTailQGe587ParametricZeroFloorSubatom] : []), + dynamicMarginSubatom, + ...(dynamicMarginSymbolicLiftSubatom ? [dynamicMarginSymbolicLiftSubatom] : []), + ...(dynamicMarginSymbolicLiftSuccessorSubatom ? [dynamicMarginSymbolicLiftSuccessorSubatom] : []), + ...(dynamicMarginExactMixedSymbolicLiftSubatom ? [dynamicMarginExactMixedSymbolicLiftSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSubatom ? [dynamicMarginExactMixedMatchingInjectionSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom ? [dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom ? [dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorSubatom ? [dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorSubatom ? [dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftSubatom ? [dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftSubatom ? [dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuSubatom] : []), + ...(dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuSubatom ? [dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuSubatom] : []), + ]; + const firstOpenMovingTermSubatom = dMaxTailQGe587ParametricZeroFloorVerified + ? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenuSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenuSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallbackSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17ResidualSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieveSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallbackSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelectorSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscapeSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLiftSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenuSubatom ?? dynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLiftSubatom ?? dynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLiftSubatom ?? dynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLiftSubatom ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39SuccessorSubatom ?? dynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessorSubatom ?? dynamicMarginExactMixedMatchingInjectionFiniteMenuSubatom ?? dynamicMarginExactMixedMatchingInjectionParametricLiftSubatom ?? dynamicMarginExactMixedMatchingInjectionSubatom ?? dynamicMarginExactMixedSymbolicLiftSubatom ?? dynamicMarginSymbolicLiftSuccessorSubatom ?? dynamicMarginSymbolicLiftSubatom ?? dynamicMarginSubatom + : dMaxTailQGe587ParametricZeroFloorSubatom + ?? dMaxTailQ587ProgressionSubatom + ?? dMaxTailQ577ProgressionSubatom + ?? dMaxTailQ571ProgressionSubatom + ?? dMaxTailQ569ProgressionSubatom + ?? dMaxTailQ563ProgressionSubatom + ?? dMaxTailQ557ProgressionSubatom + ?? dMaxTailQ547ProgressionSubatom + ?? dMaxTailQ541ProgressionSubatom + ?? dMaxTailQ523ProgressionSubatom + ?? dMaxTailQ521ProgressionSubatom + ?? dMaxTailQ509ProgressionSubatom + ?? dMaxTailQ503ProgressionSubatom + ?? dMaxTailQ499ProgressionSubatom + ?? dMaxTailQ491ProgressionSubatom + ?? dMaxTailQ487ProgressionSubatom + ?? dMaxTailQ479ProgressionSubatom + ?? dMaxTailQ467ProgressionSubatom + ?? dMaxTailQ463ProgressionSubatom + ?? dMaxTailQ461ProgressionSubatom + ?? dMaxTailQ457ProgressionSubatom + ?? dMaxTailQ449ProgressionSubatom + ?? dMaxTailQ443ProgressionSubatom + ?? dMaxTailQ439ProgressionSubatom + ?? dMaxTailQ433ProgressionSubatom + ?? dMaxTailQ431ProgressionSubatom + ?? dMaxTailQ421ProgressionSubatom + ?? dMaxTailQ419ProgressionSubatom + ?? dMaxTailQ409ProgressionSubatom + ?? dMaxTailQ401ProgressionSubatom + ?? dMaxTailQ397ProgressionSubatom + ?? dMaxTailQ389ProgressionSubatom + ?? dMaxTailQ383ProgressionSubatom + ?? dMaxTailQ379ProgressionSubatom + ?? dMaxTailQ373ProgressionSubatom + ?? dMaxTailQ367ProgressionSubatom + ?? dMaxTailQ359ProgressionSubatom + ?? dMaxTailQ353ProgressionSubatom + ?? dMaxTailQ349ProgressionSubatom + ?? dMaxTailQ347ProgressionSubatom + ?? dMaxTailQ337ProgressionSubatom + ?? dMaxTailQ331ProgressionSubatom + ?? dMaxTailQ317ProgressionSubatom + ?? dMaxTailQ313ProgressionSubatom + ?? dMaxTailQ311ProgressionSubatom + ?? dMaxTailQ307ProgressionSubatom + ?? dMaxTailQ293ProgressionSubatom + ?? dMaxTailQ283ProgressionSubatom + ?? dMaxTailQ281ProgressionSubatom + ?? dMaxTailQ277ProgressionSubatom + ?? dMaxTailQ271ProgressionSubatom + ?? dMaxTailQ269ProgressionSubatom + ?? dMaxTailQ263ProgressionSubatom + ?? dMaxTailQ257ProgressionSubatom + ?? dMaxTailQ241ProgressionSubatom + ?? dMaxTailQ239ProgressionSubatom + ?? dMaxTailQ233ProgressionSubatom + ?? dMaxTailQ229ProgressionSubatom + ?? dMaxTailQ227ProgressionSubatom + ?? dMaxTailQ223ProgressionSubatom + ?? dMaxTailQ211ProgressionSubatom + ?? dMaxTailQ199ProgressionSubatom + ?? dMaxTailQ197ProgressionSubatom + ?? dMaxTailQ193ProgressionSubatom + ?? dMaxTailQ191ProgressionSubatom + ?? dMaxTailQ181ProgressionSubatom + ?? dMaxTailQ179ProgressionSubatom + ?? dMaxTailQ173ProgressionSubatom + ?? dMaxTailQ167ProgressionSubatom + ?? dMaxTailQ163ProgressionSubatom + ?? dMaxTailQ157ProgressionSubatom + ?? dMaxTailQ151ProgressionSubatom + ?? dMaxTailQ149ProgressionSubatom + ?? dMaxTailQ139ProgressionSubatom + ?? dMaxTailQ137ProgressionSubatom + ?? dMaxTailQ131ProgressionSubatom + ?? dMaxTailQ127ProgressionSubatom + ?? dMaxTailQ113ProgressionSubatom + ?? dMaxTailQ109ProgressionSubatom + ?? dMaxTailQ107ProgressionSubatom + ?? dMaxTailQ103ProgressionSubatom + ?? dMaxTailQ101ProgressionSubatom + ?? dMaxTailQ97ProgressionSubatom + ?? dMaxTailQ89ProgressionSubatom + ?? dMaxTailQ83ProgressionSubatom + ?? dMaxTailQ79ProgressionSubatom + ?? dMaxTailQ73ProgressionSubatom + ?? dMaxTailQ71ProgressionSubatom + ?? dMaxTailQ67ProgressionSubatom + ?? dMaxTailQ61ProgressionSubatom + ?? dMaxTailQ59ProgressionSubatom + ?? dMaxTailQ53ProgressionSubatom + ?? dMaxTailQ47ProgressionSubatom + ?? dMaxTailQ43ProgressionSubatom + ?? dMaxTailQ41ProgressionSubatom + ?? dMaxTailQ37ProgressionSubatom + ?? dMaxTailQ29ProgressionSubatom + ?? dMaxTailQ251MinusProgressionSubatom + ?? dMaxTailQ31MinusProgressionSubatom + ?? dMaxTailQ23PlusProgressionSubatom + ?? dMaxTailQ11MinusProgressionSubatom + ?? dMaxTailQ19PlusProgressionSubatom + ?? dMaxTailQ17ProgressionSubatom + ?? dMaxTailRecombinationSubatom + ?? dMaxQ251ProgressionSubatom + ?? dMaxQ31ProgressionSubatom + ?? dMaxQ23ProgressionSubatom + ?? dMaxQ19ProgressionSubatom + ?? dMaxQ11ProgressionSubatom + ?? dMaxQ7ProgressionSubatom + ?? dMaxQ5ProgressionSubatom + ?? dMaxQ3ProgressionSubatom + ?? dMaxGrowthFirstSubatom + ?? dMaxGrowthSubatom + ?? dMaxSubatom; + return { + schema: 'erdos.p848_side_count_floor_atom_packet/1', + generatedAt: new Date().toISOString(), + problemId: '848', + packetId: paths?.packetId ?? `p848_side_count_floor_packet_${sanitizeP848PacketFileStem(atomId)}`, + atomId, + parentLemmaId: lift.firstOpenSymbolicLemma?.lemmaId ?? 'D2_p13_non_tight_side_count_slack_floor_lift', + parentCandidateId: lift.candidateId, + targetPrime: 13, + splitKey: stratum.splitKey, + rank: index + 1, + priority: index === 0 ? 'highest_side_count_floor_atom' : 'co_weakest_side_count_floor_atom', + status: 'symbolic_side_count_floor_atom_needed', + targetSlackLowerBound: Number.isFinite(targetFloor) ? targetFloor : null, + observedBoundedSlackFormulaFloor: Number.isFinite(observedFloor) ? observedFloor : null, + observedMarginAboveTarget: Number.isFinite(targetFloor) && Number.isFinite(observedFloor) + ? observedFloor - targetFloor + : null, + boundedWitness: { + rowCount: stratum.rowCount, + nRange: `${stratum.firstN}..${stratum.lastN}`, + minSideCountSlackFormula: stratum.minSideCountSlackFormula, + maxSideCountSlackFormula: stratum.maxSideCountSlackFormula, + minLargerSideSize: stratum.minLargerSideSize, + maxLargerSideSize: stratum.maxLargerSideSize, + minStrictBaseThreshold: stratum.minStrictBaseThreshold, + maxStrictBaseThreshold: stratum.maxStrictBaseThreshold, + minCandidateSize: stratum.minCandidateSize, + maxCandidateSize: stratum.maxCandidateSize, + minReconstructedVMax: stratum.minReconstructedVMax, + maxReconstructedVMax: stratum.maxReconstructedVMax, + minDMax: stratum.minDMax, + maxDMax: stratum.maxDMax, + minRGreater: stratum.minRGreater, + maxRGreater: stratum.maxRGreater, + minStructuralMargin: stratum.minStructuralMargin, + maxStructuralMargin: stratum.maxStructuralMargin, + formulaReplayPassed: stratum.formulaReplayPassed, + meetsTargetSlackFloor: stratum.meetsTargetSlackFloor, + }, + structuralMarginDecomposition: { + status: structuralMarginVerified + ? 'bounded_structural_margin_replay_verified_symbolic_margin_lift_needed' + : 'blocked_by_negative_bounded_structural_margin', + largerSideLabel, + targetAugmentedMarginConstant, + inequality: targetAugmentedMarginConstant === null + ? null + : `${largerSideLabel}Count + vMax + dMax + rGreater + ${targetAugmentedMarginConstant} <= candidateSize`, + boundedMarginRange: { + min: stratum.minStructuralMargin, + max: stratum.maxStructuralMargin, + }, + firstOpenSublemma: { + lemmaId: structuralMarginAtomId, + status: 'needed', + statement: targetAugmentedMarginConstant === null + ? `Prove the structural margin inequality for ${stratum.splitKey}.` + : `For every future p=13 threat row with ${stratum.splitKey}, prove ${largerSideLabel}Count + vMax + dMax + rGreater + ${targetAugmentedMarginConstant} <= candidateSize.`, + }, + movingTermSubatoms, + firstOpenMovingTermSubatom, + proofBoundary: 'This replays the bounded side-count floor as a structural margin inequality. It is not an all-N proof of the moving compatibility counts, dMax, rGreater, or candidateSize terms.', + }, + theoremObligation: { + kind: 'non_tight_p13_side_count_floor_subobligation', + statement: `For every future p=13 threat row with ${stratum.splitKey}, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) >= ${Number.isFinite(targetFloor) ? targetFloor : '(target floor)'}.`, + equivalentInequality: Number.isFinite(targetFloor) + ? `max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - ${targetFloor + 1}` + : null, + proofBoundary: 'This packet isolates one weakest non-tight side-count stratum. Its bounded witness is not an all-N proof; the symbolic side-count inequality still has to be proved or refined.', + }, + proofReduction: lift.proofReduction, + nextTheoremActions: [ + dMaxBoundProbe + ? `Treat ${dMaxSubatomId} as falsified by the extended bounded probe; do not promote dMax <= ${dMaxBudget ?? '(bounded value)'} as an all-N lemma.` + : `Prove the first moving-term subatom ${dMaxSubatomId}: ${dMaxBudget === null ? 'find a symbolic dMax bound' : `dMax <= ${dMaxBudget}`}.`, + dMaxBoundProbe + ? `Attack the successor ${dMaxGrowthSubatomId}: replace the false constant dMax bound before re-deriving the residual dynamic margin.` + : residualDynamicMarginConstant === null + ? `After dMax is bounded, prove the residual dynamic margin ${dynamicMarginSubatomId}.` + : `After dMax is bounded, prove the residual dynamic margin ${dynamicMarginSubatomId}: ${largerSideLabel}Count + vMax + rGreater + ${residualDynamicMarginConstant} <= candidateSize.`, + 'If the symbolic side-count inequality fails, emit a sharper split atom keyed by the first failing side-count term.', + 'After all co-weakest side-count floor atoms are handled, lift the remaining larger-margin strata by the same inequality template.', + ], + }; + }); +} + +function renderP848SideCountFloorPacketMarkdown(packet) { + const lines = [ + `# ${packet.atomId}`, + '', + 'This is a focused side-count floor atom for the Problem 848 p13 non-tight slack-dominance lift.', + '', + '## Summary', + '', + `- Packet id: \`${packet.packetId}\``, + `- Parent lemma: \`${packet.parentLemmaId}\``, + `- Split key: \`${packet.splitKey}\``, + `- Priority: \`${packet.priority}\``, + `- Status: \`${packet.status}\``, + `- Target slack floor: \`${packet.targetSlackLowerBound ?? '(unknown)'}\``, + `- Observed bounded slack-formula floor: \`${packet.observedBoundedSlackFormulaFloor ?? '(unknown)'}\``, + `- Observed margin above target: \`${packet.observedMarginAboveTarget ?? '(unknown)'}\``, + `- Bounded witness rows: \`${packet.boundedWitness.rowCount}\` over \`${packet.boundedWitness.nRange}\``, + '', + '## Theorem Obligation', + '', + packet.theoremObligation.statement, + '', + `Equivalent inequality: \`${packet.theoremObligation.equivalentInequality ?? '(none)'}\``, + '', + `Boundary: ${packet.theoremObligation.proofBoundary}`, + '', + '## Structural Margin Decomposition', + '', + `- Status: \`${packet.structuralMarginDecomposition?.status ?? '(none)'}\``, + `- Inequality: \`${packet.structuralMarginDecomposition?.inequality ?? '(none)'}\``, + `- Bounded margin range: \`${packet.structuralMarginDecomposition?.boundedMarginRange?.min ?? '(unknown)'}..${packet.structuralMarginDecomposition?.boundedMarginRange?.max ?? '(unknown)'}\``, + `- First open sublemma: \`${packet.structuralMarginDecomposition?.firstOpenSublemma?.lemmaId ?? '(none)'}\``, + `- First moving-term subatom: \`${packet.structuralMarginDecomposition?.firstOpenMovingTermSubatom?.atomId ?? '(none)'}\``, + `- Boundary: ${packet.structuralMarginDecomposition?.proofBoundary ?? '(none)'}`, + '', + '## Moving-Term Subatoms', + '', + ]; + for (const atom of packet.structuralMarginDecomposition?.movingTermSubatoms ?? []) { + lines.push(`- \`${atom.atomId}\` [${atom.status}]: ${atom.statement}`); + if (atom.inequality) { + lines.push(`- Inequality: \`${atom.inequality}\``); + } + if (atom.probeArtifact?.status) { + lines.push(`- Probe: \`${atom.probeArtifact.status}\`, range \`${atom.probeArtifact.probeRange ?? '(unknown)'}\`, max observed dMax \`${atom.probeArtifact.maxObservedDMax ?? '(unknown)'}\``); + } + if (atom.growthProfile?.status) { + lines.push(`- Growth profile: \`${atom.growthProfile.status}\`, first subatom \`${atom.growthProfile.firstOpenSubatomId ?? '(none)'}\``); + } + if (atom.proofArtifact?.status) { + lines.push(`- Proof artifact: \`${atom.proofArtifact.status}\`, q=\`${atom.proofArtifact.q ?? '(unknown)'}\`, next=\`${atom.proofArtifact.nextSubatomId ?? '(none)'}\``); + lines.push(`- Proof JSON: \`${atom.proofArtifact.jsonPath ?? '(none)'}\``); + } + if (atom.firstCounterexample) { + lines.push(`- First counterexample: \`N=${atom.firstCounterexample.N}, dMax=${atom.firstCounterexample.dMax}, witness=${atom.firstCounterexample.dMaxWitnessSide}:${atom.firstCounterexample.dMaxWitnessValue}\``); + } + if (atom.profileJsonPath) { + lines.push(`- Profile JSON: \`${atom.profileJsonPath}\``); + } + lines.push(`- Boundary: ${atom.proofBoundary}`); + } + lines.push( + '', + '## Proof Reduction', + '', + `- Matching saturation: ${packet.proofReduction?.matchingSaturationHypothesis ?? '(none)'}`, + `- K formula: ${packet.proofReduction?.requiredMatchingFormula ?? '(none)'}`, + `- Slack formula: ${packet.proofReduction?.derivedSlackFormula ?? '(none)'}`, + '', + '## Bounded Witness', + '', + `- Formula replay passed: \`${packet.boundedWitness.formulaReplayPassed ? 'yes' : 'no'}\``, + `- Meets target floor: \`${packet.boundedWitness.meetsTargetSlackFloor ? 'yes' : 'no'}\``, + `- Side-count slack formula range: \`${packet.boundedWitness.minSideCountSlackFormula}..${packet.boundedWitness.maxSideCountSlackFormula}\``, + `- Larger side range: \`${packet.boundedWitness.minLargerSideSize}..${packet.boundedWitness.maxLargerSideSize}\``, + `- Strict base threshold range: \`${packet.boundedWitness.minStrictBaseThreshold}..${packet.boundedWitness.maxStrictBaseThreshold}\``, + `- Candidate size range: \`${packet.boundedWitness.minCandidateSize}..${packet.boundedWitness.maxCandidateSize}\``, + `- Reconstructed vMax range: \`${packet.boundedWitness.minReconstructedVMax}..${packet.boundedWitness.maxReconstructedVMax}\``, + `- dMax range: \`${packet.boundedWitness.minDMax}..${packet.boundedWitness.maxDMax}\``, + `- rGreater range: \`${packet.boundedWitness.minRGreater}..${packet.boundedWitness.maxRGreater}\``, + '', + '## Next Theorem Actions', + '', + ); + for (const action of packet.nextTheoremActions ?? []) { + lines.push(`- ${action}`); + } + return `${lines.join('\n')}\n`; +} + +function buildP848PrimeLaneHandoffCandidate({ + laneId, + targetPrime, + packetEntries, + successorPacketEntries, + parentObligationId, +}) { + const lanePackets = (packetEntries ?? []).filter((packet) => ( + Number(packet.prime) === Number(targetPrime) + && (!parentObligationId || packet.parentObligationId === parentObligationId) + )); + if (lanePackets.length === 0) { + return null; + } + + const lanePacketIds = new Set(lanePackets.map((packet) => packet.atomId)); + const laneSuccessors = (successorPacketEntries ?? []) + .filter((packet) => lanePacketIds.has(packet.parentAtomId)); + const readySplitPackets = lanePackets + .filter((packet) => packet.splitDischargeReadinessStatus === 'split_discharge_readiness_candidate'); + const verifiedSuccessorFamilies = laneSuccessors + .filter((packet) => packet.symbolicVertexFamilyLemmaStatus === 'symbolic_vertex_family_lemma_verified'); + const totalRefinementConditions = lanePackets.reduce( + (total, packet) => total + Number(packet.vertexPresenceRefinementConditionCount ?? 0), + 0, + ); + const edgePersistenceVerifiedCount = lanePackets + .filter((packet) => packet.edgeCongruencePersistenceStatus === 'literal_constant_edge_persistence_verified').length; + const matchingKVerifiedCount = lanePackets + .filter((packet) => packet.matchingKEnvelopeCertificateStatus === 'literal_matching_sampled_k_envelope_verified').length; + const allSplitPacketsReady = readySplitPackets.length === lanePackets.length; + const allSuccessorFamiliesVerified = totalRefinementConditions > 0 + && verifiedSuccessorFamilies.length === totalRefinementConditions; + const allEdgePersistenceVerified = edgePersistenceVerifiedCount === lanePackets.length; + const allMatchingKVerified = matchingKVerifiedCount === lanePackets.length; + const lowerLayerChecks = [ + { + checkId: 'lane_split_packets_ready', + status: allSplitPacketsReady ? 'verified' : 'blocked', + evidence: `${readySplitPackets.length}/${lanePackets.length} split packets have readiness candidates`, + }, + { + checkId: 'lane_vertex_successor_families_verified', + status: allSuccessorFamiliesVerified ? 'verified' : 'blocked', + evidence: `${verifiedSuccessorFamilies.length}/${totalRefinementConditions} successor vertex-family lemmas verified`, + }, + { + checkId: 'lane_edge_persistence_verified', + status: allEdgePersistenceVerified ? 'verified' : 'blocked', + evidence: `${edgePersistenceVerifiedCount}/${lanePackets.length} split packets have literal edge persistence`, + }, + { + checkId: 'lane_matching_k_envelopes_verified', + status: allMatchingKVerified ? 'verified_sampled_envelope' : 'blocked', + evidence: `${matchingKVerifiedCount}/${lanePackets.length} split packets have matching/K-envelope certificates`, + }, + ]; + const blockingChecks = lowerLayerChecks.filter((check) => check.status === 'blocked'); + const openAllNHandoffGaps = [ + { + gapId: 'row_universe_split_coverage', + status: 'open', + sourcePacketCount: lanePackets.length, + note: 'Prove every future p=13 threatening row lands in one of the emitted split profiles, or emit the missing split profile as a new atom.', + }, + { + gapId: 'universal_k_formula_lift', + status: 'open', + sourcePacketCount: lanePackets.length, + note: 'Replace each sampled K-envelope comparison with the symbolic K(N,x) inequality for the full p=13 lane.', + }, + { + gapId: 'literal_to_parameterized_vertex_guard', + status: 'open_if_vertices_move', + sourcePacketCount: lanePackets.length, + note: 'If future rows require moving vertex formulas, re-lift vertex presence, edge persistence, and disjointness for the parameterized families.', + }, + ]; + const lowerLayersReady = blockingChecks.length === 0; + + return { + schema: 'erdos.p848_prime_lane_handoff_candidate/1', + laneId, + parentObligationId, + targetPrime, + status: lowerLayersReady + ? 'prime_lane_handoff_candidate_with_open_all_n_gaps' + : 'prime_lane_handoff_blocked_by_lower_atoms', + promotesAllNClaim: false, + splitPacketCount: lanePackets.length, + readySplitPacketCount: readySplitPackets.length, + totalRefinementConditionCount: totalRefinementConditions, + verifiedSuccessorFamilyCount: verifiedSuccessorFamilies.length, + lowerLayerChecks, + blockingChecks, + splitPackets: lanePackets.map((packet) => ({ + atomId: packet.atomId, + splitKey: packet.splitKey, + readinessStatus: packet.splitDischargeReadinessStatus, + openGapCount: packet.splitDischargeOpenGapCount, + matchingKEnvelopeSlack: packet.matchingKEnvelopeSlack, + jsonPath: packet.jsonPath, + markdownPath: packet.markdownPath, + })), + theoremCandidate: { + status: lowerLayersReady + ? 'candidate_not_promoted_all_n_gaps_open' + : 'blocked_by_lower_split_atom', + statement: `The p=${targetPrime} lane has ${readySplitPackets.length}/${lanePackets.length} split profiles assembled into theorem-facing readiness candidates.`, + openAllNHandoffGaps, + }, + proofBoundary: 'This aggregates split-discharge readiness for a prime lane. It is not a universal D-lane proof until row-universe coverage and the symbolic K(N,x) lift are discharged.', + nextTheoremAction: lowerLayersReady + ? 'Discharge row_universe_split_coverage first, then universal_k_formula_lift; do not mark the parent lane done until those all-N gaps close.' + : 'Finish the first blocked split atom before attempting prime-lane promotion.', + }; +} + +function buildP848SplitAtomPacketManifest(problem, taskList, packets, successorPackets = [], sideCountFloorPackets = []) { + const paths = getP848SplitAtomPacketPaths(problem); + const successorPaths = getP848SplitAtomSuccessorPacketPaths(problem); + const sideCountFloorPaths = getP848SideCountFloorPacketPaths(problem); + const packetEntries = packets.map((packet) => { + const packetPaths = getP848SplitAtomPacketPaths(problem, packet.atomId); + return { + atomId: packet.atomId, + packetId: packet.packetId, + parentObligationId: packet.parentObligationId, + priority: packet.priority, + prime: packet.prime, + splitKey: packet.splitKey, + status: packet.status, + jsonPath: packetPaths?.jsonPath ?? null, + markdownPath: packetPaths?.markdownPath ?? null, + commonMatchingPairCount: packet.matchingCore.commonMatchingPairCount, + vertexPresenceAtomCount: packet.summary.vertexPresenceAtomCount, + stableVertexPresenceAtomCount: packet.summary.stableVertexPresenceAtomCount, + unstableVertexPresenceAtomCount: packet.summary.unstableVertexPresenceAtomCount, + vertexPresenceRefinementStatus: packet.vertexPresenceRefinement?.status ?? null, + vertexPresenceRefinementConditionCount: packet.vertexPresenceRefinement?.conditionCount ?? 0, + edgeObstructionAtomCount: packet.summary.edgeObstructionAtomCount, + edgeObstructionCertificateStatus: packet.edgeObstructionCertificate?.status ?? null, + edgeObstructionResidueSummary: packet.edgeObstructionCertificate?.residueSummary ?? null, + edgeCongruencePersistenceStatus: packet.edgeCongruencePersistence?.status ?? null, + matchingKEnvelopeCertificateStatus: packet.matchingKEnvelopeCertificate?.status ?? null, + matchingKEnvelopeSlack: packet.matchingKEnvelopeCertificate?.kEnvelopeProof?.boundedSlackAgainstMaxK ?? null, + splitDischargeReadinessStatus: packet.splitDischargeReadiness?.status ?? null, + splitDischargeOpenGapCount: packet.splitDischargeReadiness?.openAllNHandoffGaps?.length ?? null, + readyForFirstTheoremPass: packet.summary.readyForFirstTheoremPass, + }; + }); + const successorPacketEntries = successorPackets.map((packet) => { + const packetPaths = getP848SplitAtomSuccessorPacketPaths(problem, packet.parentAtomId, packet.conditionId); + return { + packetId: packet.packetId, + successorAtomId: packet.successorAtomId, + parentAtomId: packet.parentAtomId, + conditionId: packet.conditionId, + priority: packet.priority, + status: packet.status, + successorSplitKey: packet.splitRefinement.successorSplitKey, + successorSplitModulus: packet.splitRefinement.successorSplitModulus, + affectedAtomCount: packet.checks.affectedAtomCount, + stabilizedAtomCount: packet.checks.stabilizedAtomCount, + failedAtomCount: packet.checks.failedAtomCount, + symbolicVertexFamilyLemmaStatus: packet.symbolicVertexFamilyLemma?.status ?? null, + vertexResidueModSquare: packet.symbolicVertexFamilyLemma?.vertexResidueModSquare ?? null, + jsonPath: packetPaths?.jsonPath ?? null, + markdownPath: packetPaths?.markdownPath ?? null, + }; + }); + const sideCountFloorPacketEntries = sideCountFloorPackets.map((packet) => { + const packetPaths = getP848SideCountFloorPacketPaths(problem, packet.atomId); + return { + packetId: packet.packetId, + atomId: packet.atomId, + parentLemmaId: packet.parentLemmaId, + splitKey: packet.splitKey, + priority: packet.priority, + status: packet.status, + targetSlackLowerBound: packet.targetSlackLowerBound, + observedBoundedSlackFormulaFloor: packet.observedBoundedSlackFormulaFloor, + observedMarginAboveTarget: packet.observedMarginAboveTarget, + structuralMarginDecompositionStatus: packet.structuralMarginDecomposition?.status ?? null, + firstOpenStructuralMarginLemma: packet.structuralMarginDecomposition?.firstOpenSublemma?.lemmaId ?? null, + firstOpenMovingTermSubatom: packet.structuralMarginDecomposition?.firstOpenMovingTermSubatom?.atomId ?? null, + firstOpenMovingTermSubatomStatus: packet.structuralMarginDecomposition?.firstOpenMovingTermSubatom?.status ?? null, + movingTermSubatomCount: packet.structuralMarginDecomposition?.movingTermSubatoms?.length ?? 0, + structuralMarginFloor: packet.structuralMarginDecomposition?.boundedMarginRange?.min ?? null, + boundedWitnessRowCount: packet.boundedWitness?.rowCount ?? null, + jsonPath: packetPaths?.jsonPath ?? null, + markdownPath: packetPaths?.markdownPath ?? null, + }; + }); + const firstPacket = packetEntries.find((packet) => packet.priority === 'highest_singleton_profile') + ?? packetEntries.find((packet) => packet.prime === 13) + ?? packetEntries[0] + ?? null; + const firstSuccessorPacket = successorPacketEntries.find((packet) => packet.priority === 'highest_refinement_successor') + ?? successorPacketEntries[0] + ?? null; + const firstSideCountFloorPacket = sideCountFloorPacketEntries + .find((packet) => packet.priority === 'highest_side_count_floor_atom') + ?? sideCountFloorPacketEntries[0] + ?? null; + const firstStructuralMarginMovingTermSubatom = firstSideCountFloorPacket?.firstOpenMovingTermSubatom ?? null; + const primeLaneHandoffCandidates = [ + buildP848PrimeLaneHandoffCandidate({ + laneId: 'D2_p13_matching_lower_bound', + targetPrime: 13, + parentObligationId: 'D2_p13_matching_lower_bound', + packetEntries, + successorPacketEntries, + }), + ].filter(Boolean); + + return { + schema: 'erdos.p848_split_atom_packet_manifest/1', + generatedAt: new Date().toISOString(), + problemId: '848', + sourceTaskListGeneratedAt: taskList.generatedAt, + sourcePlanId: taskList.splitCoreAtomizationPlan?.planId ?? null, + directoryPath: paths?.directoryPath ?? null, + successorDirectoryPath: successorPaths?.directoryPath ?? null, + sideCountFloorDirectoryPath: sideCountFloorPaths?.directoryPath ?? null, + manifestJsonPath: paths?.manifestJsonPath ?? null, + manifestMarkdownPath: paths?.manifestMarkdownPath ?? null, + packetCount: packetEntries.length, + successorPacketCount: successorPacketEntries.length, + sideCountFloorPacketCount: sideCountFloorPacketEntries.length, + firstPacketToAttack: firstPacket, + firstSuccessorPacketToAttack: firstSuccessorPacket, + firstSideCountFloorPacketToAttack: firstSideCountFloorPacket, + firstStructuralMarginMovingTermSubatom, + firstPrimeLaneHandoffCandidate: primeLaneHandoffCandidates[0] ?? null, + primeLaneHandoffCandidates, + packets: packetEntries, + successorPackets: successorPacketEntries, + sideCountFloorPackets: sideCountFloorPacketEntries, + }; +} + +function renderP848SplitAtomPacketManifestMarkdown(manifest) { + const lines = [ + '# Problem 848 Split Atom Packets', + '', + 'This manifest indexes the atomic split-core packets emitted from the 848 task list. Agents should use one packet at a time, starting with the highest-priority singleton p13 packet when available.', + '', + `- Source plan: \`${manifest.sourcePlanId ?? '(none)'}\``, + `- Packet count: \`${manifest.packetCount}\``, + `- Successor packet count: \`${manifest.successorPacketCount ?? 0}\``, + `- Side-count floor packet count: \`${manifest.sideCountFloorPacketCount ?? 0}\``, + `- First packet to attack: \`${manifest.firstPacketToAttack?.atomId ?? '(none)'}\``, + `- First successor packet to attack: \`${manifest.firstSuccessorPacketToAttack?.successorAtomId ?? '(none)'}\``, + `- First side-count floor packet to attack: \`${manifest.firstSideCountFloorPacketToAttack?.atomId ?? '(none)'}\``, + `- First prime-lane handoff candidate: \`${manifest.firstPrimeLaneHandoffCandidate?.laneId ?? '(none)'}\``, + '', + '## Packets', + '', + ]; + for (const packet of manifest.packets ?? []) { + lines.push(`- \`${packet.atomId}\` [${packet.priority}]: p=${packet.prime}, split=${packet.splitKey}, core=${packet.commonMatchingPairCount}, vertexAtoms=${packet.vertexPresenceAtomCount}, stableVertices=${packet.stableVertexPresenceAtomCount}, unstableVertices=${packet.unstableVertexPresenceAtomCount}, refinement=${packet.vertexPresenceRefinementStatus}/${packet.vertexPresenceRefinementConditionCount}, edgeAtoms=${packet.edgeObstructionAtomCount}, edgeCertificate=${packet.edgeObstructionCertificateStatus ?? '(none)'}, edgePersistence=${packet.edgeCongruencePersistenceStatus ?? '(none)'}, matchingK=${packet.matchingKEnvelopeCertificateStatus ?? '(none)'}, discharge=${packet.splitDischargeReadinessStatus ?? '(none)'}, ready=${packet.readyForFirstTheoremPass}`); + lines.push(`- JSON: \`${packet.jsonPath ?? '(none)'}\``); + lines.push(`- Markdown: \`${packet.markdownPath ?? '(none)'}\``); + } + lines.push('', '## Successor Packets', ''); + for (const packet of manifest.successorPackets ?? []) { + lines.push(`- \`${packet.successorAtomId}\` [${packet.priority}]: parent=${packet.parentAtomId}, condition=${packet.conditionId}, split=${packet.successorSplitKey}, affected=${packet.affectedAtomCount}, stabilized=${packet.stabilizedAtomCount}, failed=${packet.failedAtomCount}, lemma=${packet.symbolicVertexFamilyLemmaStatus}, status=${packet.status}`); + lines.push(`- JSON: \`${packet.jsonPath ?? '(none)'}\``); + lines.push(`- Markdown: \`${packet.markdownPath ?? '(none)'}\``); + } + lines.push('', '## Side-Count Floor Packets', ''); + for (const packet of manifest.sideCountFloorPackets ?? []) { + lines.push(`- \`${packet.atomId}\` [${packet.priority}]: split=${packet.splitKey}, floor=${packet.targetSlackLowerBound}, observed=${packet.observedBoundedSlackFormulaFloor}, margin=${packet.observedMarginAboveTarget}, structuralMargin=${packet.structuralMarginFloor}, sublemma=${packet.firstOpenStructuralMarginLemma ?? '(none)'}, movingTerm=${packet.firstOpenMovingTermSubatom ?? '(none)'}, rows=${packet.boundedWitnessRowCount}, status=${packet.status}`); + lines.push(`- JSON: \`${packet.jsonPath ?? '(none)'}\``); + lines.push(`- Markdown: \`${packet.markdownPath ?? '(none)'}\``); + } + lines.push('', '## Prime-Lane Handoff Candidates', ''); + for (const lane of manifest.primeLaneHandoffCandidates ?? []) { + lines.push(`- \`${lane.laneId}\` [${lane.status}]: p=${lane.targetPrime}, ready=${lane.readySplitPacketCount}/${lane.splitPacketCount}, successors=${lane.verifiedSuccessorFamilyCount}/${lane.totalRefinementConditionCount}, openAllNGaps=${lane.theoremCandidate?.openAllNHandoffGaps?.length ?? 0}`); + lines.push(`- Boundary: ${lane.proofBoundary}`); + for (const gap of lane.theoremCandidate?.openAllNHandoffGaps ?? []) { + lines.push(`- Gap \`${gap.gapId}\` [${gap.status}]: ${gap.note}`); + } + } + return `${lines.join('\n')}\n`; +} + +function writeP848SplitAtomPacketsFromTaskList(problem, taskList) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const plan = taskList.splitCoreAtomizationPlan; + const splitAtoms = Array.isArray(plan?.splitAtoms) ? plan.splitAtoms : []; + const paths = getP848SplitAtomPacketPaths(problem); + if (!paths || splitAtoms.length === 0) { + return null; + } + + ensureDir(paths.directoryPath); + const basePackets = splitAtoms.map((atom) => buildP848SplitAtomPacket(problem, plan, atom)); + const successorPackets = buildP848SplitAtomSuccessorPackets(problem, basePackets); + const sideCountFloorPackets = buildP848SideCountFloorAtomPackets(problem, plan); + const packets = basePackets.map((packet) => ({ + ...packet, + splitDischargeReadiness: buildP848SplitDischargeReadiness(packet, successorPackets), + })); + const successorPaths = getP848SplitAtomSuccessorPacketPaths(problem); + const sideCountFloorPaths = getP848SideCountFloorPacketPaths(problem); + for (const packet of packets) { + const packetPaths = getP848SplitAtomPacketPaths(problem, packet.atomId); + writeJson(packetPaths.jsonPath, packet); + writeText(packetPaths.markdownPath, renderP848SplitAtomPacketMarkdown(packet)); + } + if (successorPackets.length > 0 && successorPaths) { + ensureDir(successorPaths.directoryPath); + for (const packet of successorPackets) { + const packetPaths = getP848SplitAtomSuccessorPacketPaths(problem, packet.parentAtomId, packet.conditionId); + writeJson(packetPaths.jsonPath, packet); + writeText(packetPaths.markdownPath, renderP848SplitAtomSuccessorPacketMarkdown(packet)); + } + } + if (sideCountFloorPackets.length > 0 && sideCountFloorPaths) { + ensureDir(sideCountFloorPaths.directoryPath); + for (const packet of sideCountFloorPackets) { + const packetPaths = getP848SideCountFloorPacketPaths(problem, packet.atomId); + writeJson(packetPaths.jsonPath, packet); + writeText(packetPaths.markdownPath, renderP848SideCountFloorPacketMarkdown(packet)); + } + } + const manifest = buildP848SplitAtomPacketManifest(problem, taskList, packets, successorPackets, sideCountFloorPackets); + writeJson(paths.manifestJsonPath, manifest); + writeText(paths.manifestMarkdownPath, renderP848SplitAtomPacketManifestMarkdown(manifest)); + return { + ok: true, + packetCount: packets.length, + successorPacketCount: successorPackets.length, + sideCountFloorPacketCount: sideCountFloorPackets.length, + directoryPath: paths.directoryPath, + successorDirectoryPath: successorPaths?.directoryPath ?? null, + sideCountFloorDirectoryPath: sideCountFloorPaths?.directoryPath ?? null, + manifestJsonPath: paths.manifestJsonPath, + manifestMarkdownPath: paths.manifestMarkdownPath, + firstPacketToAttack: manifest.firstPacketToAttack, + firstSuccessorPacketToAttack: manifest.firstSuccessorPacketToAttack, + firstSideCountFloorPacketToAttack: manifest.firstSideCountFloorPacketToAttack, + }; +} + +function buildP848P13RowUniverseCoverageCandidate(problem, surface, existingPacketManifest) { + const p13PrimeLaneHandoffCandidate = (existingPacketManifest?.primeLaneHandoffCandidates ?? []) + .find((candidate) => candidate.laneId === 'D2_p13_matching_lower_bound') ?? null; + const p13ManifestPackets = (existingPacketManifest?.packets ?? []) + .filter((packet) => Number(packet.prime) === 13); + const emittedSplitKeys = p13ManifestPackets.map((packet) => packet.splitKey); + const emittedSplitKeySet = new Set(emittedSplitKeys); + const p13Evidence = surface?.activeAtomEvidence?.obligationId === 'D2_p13_matching_lower_bound' + ? surface.activeAtomEvidence + : surface?.candidatePackets?.D2_p13_matching_lower_bound ?? null; + const splitCoreWitness = surface?.proofPackets?.D2_p13_split_core_witness_extraction + ?? p13Evidence?.splitCoreWitnessPacket + ?? null; + const splitProfiles = splitCoreWitness?.profileSummary ?? []; + const matchingPatternSplitKeys = splitProfiles.map((profile) => profile.groupKey).filter(Boolean); + const missingMatchingPatternSplitKeys = matchingPatternSplitKeys + .filter((splitKey) => !emittedSplitKeys.includes(splitKey)); + const extraEmittedSplitKeys = emittedSplitKeys + .filter((splitKey) => !matchingPatternSplitKeys.includes(splitKey)); + const threatRowCount = Number(p13Evidence?.scope?.threatRowCount ?? NaN); + const tightWitnessRowCount = Number( + splitCoreWitness?.scope?.witnessRowCount + ?? p13Evidence?.matchingPatternEvidence?.witnessRowCount + ?? NaN, + ); + const boundedThreatRowsOutsideTightWitnessPacket = Number.isFinite(threatRowCount) + && Number.isFinite(tightWitnessRowCount) + ? Math.max(0, threatRowCount - tightWitnessRowCount) + : null; + const packProblemDir = getProblemPackDir(problem); + const fullVerifierPath = packProblemDir + ? path.join(packProblemDir, 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.json') + : null; + const fullVerifier = fullVerifierPath ? readJsonIfPresent(fullVerifierPath) : null; + const p13ThreatRows = (fullVerifier?.threatLiftMiningRows ?? []) + .filter((row) => Number(row?.p) === 13); + const p13ThreatRowsBySplitKey = new Map(); + const rowSplitKeyForThreat = (row) => { + const prime = Number(row?.p); + const outsider = Number(row?.outsider); + const side7 = Number(row?.compatibleSide7Count ?? row?.mixedCliqueSide7Count); + const side18 = Number(row?.compatibleSide18Count ?? row?.mixedCliqueSide18Count); + if (!Number.isFinite(prime) || !Number.isFinite(outsider) || !Number.isFinite(side7) || !Number.isFinite(side18)) { + return null; + } + const smallerSide = side7 <= side18 ? 'side7' : 'side18'; + const outsiderMod25 = Number.isFinite(Number(row?.outsiderMod25)) + ? Number(row.outsiderMod25) + : positiveModulo(outsider, 25); + return `outP2=${positiveModulo(outsider, prime * prime)}|out25=${positiveModulo(outsiderMod25, 25)}|smaller=${smallerSide}`; + }; + const addFiniteStat = (target, key, rawValue, combine) => { + const value = Number(rawValue); + if (!Number.isFinite(value)) { + return; + } + target[key] = target[key] === null ? value : combine(target[key], value); + }; + for (const row of p13ThreatRows) { + const splitKey = rowSplitKeyForThreat(row); + if (!splitKey) { + continue; + } + const stats = p13ThreatRowsBySplitKey.get(splitKey) ?? { + splitKey, + rowCount: 0, + firstN: null, + lastN: null, + minRequiredMatchingLowerBound: null, + maxRequiredMatchingLowerBound: null, + minActualMatching: null, + maxActualMatching: null, + minMatchingSlack: null, + maxMatchingSlack: null, + inEmittedTightSplitPacket: emittedSplitKeySet.has(splitKey), + }; + stats.rowCount += 1; + addFiniteStat(stats, 'firstN', row.N, Math.min); + addFiniteStat(stats, 'lastN', row.N, Math.max); + addFiniteStat(stats, 'minRequiredMatchingLowerBound', row.requiredMatchingLowerBound, Math.min); + addFiniteStat(stats, 'maxRequiredMatchingLowerBound', row.requiredMatchingLowerBound, Math.max); + addFiniteStat(stats, 'minActualMatching', row.matchingSizeInMissingCrossGraph, Math.min); + addFiniteStat(stats, 'maxActualMatching', row.matchingSizeInMissingCrossGraph, Math.max); + addFiniteStat(stats, 'minMatchingSlack', row.matchingSlack, Math.min); + addFiniteStat(stats, 'maxMatchingSlack', row.matchingSlack, Math.max); + p13ThreatRowsBySplitKey.set(splitKey, stats); + } + const boundedSplitStrata = [...p13ThreatRowsBySplitKey.values()] + .sort((left, right) => ( + Number(right.inEmittedTightSplitPacket) - Number(left.inEmittedTightSplitPacket) + || left.minMatchingSlack - right.minMatchingSlack + || right.rowCount - left.rowCount + || left.splitKey.localeCompare(right.splitKey) + )); + const emittedTightSplitStrata = boundedSplitStrata + .filter((stratum) => stratum.inEmittedTightSplitPacket); + const outsideTightSplitStrata = boundedSplitStrata + .filter((stratum) => !stratum.inEmittedTightSplitPacket); + const emittedTightSplitCoveredRowCount = emittedTightSplitStrata + .reduce((total, stratum) => total + stratum.rowCount, 0); + const outsideTightSplitRowCount = outsideTightSplitStrata + .reduce((total, stratum) => total + stratum.rowCount, 0); + const minEmittedTightSplitSlack = emittedTightSplitStrata.length > 0 + ? Math.min(...emittedTightSplitStrata.map((stratum) => stratum.minMatchingSlack).filter(Number.isFinite)) + : null; + const slackDominatedOutsideStrata = Number.isFinite(minEmittedTightSplitSlack) + ? outsideTightSplitStrata.filter((stratum) => stratum.minMatchingSlack > minEmittedTightSplitSlack) + : []; + const slackDominatedOutsideRowCount = slackDominatedOutsideStrata + .reduce((total, stratum) => total + stratum.rowCount, 0); + const outsideRowsNeedingAdditionalSplitPacket = Math.max( + 0, + outsideTightSplitRowCount - slackDominatedOutsideRowCount, + ); + const minOutsideSlack = outsideTightSplitStrata.length > 0 + ? Math.min(...outsideTightSplitStrata.map((stratum) => stratum.minMatchingSlack).filter(Number.isFinite)) + : null; + const slackDominanceMarginAboveTightFloor = Number.isFinite(minOutsideSlack) + && Number.isFinite(minEmittedTightSplitSlack) + ? minOutsideSlack - minEmittedTightSplitSlack + : null; + const boundedStratificationAudit = p13ThreatRows.length > 0 + ? { + sourceArtifact: fullVerifierPath, + auditScope: 'FULL_MIXED_BASE_STRUCTURAL_VERIFIER.threatLiftMiningRows[p=13]', + boundedThreatRowCount: p13ThreatRows.length, + splitStratumCount: boundedSplitStrata.length, + emittedTightSplitStratumCount: emittedTightSplitStrata.length, + emittedTightSplitCoveredRowCount, + outsideTightSplitStratumCount: outsideTightSplitStrata.length, + outsideTightSplitRowCount, + slackDominanceRule: 'A bounded p13 row outside the emitted tight split packets is slack-dominated when its minimum matching slack is strictly larger than the emitted tight-packet slack floor.', + minEmittedTightSplitSlack, + minOutsideSlack, + slackDominanceMarginAboveTightFloor, + slackDominatedOutsideStratumCount: slackDominatedOutsideStrata.length, + slackDominatedOutsideRowCount, + outsideRowsNeedingAdditionalSplitPacket, + allOutsideRowsSlackDominated: outsideTightSplitRowCount > 0 + && slackDominatedOutsideRowCount === outsideTightSplitRowCount, + emittedTightSplitStrata, + weakestOutsideStrata: outsideTightSplitStrata + .slice() + .sort((left, right) => ( + left.minMatchingSlack - right.minMatchingSlack + || right.rowCount - left.rowCount + || left.splitKey.localeCompare(right.splitKey) + )) + .slice(0, 8), + } + : null; + const tightSampleCovered = matchingPatternSplitKeys.length > 0 + && missingMatchingPatternSplitKeys.length === 0 + && p13PrimeLaneHandoffCandidate?.status === 'prime_lane_handoff_candidate_with_open_all_n_gaps'; + const fullBoundedUniverseCoveredByCurrentArtifact = Number.isFinite(threatRowCount) + && Number.isFinite(tightWitnessRowCount) + && threatRowCount === tightWitnessRowCount; + const boundedSlackDominatedRemainder = tightSampleCovered + && boundedStratificationAudit?.allOutsideRowsSlackDominated === true + && outsideRowsNeedingAdditionalSplitPacket === 0; + const targetNonTightSlackLowerBound = Number.isFinite(minEmittedTightSplitSlack) + ? minEmittedTightSplitSlack + 1 + : null; + const nonTightSlackFormulaRows = []; + const nonTightSlackFormulaStrata = new Map(); + for (const row of p13ThreatRows) { + const splitKey = rowSplitKeyForThreat(row); + if (!splitKey || emittedSplitKeySet.has(splitKey)) { + continue; + } + const side7 = Number(row.compatibleSide7Count); + const side18 = Number(row.compatibleSide18Count); + const strictBaseThreshold = Number(row.strictBaseThreshold); + const actualMatching = Number(row.matchingSizeInMissingCrossGraph); + const requiredMatchingLowerBound = Number.isFinite(Number(row.requiredMatchingLowerBound)) + ? Number(row.requiredMatchingLowerBound) + : side7 + side18 - strictBaseThreshold + 1; + const numericFieldsPresent = [ + side7, + side18, + strictBaseThreshold, + actualMatching, + requiredMatchingLowerBound, + Number(row.matchingSlack), + ].every(Number.isFinite); + const smallerSideSize = Math.min(side7, side18); + const largerSideSize = Math.max(side7, side18); + const largerSideLabel = side7 >= side18 ? 'side7' : 'side18'; + const requiredFormula = side7 + side18 - strictBaseThreshold + 1; + const sideCountSlackFormula = strictBaseThreshold - 1 - largerSideSize; + const candidateSize = Number(row.candidateSize); + const dMax = Number(row.dMax); + const rGreater = Number(row.rGreater); + const reconstructedVMax = [ + candidateSize, + strictBaseThreshold, + dMax, + rGreater, + ].every(Number.isFinite) + ? candidateSize - strictBaseThreshold - dMax - rGreater + : Number.NaN; + const targetAugmentedMarginConstant = Number.isFinite(targetNonTightSlackLowerBound) + ? targetNonTightSlackLowerBound + 1 + : Number.NaN; + const structuralMargin = [ + candidateSize, + largerSideSize, + reconstructedVMax, + dMax, + rGreater, + targetAugmentedMarginConstant, + ].every(Number.isFinite) + ? candidateSize - largerSideSize - reconstructedVMax - dMax - rGreater - targetAugmentedMarginConstant + : Number.NaN; + const observedSlack = actualMatching - requiredMatchingLowerBound; + const formulaReplayPassed = numericFieldsPresent + && requiredMatchingLowerBound === requiredFormula + && actualMatching === smallerSideSize + && Number(row.matchingSlack) === observedSlack + && observedSlack === sideCountSlackFormula; + const meetsTargetSlackFloor = Number.isFinite(targetNonTightSlackLowerBound) + && sideCountSlackFormula >= targetNonTightSlackLowerBound; + nonTightSlackFormulaRows.push({ + N: Number(row.N), + outsider: Number(row.outsider), + splitKey, + side7, + side18, + strictBaseThreshold, + requiredMatchingLowerBound, + actualMatching, + smallerSideSize, + largerSideSize, + largerSideLabel, + observedSlack, + sideCountSlackFormula, + candidateSize, + dMax, + rGreater, + reconstructedVMax, + targetAugmentedMarginConstant, + structuralMargin, + formulaReplayPassed, + meetsTargetSlackFloor, + }); + const stats = nonTightSlackFormulaStrata.get(splitKey) ?? { + splitKey, + rowCount: 0, + firstN: null, + lastN: null, + minSideCountSlackFormula: null, + maxSideCountSlackFormula: null, + minLargerSideSize: null, + maxLargerSideSize: null, + minStrictBaseThreshold: null, + maxStrictBaseThreshold: null, + largerSideLabel, + minCandidateSize: null, + maxCandidateSize: null, + minReconstructedVMax: null, + maxReconstructedVMax: null, + minDMax: null, + maxDMax: null, + minRGreater: null, + maxRGreater: null, + minStructuralMargin: null, + maxStructuralMargin: null, + formulaReplayPassed: true, + meetsTargetSlackFloor: true, + }; + stats.rowCount += 1; + addFiniteStat(stats, 'firstN', row.N, Math.min); + addFiniteStat(stats, 'lastN', row.N, Math.max); + addFiniteStat(stats, 'minSideCountSlackFormula', sideCountSlackFormula, Math.min); + addFiniteStat(stats, 'maxSideCountSlackFormula', sideCountSlackFormula, Math.max); + addFiniteStat(stats, 'minLargerSideSize', largerSideSize, Math.min); + addFiniteStat(stats, 'maxLargerSideSize', largerSideSize, Math.max); + addFiniteStat(stats, 'minStrictBaseThreshold', strictBaseThreshold, Math.min); + addFiniteStat(stats, 'maxStrictBaseThreshold', strictBaseThreshold, Math.max); + addFiniteStat(stats, 'minCandidateSize', candidateSize, Math.min); + addFiniteStat(stats, 'maxCandidateSize', candidateSize, Math.max); + addFiniteStat(stats, 'minReconstructedVMax', reconstructedVMax, Math.min); + addFiniteStat(stats, 'maxReconstructedVMax', reconstructedVMax, Math.max); + addFiniteStat(stats, 'minDMax', dMax, Math.min); + addFiniteStat(stats, 'maxDMax', dMax, Math.max); + addFiniteStat(stats, 'minRGreater', rGreater, Math.min); + addFiniteStat(stats, 'maxRGreater', rGreater, Math.max); + addFiniteStat(stats, 'minStructuralMargin', structuralMargin, Math.min); + addFiniteStat(stats, 'maxStructuralMargin', structuralMargin, Math.max); + stats.formulaReplayPassed = stats.formulaReplayPassed && formulaReplayPassed; + stats.meetsTargetSlackFloor = stats.meetsTargetSlackFloor && meetsTargetSlackFloor; + nonTightSlackFormulaStrata.set(splitKey, stats); + } + const nonTightSlackFormulaStratumSummaries = [...nonTightSlackFormulaStrata.values()] + .sort((left, right) => ( + left.minSideCountSlackFormula - right.minSideCountSlackFormula + || right.rowCount - left.rowCount + || left.splitKey.localeCompare(right.splitKey) + )); + const failedSlackFormulaRows = nonTightSlackFormulaRows + .filter((row) => !row.formulaReplayPassed || !row.meetsTargetSlackFloor); + const slackFormulaReplayVerified = boundedSlackDominatedRemainder + && nonTightSlackFormulaRows.length === outsideTightSplitRowCount + && failedSlackFormulaRows.length === 0; + const slackDominanceSymbolicLiftCandidate = boundedSlackDominatedRemainder + ? { + candidateId: 'D2_p13_slack_dominance_symbolic_lift', + status: slackFormulaReplayVerified + ? 'bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed' + : 'blocked_by_slack_formula_replay_failure', + promotesAllNClaim: false, + targetPrime: 13, + boundedRowCount: nonTightSlackFormulaRows.length, + boundedStratumCount: nonTightSlackFormulaStratumSummaries.length, + targetTightSlackFloor: minEmittedTightSplitSlack, + targetNonTightSlackLowerBound, + observedMinNonTightSlack: minOutsideSlack, + failedFormulaReplayRowCount: failedSlackFormulaRows.length, + firstFailedFormulaReplayRows: failedSlackFormulaRows.slice(0, 5), + proofReduction: { + statement: 'For non-tight p13 rows, reduce slack dominance to a side-count inequality after matching saturation.', + matchingSaturationHypothesis: 'matchingSizeInMissingCrossGraph = min(compatibleSide7Count, compatibleSide18Count)', + requiredMatchingFormula: 'K = compatibleSide7Count + compatibleSide18Count - strictBaseThreshold + 1', + derivedSlackFormula: 'matchingSlack = strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count)', + sufficientSideCountInequality: Number.isFinite(targetNonTightSlackLowerBound) + ? `max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 1 - ${targetNonTightSlackLowerBound}` + : null, + }, + boundedFormulaChecks: [ + { + checkId: 'non_tight_row_formula_replay', + status: failedSlackFormulaRows.length === 0 ? 'verified_bounded' : 'failed', + evidence: `${nonTightSlackFormulaRows.length - failedSlackFormulaRows.length}/${nonTightSlackFormulaRows.length} bounded non-tight p13 rows replay the slack formula and target floor`, + }, + { + checkId: 'future_symbolic_side_count_floor', + status: 'open_symbolic_lift', + evidence: 'The bounded formula replay names the exact side-count inequality still needed for all future p13 non-tight rows.', + }, + ], + formulaStrata: nonTightSlackFormulaStratumSummaries, + weakestFormulaStrata: nonTightSlackFormulaStratumSummaries.slice(0, 8), + firstOpenSymbolicLemma: { + lemmaId: 'D2_p13_non_tight_side_count_slack_floor_lift', + status: 'needed', + statement: 'For every future p=13 threat row outside the three tight split keys, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) stays above the tight slack floor.', + }, + proofBoundary: 'This candidate verifies the bounded algebraic slack reduction and side-count floor; it does not prove the all-N side-count inequality.', + } + : null; + const currentCoverageScope = boundedSlackDominatedRemainder + ? 'bounded_p13_threat_rows_tight_splits_plus_slack_dominated_remainder' + : 'matching_pattern_tight_witness_rows'; + + return { + schema: 'erdos.p848_row_universe_split_coverage_candidate/1', + coverageId: 'D2_p13_row_universe_split_coverage', + parentObligationId: 'D2_p13_matching_lower_bound', + targetPrime: 13, + status: tightSampleCovered + ? fullBoundedUniverseCoveredByCurrentArtifact + ? 'bounded_row_universe_covered_symbolic_lift_still_needed' + : boundedSlackDominatedRemainder + ? 'bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder' + : 'tight_sample_covered_full_row_universe_stratification_needed' + : 'blocked_by_split_packet_coverage', + promotesAllNClaim: false, + currentCoverage: { + coverageScope: currentCoverageScope, + threatRowCount: p13ThreatRows.length > 0 ? p13ThreatRows.length : Number.isFinite(threatRowCount) ? threatRowCount : null, + tightWitnessRowCount: Number.isFinite(tightWitnessRowCount) ? tightWitnessRowCount : null, + boundedThreatRowsOutsideTightWitnessPacket, + boundedThreatRowsCoveredByEmittedTightSplitStrata: boundedStratificationAudit?.emittedTightSplitCoveredRowCount ?? null, + boundedThreatRowsOutsideEmittedTightSplitStrata: boundedStratificationAudit?.outsideTightSplitRowCount ?? null, + boundedThreatRowsSlackDominatedOutsideTightSplitStrata: boundedStratificationAudit?.slackDominatedOutsideRowCount ?? null, + boundedThreatRowsNeedingAdditionalSplitPacket: boundedStratificationAudit?.outsideRowsNeedingAdditionalSplitPacket ?? null, + splitProfileCount: matchingPatternSplitKeys.length, + emittedP13SplitPacketCount: p13ManifestPackets.length, + matchingPatternSplitKeys, + emittedSplitKeys, + missingMatchingPatternSplitKeys, + extraEmittedSplitKeys, + allTightSampleSplitKeysEmitted: missingMatchingPatternSplitKeys.length === 0, + allP13SplitPacketsReady: p13PrimeLaneHandoffCandidate?.readySplitPacketCount === p13PrimeLaneHandoffCandidate?.splitPacketCount, + allBoundedP13ThreatRowsStratified: fullBoundedUniverseCoveredByCurrentArtifact || boundedSlackDominatedRemainder, + }, + boundedStratificationAudit, + slackDominanceSymbolicLiftCandidate, + lowerLayerChecks: [ + { + checkId: 'tight_matching_pattern_split_keys_emitted', + status: missingMatchingPatternSplitKeys.length === 0 ? 'verified' : 'blocked', + evidence: `${matchingPatternSplitKeys.length - missingMatchingPatternSplitKeys.length}/${matchingPatternSplitKeys.length} tight split keys have emitted packets`, + }, + { + checkId: 'tight_matching_pattern_split_packets_ready', + status: p13PrimeLaneHandoffCandidate?.status === 'prime_lane_handoff_candidate_with_open_all_n_gaps' + ? 'verified' + : 'blocked', + evidence: p13PrimeLaneHandoffCandidate?.status ?? null, + }, + { + checkId: 'full_bounded_threat_universe_stratified', + status: fullBoundedUniverseCoveredByCurrentArtifact || boundedSlackDominatedRemainder + ? 'verified_bounded' + : 'missing_stratification_atom', + evidence: boundedStratificationAudit + ? `${boundedStratificationAudit.emittedTightSplitCoveredRowCount}/${boundedStratificationAudit.boundedThreatRowCount} bounded p13 rows are in emitted tight split strata; ${boundedStratificationAudit.slackDominatedOutsideRowCount}/${boundedStratificationAudit.outsideTightSplitRowCount} outside rows are slack-dominated above tight floor ${boundedStratificationAudit.minEmittedTightSplitSlack}` + : Number.isFinite(threatRowCount) && Number.isFinite(tightWitnessRowCount) + ? `${tightWitnessRowCount}/${threatRowCount} bounded p13 threat rows are in the tight matching-pattern split packet` + : null, + }, + { + checkId: 'bounded_slack_dominated_remainder', + status: boundedSlackDominatedRemainder + ? 'verified_bounded' + : boundedStratificationAudit + ? 'needs_additional_split_or_slack_proof' + : 'not_audited', + evidence: boundedStratificationAudit + ? `${boundedStratificationAudit.slackDominatedOutsideRowCount}/${boundedStratificationAudit.outsideTightSplitRowCount} bounded outside-tight p13 rows have min slack > ${boundedStratificationAudit.minEmittedTightSplitSlack}` + : null, + }, + { + checkId: 'future_all_n_row_universe_covered', + status: 'open_symbolic_lift', + evidence: boundedSlackDominatedRemainder + ? 'The bounded p13 row universe is stratified, but the slack-dominance split still needs a symbolic all-N lift.' + : 'No repo-owned all-N row-universe theorem has been attached to this handoff candidate yet.', + }, + ], + emittedMissingAtom: fullBoundedUniverseCoveredByCurrentArtifact + ? { + atomId: 'D2_p13_row_universe_symbolic_lift', + status: 'needed', + statement: 'Prove every future p=13 threatening row falls into one of the emitted split profiles.', + } + : boundedSlackDominatedRemainder + ? { + atomId: 'D2_p13_slack_dominance_symbolic_lift', + status: 'needed', + statement: 'Lift the bounded p=13 row stratification into a symbolic theorem: the 49 non-tight residue/side strata remain slack-dominated above the tight split floor for all future rows, or the first failing stratum emits a new deterministic split packet.', + } + : { + atomId: 'D2_p13_row_universe_stratification_lift', + status: 'needed', + statement: 'Stratify the p=13 bounded threat universe beyond the tight matching-pattern witnesses: either prove non-tight rows have an easier slack-dominated matching bound, or emit additional split profiles for them before the all-N lift.', + }, + proofBoundary: boundedSlackDominatedRemainder + ? 'This is a bounded row-universe stratification audit. It verifies that the current bounded p13 threat rows outside the tight packets are slack-dominated; it does not prove the all-N slack theorem.' + : 'This is a row-universe coverage audit and missing-atom emitter. It verifies tight-sample split coverage only; it does not prove D2 for all p=13 rows.', + nextTheoremAction: fullBoundedUniverseCoveredByCurrentArtifact + ? 'Prove the symbolic all-N row-universe lift for the emitted p13 split profiles.' + : boundedSlackDominatedRemainder + ? 'Prove D2_p13_slack_dominance_symbolic_lift: turn the bounded slack-dominated remainder into a symbolic all-N row-family theorem.' + : 'Attack D2_p13_row_universe_stratification_lift: separate non-tight p13 threat rows into slack-dominated families or emit additional split packets.', + }; +} + +function buildP848SplitCoreAtomizationPlan(problem, formalizationWork) { + if (String(problem?.problemId ?? '') !== '848') { + return null; + } + const surface = formalizationWork.currentWork?.packetData?.structuralLiftAtomicSurface ?? null; + const d2Packet = surface?.proofPackets?.D2_p13_split_core_witness_extraction ?? null; + const d3Packet = surface?.proofPackets?.D3_p17_split_core_witness_extraction ?? null; + if (!surface || (!d2Packet && !d3Packet)) { + return null; + } + + const buildSplitRows = (packet, prime, parentObligationId) => { + const profilesByKey = new Map((packet?.profileSummary ?? []).map((profile) => [profile.groupKey, profile])); + return (packet?.symbolicSubgoals ?? []).map((subgoal, index) => { + const profile = profilesByKey.get(subgoal.groupKey) ?? {}; + const witnessCount = Number(profile.witnessCount ?? 0); + return { + atomId: subgoal.subgoalId, + prime, + parentObligationId, + splitKey: subgoal.groupKey, + status: 'needs_symbolic_persistence_proof', + priority: prime === 13 && witnessCount === 1 + ? 'highest_singleton_profile' + : prime === 13 + ? 'high_p13_active_lane' + : 'supporting_p17_companion_lane', + witnessCount, + nRange: profile.nRange ?? null, + commonMatchingPairCount: profile.commonMatchingPairCount ?? null, + commonMatchingPairExportComplete: profile.commonMatchingPairExportComplete ?? null, + commonMatchingPairs: profile.commonMatchingPairs ?? [], + requiredMatchingLowerBoundRange: profile.requiredMatchingLowerBoundRange ?? null, + minMatchingSlack: profile.minMatchingSlack ?? null, + boundedTarget: subgoal.boundedTarget ?? null, + goal: subgoal.goal, + falsifierBoundary: subgoal.falsifierBoundary, + }; + }); + }; + + const splitAtomsWithoutArtifacts = [ + ...buildSplitRows(d2Packet, 13, 'D2_p13_matching_lower_bound'), + ...buildSplitRows(d3Packet, 17, 'D3_p17_matching_lower_bound'), + ]; + const packetRootPaths = getP848SplitAtomPacketPaths(problem); + const splitAtoms = splitAtomsWithoutArtifacts.map((atom) => { + const packetPaths = getP848SplitAtomPacketPaths(problem, atom.atomId); + return { + ...atom, + packetArtifact: packetPaths + ? { + packetId: packetPaths.packetId, + jsonPath: packetPaths.jsonPath, + markdownPath: packetPaths.markdownPath, + jsonPresent: fs.existsSync(packetPaths.jsonPath), + markdownPresent: fs.existsSync(packetPaths.markdownPath), + } + : null, + }; + }); + const existingPacketManifest = packetRootPaths?.manifestJsonPath + ? readJsonIfPresent(packetRootPaths.manifestJsonPath) + : null; + const successorPacketEntries = Array.isArray(existingPacketManifest?.successorPackets) + ? existingPacketManifest.successorPackets + : []; + const sideCountFloorPacketEntries = Array.isArray(existingPacketManifest?.sideCountFloorPackets) + ? existingPacketManifest.sideCountFloorPackets + : []; + const firstSideCountFloorPacket = existingPacketManifest?.firstSideCountFloorPacketToAttack + ?? sideCountFloorPacketEntries.find((packet) => packet.priority === 'highest_side_count_floor_atom') + ?? sideCountFloorPacketEntries[0] + ?? null; + const firstSideCountFloorMovingTermSubatom = firstSideCountFloorPacket?.firstOpenMovingTermSubatom ?? null; + const firstSideCountFloorMovingTermIsDMaxGrowth = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_growth_'); + const firstSideCountFloorMovingTermIsDMaxQ2Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q2_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ3Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q3_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ5Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q5_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ7Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q7_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ11Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q11_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ19Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q19_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ23Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q23_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ31Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q31_progression_'); + const firstSideCountFloorMovingTermIsDMaxQ251Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_q251_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailRecombination = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_recombination_'); + const firstSideCountFloorMovingTermIsDMaxTailQ17Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q17_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q19_plus_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q11_minus_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q23_plus_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q31_minus_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q251_minus_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ29Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q29_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ37Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q37_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ41Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q41_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ43Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q43_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ47Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q47_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ53Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q53_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ59Progression = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q59_progression_'); + const firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_residual_dynamic_margin_symbolic_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_successor_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_symbolic_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor = firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + || firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor; + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_'); + const firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_exact_mixed_matching_injection_'); + const firstSideCountFloorMovingTermIsDynamicMargin = firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + || firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + || firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + || firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dynamic_margin_'); + const firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloorAtom = String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_'); + const firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloor = firstSideCountFloorMovingTermIsDynamicMargin + || firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloorAtom; + const firstSideCountFloorMovingTermIsDMaxTailQ587Progression = firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloor + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q587_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ577Progression = firstSideCountFloorMovingTermIsDMaxTailQ587Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q577_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ571Progression = firstSideCountFloorMovingTermIsDMaxTailQ577Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q571_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ569Progression = firstSideCountFloorMovingTermIsDMaxTailQ571Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q569_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ563Progression = firstSideCountFloorMovingTermIsDMaxTailQ569Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q563_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ557Progression = firstSideCountFloorMovingTermIsDMaxTailQ563Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q557_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ547Progression = firstSideCountFloorMovingTermIsDMaxTailQ557Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q547_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ541Progression = firstSideCountFloorMovingTermIsDMaxTailQ547Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q541_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ523Progression = firstSideCountFloorMovingTermIsDMaxTailQ541Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q523_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ521Progression = firstSideCountFloorMovingTermIsDMaxTailQ523Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q521_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ509Progression = firstSideCountFloorMovingTermIsDMaxTailQ521Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q509_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ503Progression = firstSideCountFloorMovingTermIsDMaxTailQ509Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q503_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ499Progression = firstSideCountFloorMovingTermIsDMaxTailQ503Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q499_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ491Progression = firstSideCountFloorMovingTermIsDMaxTailQ499Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q491_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ487Progression = firstSideCountFloorMovingTermIsDMaxTailQ491Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q487_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ479Progression = firstSideCountFloorMovingTermIsDMaxTailQ487Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q479_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ467Progression = firstSideCountFloorMovingTermIsDMaxTailQ479Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q467_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ463Progression = firstSideCountFloorMovingTermIsDMaxTailQ467Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q463_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ461Progression = firstSideCountFloorMovingTermIsDMaxTailQ463Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q461_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ457Progression = firstSideCountFloorMovingTermIsDMaxTailQ461Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q457_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ449Progression = firstSideCountFloorMovingTermIsDMaxTailQ457Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q449_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ443Progression = firstSideCountFloorMovingTermIsDMaxTailQ449Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q443_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ439Progression = firstSideCountFloorMovingTermIsDMaxTailQ443Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q439_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ433Progression = firstSideCountFloorMovingTermIsDMaxTailQ439Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q433_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ431Progression = firstSideCountFloorMovingTermIsDMaxTailQ433Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q431_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ421Progression = firstSideCountFloorMovingTermIsDMaxTailQ431Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q421_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ419Progression = firstSideCountFloorMovingTermIsDMaxTailQ421Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q419_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ409Progression = firstSideCountFloorMovingTermIsDMaxTailQ419Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q409_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ401Progression = firstSideCountFloorMovingTermIsDMaxTailQ409Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q401_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ397Progression = firstSideCountFloorMovingTermIsDMaxTailQ401Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q397_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ389Progression = firstSideCountFloorMovingTermIsDMaxTailQ397Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q389_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ383Progression = firstSideCountFloorMovingTermIsDMaxTailQ389Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q383_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ379Progression = firstSideCountFloorMovingTermIsDMaxTailQ383Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q379_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ373Progression = firstSideCountFloorMovingTermIsDMaxTailQ379Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q373_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ367Progression = firstSideCountFloorMovingTermIsDMaxTailQ373Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q367_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ359Progression = firstSideCountFloorMovingTermIsDMaxTailQ367Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q359_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ353Progression = firstSideCountFloorMovingTermIsDMaxTailQ359Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q353_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ349Progression = firstSideCountFloorMovingTermIsDMaxTailQ353Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q349_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ347Progression = firstSideCountFloorMovingTermIsDMaxTailQ349Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q347_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ337Progression = firstSideCountFloorMovingTermIsDMaxTailQ347Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q337_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ331Progression = firstSideCountFloorMovingTermIsDMaxTailQ337Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q331_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ317Progression = firstSideCountFloorMovingTermIsDMaxTailQ331Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q317_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ313Progression = firstSideCountFloorMovingTermIsDMaxTailQ317Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q313_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ311Progression = firstSideCountFloorMovingTermIsDMaxTailQ313Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q311_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ307Progression = firstSideCountFloorMovingTermIsDMaxTailQ311Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q307_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ293Progression = firstSideCountFloorMovingTermIsDMaxTailQ307Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q293_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ283Progression = firstSideCountFloorMovingTermIsDMaxTailQ293Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q283_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ281Progression = firstSideCountFloorMovingTermIsDMaxTailQ283Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q281_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ277Progression = firstSideCountFloorMovingTermIsDMaxTailQ281Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q277_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ271Progression = firstSideCountFloorMovingTermIsDMaxTailQ277Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q271_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ269Progression = firstSideCountFloorMovingTermIsDMaxTailQ271Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q269_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ263Progression = firstSideCountFloorMovingTermIsDMaxTailQ269Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q263_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ257Progression = firstSideCountFloorMovingTermIsDMaxTailQ263Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q257_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ241Progression = firstSideCountFloorMovingTermIsDMaxTailQ257Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q241_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ239Progression = firstSideCountFloorMovingTermIsDMaxTailQ241Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q239_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ233Progression = firstSideCountFloorMovingTermIsDMaxTailQ239Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q233_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ229Progression = firstSideCountFloorMovingTermIsDMaxTailQ233Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q229_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ227Progression = firstSideCountFloorMovingTermIsDMaxTailQ229Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q227_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ223Progression = firstSideCountFloorMovingTermIsDMaxTailQ227Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q223_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ211Progression = firstSideCountFloorMovingTermIsDMaxTailQ223Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q211_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ199Progression = firstSideCountFloorMovingTermIsDMaxTailQ211Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q199_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ197Progression = firstSideCountFloorMovingTermIsDMaxTailQ199Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q197_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ193Progression = firstSideCountFloorMovingTermIsDMaxTailQ197Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q193_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ191Progression = firstSideCountFloorMovingTermIsDMaxTailQ193Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q191_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ181Progression = firstSideCountFloorMovingTermIsDMaxTailQ191Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q181_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ179Progression = firstSideCountFloorMovingTermIsDMaxTailQ181Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q179_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ173Progression = firstSideCountFloorMovingTermIsDMaxTailQ179Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q173_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ167Progression = firstSideCountFloorMovingTermIsDMaxTailQ173Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q167_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ163Progression = firstSideCountFloorMovingTermIsDMaxTailQ167Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q163_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ157Progression = firstSideCountFloorMovingTermIsDMaxTailQ163Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q157_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ151Progression = firstSideCountFloorMovingTermIsDMaxTailQ157Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q151_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ149Progression = firstSideCountFloorMovingTermIsDMaxTailQ151Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q149_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ139Progression = firstSideCountFloorMovingTermIsDMaxTailQ149Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q139_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ137Progression = firstSideCountFloorMovingTermIsDMaxTailQ139Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q137_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ131Progression = firstSideCountFloorMovingTermIsDMaxTailQ137Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q131_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ127Progression = firstSideCountFloorMovingTermIsDMaxTailQ131Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q127_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ113Progression = firstSideCountFloorMovingTermIsDMaxTailQ127Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q113_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ109Progression = firstSideCountFloorMovingTermIsDMaxTailQ113Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q109_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ107Progression = firstSideCountFloorMovingTermIsDMaxTailQ109Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q107_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ103Progression = firstSideCountFloorMovingTermIsDMaxTailQ107Progression + || String(firstSideCountFloorMovingTermSubatom ?? '') + .startsWith('D2_p13_dmax_tail_q103_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ101Progression = firstSideCountFloorMovingTermIsDMaxTailQ103Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q101_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ97Progression = firstSideCountFloorMovingTermIsDMaxTailQ101Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q97_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ89Progression = firstSideCountFloorMovingTermIsDMaxTailQ97Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q89_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ83Progression = firstSideCountFloorMovingTermIsDMaxTailQ89Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q83_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ79Progression = firstSideCountFloorMovingTermIsDMaxTailQ83Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q79_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ73Progression = firstSideCountFloorMovingTermIsDMaxTailQ79Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q73_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ71Progression = firstSideCountFloorMovingTermIsDMaxTailQ73Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q71_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ67Progression = firstSideCountFloorMovingTermIsDMaxTailQ71Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q67_progression_'); + const firstSideCountFloorMovingTermIsDMaxTailQ61Progression = firstSideCountFloorMovingTermIsDMaxTailQ67Progression + || String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q61_progression_'); + const dMaxConstantBoundFinished = firstSideCountFloorMovingTermIsDMaxGrowth + || firstSideCountFloorMovingTermIsDMaxQ2Progression + || firstSideCountFloorMovingTermIsDMaxQ3Progression + || firstSideCountFloorMovingTermIsDMaxQ5Progression + || firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + || firstSideCountFloorMovingTermIsDMaxTailRecombination + || firstSideCountFloorMovingTermIsDMaxTailQ17Progression + || firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + || firstSideCountFloorMovingTermIsDMaxTailQ67Progression + || firstSideCountFloorMovingTermIsDMaxTailQ71Progression + || firstSideCountFloorMovingTermIsDMaxTailQ73Progression + || firstSideCountFloorMovingTermIsDMaxTailQ79Progression + || firstSideCountFloorMovingTermIsDMaxTailQ83Progression + || firstSideCountFloorMovingTermIsDMaxTailQ89Progression + || firstSideCountFloorMovingTermIsDMaxTailQ97Progression + || firstSideCountFloorMovingTermIsDMaxTailQ101Progression + || firstSideCountFloorMovingTermIsDMaxTailQ103Progression + || firstSideCountFloorMovingTermIsDMaxTailQ107Progression + || firstSideCountFloorMovingTermIsDMaxTailQ109Progression + || firstSideCountFloorMovingTermIsDMaxTailQ113Progression + || firstSideCountFloorMovingTermIsDMaxTailQ127Progression + || firstSideCountFloorMovingTermIsDMaxTailQ131Progression + || firstSideCountFloorMovingTermIsDMaxTailQ137Progression; + const dMaxGrowthProfileFirstSubatomEmitted = firstSideCountFloorMovingTermIsDMaxQ2Progression + || firstSideCountFloorMovingTermIsDMaxQ3Progression + || firstSideCountFloorMovingTermIsDMaxQ5Progression + || firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + || firstSideCountFloorMovingTermIsDMaxTailRecombination + || firstSideCountFloorMovingTermIsDMaxTailQ17Progression + || firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + || firstSideCountFloorMovingTermIsDMaxTailQ67Progression + || firstSideCountFloorMovingTermIsDMaxTailQ71Progression + || firstSideCountFloorMovingTermIsDMaxTailQ73Progression + || firstSideCountFloorMovingTermIsDMaxTailQ79Progression + || firstSideCountFloorMovingTermIsDMaxTailQ83Progression + || firstSideCountFloorMovingTermIsDMaxTailQ89Progression + || firstSideCountFloorMovingTermIsDMaxTailQ97Progression + || firstSideCountFloorMovingTermIsDMaxTailQ101Progression + || firstSideCountFloorMovingTermIsDMaxTailQ103Progression + || firstSideCountFloorMovingTermIsDMaxTailQ107Progression + || firstSideCountFloorMovingTermIsDMaxTailQ109Progression + || firstSideCountFloorMovingTermIsDMaxTailQ113Progression + || firstSideCountFloorMovingTermIsDMaxTailQ127Progression + || firstSideCountFloorMovingTermIsDMaxTailQ131Progression + || firstSideCountFloorMovingTermIsDMaxTailQ137Progression; + const firstSuccessorPacket = existingPacketManifest?.firstSuccessorPacketToAttack + ?? successorPacketEntries.find((packet) => packet.priority === 'highest_refinement_successor') + ?? successorPacketEntries[0] + ?? null; + const allSuccessorPacketFilesPresent = successorPacketEntries.length > 0 + && successorPacketEntries.every((packet) => ( + packet.jsonPath && fs.existsSync(packet.jsonPath) + && packet.markdownPath && fs.existsSync(packet.markdownPath) + )); + const firstPacketRefinementConditionCount = Number( + existingPacketManifest?.firstPacketToAttack?.vertexPresenceRefinementConditionCount ?? 0, + ); + const verifiedSuccessorFamilyCount = successorPacketEntries + .filter((packet) => packet.symbolicVertexFamilyLemmaStatus === 'symbolic_vertex_family_lemma_verified').length; + const firstUnverifiedSuccessorPacket = successorPacketEntries + .find((packet) => packet.symbolicVertexFamilyLemmaStatus !== 'symbolic_vertex_family_lemma_verified') ?? null; + const allMaterializedSuccessorFamiliesVerified = successorPacketEntries.length > 0 + && verifiedSuccessorFamilyCount === successorPacketEntries.length; + const firstManifestPacket = existingPacketManifest?.firstPacketToAttack + ?? (existingPacketManifest?.packets ?? []).find((packet) => packet.priority === 'highest_singleton_profile') + ?? null; + const p13PrimeLaneHandoffCandidate = (existingPacketManifest?.primeLaneHandoffCandidates ?? []) + .find((candidate) => candidate.laneId === 'D2_p13_matching_lower_bound') ?? null; + const existingManifestPacketEntries = Array.isArray(existingPacketManifest?.packets) + ? existingPacketManifest.packets + : []; + const firstPacketEdgeObstructionCertificateStatus = firstManifestPacket?.edgeObstructionCertificateStatus ?? null; + const firstPacketLiteralEdgeObstructionsCertified = firstPacketEdgeObstructionCertificateStatus + === 'literal_edge_obstruction_certificate_verified'; + const firstPacketEdgeCongruencePersistenceStatus = firstManifestPacket?.edgeCongruencePersistenceStatus ?? null; + const firstPacketEdgeCongruencePersistenceVerified = firstPacketEdgeCongruencePersistenceStatus + === 'literal_constant_edge_persistence_verified'; + const verifiedEdgeCongruencePacketCount = existingManifestPacketEntries + .filter((packet) => packet.edgeCongruencePersistenceStatus === 'literal_constant_edge_persistence_verified').length; + const allManifestPacketsEdgeCongruenceVerified = existingManifestPacketEntries.length > 0 + && verifiedEdgeCongruencePacketCount === existingManifestPacketEntries.length; + const firstPacketMatchingKEnvelopeCertificateStatus = firstManifestPacket?.matchingKEnvelopeCertificateStatus ?? null; + const firstPacketMatchingKEnvelopeVerified = firstPacketMatchingKEnvelopeCertificateStatus + === 'literal_matching_sampled_k_envelope_verified'; + const verifiedMatchingKEnvelopePacketCount = existingManifestPacketEntries + .filter((packet) => packet.matchingKEnvelopeCertificateStatus === 'literal_matching_sampled_k_envelope_verified').length; + const allManifestPacketsMatchingKEnvelopeVerified = existingManifestPacketEntries.length > 0 + && verifiedMatchingKEnvelopePacketCount === existingManifestPacketEntries.length; + const firstPacketSplitDischargeReadinessStatus = firstManifestPacket?.splitDischargeReadinessStatus ?? null; + const firstPacketSplitDischargeReady = firstPacketSplitDischargeReadinessStatus + === 'split_discharge_readiness_candidate'; + const splitDischargeReadyPacketCount = existingManifestPacketEntries + .filter((packet) => packet.splitDischargeReadinessStatus === 'split_discharge_readiness_candidate').length; + const p13ManifestPacketEntries = existingManifestPacketEntries + .filter((packet) => Number(packet.prime) === 13); + const p13SplitDischargeReadyPacketCount = p13ManifestPacketEntries + .filter((packet) => packet.splitDischargeReadinessStatus === 'split_discharge_readiness_candidate').length; + const allP13SplitDischargeReady = p13ManifestPacketEntries.length > 0 + && p13SplitDischargeReadyPacketCount === p13ManifestPacketEntries.length; + const p13PrimeLaneHandoffReady = p13PrimeLaneHandoffCandidate?.status + === 'prime_lane_handoff_candidate_with_open_all_n_gaps'; + const firstOpenP13HandoffGap = p13PrimeLaneHandoffCandidate?.theoremCandidate?.openAllNHandoffGaps?.[0] ?? null; + const p13RowUniverseCoverageCandidate = buildP848P13RowUniverseCoverageCandidate(problem, surface, existingPacketManifest); + const nextUndischargedP13Packet = existingManifestPacketEntries.find((packet) => ( + Number(packet.prime) === 13 + && packet.splitDischargeReadinessStatus !== 'split_discharge_readiness_candidate' + )) ?? null; + const allCommonCorePairsExported = splitAtoms.length > 0 + && splitAtoms.every((atom) => atom.commonMatchingPairExportComplete === true); + const allSplitAtomPacketArtifactsPlanned = splitAtoms.length > 0 + && splitAtoms.every((atom) => Boolean(atom.packetArtifact?.jsonPath && atom.packetArtifact?.markdownPath)); + const allSplitAtomPacketFilesPresent = splitAtoms.length > 0 + && splitAtoms.every((atom) => atom.packetArtifact?.jsonPresent === true && atom.packetArtifact?.markdownPresent === true) + && Boolean(packetRootPaths?.manifestJsonPath && fs.existsSync(packetRootPaths.manifestJsonPath)) + && Boolean(packetRootPaths?.manifestMarkdownPath && fs.existsSync(packetRootPaths.manifestMarkdownPath)); + const highestPriorityAtom = splitAtoms.find((atom) => atom.priority === 'highest_singleton_profile') + ?? splitAtoms.find((atom) => atom.prime === 13) + ?? splitAtoms[0] + ?? null; + const totalCommonCoreEdges = splitAtoms.reduce((total, atom) => total + Number(atom.commonMatchingPairCount ?? 0), 0); + + return { + planId: 'p848_split_core_atomization_master_plan_v1', + status: 'active', + scope: { + problemId: '848', + activeParentObligationId: surface.activeAtom?.obligationId ?? 'D2_p13_matching_lower_bound', + targetObligationId: surface.targetAtom?.obligationId ?? 'D4_matching_bound_implies_sMaxMixed_bound', + splitAtomCount: splitAtoms.length, + totalCommonCoreEdges, + d2SplitCount: d2Packet?.scope?.splitProfileCount ?? 0, + d3SplitCount: d3Packet?.scope?.splitProfileCount ?? 0, + }, + packetManifest: packetRootPaths + ? { + status: allSplitAtomPacketArtifactsPlanned ? 'planned' : 'blocked', + directoryPath: packetRootPaths.directoryPath, + manifestJsonPath: packetRootPaths.manifestJsonPath, + manifestMarkdownPath: packetRootPaths.manifestMarkdownPath, + packetCount: splitAtoms.length, + successorPacketCount: successorPacketEntries.length, + sideCountFloorPacketCount: sideCountFloorPacketEntries.length, + firstPacketRefinementConditionCount, + verifiedSuccessorFamilyCount, + allPacketFilesPresent: allSplitAtomPacketFilesPresent, + allSuccessorPacketFilesPresent, + allMaterializedSuccessorFamiliesVerified, + firstPacketEdgeObstructionCertificateStatus, + firstPacketLiteralEdgeObstructionsCertified, + firstPacketEdgeCongruencePersistenceStatus, + firstPacketEdgeCongruencePersistenceVerified, + verifiedEdgeCongruencePacketCount, + allManifestPacketsEdgeCongruenceVerified, + firstPacketMatchingKEnvelopeCertificateStatus, + firstPacketMatchingKEnvelopeVerified, + verifiedMatchingKEnvelopePacketCount, + allManifestPacketsMatchingKEnvelopeVerified, + firstPacketSplitDischargeReadinessStatus, + firstPacketSplitDischargeReady, + splitDischargeReadyPacketCount, + p13SplitDischargeReadyPacketCount, + allP13SplitDischargeReady, + p13PrimeLaneHandoffStatus: p13PrimeLaneHandoffCandidate?.status ?? null, + p13PrimeLaneHandoffOpenGapCount: p13PrimeLaneHandoffCandidate?.theoremCandidate?.openAllNHandoffGaps?.length ?? null, + p13PrimeLaneHandoffFirstOpenGap: firstOpenP13HandoffGap?.gapId ?? null, + p13RowUniverseCoverageStatus: p13RowUniverseCoverageCandidate?.status ?? null, + p13RowUniverseCoverageScope: p13RowUniverseCoverageCandidate?.currentCoverage?.coverageScope ?? null, + p13RowUniverseFirstMissingAtom: p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId ?? null, + p13SlackDominanceLiftStatus: p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.status ?? null, + p13SlackDominanceFirstOpenLemma: p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.firstOpenSymbolicLemma?.lemmaId ?? null, + firstSideCountFloorPacketToAttack: firstSideCountFloorPacket?.atomId ?? null, + firstSideCountFloorStructuralMarginLemma: firstSideCountFloorPacket?.firstOpenStructuralMarginLemma ?? null, + firstSideCountFloorMovingTermSubatom, + nextUndischargedP13PacketToAttack: nextUndischargedP13Packet?.atomId ?? null, + firstPacketToAttack: highestPriorityAtom?.atomId ?? null, + firstSuccessorPacketToAttack: firstSuccessorPacket?.successorAtomId ?? null, + firstUnverifiedSuccessorPacketToAttack: firstUnverifiedSuccessorPacket?.successorAtomId ?? null, + refreshCommand: `erdos problem task-list-refresh ${problem.problemId}`, + } + : null, + northStar: 'Make the D2/D3 matching lower-bound proof deterministic by turning every split-core persistence claim into replayable vertex, edge, congruence, matching, and K-envelope atoms.', + deterministicRule: 'No split may be promoted from bounded witness support to theorem support until every layer below has a pass/fail checker and every failure emits a smaller successor atom.', + mostConfusingPart: { + question: 'Are the common matching pairs literal fixed vertices, or formulaic residue-family vertices that move with N?', + whyItMatters: 'This determines whether the proof obligation is fixed vertex presence across a split, or extraction of a parameterized vertex formula before edge persistence can be proved.', + firstPlaceToAttack: highestPriorityAtom?.atomId ?? null, + reason: highestPriorityAtom + ? `Start with ${highestPriorityAtom.atomId} because it is the sharpest active split atom: ${highestPriorityAtom.priority}.` + : 'No split atom is available yet.', + }, + rowUniverseCoverage: p13RowUniverseCoverageCandidate, + slackDominanceSymbolicLift: p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate ?? null, + masterLayers: [ + { + layerId: 'A0_input_universe_freeze', + status: d2Packet || d3Packet ? 'done_bounded' : 'blocked', + objective: 'Freeze the exact threatening-outsider row universe, prime lanes, and K(N,x) formula used by D1.', + deterministicOutput: 'A row-universe manifest keyed by prime, N, outsider, side counts, K(N,x), actual matching, and smaller-side size.', + currentEvidence: surface.proofPackets?.D1_residue_block_matching_injection?.checkerId ?? null, + }, + { + layerId: 'A1_split_profile_inventory', + status: splitAtoms.length > 0 ? 'done_bounded' : 'blocked', + objective: 'Freeze the p13 and p17 split keys and attach each bounded split-core witness packet to a parent D-lane obligation.', + deterministicOutput: 'One split atom per residue/smaller-side profile.', + currentEvidence: splitAtoms.map((atom) => atom.atomId), + }, + { + layerId: 'A2_full_common_core_pair_export', + status: allCommonCorePairsExported ? 'done' : 'next', + objective: 'Export the full common matching core for each split, not only a pair sample.', + deterministicOutput: 'For every split atom, a complete ordered list of common matching pairs with left/right values and residues modulo 25, p, and p^2.', + falsifierBoundary: 'A split packet reports commonMatchingPairCount but cannot provide exactly that many explicit pair records.', + }, + { + layerId: 'A3_vertex_presence_atoms', + status: allCommonCorePairsExported && allSplitAtomPacketArtifactsPlanned ? 'next' : 'pending_A2', + objective: 'Prove every left/right vertex used by the split core is present on the correct compatible side for every row in the split.', + deterministicOutput: 'One pass/fail vertex-presence certificate per split-core vertex family.', + falsifierBoundary: 'A core vertex leaves the compatible side, changes side, or requires an unstated N-dependent formula.', + }, + { + layerId: 'A4_edge_obstruction_atoms', + status: allCommonCorePairsExported && allSplitAtomPacketArtifactsPlanned ? 'next' : 'pending_A2', + objective: 'For every selected pair, identify the exact reason the cross edge is missing.', + deterministicOutput: 'One obstruction certificate per pair, preferably a square-divisor witness or explicit modular contradiction.', + falsifierBoundary: 'A selected pair is compatible in any row of the split or lacks a stable obstruction witness.', + }, + { + layerId: 'A5_congruence_persistence_atoms', + status: allManifestPacketsEdgeCongruenceVerified + ? 'done_literal' + : allCommonCorePairsExported && allSplitAtomPacketArtifactsPlanned + ? 'next' + : 'pending_A4', + objective: 'Prove each edge obstruction is implied by the split congruence assumptions, not by accidental sampled N values.', + deterministicOutput: 'A symbolic congruence proof per obstruction family.', + falsifierBoundary: 'The obstruction depends on a sampled representative rather than the split key and row-universe hypotheses.', + }, + { + layerId: 'A6_matching_disjointness_atoms', + status: allManifestPacketsMatchingKEnvelopeVerified + ? 'done_literal' + : allCommonCorePairsExported && allSplitAtomPacketArtifactsPlanned + ? 'next' + : 'pending_A2', + objective: 'Prove the exported pairs form a matching by checking left and right uniqueness.', + deterministicOutput: 'A deterministic disjointness certificate per split core.', + falsifierBoundary: 'Two core pairs reuse a left or right vertex after parameterization.', + }, + { + layerId: 'A7_K_envelope_atoms', + status: allManifestPacketsMatchingKEnvelopeVerified + ? 'done_sampled_envelope' + : 'bounded_done_symbolic_pending', + objective: 'Prove the symbolic core size is always at least the required K(N,x) throughout the split.', + deterministicOutput: 'One K-envelope inequality certificate per split.', + currentEvidence: splitAtoms.map((atom) => ({ + atomId: atom.atomId, + commonMatchingPairCount: atom.commonMatchingPairCount, + requiredMatchingLowerBoundRange: atom.requiredMatchingLowerBoundRange, + })), + }, + { + layerId: 'A8_split_discharge_atoms', + status: allP13SplitDischargeReady + ? 'p13_readiness_complete_p17_pending' + : splitDischargeReadyPacketCount > 0 + ? 'partial_readiness' + : 'pending_A3_A4_A5_A6_A7', + objective: 'Promote each split from bounded support to a symbolic split lemma only after all lower atoms pass.', + deterministicOutput: 'One theorem-facing split lemma per split key.', + falsifierBoundary: 'Any lower atom fails or emits a new sub-split that is not yet discharged.', + }, + { + layerId: 'A9_prime_lane_promotion', + status: allP13SplitDischargeReady ? 'p13_ready_for_D2_promotion' : 'pending_A8', + objective: 'Promote D2 once all p13 split lemmas pass, and promote D3 once all p17 split lemmas pass.', + deterministicOutput: 'D2_p13_matching_lower_bound and D3_p17_matching_lower_bound can feed D4 without bounded-only caveats.', + falsifierBoundary: 'A prime lane has an uncovered split, an unproved split, or an unbounded K envelope.', + }, + ], + splitAtoms, + adjacentAtomizedLayers: [ + { + layerId: 'B1_split_coverage_universe', + status: 'needed', + reason: 'The split-core proof should not silently assume every future threatening row belongs to the current split keys.', + focusPlan: 'Create a checker that partitions every bounded threatening row by the split key and emits new split obligations whenever a refreshed verifier discovers a new key.', + }, + { + layerId: 'B2_vertex_formula_extraction', + status: 'needed_if_vertices_move', + reason: 'If core vertices are not literal constants across N, we need formulas for the moving vertex families before edge persistence is meaningful.', + focusPlan: 'Mine affine/residue formulas for common-core left/right vertices and verify them against every sampled witness row.', + }, + { + layerId: 'B3_obstruction_witness_normal_form', + status: 'needed', + reason: 'Edge persistence becomes deterministic only when every missing edge has a normalized obstruction witness.', + focusPlan: 'Normalize each missing edge into product-plus-one divisibility, square-witness, or explicit incompatibility schema.', + }, + { + layerId: 'B4_all_N_handoff_guard', + status: 'needed_later', + reason: 'Even after split cores are symbolic, the final 848 decision still needs a clean handoff from D2/D3/D4 into the all-N threshold route.', + focusPlan: 'Keep this separate from split-core work; do not let final threshold or endpoint-regime logic pollute the matching-core proof.', + }, + ], + recommendedImmediateTasks: [ + { + taskId: 'implement_full_common_core_pair_export', + status: allCommonCorePairsExported ? 'done' : 'next', + task: 'Extend the matching-pattern miner so every split profile exports the full common matching core, not only commonMatchingPairSample.', + completionRule: 'Each split profile has commonMatchingPairs.length === commonMatchingPairCount for p13 and p17.', + }, + { + taskId: 'emit_split_atom_packets', + status: allCommonCorePairsExported && allSplitAtomPacketArtifactsPlanned + ? 'done' + : 'blocked_by_full_common_core_export', + task: 'Generate one atom packet per split with inputs, common pairs, K envelope, required lower-bound range, and falsifier boundary.', + completionRule: 'The task list points at concrete split atom IDs instead of one broad D2/D3 persistence phrase.', + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'materialize_square_residue_successor_packets', + status: successorPacketEntries.length >= 2 && allSuccessorPacketFilesPresent + ? 'done' + : 'highest', + task: 'Materialize square-residue successor packets for every p13 split profile so D2 can be discharged profile-by-profile.', + completionRule: 'The packet manifest lists verified successor packet files for every p13 refinement condition.', + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'attack_top_square_residue_successor', + status: firstSuccessorPacket + ? firstSuccessorPacket.symbolicVertexFamilyLemmaStatus === 'symbolic_vertex_family_lemma_verified' + ? 'done_symbolic_family_verified' + : 'highest' + : 'blocked_by_successor_materialization', + task: firstSuccessorPacket + ? `Attack successor ${firstSuccessorPacket.successorAtomId}: prove the ${firstSuccessorPacket.affectedAtomCount} affected vertex-presence atoms as a symbolic square-residue subfamily.` + : 'Attack the top square-residue successor after it is materialized.', + completionRule: 'The successor packet is promoted to a symbolic vertex-family lemma or emits a still smaller deterministic obstruction.', + command: null, + packetAtomId: firstSuccessorPacket?.successorAtomId ?? null, + packetId: firstSuccessorPacket?.packetId ?? null, + packetJsonPath: firstSuccessorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSuccessorPacket?.markdownPath ?? null, + }, + { + taskId: firstUnverifiedSuccessorPacket + ? 'attack_next_square_residue_successor' + : 'materialize_remaining_square_residue_successor_packets', + status: firstUnverifiedSuccessorPacket + ? 'highest' + : allMaterializedSuccessorFamiliesVerified + && firstPacketRefinementConditionCount > successorPacketEntries.length + ? 'highest' + : 'blocked_by_successor_family_proofs', + task: firstUnverifiedSuccessorPacket + ? `Attack successor ${firstUnverifiedSuccessorPacket.successorAtomId}: prove the ${firstUnverifiedSuccessorPacket.affectedAtomCount} affected vertex-presence atoms as a symbolic square-residue subfamily.` + : `Materialize the remaining square-residue successor packets; ${successorPacketEntries.length} of ${firstPacketRefinementConditionCount || '(unknown)'} refinement conditions currently have packet files.`, + completionRule: firstUnverifiedSuccessorPacket + ? 'The successor packet is promoted to a symbolic vertex-family lemma or emits a smaller deterministic obstruction.' + : 'Every refinement condition from the singleton p13 packet has a successor packet file and symbolic family check.', + command: null, + packetAtomId: firstUnverifiedSuccessorPacket?.successorAtomId ?? null, + packetId: firstUnverifiedSuccessorPacket?.packetId ?? null, + packetJsonPath: firstUnverifiedSuccessorPacket?.jsonPath ?? null, + packetMarkdownPath: firstUnverifiedSuccessorPacket?.markdownPath ?? null, + }, + { + taskId: 'emit_singleton_edge_obstruction_certificate', + status: firstPacketLiteralEdgeObstructionsCertified + ? 'done_literal_edge_certificate_verified' + : allMaterializedSuccessorFamiliesVerified + ? 'highest' + : 'blocked_by_vertex_successor_family_proofs', + task: highestPriorityAtom + ? `Emit the literal edge-obstruction certificate for singleton p13 packet ${highestPriorityAtom.atomId}, proving every exported cross-edge obstruction has a checked squarefree product-plus-one certificate.` + : 'Emit the literal edge-obstruction certificate for the first singleton p13 packet.', + completionRule: 'The first packet manifest reports literal_edge_obstruction_certificate_verified for the singleton p13 packet.', + command: `erdos problem task-list-refresh ${problem.problemId}`, + packetAtomId: highestPriorityAtom?.atomId ?? null, + packetId: highestPriorityAtom?.packetArtifact?.packetId ?? null, + packetJsonPath: highestPriorityAtom?.packetArtifact?.jsonPath ?? null, + packetMarkdownPath: highestPriorityAtom?.packetArtifact?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'promote_singleton_edge_congruence_persistence', + status: firstPacketEdgeCongruencePersistenceVerified + ? 'done_literal_edge_persistence_verified' + : firstPacketLiteralEdgeObstructionsCertified && allMaterializedSuccessorFamiliesVerified + ? 'highest' + : 'blocked_by_edge_obstruction_certificate', + task: highestPriorityAtom + ? `Promote the singleton p13 packet ${highestPriorityAtom.atomId} from literal edge-obstruction certificates into A5 congruence-persistence families.` + : 'Promote the first singleton p13 packet from literal edge-obstruction certificates into A5 congruence-persistence families.', + completionRule: 'Each edge-obstruction family is either proved from the split hypotheses or emits a sharper deterministic successor atom.', + command: null, + packetAtomId: highestPriorityAtom?.atomId ?? null, + packetId: highestPriorityAtom?.packetArtifact?.packetId ?? null, + packetJsonPath: highestPriorityAtom?.packetArtifact?.jsonPath ?? null, + packetMarkdownPath: highestPriorityAtom?.packetArtifact?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'promote_singleton_matching_disjointness_and_k_envelope', + status: firstPacketMatchingKEnvelopeVerified + ? 'done_literal_matching_sampled_k_verified' + : firstPacketEdgeCongruencePersistenceVerified && allMaterializedSuccessorFamiliesVerified + ? 'highest' + : 'blocked_by_edge_congruence_persistence', + task: highestPriorityAtom + ? `Promote singleton p13 packet ${highestPriorityAtom.atomId} through A6 matching disjointness and A7 K-envelope checks.` + : 'Promote the first singleton p13 packet through A6 matching disjointness and A7 K-envelope checks.', + completionRule: 'The literal matching pairs are pairwise disjoint and the common-core count dominates the required K-envelope without bounded-only overclaim.', + command: null, + packetAtomId: highestPriorityAtom?.atomId ?? null, + packetId: highestPriorityAtom?.packetArtifact?.packetId ?? null, + packetJsonPath: highestPriorityAtom?.packetArtifact?.jsonPath ?? null, + packetMarkdownPath: highestPriorityAtom?.packetArtifact?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'assemble_singleton_split_discharge_readiness', + status: firstPacketSplitDischargeReady + ? 'done_split_discharge_readiness_candidate' + : firstPacketMatchingKEnvelopeVerified + ? 'highest' + : 'blocked_by_matching_k_envelope_certificate', + task: highestPriorityAtom + ? `Assemble split-discharge readiness for singleton p13 packet ${highestPriorityAtom.atomId} from verified vertex successors, edge persistence, matching disjointness, and sampled K-envelope certificates.` + : 'Assemble split-discharge readiness for the first singleton p13 packet.', + completionRule: 'The packet either becomes a theorem-facing split lemma candidate with explicit all-N handoff gaps, or emits the first missing lower atom.', + command: null, + packetAtomId: highestPriorityAtom?.atomId ?? null, + packetId: highestPriorityAtom?.packetArtifact?.packetId ?? null, + packetJsonPath: highestPriorityAtom?.packetArtifact?.jsonPath ?? null, + packetMarkdownPath: highestPriorityAtom?.packetArtifact?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'attack_next_p13_split_profile', + status: allP13SplitDischargeReady + ? 'done_p13_split_readiness_candidates' + : firstPacketSplitDischargeReady && nextUndischargedP13Packet + ? 'highest' + : 'blocked_by_singleton_split_readiness', + task: nextUndischargedP13Packet + ? `Attack next p13 split profile ${nextUndischargedP13Packet.atomId}: emit or verify its vertex successor families, then assemble split-discharge readiness.` + : allP13SplitDischargeReady + ? 'All p13 split profiles have split-discharge readiness candidates; promote the D2 p13 lane through the explicit all-N handoff gaps next.' + : 'Attack the next p13 split profile after singleton readiness is assembled.', + completionRule: allP13SplitDischargeReady + ? 'D2 promotion either discharges the row-universe and symbolic-K handoff gaps or emits the first missing all-N atom.' + : 'The next p13 split either reaches split-discharge readiness or emits the first lower atom still missing.', + command: null, + packetAtomId: nextUndischargedP13Packet?.atomId ?? null, + packetId: nextUndischargedP13Packet?.packetId ?? null, + packetJsonPath: nextUndischargedP13Packet?.jsonPath ?? null, + packetMarkdownPath: nextUndischargedP13Packet?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'promote_d2_p13_all_n_handoff', + status: p13RowUniverseCoverageCandidate?.status === 'tight_sample_covered_full_row_universe_stratification_needed' + ? 'done_missing_atom_emitted' + : p13RowUniverseCoverageCandidate?.status === 'bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder' + ? 'done_bounded_row_universe_stratified' + : p13PrimeLaneHandoffReady + ? 'highest' + : allP13SplitDischargeReady + ? 'highest' + : 'blocked_by_p13_split_readiness', + task: p13RowUniverseCoverageCandidate?.status === 'tight_sample_covered_full_row_universe_stratification_needed' + ? `Row-universe coverage narrowed: ${p13RowUniverseCoverageCandidate.emittedMissingAtom.atomId} is now the first missing all-N atom before D2 can be promoted.` + : p13RowUniverseCoverageCandidate?.status === 'bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder' + ? `Bounded p13 row-universe stratification is audited; ${p13RowUniverseCoverageCandidate.emittedMissingAtom.atomId} is now the symbolic all-N lift before D2 can be promoted.` + : p13PrimeLaneHandoffReady + ? `Promote D2 p13 lane by discharging handoff gap ${firstOpenP13HandoffGap?.gapId ?? 'row_universe_split_coverage'} without treating sampled split readiness as an all-N proof.` + : 'Assemble the D2 p13 prime-lane handoff candidate from all p13 split-discharge readiness packets.', + completionRule: 'The D2 p13 lane either closes row-universe coverage and symbolic K(N,x), or emits the first missing all-N atom.', + command: null, + packetAtomId: p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId ?? null, + packetId: p13PrimeLaneHandoffCandidate?.laneId ?? p13RowUniverseCoverageCandidate?.coverageId ?? null, + packetJsonPath: null, + packetMarkdownPath: null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'attack_d2_p13_row_universe_stratification_lift', + status: p13RowUniverseCoverageCandidate?.status === 'bounded_row_universe_stratified_tight_splits_plus_slack_dominated_remainder' + ? 'done_bounded_slack_stratification_audited' + : p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId === 'D2_p13_row_universe_stratification_lift' + ? 'highest' + : 'blocked_by_row_universe_coverage_audit', + task: p13RowUniverseCoverageCandidate?.emittedMissingAtom?.statement + ?? 'Attack the first missing p13 row-universe coverage atom after the audit emits it.', + completionRule: 'Every bounded p13 threat row is either assigned to a split profile, proved slack-dominated outside the tight split packet, or emitted as a new deterministic split atom.', + command: null, + packetAtomId: p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId ?? null, + packetId: p13RowUniverseCoverageCandidate?.coverageId ?? null, + packetJsonPath: null, + packetMarkdownPath: null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_d2_p13_slack_dominance_symbolic_lift', + status: p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.status === 'bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed' + ? 'done_bounded_formula_reduction_emitted' + : p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId === 'D2_p13_slack_dominance_symbolic_lift' + ? 'highest' + : 'blocked_by_bounded_row_universe_stratification', + task: p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.status === 'bounded_slack_formula_replay_verified_symbolic_side_count_lift_needed' + ? `Slack dominance reduced to ${p13RowUniverseCoverageCandidate.slackDominanceSymbolicLiftCandidate.firstOpenSymbolicLemma.lemmaId}; prove the side-count floor next.` + : p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId === 'D2_p13_slack_dominance_symbolic_lift' + ? p13RowUniverseCoverageCandidate.emittedMissingAtom.statement + : 'After the bounded p13 row universe is stratified, lift the non-tight slack-dominance audit into a symbolic all-N theorem.', + completionRule: 'The 49 non-tight p13 residue/side strata either get a symbolic slack-dominance proof, or the first failing stratum emits a deterministic successor split atom.', + command: null, + packetAtomId: p13RowUniverseCoverageCandidate?.emittedMissingAtom?.atomId === 'D2_p13_slack_dominance_symbolic_lift' + ? p13RowUniverseCoverageCandidate.emittedMissingAtom.atomId + : null, + packetId: p13RowUniverseCoverageCandidate?.coverageId ?? null, + packetJsonPath: null, + packetMarkdownPath: null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_d2_p13_non_tight_side_count_slack_floor_lift', + status: firstSideCountFloorPacket + ? 'done_weakest_side_count_atoms_emitted' + : p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.firstOpenSymbolicLemma?.lemmaId === 'D2_p13_non_tight_side_count_slack_floor_lift' + ? 'highest' + : 'blocked_by_slack_formula_reduction', + task: firstSideCountFloorPacket + ? `Weakest side-count floor atom packets are emitted; attack ${firstSideCountFloorPacket.atomId} next.` + : p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.firstOpenSymbolicLemma?.statement + ?? 'Prove the side-count floor after the non-tight p13 slack formula reduction is available.', + completionRule: 'Either prove max(side7, side18) <= strictBaseThreshold - 1 - targetSlack for all non-tight p13 rows, or emit the weakest failing residue/side stratum as a deterministic atom.', + command: null, + packetAtomId: p13RowUniverseCoverageCandidate?.slackDominanceSymbolicLiftCandidate?.firstOpenSymbolicLemma?.lemmaId ?? null, + packetId: p13RowUniverseCoverageCandidate?.coverageId ?? null, + packetJsonPath: null, + packetMarkdownPath: null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'attack_weakest_p13_side_count_floor_atom', + status: firstSideCountFloorPacket?.structuralMarginDecompositionStatus === 'bounded_structural_margin_replay_verified_symbolic_margin_lift_needed' + ? 'done_structural_margin_decomposition_emitted' + : firstSideCountFloorPacket + ? 'highest' + : 'blocked_by_side_count_floor_packet_emission', + task: firstSideCountFloorPacket + ? `Attack weakest p13 side-count floor atom ${firstSideCountFloorPacket.atomId}: prove its side-count inequality or split the first failing term.` + : 'Emit the weakest p13 side-count floor atom before attacking it.', + completionRule: 'The weakest side-count floor packet either becomes a symbolic side-count lemma or emits a sharper deterministic sub-atom.', + command: null, + packetAtomId: firstSideCountFloorPacket?.atomId ?? null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_structural_margin_atom', + status: firstSideCountFloorPacket?.firstOpenMovingTermSubatom + ? 'done_moving_term_subatoms_emitted' + : firstSideCountFloorPacket?.firstOpenStructuralMarginLemma + ? 'highest' + : 'blocked_by_side_count_floor_decomposition', + task: firstSideCountFloorPacket?.firstOpenStructuralMarginLemma + ? `Prove structural margin lemma ${firstSideCountFloorPacket.firstOpenStructuralMarginLemma} for ${firstSideCountFloorPacket.splitKey}, or emit the first moving-term sub-atom.` + : 'Decompose the weakest side-count floor atom into a structural margin lemma before proving it.', + completionRule: 'The structural margin inequality either gets a symbolic bound for candidateSize, vMax, dMax, rGreater, and the larger side count, or emits the first moving term as a sharper atom.', + command: null, + packetAtomId: firstSideCountFloorPacket?.firstOpenStructuralMarginLemma ?? null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_bound_atom', + status: dMaxConstantBoundFinished + ? 'done_constant_bound_falsified_successor_atom_emitted' + : firstSideCountFloorMovingTermSubatom + ? 'highest' + : 'blocked_by_structural_margin_atom', + task: dMaxConstantBoundFinished + ? 'The original dMax constant-bound atom is closed by a bounded falsifier and successor growth profile; continue with the current downstream moving-term atom.' + : firstSideCountFloorPacket?.firstOpenMovingTermSubatom + ? `Prove moving-term atom ${firstSideCountFloorPacket.firstOpenMovingTermSubatom} for ${firstSideCountFloorPacket.splitKey}, or emit a sharper same-prime degree sub-atom.` + : 'Wait for the structural margin atom to emit its first moving-term subatom.', + completionRule: 'The dMax subatom either proves the uniform same-prime degree bound used by the structural margin, or emits the sharper term family that controls dMax.', + command: null, + packetAtomId: dMaxConstantBoundFinished ? null : firstSideCountFloorPacket?.firstOpenMovingTermSubatom ?? null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'attack_weakest_p13_dmax_growth_atom', + status: firstSideCountFloorMovingTermIsDynamicMargin + ? 'done_dmax_growth_tail_profile_closed' + : dMaxGrowthProfileFirstSubatomEmitted + ? 'done_growth_profile_subatom_emitted' + : firstSideCountFloorMovingTermIsDMaxGrowth + ? 'highest' + : 'blocked_by_dmax_bound_atom', + task: firstSideCountFloorMovingTermIsDynamicMargin + ? `The dMax growth tail profile is closed through q>=587 for ${firstSideCountFloorPacket?.splitKey ?? '(unknown split)'}; attack the residual dynamic margin next.` + : dMaxGrowthProfileFirstSubatomEmitted + ? `dMax growth profile emitted first subatom ${firstSideCountFloorMovingTermSubatom}; attack that floor-function progression next.` + : firstSideCountFloorMovingTermIsDMaxGrowth + ? `Attack dMax growth atom ${firstSideCountFloorMovingTermSubatom} for ${firstSideCountFloorPacket.splitKey}: replace the false constant dMax bound with a symbolic same-prime degree-growth envelope.` + : 'Wait for the dMax constant-bound atom to either prove or emit a degree-growth successor.', + completionRule: 'The dMax growth atom either proves a symbolic envelope for the same-prime degree term or emits the first residue/floor-function sub-split controlling the degree growth.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMargin ? null : firstSideCountFloorMovingTermSubatom, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q2_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ3Progression + || firstSideCountFloorMovingTermIsDMaxQ5Progression + || firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q2_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ2Progression + ? 'highest' + : 'blocked_by_dmax_growth_profile', + task: firstSideCountFloorMovingTermIsDMaxQ2Progression + ? `Prove q=2 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: bound the m = 437 + 676*t contribution with base-residue and lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ3Progression + || firstSideCountFloorMovingTermIsDMaxQ5Progression + || firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=2 dMax progression upper-bound certificate is present; continue the higher-q progression chain.' + : 'Wait for the dMax growth profile to emit its first square-divisor progression atom.', + completionRule: 'The q=2 progression contribution is bounded by a floor-function with exclusions, or the first unresolved exclusion class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ2Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q3_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ5Progression + || firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q3_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ3Progression + ? 'highest' + : 'blocked_by_q2_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ3Progression + ? `Prove q=3 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for q=2 overlap/base-residue/lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ5Progression + || firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=3 dMax progression upper-bound certificate is present; continue the higher-q progression chain.' + : 'Wait for the q=2 progression proof to emit the q=3 square-divisor progression atom.', + completionRule: 'The q=3 progression contribution is bounded by CRT floor-functions, or the first unresolved q=3 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ3Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q5_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q5_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ5Progression + ? 'highest' + : 'blocked_by_q3_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ5Progression + ? `Prove q=5 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for q=2/q=3 overlap plus base-residue/lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ7Progression + || firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=5 dMax progression upper-bound certificate is present; attack the q=7 progression next.' + : 'Wait for the q=3 progression proof to emit the q=5 square-divisor progression atom.', + completionRule: 'The q=5 progression contribution is bounded by CRT floor-functions, or the first unresolved q=5 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ5Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q7_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q7_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ7Progression + ? 'highest' + : 'blocked_by_q5_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ7Progression + ? `Prove q=7 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for prior-q overlap plus lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ11Progression + || firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=7 dMax progression upper-bound certificate is present; attack the q=11 progression next.' + : 'Wait for the q=5 progression proof to emit the q=7 square-divisor progression atom.', + completionRule: 'The q=7 progression contribution is bounded by CRT floor-functions, or the first unresolved q=7 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ7Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q11_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q11_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ11Progression + ? 'highest' + : 'blocked_by_q7_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ11Progression + ? `Prove q=11 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for prior-q overlap plus lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ19Progression + || firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=11 dMax progression upper-bound certificate is present; attack the q=19 progression next.' + : 'Wait for the q=7 progression proof to emit the q=11 square-divisor progression atom.', + completionRule: 'The q=11 progression contribution is bounded by CRT floor-functions, or the first unresolved q=11 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ11Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q19_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q19_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ19Progression + ? 'highest' + : 'blocked_by_q11_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ19Progression + ? `Prove q=19 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for prior-q overlap plus lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ23Progression + || firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=19 dMax progression upper-bound certificate is present; attack the q=23 progression next.' + : 'Wait for the q=11 progression proof to emit the q=19 square-divisor progression atom.', + completionRule: 'The q=19 progression contribution is bounded by CRT floor-functions, or the first unresolved q=19 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ19Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q23_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ31Progression + || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q23_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ23Progression + ? 'highest' + : 'blocked_by_q19_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ23Progression + ? `Prove q=23 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for prior-q overlap plus lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ31Progression || firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=23 dMax progression upper-bound certificate is present; attack the q=31 progression next.' + : 'Wait for the q=19 progression proof to emit the q=23 square-divisor progression atom.', + completionRule: 'The q=23 progression contribution is bounded by CRT floor-functions, or the first unresolved q=23 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ23Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q31_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'done_q31_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ31Progression + ? 'highest' + : 'blocked_by_q23_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ31Progression + ? `Prove q=31 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for prior-q overlap plus lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'The q=31 dMax progression upper-bound certificate is present; attack the q=251 progression next.' + : 'Wait for the q=23 progression proof to emit the q=31 square-divisor progression atom.', + completionRule: 'The q=31 progression contribution is bounded by CRT floor-functions, or the first unresolved q=31 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ31Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_q251_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailRecombination + || firstSideCountFloorMovingTermIsDMaxTailQ17Progression + || firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q251_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxQ251Progression + ? 'highest' + : 'blocked_by_q31_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxQ251Progression + ? `Prove q=251 dMax progression atom ${firstSideCountFloorMovingTermSubatom}: derive the CRT floor-function contribution and account for prior-q overlap plus lower-witness exclusions.` + : firstSideCountFloorMovingTermIsDMaxTailRecombination + || firstSideCountFloorMovingTermIsDMaxTailQ17Progression + || firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=251 dMax progression upper-bound certificate is present; attack the tail/recombination envelope next.' + : 'Wait for the q=31 progression proof to emit the q=251 square-divisor progression atom.', + completionRule: 'The q=251 progression contribution is bounded by CRT floor-functions, or the first unresolved q=251 exclusion/overlap class becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxQ251Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_recombination_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ17Progression + || firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_tail_scaffold_q13_residue_exclusion_verified' + : firstSideCountFloorMovingTermIsDMaxTailRecombination + ? 'highest' + : 'blocked_by_q251_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailRecombination + ? `Prove dMax tail/recombination atom ${firstSideCountFloorMovingTermSubatom}: combine verified q-components with a symbolic tail estimate for remaining same-prime square-divisor events.` + : firstSideCountFloorMovingTermIsDMaxTailQ17Progression + || firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The tail/recombination scaffold excludes q=13 by split residue; attack the first unresolved tail prime q=17 next.' + : 'Wait for the q=251 progression proof to emit the tail/recombination atom.', + completionRule: 'The verified q-components plus a tail estimate imply the required symbolic dMax growth envelope, or the first unresolved tail range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailRecombination ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q17_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q17_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ17Progression + ? 'highest' + : 'blocked_by_tail_recombination_scaffold', + task: firstSideCountFloorMovingTermIsDMaxTailQ17Progression + ? `Prove dMax tail q=17 progression atom ${firstSideCountFloorMovingTermSubatom}: derive both witness-side CRT floor bounds and decide whether q=17 is a bounded-only gap or a symbolic tail component.` + : firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=17 tail-prime upper-bound certificate is present; attack the plus-side q=19 tail complement next.' + : 'Wait for the tail/recombination scaffold to emit the first unresolved tail-prime atom.', + completionRule: 'The q=17 tail progression contribution is bounded by CRT floor functions for both same-prime witnesses, or the next unresolved tail prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ17Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q19_plus_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q19_plus_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + ? 'highest' + : 'blocked_by_q17_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression + ? `Prove dMax tail plus-side q=19 progression atom ${firstSideCountFloorMovingTermSubatom}: certify the non-observed plus-side complement left open by the minus-side q=19 packet.` + : firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The plus-side q=19 tail complement is certified; backfill the earlier minus-side q=11 complement next.' + : 'Wait for the q=17 tail progression proof to emit the next side-specific q=19 tail atom.', + completionRule: 'The plus-side q=19 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ19PlusProgression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q11_minus_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q11_minus_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + ? 'highest' + : 'blocked_by_q19_plus_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression + ? `Prove dMax tail minus-side q=11 progression atom ${firstSideCountFloorMovingTermSubatom}: backfill the non-observed complement left open by the plus-side q=11 packet.` + : firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The minus-side q=11 tail complement is certified; attack the plus-side q=23 complement next.' + : 'Wait for the plus-side q=19 complement proof to emit the q=11 minus-side backfill atom.', + completionRule: 'The minus-side q=11 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ11MinusProgression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q23_plus_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q23_plus_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + ? 'highest' + : 'blocked_by_q11_minus_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression + ? `Prove dMax tail plus-side q=23 progression atom ${firstSideCountFloorMovingTermSubatom}: certify the non-observed plus-side complement left open by the minus-side q=23 packet.` + : firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The plus-side q=23 tail complement is certified; attack the minus-side q=31 complement next.' + : 'Wait for the minus-side q=11 complement proof to emit the plus-side q=23 tail atom.', + completionRule: 'The plus-side q=23 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ23PlusProgression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q31_minus_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q31_minus_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + ? 'highest' + : 'blocked_by_q23_plus_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression + ? `Prove dMax tail minus-side q=31 progression atom ${firstSideCountFloorMovingTermSubatom}: certify the non-observed minus-side complement left open by the plus-side q=31 packet.` + : firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + || firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The minus-side q=31 tail complement is certified; attack the minus-side q=251 complement next.' + : 'Wait for the plus-side q=23 complement proof to emit the minus-side q=31 tail atom.', + completionRule: 'The minus-side q=31 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ31MinusProgression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q251_minus_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q251_minus_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + ? 'highest' + : 'blocked_by_q31_minus_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression + ? `Prove dMax tail minus-side q=251 progression atom ${firstSideCountFloorMovingTermSubatom}: certify the non-observed minus-side complement left open by the plus-side q=251 packet.` + : firstSideCountFloorMovingTermIsDMaxTailQ29Progression + || firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The minus-side q=251 tail complement is certified; attack the first remaining non-observed q=29 tail prime next.' + : 'Wait for the minus-side q=31 complement proof to emit the minus-side q=251 tail atom.', + completionRule: 'The minus-side q=251 tail contribution is bounded by its CRT floor function, or the next unresolved tail range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ251MinusProgression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q29_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q29_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ29Progression + ? 'highest' + : 'blocked_by_q251_minus_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ29Progression + ? `Prove dMax tail q=29 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the first remaining non-observed tail prime.` + : firstSideCountFloorMovingTermIsDMaxTailQ37Progression + || firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=29 residual tail-prime component is certified; attack q=37 next, starting with the plus-side witness-divisibility exclusion.' + : 'Wait for the minus-side q=251 complement proof to emit the q=29 residual tail-prime atom.', + completionRule: 'The q=29 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ29Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q37_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q37_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ37Progression + ? 'highest' + : 'blocked_by_q29_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ37Progression + ? `Prove dMax tail q=37 progression atom ${firstSideCountFloorMovingTermSubatom}: combine the plus-side witness-divisibility exclusion with the minus-side CRT floor bound.` + : firstSideCountFloorMovingTermIsDMaxTailQ41Progression + || firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=37 residual tail-prime component is certified; attack q=41 next as the first two-sided residual tail-prime CRT floor-bound.' + : 'Wait for the q=29 tail-prime proof to emit the q=37 residual tail-prime atom.', + completionRule: 'The q=37 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ37Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q41_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q41_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ41Progression + ? 'highest' + : 'blocked_by_q37_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ41Progression + ? `Prove dMax tail q=41 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : firstSideCountFloorMovingTermIsDMaxTailQ43Progression + || firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=41 residual tail-prime component is certified; attack q=43 next, starting with the plus-side witness-divisibility exclusion.' + : 'Wait for the q=37 tail-prime proof to emit the q=41 residual tail-prime atom.', + completionRule: 'The q=41 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ41Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q43_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q43_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ43Progression + ? 'highest' + : 'blocked_by_q41_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ43Progression + ? `Prove dMax tail q=43 progression atom ${firstSideCountFloorMovingTermSubatom}: combine the plus-side witness-divisibility exclusion with the minus-side CRT floor bound.` + : firstSideCountFloorMovingTermIsDMaxTailQ47Progression + || firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=43 residual tail-prime component is certified; attack q=47 next as a two-sided residual tail-prime CRT floor-bound.' + : 'Wait for the q=41 tail-prime proof to emit the q=43 residual tail-prime atom.', + completionRule: 'The q=43 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ43Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q47_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'done_q47_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ47Progression + ? 'highest' + : 'blocked_by_q43_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ47Progression + ? `Prove dMax tail q=47 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : firstSideCountFloorMovingTermIsDMaxTailQ53Progression + || firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'The q=47 residual tail-prime component is certified; attack q=53 next as a two-sided residual tail-prime CRT floor-bound.' + : 'Wait for the q=43 tail-prime proof to emit the q=47 residual tail-prime atom.', + completionRule: 'The q=47 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ47Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q53_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + || firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'done_q53_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ53Progression + ? 'highest' + : 'blocked_by_q47_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ53Progression + ? `Prove dMax tail q=53 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : firstSideCountFloorMovingTermIsDMaxTailQ59Progression + || firstSideCountFloorMovingTermIsDMaxTailQ61Progression + || firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'The q=53 residual tail-prime component is certified; attack q=59 next as a two-sided residual tail-prime CRT floor-bound.' + : 'Wait for the q=47 tail-prime proof to emit the q=53 residual tail-prime atom.', + completionRule: 'The q=53 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ53Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q59_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ61Progression + || firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'done_q59_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ59Progression + ? 'highest' + : 'blocked_by_q53_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ59Progression + ? `Prove dMax tail q=59 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : firstSideCountFloorMovingTermIsDMaxTailQ61Progression + || firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'The q=59 residual tail-prime component is certified; attack q=61 next as a two-sided residual tail-prime CRT floor-bound.' + : 'Wait for the q=53 tail-prime proof to emit the q=59 residual tail-prime atom.', + completionRule: 'The q=59 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQ59Progression ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q61_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'done_q61_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? 'highest' + : 'blocked_by_q59_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'The q=61 residual tail-prime component is certified; attack q=67 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ61Progression + ? `Prove dMax tail q=61 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=59 tail-prime proof to emit the q=61 residual tail-prime atom.', + completionRule: 'The q=61 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q61_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q67_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ71Progression + ? 'done_q67_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? 'highest' + : 'blocked_by_q61_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ71Progression + ? 'The q=67 residual tail-prime component is certified; attack q=71 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ67Progression + ? `Prove dMax tail q=67 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=61 tail-prime proof to emit the q=67 residual tail-prime atom.', + completionRule: 'The q=67 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q67_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q71_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ73Progression + ? 'done_q71_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ71Progression + ? 'highest' + : 'blocked_by_q67_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ73Progression + ? 'The q=71 residual tail-prime component is certified; attack q=73 next, starting with the minus-side witness-divisibility exclusion.' + : firstSideCountFloorMovingTermIsDMaxTailQ71Progression + ? `Prove dMax tail q=71 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=67 tail-prime proof to emit the q=71 residual tail-prime atom.', + completionRule: 'The q=71 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q71_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q73_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ79Progression + ? 'done_q73_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ73Progression + ? 'highest' + : 'blocked_by_q71_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ79Progression + ? 'The q=73 residual tail-prime component is certified; attack q=79 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ73Progression + ? `Prove dMax tail q=73 progression atom ${firstSideCountFloorMovingTermSubatom}: combine the minus-side witness-divisibility exclusion with the plus-side CRT floor bound.` + : 'Wait for the q=71 tail-prime proof to emit the q=73 residual tail-prime atom.', + completionRule: 'The q=73 tail contribution is bounded by the plus-side CRT floor function and minus-side exclusion, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q73_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q79_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ83Progression + ? 'done_q79_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ79Progression + ? 'highest' + : 'blocked_by_q73_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ83Progression + ? 'The q=79 residual tail-prime component is certified; attack q=83 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ79Progression + ? `Prove dMax tail q=79 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=73 tail-prime proof to emit the q=79 residual tail-prime atom.', + completionRule: 'The q=79 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q79_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q83_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ89Progression + ? 'done_q83_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ83Progression + ? 'highest' + : 'blocked_by_q79_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ89Progression + ? 'The q=83 residual tail-prime component is certified; attack q=89 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ83Progression + ? `Prove dMax tail q=83 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=79 tail-prime proof to emit the q=83 residual tail-prime atom.', + completionRule: 'The q=83 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q83_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q89_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ97Progression + ? 'done_q89_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ89Progression + ? 'highest' + : 'blocked_by_q83_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ97Progression + ? 'The q=89 residual tail-prime component is certified; attack q=97 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ89Progression + ? `Prove dMax tail q=89 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=83 tail-prime proof to emit the q=89 residual tail-prime atom.', + completionRule: 'The q=89 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q89_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q97_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ101Progression + ? 'done_q97_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ97Progression + ? 'highest' + : 'blocked_by_q89_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ101Progression + ? 'The q=97 residual tail-prime component is certified; attack q=101 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ97Progression + ? `Prove dMax tail q=97 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=89 tail-prime proof to emit the q=97 residual tail-prime atom.', + completionRule: 'The q=97 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q97_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q101_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ103Progression + ? 'done_q101_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ101Progression + ? 'highest' + : 'blocked_by_q97_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ103Progression + ? 'The q=101 residual tail-prime component is certified; attack q=103 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ101Progression + ? `Prove dMax tail q=101 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=97 tail-prime proof to emit the q=101 residual tail-prime atom.', + completionRule: 'The q=101 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q101_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q103_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ107Progression + ? 'done_q103_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ103Progression + ? 'highest' + : 'blocked_by_q101_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ107Progression + ? 'The q=103 residual tail-prime component is certified; attack q=107 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ103Progression + ? `Prove dMax tail q=103 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=101 tail-prime proof to emit the q=103 residual tail-prime atom.', + completionRule: 'The q=103 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q103_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q107_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ109Progression + ? 'done_q107_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ107Progression + ? 'highest' + : 'blocked_by_q103_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ109Progression + ? 'The q=107 residual tail-prime component is certified; attack q=109 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ107Progression + ? `Prove dMax tail q=107 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=103 tail-prime proof to emit the q=107 residual tail-prime atom.', + completionRule: 'The q=107 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q107_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q109_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ113Progression + ? 'done_q109_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ109Progression + ? 'highest' + : 'blocked_by_q107_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ113Progression + ? 'The q=109 residual tail-prime component is certified; attack q=113 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ109Progression + ? `Prove dMax tail q=109 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=107 tail-prime proof to emit the q=109 residual tail-prime atom.', + completionRule: 'The q=109 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q109_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q113_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ127Progression + ? 'done_q113_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ113Progression + ? 'highest' + : 'blocked_by_q109_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ127Progression + ? 'The q=113 residual tail-prime component is certified; attack q=127 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ113Progression + ? `Prove dMax tail q=113 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=109 tail-prime proof to emit the q=113 residual tail-prime atom.', + completionRule: 'The q=113 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q113_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q127_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ131Progression + ? 'done_q127_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ127Progression + ? 'highest' + : 'blocked_by_q113_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ131Progression + ? 'The q=127 residual tail-prime component is certified; attack q=131 next, combining the minus-side witness-divisibility exclusion with the plus-side CRT floor bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ127Progression + ? `Prove dMax tail q=127 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=113 tail-prime proof to emit the q=127 residual tail-prime atom.', + completionRule: 'The q=127 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q127_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q131_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ137Progression + ? 'done_q131_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ131Progression + ? 'highest' + : 'blocked_by_q127_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ137Progression + ? 'The q=131 residual tail-prime component is certified; attack q=137 next as a two-sided residual tail-prime CRT floor-bound.' + : firstSideCountFloorMovingTermIsDMaxTailQ131Progression + ? `Prove dMax tail q=131 progression atom ${firstSideCountFloorMovingTermSubatom}: combine the minus-side witness-divisibility exclusion with the plus-side CRT floor bound.` + : 'Wait for the q=127 tail-prime proof to emit the q=131 residual tail-prime atom.', + completionRule: 'The q=131 tail contribution is bounded by the minus-side exclusion and plus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q131_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q137_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ139Progression + ? 'done_q137_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ137Progression + ? 'highest' + : 'blocked_by_q131_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ137Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ139Progression + ? 'The q=137 residual tail-prime component is certified; attack q=139 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=137 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=131 tail-prime proof to emit the q=137 residual tail-prime atom.', + completionRule: 'The q=137 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q137_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q139_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ149Progression + ? 'done_q139_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ139Progression + ? 'highest' + : 'blocked_by_q137_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ139Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ149Progression + ? 'The q=139 residual tail-prime component is certified; attack q=149 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=139 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=137 tail-prime proof to emit the q=139 residual tail-prime atom.', + completionRule: 'The q=139 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q139_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q149_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ151Progression + ? 'done_q149_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ149Progression + ? 'highest' + : 'blocked_by_q139_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ149Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ151Progression + ? 'The q=149 residual tail-prime component is certified; attack q=151 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=149 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=139 tail-prime proof to emit the q=149 residual tail-prime atom.', + completionRule: 'The q=149 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q149_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q151_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ157Progression + ? 'done_q151_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ151Progression + ? 'highest' + : 'blocked_by_q149_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ151Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ157Progression + ? 'The q=151 residual tail-prime component is certified; attack q=157 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=151 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=149 tail-prime proof to emit the q=151 residual tail-prime atom.', + completionRule: 'The q=151 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q151_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q157_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ163Progression + ? 'done_q157_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ157Progression + ? 'highest' + : 'blocked_by_q151_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ157Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ163Progression + ? 'The q=157 residual tail-prime component is certified; attack q=163 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=157 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=151 tail-prime proof to emit the q=157 residual tail-prime atom.', + completionRule: 'The q=157 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q157_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q163_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ167Progression + ? 'done_q163_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ163Progression + ? 'highest' + : 'blocked_by_q157_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ163Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ167Progression + ? 'The q=163 residual tail-prime component is certified; attack q=167 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=163 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=157 tail-prime proof to emit the q=163 residual tail-prime atom.', + completionRule: 'The q=163 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q163_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q167_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ173Progression + ? 'done_q167_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ167Progression + ? 'highest' + : 'blocked_by_q163_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ167Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ173Progression + ? 'The q=167 residual tail-prime component is certified; attack q=173 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=167 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=163 tail-prime proof to emit the q=167 residual tail-prime atom.', + completionRule: 'The q=167 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q167_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q173_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ179Progression + ? 'done_q173_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ173Progression + ? 'highest' + : 'blocked_by_q167_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ173Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ179Progression + ? 'The q=173 residual tail-prime component is certified; attack q=179 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=173 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=167 tail-prime proof to emit the q=173 residual tail-prime atom.', + completionRule: 'The q=173 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q173_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q179_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ181Progression + ? 'done_q179_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ179Progression + ? 'highest' + : 'blocked_by_q173_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ179Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ181Progression + ? 'The q=179 residual tail-prime component is certified; attack q=181 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=179 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=173 tail-prime proof to emit the q=179 residual tail-prime atom.', + completionRule: 'The q=179 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q179_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q181_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ191Progression + ? 'done_q181_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ181Progression + ? 'highest' + : 'blocked_by_q179_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ181Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ191Progression + ? 'The q=181 residual tail-prime component is certified; attack q=191 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=181 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=179 tail-prime proof to emit the q=181 residual tail-prime atom.', + completionRule: 'The q=181 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q181_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q191_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ193Progression + ? 'done_q191_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ191Progression + ? 'highest' + : 'blocked_by_q181_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ191Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ193Progression + ? 'The q=191 residual tail-prime component is certified; attack q=193 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=191 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=181 tail-prime proof to emit the q=191 residual tail-prime atom.', + completionRule: 'The q=191 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q191_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q193_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ197Progression + ? 'done_q193_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ193Progression + ? 'highest' + : 'blocked_by_q191_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ193Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ197Progression + ? 'The q=193 residual tail-prime component is certified; attack q=197 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=193 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=191 tail-prime proof to emit the q=193 residual tail-prime atom.', + completionRule: 'The q=193 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q193_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q197_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ199Progression + ? 'done_q197_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ197Progression + ? 'highest' + : 'blocked_by_q193_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ197Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ199Progression + ? 'The q=197 residual tail-prime component is certified; attack q=199 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=197 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=193 tail-prime proof to emit the q=197 residual tail-prime atom.', + completionRule: 'The q=197 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q197_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q199_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ211Progression + ? 'done_q199_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ199Progression + ? 'highest' + : 'blocked_by_q197_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ199Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ211Progression + ? 'The q=199 residual tail-prime component is certified; attack q=211 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=199 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=197 tail-prime proof to emit the q=199 residual tail-prime atom.', + completionRule: 'The q=199 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q199_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q211_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ223Progression + ? 'done_q211_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ211Progression + ? 'highest' + : 'blocked_by_q199_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ211Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ223Progression + ? 'The q=211 residual tail-prime component is certified; attack q=223 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=211 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=199 tail-prime proof to emit the q=211 residual tail-prime atom.', + completionRule: 'The q=211 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q211_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q223_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ227Progression + ? 'done_q223_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ223Progression + ? 'highest' + : 'blocked_by_q211_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ223Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ227Progression + ? 'The q=223 residual tail-prime component is certified; attack q=227 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=223 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=211 tail-prime proof to emit the q=223 residual tail-prime atom.', + completionRule: 'The q=223 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q223_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q227_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ229Progression + ? 'done_q227_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ227Progression + ? 'highest' + : 'blocked_by_q223_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ227Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ229Progression + ? 'The q=227 residual tail-prime component is certified; attack q=229 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=227 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=223 tail-prime proof to emit the q=227 residual tail-prime atom.', + completionRule: 'The q=227 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q227_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q229_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ233Progression + ? 'done_q229_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ229Progression + ? 'highest' + : 'blocked_by_q227_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ229Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ233Progression + ? 'The q=229 residual tail-prime component is certified; attack q=233 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=229 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=227 tail-prime proof to emit the q=229 residual tail-prime atom.', + completionRule: 'The q=229 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q229_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q233_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ239Progression + ? 'done_q233_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ233Progression + ? 'highest' + : 'blocked_by_q229_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ233Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ239Progression + ? 'The q=233 residual tail-prime component is certified; attack q=239 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=233 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=229 tail-prime proof to emit the q=233 residual tail-prime atom.', + completionRule: 'The q=233 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q233_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q239_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ241Progression + ? 'done_q239_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ239Progression + ? 'highest' + : 'blocked_by_q233_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ239Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ241Progression + ? 'The q=239 residual tail-prime component is certified; attack q=241 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=239 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=233 tail-prime proof to emit the q=239 residual tail-prime atom.', + completionRule: 'The q=239 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q239_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q241_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ257Progression + ? 'done_q241_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ241Progression + ? 'highest' + : 'blocked_by_q239_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ241Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ257Progression + ? 'The q=241 residual tail-prime component is certified; q=251 is already covered, so attack q=257 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=241 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=239 tail-prime proof to emit the q=241 residual tail-prime atom.', + completionRule: 'The q=241 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q241_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q257_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ263Progression + ? 'done_q257_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ257Progression + ? 'highest' + : 'blocked_by_q241_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ257Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ263Progression + ? 'The q=257 residual tail-prime component is certified; attack q=263 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=257 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=241 tail-prime proof to emit the q=257 residual tail-prime atom.', + completionRule: 'The q=257 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q257_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q263_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ269Progression + ? 'done_q263_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ263Progression + ? 'highest' + : 'blocked_by_q257_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ263Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ269Progression + ? 'The q=263 residual tail-prime component is certified; attack q=269 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=263 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=257 tail-prime proof to emit the q=263 residual tail-prime atom.', + completionRule: 'The q=263 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q263_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q269_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ271Progression + ? 'done_q269_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ269Progression + ? 'highest' + : 'blocked_by_q263_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ269Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ271Progression + ? 'The q=269 residual tail-prime component is certified; attack q=271 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=269 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=263 tail-prime proof to emit the q=269 residual tail-prime atom.', + completionRule: 'The q=269 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q269_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q271_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ277Progression + ? 'done_q271_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ271Progression + ? 'highest' + : 'blocked_by_q269_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ271Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ277Progression + ? 'The q=271 residual tail-prime component is certified; attack q=277 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=271 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=269 tail-prime proof to emit the q=271 residual tail-prime atom.', + completionRule: 'The q=271 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q271_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q277_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ281Progression + ? 'done_q277_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ277Progression + ? 'highest' + : 'blocked_by_q271_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ277Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ281Progression + ? 'The q=277 residual tail-prime component is certified; attack q=281 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=277 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=271 tail-prime proof to emit the q=277 residual tail-prime atom.', + completionRule: 'The q=277 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q277_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q281_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ283Progression + ? 'done_q281_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ281Progression + ? 'highest' + : 'blocked_by_q277_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ281Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ283Progression + ? 'The q=281 residual tail-prime component is certified; attack q=283 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=281 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=277 tail-prime proof to emit the q=281 residual tail-prime atom.', + completionRule: 'The q=281 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q281_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q283_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ293Progression + ? 'done_q283_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ283Progression + ? 'highest' + : 'blocked_by_q281_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ283Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ293Progression + ? 'The q=283 residual tail-prime component is certified; attack q=293 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=283 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=281 tail-prime proof to emit the q=283 residual tail-prime atom.', + completionRule: 'The q=283 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q283_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q293_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ307Progression + ? 'done_q293_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ293Progression + ? 'highest' + : 'blocked_by_q283_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ293Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ307Progression + ? 'The q=293 residual tail-prime component is certified; attack q=307 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=293 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=283 tail-prime proof to emit the q=293 residual tail-prime atom.', + completionRule: 'The q=293 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q293_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q307_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ311Progression + ? 'done_q307_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ307Progression + ? 'highest' + : 'blocked_by_q293_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ307Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ311Progression + ? 'The q=307 residual tail-prime component is certified; attack q=311 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=307 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=293 tail-prime proof to emit the q=307 residual tail-prime atom.', + completionRule: 'The q=307 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q307_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q311_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ313Progression + ? 'done_q311_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ311Progression + ? 'highest' + : 'blocked_by_q307_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ311Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ313Progression + ? 'The q=311 residual tail-prime component is certified; attack q=313 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=311 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=307 tail-prime proof to emit the q=311 residual tail-prime atom.', + completionRule: 'The q=311 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q311_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q313_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ317Progression + ? 'done_q313_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ313Progression + ? 'highest' + : 'blocked_by_q311_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ313Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ317Progression + ? 'The q=313 residual tail-prime component is certified; attack q=317 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=313 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=311 tail-prime proof to emit the q=313 residual tail-prime atom.', + completionRule: 'The q=313 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q313_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q317_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ331Progression + ? 'done_q317_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ317Progression + ? 'highest' + : 'blocked_by_q313_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ317Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ331Progression + ? 'The q=317 residual tail-prime component is certified; attack q=331 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=317 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=313 tail-prime proof to emit the q=317 residual tail-prime atom.', + completionRule: 'The q=317 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q317_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q331_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ337Progression + ? 'done_q331_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ331Progression + ? 'highest' + : 'blocked_by_q317_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ331Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ337Progression + ? 'The q=331 residual tail-prime component is certified; attack q=337 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=331 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=317 tail-prime proof to emit the q=331 residual tail-prime atom.', + completionRule: 'The q=331 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q331_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q337_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ347Progression + ? 'done_q337_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ337Progression + ? 'highest' + : 'blocked_by_q331_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ337Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ347Progression + ? 'The q=337 residual tail-prime component is certified; attack q=347 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=337 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=331 tail-prime proof to emit the q=337 residual tail-prime atom.', + completionRule: 'The q=337 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q337_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q347_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ349Progression + ? 'done_q347_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ347Progression + ? 'highest' + : 'blocked_by_q337_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ347Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ349Progression + ? 'The q=347 residual tail-prime component is certified; attack q=349 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=347 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=337 tail-prime proof to emit the q=347 residual tail-prime atom.', + completionRule: 'The q=347 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q347_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q349_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ353Progression + ? 'done_q349_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ349Progression + ? 'highest' + : 'blocked_by_q347_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ349Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ353Progression + ? 'The q=349 residual tail-prime component is certified; attack q=353 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=349 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=347 tail-prime proof to emit the q=349 residual tail-prime atom.', + completionRule: 'The q=349 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q349_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q353_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ359Progression + ? 'done_q353_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ353Progression + ? 'highest' + : 'blocked_by_q349_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ353Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ359Progression + ? 'The q=353 residual tail-prime component is certified; attack q=359 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=353 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=349 tail-prime proof to emit the q=353 residual tail-prime atom.', + completionRule: 'The q=353 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q353_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q359_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ367Progression + ? 'done_q359_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ359Progression + ? 'highest' + : 'blocked_by_q353_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ359Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ367Progression + ? 'The q=359 residual tail-prime component is certified; attack q=367 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=359 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=353 tail-prime proof to emit the q=359 residual tail-prime atom.', + completionRule: 'The q=359 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q359_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q367_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ373Progression + ? 'done_q367_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ367Progression + ? 'highest' + : 'blocked_by_q359_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ367Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ373Progression + ? 'The q=367 residual tail-prime component is certified; attack q=373 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=367 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=359 tail-prime proof to emit the q=367 residual tail-prime atom.', + completionRule: 'The q=367 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q367_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q373_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ379Progression + ? 'done_q373_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ373Progression + ? 'highest' + : 'blocked_by_q367_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ373Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ379Progression + ? 'The q=373 residual tail-prime component is certified; attack q=379 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=373 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=367 tail-prime proof to emit the q=373 residual tail-prime atom.', + completionRule: 'The q=373 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q373_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q379_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ383Progression + ? 'done_q379_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ379Progression + ? 'highest' + : 'blocked_by_q373_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ379Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ383Progression + ? 'The q=379 residual tail-prime component is certified; attack q=383 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=379 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=373 tail-prime proof to emit the q=379 residual tail-prime atom.', + completionRule: 'The q=379 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q379_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q383_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ389Progression + ? 'done_q383_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ383Progression + ? 'highest' + : 'blocked_by_q379_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ383Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ389Progression + ? 'The q=383 residual tail-prime component is certified; attack q=389 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=383 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=379 tail-prime proof to emit the q=383 residual tail-prime atom.', + completionRule: 'The q=383 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q383_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q389_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ397Progression + ? 'done_q389_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ389Progression + ? 'highest' + : 'blocked_by_q383_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ389Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ397Progression + ? 'The q=389 residual tail-prime component is certified; attack q=397 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=389 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=383 tail-prime proof to emit the q=389 residual tail-prime atom.', + completionRule: 'The q=389 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q389_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q397_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ401Progression + ? 'done_q397_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ397Progression + ? 'highest' + : 'blocked_by_q389_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ397Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ401Progression + ? 'The q=397 residual tail-prime component is certified; attack q=401 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=397 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=389 tail-prime proof to emit the q=397 residual tail-prime atom.', + completionRule: 'The q=397 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q397_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q401_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ409Progression + ? 'done_q401_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ401Progression + ? 'highest' + : 'blocked_by_q397_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ401Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ409Progression + ? 'The q=401 residual tail-prime component is certified; attack q=409 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=401 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=397 tail-prime proof to emit the q=401 residual tail-prime atom.', + completionRule: 'The q=401 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q401_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q409_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ419Progression + ? 'done_q409_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ409Progression + ? 'highest' + : 'blocked_by_q401_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ409Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ419Progression + ? 'The q=409 residual tail-prime component is certified; attack q=419 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=409 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=401 tail-prime proof to emit the q=409 residual tail-prime atom.', + completionRule: 'The q=409 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q409_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q419_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ421Progression + ? 'done_q419_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ419Progression + ? 'highest' + : 'blocked_by_q409_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ419Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ421Progression + ? 'The q=419 residual tail-prime component is certified; attack q=421 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=419 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=409 tail-prime proof to emit the q=419 residual tail-prime atom.', + completionRule: 'The q=419 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q419_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q421_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ431Progression + ? 'done_q421_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ421Progression + ? 'highest' + : 'blocked_by_q419_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ421Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ431Progression + ? 'The q=421 residual tail-prime component is certified; attack q=431 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=421 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=419 tail-prime proof to emit the q=421 residual tail-prime atom.', + completionRule: 'The q=421 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q421_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q431_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ433Progression + ? 'done_q431_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ431Progression + ? 'highest' + : 'blocked_by_q421_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ431Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ433Progression + ? 'The q=431 residual tail-prime component is certified; attack q=433 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=431 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=421 tail-prime proof to emit the q=431 residual tail-prime atom.', + completionRule: 'The q=431 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q431_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q433_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ439Progression + ? 'done_q433_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ433Progression + ? 'highest' + : 'blocked_by_q431_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ433Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ439Progression + ? 'The q=433 residual tail-prime component is certified; attack q=439 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=433 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=431 tail-prime proof to emit the q=433 residual tail-prime atom.', + completionRule: 'The q=433 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q433_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q439_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ443Progression + ? 'done_q439_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ439Progression + ? 'highest' + : 'blocked_by_q433_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ439Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ443Progression + ? 'The q=439 residual tail-prime component is certified; attack q=443 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=439 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=433 tail-prime proof to emit the q=439 residual tail-prime atom.', + completionRule: 'The q=439 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q439_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q443_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ449Progression + ? 'done_q443_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ443Progression + ? 'highest' + : 'blocked_by_q439_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ443Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ449Progression + ? 'The q=443 residual tail-prime component is certified; attack q=449 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=443 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=439 tail-prime proof to emit the q=443 residual tail-prime atom.', + completionRule: 'The q=443 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q443_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q449_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ457Progression + ? 'done_q449_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ449Progression + ? 'highest' + : 'blocked_by_q443_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ449Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ457Progression + ? 'The q=449 residual tail-prime component is certified; attack q=457 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=449 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=443 tail-prime proof to emit the q=449 residual tail-prime atom.', + completionRule: 'The q=449 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q449_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q457_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ461Progression + ? 'done_q457_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ457Progression + ? 'highest' + : 'blocked_by_q449_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ457Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ461Progression + ? 'The q=457 residual tail-prime component is certified; attack q=461 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=457 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=449 tail-prime proof to emit the q=457 residual tail-prime atom.', + completionRule: 'The q=457 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q457_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q461_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ463Progression + ? 'done_q461_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ461Progression + ? 'highest' + : 'blocked_by_q457_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ461Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ463Progression + ? 'The q=461 residual tail-prime component is certified; attack q=463 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=461 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=457 tail-prime proof to emit the q=461 residual tail-prime atom.', + completionRule: 'The q=461 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q461_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q463_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ467Progression + ? 'done_q463_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ463Progression + ? 'highest' + : 'blocked_by_q461_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ463Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ467Progression + ? 'The q=463 residual tail-prime component is certified; attack q=467 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=463 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=461 tail-prime proof to emit the q=463 residual tail-prime atom.', + completionRule: 'The q=463 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q463_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q467_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ479Progression + ? 'done_q467_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ467Progression + ? 'highest' + : 'blocked_by_q463_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ467Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ479Progression + ? 'The q=467 residual tail-prime component is certified; attack q=479 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=467 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=463 tail-prime proof to emit the q=467 residual tail-prime atom.', + completionRule: 'The q=467 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q467_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q479_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ487Progression + ? 'done_q479_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ479Progression + ? 'highest' + : 'blocked_by_q467_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ479Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ487Progression + ? 'The q=479 residual tail-prime component is certified; attack q=487 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=479 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=467 tail-prime proof to emit the q=479 residual tail-prime atom.', + completionRule: 'The q=479 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q479_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q487_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ491Progression + ? 'done_q487_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ487Progression + ? 'highest' + : 'blocked_by_q479_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ487Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ491Progression + ? 'The q=487 residual tail-prime component is certified; attack q=491 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=487 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=479 tail-prime proof to emit the q=487 residual tail-prime atom.', + completionRule: 'The q=487 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q487_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q491_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ499Progression + ? 'done_q491_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ491Progression + ? 'highest' + : 'blocked_by_q487_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ491Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ499Progression + ? 'The q=491 residual tail-prime component is certified; attack q=499 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=491 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=487 tail-prime proof to emit the q=491 residual tail-prime atom.', + completionRule: 'The q=491 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q491_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q499_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ503Progression + ? 'done_q499_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ499Progression + ? 'highest' + : 'blocked_by_q491_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ499Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ503Progression + ? 'The q=499 residual tail-prime component is certified; attack q=503 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=499 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=491 tail-prime proof to emit the q=499 residual tail-prime atom.', + completionRule: 'The q=499 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q499_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q503_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ509Progression + ? 'done_q503_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ503Progression + ? 'highest' + : 'blocked_by_q499_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ503Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ509Progression + ? 'The q=503 residual tail-prime component is certified; attack q=509 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=503 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=499 tail-prime proof to emit the q=503 residual tail-prime atom.', + completionRule: 'The q=503 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q503_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q509_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ521Progression + ? 'done_q509_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ509Progression + ? 'highest' + : 'blocked_by_q503_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ509Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ521Progression + ? 'The q=509 residual tail-prime component is certified; attack q=521 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=509 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=503 tail-prime proof to emit the q=509 residual tail-prime atom.', + completionRule: 'The q=509 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q509_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q521_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ523Progression + ? 'done_q521_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ521Progression + ? 'highest' + : 'blocked_by_q509_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ521Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ523Progression + ? 'The q=521 residual tail-prime component is certified; attack q=523 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=521 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=509 tail-prime proof to emit the q=521 residual tail-prime atom.', + completionRule: 'The q=521 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q521_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q523_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ541Progression + ? 'done_q523_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ523Progression + ? 'highest' + : 'blocked_by_q521_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ523Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ541Progression + ? 'The q=523 residual tail-prime component is certified; attack q=541 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=523 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=521 tail-prime proof to emit the q=523 residual tail-prime atom.', + completionRule: 'The q=523 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q523_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q541_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ547Progression + ? 'done_q541_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ541Progression + ? 'highest' + : 'blocked_by_q523_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ541Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ547Progression + ? 'The q=541 residual tail-prime component is certified; attack q=547 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=541 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=523 tail-prime proof to emit the q=541 residual tail-prime atom.', + completionRule: 'The q=541 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q541_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q547_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ557Progression + ? 'done_q547_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ547Progression + ? 'highest' + : 'blocked_by_q541_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ547Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ557Progression + ? 'The q=547 residual tail-prime component is certified; attack q=557 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=547 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=541 tail-prime proof to emit the q=547 residual tail-prime atom.', + completionRule: 'The q=547 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q547_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q557_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ563Progression + ? 'done_q557_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ557Progression + ? 'highest' + : 'blocked_by_q547_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ557Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ563Progression + ? 'The q=557 residual tail-prime component is certified; attack q=563 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=557 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=547 tail-prime proof to emit the q=557 residual tail-prime atom.', + completionRule: 'The q=557 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q557_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q563_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ569Progression + ? 'done_q563_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ563Progression + ? 'highest' + : 'blocked_by_q557_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ563Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ569Progression + ? 'The q=563 residual tail-prime component is certified; attack q=569 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=563 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=557 tail-prime proof to emit the q=563 residual tail-prime atom.', + completionRule: 'The q=563 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q563_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q569_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ571Progression + ? 'done_q569_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ569Progression + ? 'highest' + : 'blocked_by_q563_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ569Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ571Progression + ? 'The q=569 residual tail-prime component is certified; attack q=571 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=569 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=563 tail-prime proof to emit the q=569 residual tail-prime atom.', + completionRule: 'The q=569 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q569_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q571_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ577Progression + ? 'done_q571_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ571Progression + ? 'highest' + : 'blocked_by_q569_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ571Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ577Progression + ? 'The q=571 residual tail-prime component is certified; attack q=577 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=571 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=569 tail-prime proof to emit the q=571 residual tail-prime atom.', + completionRule: 'The q=571 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q571_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q577_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQ587Progression + ? 'done_q577_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ577Progression + ? 'highest' + : 'blocked_by_q571_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ577Progression + ? firstSideCountFloorMovingTermIsDMaxTailQ587Progression + ? 'The q=577 residual tail-prime component is certified; attack q=587 next as a two-sided residual tail-prime CRT floor-bound.' + : `Prove dMax tail q=577 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=571 tail-prime proof to emit the q=577 residual tail-prime atom.', + completionRule: 'The q=577 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q577_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_weakest_p13_dmax_tail_q587_progression_atom', + status: firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloor + ? 'done_q587_tail_progression_upper_bound_verified' + : firstSideCountFloorMovingTermIsDMaxTailQ587Progression + ? 'highest' + : 'blocked_by_q577_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDMaxTailQ587Progression + ? firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloor + ? 'The q=587 residual tail-prime component is certified; lift the bounded q>=587 zero-floor profile before any aggregate dMax tail claim.' + : `Prove dMax tail q=587 progression atom ${firstSideCountFloorMovingTermSubatom}: certify both same-prime witness-side CRT floor bounds for the next residual tail prime.` + : 'Wait for the q=577 tail-prime proof to emit the q=587 residual tail-prime atom.', + completionRule: 'The q=587 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.', + command: null, + packetAtomId: String(firstSideCountFloorMovingTermSubatom ?? '').startsWith('D2_p13_dmax_tail_q587_progression_') + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dmax_tail_q_ge_587_parametric_zero_floor_lift', + status: firstSideCountFloorMovingTermIsDynamicMargin + ? 'done_q_ge_587_bounded_zero_floor_lift_verified' + : firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloorAtom + ? 'highest' + : 'blocked_by_q587_tail_progression_certificate', + task: firstSideCountFloorMovingTermIsDynamicMargin + ? 'The q>=587 bounded zero-floor lift is verified; attack the residual dynamic margin next.' + : firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloorAtom + ? `Lift bounded q>=587 tail atom ${firstSideCountFloorMovingTermSubatom}: convert the zero-floor CRT range profile into a parametric or aggregate tail lemma.` + : 'Wait for the q=587 tail-prime proof to emit the q>=587 parametric zero-floor lift atom.', + completionRule: 'The q>=587 tail profile is converted into a theorem-facing aggregate lemma, or the first concrete exceptional prime/range is emitted.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloorAtom ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_side18_residual_dynamic_margin_atom', + status: firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + ? 'done_bounded_dynamic_margin_replay_verified' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'done_exact_mixed_matching_profile_emitted_parametric_lift_needed' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'done_exact_mixed_symbolic_lift_decomposed' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'done_bounded_exact_mixed_successor_profile_verified' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMargin + ? 'highest' + : firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloor + ? 'blocked_by_q_ge_587_tail_lift' + : 'blocked_by_dmax_tail_growth_profile', + task: firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + ? 'The bounded residual dynamic-margin replay is verified; lift the side18 threshold inequality symbolically next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'The bounded exact mixed matching-injection profile is verified; prove the parametric prefix-extension lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'The exact mixed-margin symbolic lift is decomposed; prove the matching-injection sublemma next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'The bounded exact mixed-margin successor profile is verified; lift matching saturation and exact mixed margin symbolically next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? `Prove exact mixed-margin successor atom ${firstSideCountFloorMovingTermSubatom}: the prior side18 threshold lift is falsified, so use matching saturation plus exact mixed margin, or emit a sharper root-universe/rGreater successor.` + : firstSideCountFloorMovingTermIsDynamicMargin + ? `Prove residual dynamic margin atom ${firstSideCountFloorMovingTermSubatom}: side18Count + vMax + rGreater + 39 <= candidateSize, or emit the first sharper side-count/rGreater successor atom.` + : firstSideCountFloorMovingTermIsDMaxTailQGe587ParametricZeroFloor + ? 'Wait for the q>=587 aggregate tail lift to close before re-deriving the residual dynamic margin.' + : 'Wait for the dMax growth and tail profile subatoms to close before attacking the residual dynamic margin.', + completionRule: firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'The exact mixed-margin successor proves matching saturation and positive exact margin for this split, or emits the first sharper residue/root-universe obstruction.' + : 'The side18 residual dynamic margin is proved symbolically, or the first exact moving-count/rGreater obstruction becomes the next atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMargin + && !firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_side18_residual_dynamic_margin_symbolic_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'done_symbolic_lift_falsified_exact_mixed_matching_profile_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'done_symbolic_lift_falsified_exact_mixed_decomposition_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'done_symbolic_lift_falsified_successor_profile_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'done_symbolic_lift_falsified_successor_atom_emitted' + : firstSideCountFloorMovingTermIsDynamicMargin + ? 'blocked_by_dynamic_margin_bounded_replay' + : 'blocked_by_residual_dynamic_margin_atom', + task: firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + ? `Lift residual dynamic margin symbolic atom ${firstSideCountFloorMovingTermSubatom}: prove strictBaseThreshold - 1 - side18Count >= 20 for the split, or emit the first exact future-row obstruction.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'The false side18 threshold lift has been replaced by an exact mixed-margin decomposition, and the bounded matching profile now points to a parametric injection lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'The false side18 threshold lift has been replaced by an exact mixed-margin decomposition; prove the matching injection next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'The side18 threshold symbolic lift is falsified and the bounded exact mixed-margin successor profile is verified; lift the exact mixed-margin successor next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'The side18 threshold symbolic lift is falsified by an extended root-universe row; attack the exact mixed-margin successor instead.' + : firstSideCountFloorMovingTermIsDynamicMargin + ? 'Wait for the bounded residual dynamic-margin replay to expose the symbolic side18 threshold target.' + : 'Wait for the residual dynamic-margin atom to become the active moving-term subatom.', + completionRule: 'The side18 threshold inequality is proved symbolically for this split, or the first exact obstruction becomes a sharper side-count/rGreater successor atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_symbolic_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'done_symbolic_lift_decomposed_matching_profile_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'done_symbolic_lift_decomposed_first_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + ? 'blocked_by_side18_threshold_symbolic_lift' + : firstSideCountFloorMovingTermIsDynamicMargin + ? 'blocked_by_residual_dynamic_margin_atom' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? `Lift exact mixed-margin symbolic atom ${firstSideCountFloorMovingTermSubatom}: prove smaller-side matching saturation and strictBaseThreshold - mixedBaseCliqueSize >= 1 for the outsider-6323 family, or emit the first exact residue/root-universe obstruction.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'The exact mixed-margin symbolic lift is reduced and the bounded matching profile is emitted; prove the parametric matching-injection lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'The exact mixed-margin symbolic lift is reduced to matching-injection plus margin-floor sublemmas; prove matching injection first.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor to emit the symbolic matching-saturation lift.' + : firstSideCountFloorMovingTermIsDynamicMarginSymbolicLift + ? 'Wait for the side18 threshold symbolic lift to either prove or emit the exact mixed-margin successor.' + : firstSideCountFloorMovingTermIsDynamicMargin + ? 'Wait for the residual dynamic-margin phase to reach the exact mixed-margin successor.' + : 'Wait for the dynamic-margin phase to open.', + completionRule: 'The exact mixed-margin successor is proved symbolically for the outsider-6323 family, or the first residue/root-universe obstruction becomes the next deterministic atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'done_q17_residual_window_relaxed_fallback_menu_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'done_q17_residual_p13_expanded_fallback_menu_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'done_p7_q17_residual_cross_bad_fallback_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'done_squarefree_sieve_p7_q17_residual_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'done_period_shifted_endpoint_menu_sieve_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'done_p7_fallback_period_shifted_endpoint_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'done_small_prime_crt_endpoint_reduced_cross_squarefree_fallback_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'done_right_compatibility_escape_profile_small_prime_selector_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'done_exception_window_falsified_escape_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'done_selected_cross_squarefree_exception_window_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'done_selected_cross_squarefree_exception_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_direct_selector_lift_proved_cross_squarefree_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'done_residue_direct_selector_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'done_delta_staircase_generalization_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? 'done_finite_menu_falsified_direct_delta_successor_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'done_bounded_online_augmenting_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'done_bounded_prefix_matching_profile_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'The q17 residual p13-expanded fallback menu is falsified and repaired only after relaxing the local window; prove the window-relaxed fallback selector next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'The q17 residual seed fallback menu is falsified and repaired by a p=13 endpoint seed; prove the expanded fallback menu next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'The q17 residual fallback is falsified by a certified cross-bad row; prove the small-prime fallback selector next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'The squarefree sieve has been decomposed into a p=7 period-shift selector plus q=17 residual fallback; prove that residual lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'The period-shifted endpoint menu has been reduced to a squarefree sieve/hitting lemma; prove that theorem next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'The p=7 cross-squarefree fallback is reduced to a period-shifted endpoint menu; prove that menu next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'The small-prime CRT selector has a symbolic p=7 endpoint reduction; prove the cross-squarefree fallback next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'The right-compatibility escape lift has a bounded small-prime CRT profile; prove the small-prime selector next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'The finite exception window is falsified; prove the right-compatibility escape lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'The selected cross-squarefree exception menu is reduced to a finite-window theorem lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'The selected cross-squarefree lift is falsified; prove the exception/replacement menu next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The residue direct-selector sublemma is proved; prove selected cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'The residue-parametric lift has been decomposed; prove the direct-selector sublemma next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'The matching-injection lane has outgrown singleton direct deltas; prove the residue-parametric delta-selection lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? 'The mined finite menu has been falsified by bounded future event rows; prove the current direct-delta successor branch next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'The matching-injection lane has been narrowed to the finite augmenting-path menu; prove that menu next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'The bounded prefix matching-injection profile is emitted; prove the parametric prefix-extension lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? `Prove exact mixed matching-injection atom ${firstSideCountFloorMovingTermSubatom}: construct a side7-to-side18 missing-cross injection for outsider 6323, or emit the first unmatched residue/root-universe obstruction.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into its matching-injection sublemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'The matching injection saturates the side7-compatible set for this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_direct_selector_lift_proved_cross_squarefree_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'done_residue_direct_selector_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'done_delta_staircase_generalization_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? 'done_finite_menu_falsified_direct_delta_successor_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'done_bounded_online_augmenting_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The residue direct-selector sublemma is proved; prove selected cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'The residue-parametric lift has been decomposed; prove the direct-selector sublemma next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'The direct-delta staircase now has enough bounded failures to target the residue-parametric delta-selection lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? 'The finite augmenting menu was tested and falsified; prove the current direct-delta successor branch next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'The bounded online augmentation profile is emitted; prove the finite direct/replacement augmenting menu next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? `Prove parametric exact mixed matching-injection lift ${firstSideCountFloorMovingTermSubatom}: turn the bounded prefix/core profile into an online side7-to-side18 insertion rule, or emit the first future event-row obstruction.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A parametric insertion/replacement rule saturates side7 for every future row in this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_direct_selector_lift_proved_cross_squarefree_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'done_residue_direct_selector_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'done_delta_staircase_generalization_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? 'done_falsified_direct_delta_successor_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The finite menu/direct-delta lane has been replaced by a proved direct selector; prove selected cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'The finite menu/direct-delta lane has been generalized into a residue direct-selector sublemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'The finite menu and direct-delta extensions now point to a residue-parametric selection rule instead of another singleton delta.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? 'The finite menu and its first direct-delta extension have bounded falsifiers; prove the current direct-delta successor branch next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? `Prove finite augmenting-path menu ${firstSideCountFloorMovingTermSubatom}: discharge the direct insertion residue/delta cases plus the short replacement paths, or emit the first future event-row obstruction.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A finite direct/replacement augmenting-path menu saturates side7 for every future event row, or the first event outside the menu becomes the next deterministic atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaSuccessor + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_direct_selector_lift_proved_cross_squarefree_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'done_residue_direct_selector_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'done_delta_staircase_generalization_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'done_falsified_direct_delta_minus39_successor_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The direct-delta staircase has been replaced by a proved four-slot direct selector; prove selected cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'The direct-delta staircase has been decomposed into the residue direct-selector sublemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'The direct delta -39 successor exposed another bounded repair; prove the residue-parametric delta-selection lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'The direct delta -1089 extension fails first at side7 vertex 164507; prove the direct delta -39 successor branch next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? `Prove direct delta -1089 successor ${firstSideCountFloorMovingTermSubatom}: show the 73607 -> 72518 missing-cross edge branch extends symbolically, or emit the first future row requiring another delta/path.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'The delta -1089 branch is proved and merged into the menu, or the first future row requiring another direct delta or longer augmenting path becomes the next deterministic atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_direct_selector_lift_proved_cross_squarefree_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'done_residue_direct_selector_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'done_delta_staircase_generalization_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The direct delta -39 branch has been generalized into a proved four-slot direct selector; prove selected cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'The direct delta -39 branch has been generalized into the residue direct-selector sublemma; do not add singleton delta -1664.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'The direct delta -39 branch is falsified at side7 vertex 468707; continue with the residue-parametric delta-selection lift instead of adding singleton delta -1664.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? `Prove direct delta -39 successor ${firstSideCountFloorMovingTermSubatom}: show the 164507 -> 164468 missing-cross edge branch extends symbolically, or emit the first future row requiring another delta/path.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 successor check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'The delta -39 branch is proved and merged into the menu, or the first future row requiring another direct delta or longer augmenting path becomes the next deterministic atom.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_direct_selector_lift_proved_cross_squarefree_sublemma_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'done_reduced_to_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The residue-parametric delta-selection lift now has a proved direct-selector sublemma; prove selected cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'The residue-parametric delta-selection lift has been reduced to the direct-selector sublemma; prove that sublemma next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? `Prove residue-parametric delta-selection lift ${firstSideCountFloorMovingTermSubatom}: replace one-off direct-delta repairs with a rule covering every future side7-compatible event row, or emit the first obstruction outside the residue-parametric menu.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 successor check to either prove that branch or trigger the residue-parametric delta-selection lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 successor check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A residue/block delta-selection theorem saturates side7 without adding singleton delta siblings, or the first uncovered event row becomes the next obstruction packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'done_symbolic_direct_selector_lift_proved_cross_exception_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'done_symbolic_direct_selector_lift_proved' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'The four-slot direct selector is proved and the selected cross-squarefree lift has emitted an exception menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'The four-slot mod-4 selector proves every future side7 event row has an active side18-compatible endpoint; prove cross-squarefreeness next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? `Prove residue direct-selector lift ${firstSideCountFloorMovingTermSubatom}: every future side7-compatible event row needs a residue-selected side18-compatible direct endpoint, or emit the first row with no selected endpoint.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to its first direct-selector sublemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 successor check to either prove that branch or trigger the residue-parametric delta-selection lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 successor check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A residue/mod-square selector produces a side18-compatible direct endpoint for every future side7 event row, or the first uncovered event row becomes the next obstruction packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'done_falsified_exception_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'The selected four-slot endpoint is falsified by a square-divisor exception; prove the replacement menu next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? `Prove selected cross-squarefree lift ${firstSideCountFloorMovingTermSubatom}: the four-slot endpoint must have squarefree left * right + 1 for every future side7-compatible row, or emit the first square-divisor exception packet.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'The selected four-slot endpoint is a squarefree missing-cross edge for every future side7 row, or the first square-divisor exception becomes a bounded replacement-path packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'done_bounded_exception_menu_reduced_to_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'The selected cross-squarefree exception menu has a bounded finite-window profile; prove the finite-window lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? `Prove selected cross-squarefree exception menu ${firstSideCountFloorMovingTermSubatom}: replace the failing previous-93 endpoint for the left=8107 obstruction class with a symbolic side18-compatible squarefree-cross endpoint, or emit the first uncovered replacement row.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic replacement menu handles the selected endpoint square-divisor exceptions without adding singleton deltas, or the first uncovered replacement row becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'done_falsified_right_compatibility_escape_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'The finite 27-delta exception window is falsified at left=1138307; prove the right-compatibility escape lift next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? `Prove selected cross-squarefree exception finite-window lift ${firstSideCountFloorMovingTermSubatom}: every selected-cross square-divisor exception must have a replacement right from the 27-delta menu, or emit the first uncovered row.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic finite-window lift covers all selected-cross exceptions without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'done_squarefree_sieve_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'done_period_shifted_endpoint_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'done_p7_endpoint_cross_squarefree_fallback_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'done_bounded_small_prime_crt_selector_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'The right-compatibility escape lift has been reduced through the period-shifted endpoint menu to a squarefree sieve/hitting lemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'The right-compatibility escape lift has been reduced through p=7 fallback profiling to the period-shifted endpoint menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'The right-compatibility escape lift is reduced through the small-prime CRT endpoint lemma; prove the p=7 cross-squarefree fallback next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'The right-compatibility escape lift is reduced to a bounded small-prime CRT selector profile.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? `Prove selected cross-squarefree exception right-compatibility escape lift ${firstSideCountFloorMovingTermSubatom}: use the left=1138307 uncovered row to build a symbolic side18 repair selector beyond the failed 27-delta window, or emit the first row with no bounded escape repair.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'Wait for the selected cross-squarefree exception finite-window lift to prove or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic right-compatibility escape selector replaces the finite-window miss family without adding singleton delta siblings, or the first row with no bounded side18 squarefree repair becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'done_squarefree_sieve_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'done_period_shifted_endpoint_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'done_p7_endpoint_reduction_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'The small-prime CRT selector, p=7 endpoint fallback, and period-shifted endpoint menu are reduced to a squarefree sieve/hitting lemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'The small-prime CRT selector and p=7 endpoint fallback have been reduced to the period-shifted endpoint-menu theorem target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'The small-prime CRT selector has a symbolic p=7 endpoint reduction; selected cross-squarefreeness is now isolated in the fallback atom.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? `Prove selected cross-squarefree exception small-prime CRT escape selector lift ${firstSideCountFloorMovingTermSubatom}: derive the finite local side18 repair selector from the small primes {7,11,13,17,19,23,31,37,41}, or emit the first finite-window miss outside that rule.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'Wait for the selected cross-squarefree exception right-compatibility escape profile to reduce to a small-prime selector or emit a no-repair obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'Wait for the selected cross-squarefree exception finite-window lift to prove or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic small-prime CRT selector handles the right-compatibility escape rows, or the first finite-window miss outside that selector becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'done_squarefree_sieve_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'done_period_shifted_endpoint_menu_profile_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'blocked_by_small_prime_crt_endpoint_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'The p=7 endpoint cross-bad rows are reduced through the period-shifted endpoint menu to a squarefree sieve/hitting lemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'The p=7 endpoint cross-bad rows are profiled into a period-shifted endpoint-menu target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? `Prove selected cross-squarefree exception p=7 endpoint cross-squarefree fallback lift ${firstSideCountFloorMovingTermSubatom}: starting from d_7(left)=-14-25*((2*left-27) mod 49), handle the p=7 endpoint cross-bad rows with a small-prime fallback selector, or emit the first fallback miss.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'Wait for the small-prime CRT selector to emit its p=7 endpoint reduction or a selector obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'Wait for the selected cross-squarefree exception right-compatibility escape profile to reduce to a small-prime selector or emit a no-repair obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'Wait for the selected cross-squarefree exception finite-window lift to prove or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic cross-squarefree fallback selector handles the p=7 endpoint cross-bad rows, or the first finite-window miss outside that fallback rule becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'done_squarefree_sieve_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'blocked_by_p7_endpoint_cross_squarefree_fallback_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'blocked_by_small_prime_crt_endpoint_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'The period-shifted endpoint menu replay is reduced to a squarefree sieve/hitting lemma.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? `Prove selected cross-squarefree exception period-shifted endpoint-menu lift ${firstSideCountFloorMovingTermSubatom}: show the small-prime shifted endpoint menu supplies a squarefree cross product for every p=7 endpoint cross-bad row, or emit the first future row outside the menu.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'Wait for the p=7 endpoint fallback profile to emit the period-shifted endpoint-menu target or a fallback miss.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'Wait for the small-prime CRT selector to emit its p=7 endpoint reduction or a selector obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'Wait for the selected cross-squarefree exception right-compatibility escape profile to reduce to a small-prime selector or emit a no-repair obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'Wait for the selected cross-squarefree exception finite-window lift to prove or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic finite endpoint-menu lift covers all p=7 endpoint cross-bad rows without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'done_q17_residual_window_relaxed_fallback_menu_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'done_q17_residual_p13_expanded_fallback_menu_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'done_p7_q17_residual_cross_bad_fallback_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'done_p7_shift_q17_residual_lift_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'blocked_by_period_shifted_endpoint_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'blocked_by_p7_endpoint_cross_squarefree_fallback_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'blocked_by_small_prime_crt_endpoint_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed selector target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'The q17 residual seed fallback emitted the p13-expanded fallback menu target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'The p7/q17 residual profile emitted the q17 cross-bad fallback selector target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'The squarefree sieve profile is decomposed into a p=7 period-shift selector plus q=17 residual-class fallback.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? `Prove selected cross-squarefree exception period-shifted endpoint-menu squarefree sieve lift ${firstSideCountFloorMovingTermSubatom}: prove the squarefree hitting lemma for the local endpoint menu, or emit the first row where every menu endpoint is cross-blocked.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'Wait for the period-shifted endpoint menu replay to reduce to a squarefree sieve/hitting lemma or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'Wait for the p=7 endpoint fallback profile to emit the period-shifted endpoint-menu target or a fallback miss.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'Wait for the small-prime CRT selector to emit its p=7 endpoint reduction or a selector obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'Wait for the selected cross-squarefree exception right-compatibility escape profile to reduce to a small-prime selector or emit a no-repair obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'Wait for the selected cross-squarefree exception finite-window lift to prove or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic sieve/hitting lemma proves cross-squarefree endpoint existence for the menu, or the first fully cross-blocked row becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'done_q17_residual_window_relaxed_fallback_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'done_q17_residual_p13_expanded_fallback_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'done_q17_residual_cross_bad_fallback_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'blocked_by_period_shifted_endpoint_menu_squarefree_sieve_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'blocked_by_period_shifted_endpoint_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'blocked_by_p7_endpoint_cross_squarefree_fallback_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'blocked_by_small_prime_crt_endpoint_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'The q17 residual p13-expanded fallback menu is falsified and routed to a window-relaxed fallback selector.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'The q17 residual seed fallback is falsified and routed to the p13-expanded fallback menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'The q17 residual fallback is falsified at the first post-20M residual cross-bad row; prove the fallback selector next.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? `Prove selected cross-squarefree exception period-shifted endpoint-menu p7-shift q17 residual lift ${firstSideCountFloorMovingTermSubatom}: prove the p=7 period-shift squarefree selector and the q=17 fallback on left == 5882 mod 11025, or emit the first residual row where q17 is cross-blocked.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'Wait for the squarefree sieve profile to decompose into a p7-shift residual theorem or emit a fully cross-blocked row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'Wait for the period-shifted endpoint menu replay to reduce to a squarefree sieve/hitting lemma or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'Wait for the p=7 endpoint fallback profile to emit the period-shifted endpoint-menu target or a fallback miss.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'Wait for the small-prime CRT selector to emit its p=7 endpoint reduction or a selector obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'Wait for the selected cross-squarefree exception right-compatibility escape profile to reduce to a small-prime selector or emit a no-repair obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'Wait for the selected cross-squarefree exception finite-window lift to prove or emit its first uncovered row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'Wait for the selected cross-squarefree exception menu to emit its finite-window lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'Wait for the selected cross-squarefree lift to either prove or emit the first square-divisor exception.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'Wait for the residue direct-selector lift to prove endpoint existence before proving selected cross-squarefreeness.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'Wait for the residue-parametric delta-selection lift to reduce to direct-selector and cross-squarefree sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'Wait for the direct delta -39 check to trigger the residue-parametric lift.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'Wait for the direct delta -1089 check to either prove that branch or expose the next direct-delta obstruction.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'Wait for the finite augmenting menu check to either prove the menu or expose the first new direct-delta branch.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'Wait for the parametric lift profile to expose the finite augmenting-path menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'Wait for the bounded matching-injection profile to identify the parametric insertion target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'Wait for the exact mixed-margin symbolic lift to decompose into matching-injection sublemmas.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'Wait for the exact mixed-margin successor profile to expose the symbolic lift.' + : 'Wait for the dynamic-margin exact mixed phase to open.', + completionRule: 'A symbolic p7-shift plus q17 residual lemma proves cross-squarefree endpoint existence for the menu, or the first q17 residual cross-bad row becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'done_window_relaxed_fallback_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'done_p13_expanded_fallback_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'blocked_by_p7_shift_q17_residual_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'blocked_by_period_shifted_endpoint_menu_squarefree_sieve_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'blocked_by_period_shifted_endpoint_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'blocked_by_p7_endpoint_cross_squarefree_fallback_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'blocked_by_small_prime_crt_endpoint_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'The q17 residual seed fallback menu is falsified and the p13-expanded fallback menu is the active theorem target.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? `Prove selected cross-squarefree exception q17 residual cross-bad fallback lift ${firstSideCountFloorMovingTermSubatom}: show a small-prime local endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully fallback-blocked row.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'Wait for the p7-shift q17 residual check to either prove the q17 fallback or emit its first cross-bad row.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'Wait for the squarefree sieve profile to decompose into a residual fallback target.' + : 'Wait for the selected cross-squarefree exception endpoint-menu lane to reach the q17 residual fallback.', + completionRule: 'A symbolic fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully fallback-blocked row becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'done_window_relaxed_fallback_menu_emitted' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'blocked_by_q17_residual_seed_fallback_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuP7ShiftQ17Residual + ? 'blocked_by_p7_shift_q17_residual_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuSquarefreeSieve + ? 'blocked_by_period_shifted_endpoint_menu_squarefree_sieve_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenu + ? 'blocked_by_period_shifted_endpoint_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionP7EndpointCrossSquarefreeFallback + ? 'blocked_by_p7_endpoint_cross_squarefree_fallback_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionSmallPrimeCrtEscapeSelector + ? 'blocked_by_small_prime_crt_endpoint_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionRightCompatibilityEscape + ? 'blocked_by_right_compatibility_escape_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionWindowLift + ? 'blocked_by_exception_window_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionMenu + ? 'blocked_by_exception_menu_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeLift + ? 'blocked_by_selected_cross_squarefree_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueDirectSelectorLift + ? 'blocked_by_direct_selector_lift' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionResidueParametricDeltaSelectionLift + ? 'blocked_by_residue_parametric_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus39Successor + ? 'blocked_by_direct_delta_minus39_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionDirectDeltaMinus1089Successor + ? 'blocked_by_direct_delta_minus1089_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionFiniteMenu + ? 'blocked_by_finite_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionParametricLift + ? 'blocked_by_parametric_lift_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjection + ? 'blocked_by_bounded_matching_profile' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSymbolicLift + ? 'blocked_by_exact_mixed_symbolic_reduction' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedSuccessor + ? 'blocked_by_exact_mixed_successor_profile' + : 'blocked_by_dynamic_margin_phase', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'The q17 residual p13-expanded fallback menu is falsified and routed to the window-relaxed fallback menu.' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? `Prove selected cross-squarefree exception q17 residual p13-expanded fallback menu lift ${firstSideCountFloorMovingTermSubatom}: show the expanded local endpoint menu {11,13,19,23,31} supplies a squarefree side18-compatible right endpoint, or emit the first fully expanded-menu-blocked row.` + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'Wait for the q17 residual seed fallback menu to prove or emit its first fully blocked row.' + : 'Wait for the q17 residual cross-bad lane to reach the expanded fallback-menu target.', + completionRule: 'A symbolic expanded fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully expanded-menu-blocked row becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + && !firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? firstSideCountFloorMovingTermSubatom + : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'prove_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift', + status: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? 'highest' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualP13ExpandedFallbackMenu + ? 'blocked_by_p13_expanded_fallback_menu_check' + : firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualCrossBadFallback + ? 'blocked_by_q17_residual_seed_fallback_check' + : 'blocked_by_q17_residual_cross_bad_lane', + task: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu + ? `Prove selected cross-squarefree exception q17 residual window-relaxed fallback menu lift ${firstSideCountFloorMovingTermSubatom}: show the 25000-window endpoint menu supplies a squarefree side18-compatible right endpoint, or emit the first fully window-relaxed blocked row.` + : 'Wait for the q17 residual p13-expanded fallback menu to prove or emit its first 10000-window obstruction.', + completionRule: 'A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.', + command: null, + packetAtomId: firstSideCountFloorMovingTermIsDynamicMarginExactMixedMatchingInjectionSelectedCrossSquarefreeExceptionPeriodShiftedEndpointMenuQ17ResidualWindowRelaxedFallbackMenu ? firstSideCountFloorMovingTermSubatom : null, + packetId: firstSideCountFloorPacket?.packetId ?? null, + packetJsonPath: firstSideCountFloorPacket?.jsonPath ?? null, + packetMarkdownPath: firstSideCountFloorPacket?.markdownPath ?? null, + manifestJsonPath: packetRootPaths?.manifestJsonPath ?? null, + manifestMarkdownPath: packetRootPaths?.manifestMarkdownPath ?? null, + }, + { + taskId: 'start_singleton_p13_profile', + status: firstSuccessorPacket ? 'done_successor_packets_emitted' : 'highest', + task: 'Attack the singleton p13 split outP2=99|out25=14|smaller=side7 first to determine whether it is a real symbolic class or an under-split boundary artifact.', + completionRule: 'The singleton split either gets a persistence atom or emits a sharper split key.', + command: null, + packetAtomId: highestPriorityAtom?.atomId ?? null, + packetId: highestPriorityAtom?.packetArtifact?.packetId ?? null, + packetJsonPath: highestPriorityAtom?.packetArtifact?.jsonPath ?? null, + packetMarkdownPath: highestPriorityAtom?.packetArtifact?.markdownPath ?? null, + }, + ], + }; +} + +function buildProblemNextNeededSteps(problem, claimPass, formalizationWork) { + const remainingGaps = Array.isArray(formalizationWork.currentWork?.remainingGaps) + ? formalizationWork.currentWork.remainingGaps + : []; + const recommendations = Array.isArray(claimPass.recommendations) + ? claimPass.recommendations + : []; + const breakpointScout = getP848ExactBreakpointScout(problem); + const breakpointCertificate = getP848ExactBreakpointCertificate(problem); + const structuralVerifierAudit = getP848ExternalStructuralVerifierAudit(problem); + const baseSideScout = getP848BaseSideScout(problem); + const structuralTwoSideScout = getP848StructuralTwoSideScout(problem); + const mixedBaseFailureScout = getP848MixedBaseFailureScout(problem); + const fullMixedBaseStructuralVerifier = getP848FullMixedBaseStructuralVerifier(problem); + const structuralLiftMiner = getP848StructuralLiftMiner(problem); + const packProblemDir = getProblemPackDir(problem); + const intervalQueuePath = packProblemDir ? path.join(packProblemDir, 'INTERVAL_WORK_QUEUE.yaml') : null; + const intervalQueue = intervalQueuePath ? readYamlIfPresent(intervalQueuePath) : null; + const latestVerifiedInterval = claimPass.currentState?.latestVerifiedInterval ?? null; + const finiteGapStrategy = buildP848FiniteGapStrategy(problem, latestVerifiedInterval, intervalQueue, breakpointCertificate); + const splitCoreAtomizationPlan = buildP848SplitCoreAtomizationPlan(problem, formalizationWork); + const steps = []; + + for (const gap of remainingGaps.slice(0, 3)) { + steps.push({ + stepId: `gap_${steps.length + 1}`, + status: 'next', + task: gap, + source: 'formalization_work', + command: formalizationWork.commands?.formalizationWorkRefresh ?? `erdos problem formalization-work-refresh ${problem.problemId}`, + }); + } + + for (const recommendation of recommendations.slice(0, 4)) { + steps.push({ + stepId: recommendation.recommendation_id, + status: recommendation.priority ?? 'next', + task: recommendation.reason ?? recommendation.recommendation_id, + source: recommendation.lane ?? 'claim_pass', + command: recommendation.command ?? recommendation.entryCommand ?? `erdos problem claim-pass ${problem.problemId}`, + }); + } + + if (finiteGapStrategy?.status === 'ready') { + steps.push({ + stepId: 'finite_gap_strategy_handoff', + status: 'high', + task: `Use the finite-gap strategy readout: endpoint rollout is useful, but exact-only closure would still require about ${finiteGapStrategy.projectedEndpointChecksToOperationalThresholdLabel} endpoint checks to reach the imported ${finiteGapStrategy.operationalThreshold.raw} handoff.`, + source: 'finite_gap_strategy', + command: `erdos problem task-list-refresh ${problem.problemId}`, + }); + } + + if (String(problem?.problemId ?? '') === '848') { + if (splitCoreAtomizationPlan) { + for (const task of splitCoreAtomizationPlan.recommendedImmediateTasks ?? []) { + steps.push({ + stepId: task.taskId, + status: task.status, + task: task.task, + source: 'split_core_atomization_plan', + command: task.command !== undefined ? task.command : `erdos problem task-list-refresh ${problem.problemId}`, + completionRule: task.completionRule ?? null, + packetAtomId: task.packetAtomId ?? null, + packetId: task.packetId ?? null, + packetJsonPath: task.packetJsonPath ?? null, + packetMarkdownPath: task.packetMarkdownPath ?? null, + manifestJsonPath: task.manifestJsonPath ?? null, + manifestMarkdownPath: task.manifestMarkdownPath ?? null, + }); + } + } + + const audit = structuralVerifierAudit?.audit ?? null; + const blockerIds = (audit?.checks ?? []) + .filter((check) => check.status === 'failed' && check.severity === 'blocker') + .map((check) => check.checkId); + steps.push({ + stepId: 'structural_verifier_import_audit', + status: blockerIds.length > 0 || !audit ? 'high' : 'ready', + task: audit + ? `Use the structural-verifier import audit: status ${audit.status}${blockerIds.length > 0 ? `, blockers ${blockerIds.join(', ')}` : ''}.` + : 'Run the structural-verifier import audit before absorbing external outsider-clique computation into repo-owned coverage.', + source: 'external_structural_verifier_audit', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action structural_verifier_audit`, + }); + + const sideScout = baseSideScout?.scout ?? null; + steps.push({ + stepId: 'base_side_scout', + status: sideScout?.summary?.maxSide18ExceedsSide7 ? 'high' : 'ready', + task: sideScout + ? `Use the base-side scout: status ${sideScout.status} over ${sideScout.summary?.interval}; max side18-minus-side7 is ${sideScout.summary?.globalMaxSide18Minus7}.` + : 'Run the base-side scout to test whether the external one-sided 7 mod 25 base mask is safe against the 18 mod 25 side.', + source: 'structural_base_side_scout', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action base_side_scout --base-side-max 2000`, + }); + + const twoSideScout = structuralTwoSideScout?.scout ?? null; + const fullMixedVerifierPass = fullMixedBaseStructuralVerifier?.verifier?.summary?.allMixedChecksPass === true; + const twoSideRange = parseP848ClosedIntegerRange(twoSideScout?.summary?.assessedRange); + const structuralMinForCommand = twoSideRange?.min ?? 7307; + const structuralMaxForCommand = twoSideRange?.max ?? 10000; + steps.push({ + stepId: 'structural_two_side_scout', + status: twoSideScout?.summary?.allUnionChecksPass || fullMixedVerifierPass ? 'ready' : 'high', + task: twoSideScout + ? `Use the two-sided structural scout: status ${twoSideScout.status} over ${twoSideScout.summary?.assessedRange}; union failures ${twoSideScout.summary?.unionFailureCount}${fullMixedVerifierPass ? ' repaired by the full mixed-base verifier' : ''}.` + : 'Run the two-sided structural scout so the outsider-clique verifier lane covers both principal base sides with a safe union-mask bound.', + source: 'structural_two_side_scout', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action structural_two_side_scout --structural-min ${structuralMinForCommand} --structural-max ${structuralMaxForCommand}`, + }); + + const mixedScout = mixedBaseFailureScout?.scout ?? null; + steps.push({ + stepId: 'mixed_base_failure_scout', + status: mixedScout?.summary?.allAnalyzedRowsMixedPass ? 'ready' : 'high', + task: mixedScout + ? `Use the mixed-base failure scout: status ${mixedScout.status}; analyzed ${mixedScout.summary?.analyzedRowCount} union-failure rows with ${mixedScout.summary?.mixedFailureCount} mixed-base failures.` + : 'Run the mixed-base failure scout on the two-sided structural union failures to test whether exact mixed-base cliques repair the safe-union overcount.', + source: 'mixed_base_failure_scout', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action mixed_base_failure_scout --mixed-base-max-rows 40`, + }); + if (mixedScout?.summary?.allAnalyzedRowsMixedPass) { + const fullMixedVerifier = fullMixedBaseStructuralVerifier?.verifier ?? null; + steps.push({ + stepId: 'full_mixed_base_structural_verifier', + status: fullMixedVerifier?.summary?.allMixedChecksPass ? 'ready' : 'high', + task: fullMixedVerifier + ? `Use the full mixed-base structural verifier: status ${fullMixedVerifier.status} over ${fullMixedVerifier.summary?.assessedRange}; exact threatening-outsider checks ${fullMixedVerifier.summary?.threateningOutsiderCheckCount}, mixed failures ${fullMixedVerifier.summary?.mixedFailureCount}.` + : 'Promote the mixed-base repair from sampled union-failure rows into the full two-sided structural verifier by replacing the safe union-base overcount with exact mixed-base clique checks at every structural breakpoint and threatening active outsider.', + source: 'full_mixed_base_structural_verifier', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action full_mixed_base_structural_verifier --structural-min ${structuralMinForCommand} --structural-max ${structuralMaxForCommand}`, + }); + if (fullMixedVerifier?.summary?.allMixedChecksPass) { + const structuralLift = structuralLiftMiner?.miner ?? null; + steps.push({ + stepId: 'structural_lift_miner', + status: structuralLift ? 'ready' : 'high', + task: structuralLift + ? `Use the structural lift miner: status ${structuralLift.status}; mined ${structuralLift.summary?.minedExactRowCount} exact mixed rows; next theorem lane ${structuralLift.summary?.nextTheoremLane}.` + : 'Mine the full mixed-base structural verifier into theorem-facing lift obligations before extending bounded search again.', + source: 'structural_lift_miner', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action structural_lift_miner`, + }); + } + } + } + + if (breakpointCertificate?.certificate?.status === 'certified_from_endpoint_monotonicity') { + steps.push({ + stepId: 'regime_b_endpoint_verifier_backend', + status: 'high', + task: `Continue the active endpoint-monotonicity exact verifier beyond ${breakpointCertificate.certificate.summary.interval} (${breakpointCertificate.certificate.summary.endpointCheckCount} endpoint checks cover ${breakpointCertificate.certificate.summary.rowCount} rows; compression ${breakpointCertificate.certificate.summary.compressionRatio.toFixed(2)}x).`, + source: 'exact_breakpoint_certificate', + command: `erdos number-theory dispatch ${problem.problemId} --apply --action exact_followup_rollout --exact-chunks 5 --exact-chunk-size 1000 --endpoint-monotonicity`, + }); + } else if (breakpointScout?.scout?.summary) { + steps.push({ + stepId: 'regime_b_breakpoint_scout_to_certificate', + status: 'high', + task: `Convert the exact breakpoint scout over ${breakpointScout.scout.summary.interval} (${breakpointScout.scout.summary.plateauCount} plateaus) into a structured-breakpoint certificate, or record the monotonicity obstruction that prevents promotion.`, + source: 'exact_breakpoint_scout', + command: `node packs/number-theory/problems/848/compute/problem848_exact_breakpoint_scout.mjs --results packs/number-theory/problems/848/EXACT_SMALL_N_${String(breakpointScout.scout.summary.interval ?? '').replace('..', '_')}_RESULTS.json --json-output packs/number-theory/problems/848/EXACT_BREAKPOINT_SCOUT.json`, + }); + } + + return steps; +} + +function pickProblemAgentPrimaryAction(currentTasks, nextNeededSteps) { + const priorityRank = { + highest: 0, + next: 1, + high: 2, + }; + const candidate = [...(nextNeededSteps ?? [])] + .filter((step) => Object.hasOwn(priorityRank, step.status)) + .sort((left, right) => priorityRank[left.status] - priorityRank[right.status])[0] + ?? null; + if (candidate) { + return { + source: candidate.source ?? 'next_needed_steps', + stepId: candidate.stepId, + status: candidate.status, + task: candidate.task, + command: candidate.command ?? null, + completionRule: candidate.completionRule ?? null, + packetAtomId: candidate.packetAtomId ?? null, + packetId: candidate.packetId ?? null, + packetJsonPath: candidate.packetJsonPath ?? null, + packetMarkdownPath: candidate.packetMarkdownPath ?? null, + manifestJsonPath: candidate.manifestJsonPath ?? null, + manifestMarkdownPath: candidate.manifestMarkdownPath ?? null, + }; + } + + const task = (currentTasks ?? []).find((item) => item.taskId === 'discharge_first_remaining_gap') + ?? (currentTasks ?? []).find((item) => item.taskId === 'execute_current_work_packet') + ?? (currentTasks ?? []).find((item) => item.status === 'ready') + ?? null; + if (!task) { + return null; + } + + return { + source: 'current_tasks', + stepId: task.taskId, + status: task.status, + task: task.task, + command: task.command ?? null, + completionRule: task.completionRule ?? null, + }; +} + +function buildProblemAgentFlow(problem, { + currentTasks, + nextNeededSteps, + granularBreakdownMode, + orpModeOverlays, + commands, +}) { + const primaryNextAction = pickProblemAgentPrimaryAction(currentTasks, nextNeededSteps); + const situationalOverlays = (orpModeOverlays?.overlays ?? []) + .filter((overlay) => overlay.modeId !== granularBreakdownMode?.modeId) + .map((overlay) => ({ + modeId: overlay.modeId, + role: overlay.role, + useWhen: overlay.useWhen, + command: overlay.command, + loopPlacement: overlay.loopPlacement, + outputExpectation: overlay.outputExpectation, + })); + + return { + schema: 'erdos.problem_agent_flow/1', + status: primaryNextAction ? 'ready' : 'blocked_no_primary_action', + audience: 'agent', + problemId: problem.problemId, + purpose: 'Give agents one compact execution contract without forcing humans or agents through every task-list section.', + operatingRule: 'Read this object first; execute the primary next action unless a guardrail blocks it or the task list is stale.', + primaryNextAction, + modePolicy: { + defaultAction: 'execute_primary_next_action', + doNotRunEveryMode: true, + selectionRule: orpModeOverlays?.selectionRule ?? 'Use an ORP mode only when it reduces ambiguity or friction.', + granularBreakdown: granularBreakdownMode + ? { + modeId: granularBreakdownMode.modeId, + useWhen: 'Use when the primary action is broad, fuzzy, theorem-heavy, or has unclear dependencies.', + fullBreakdownCommand: granularBreakdownMode.commands.fullBreakdown, + nudgeCommand: granularBreakdownMode.commands.nudge, + compressionRule: 'After any breakdown, compress back to one active target and one verification command.', + } + : null, + situationalOverlays, + }, + executionLoop: [ + 'Load agentFlow.primaryNextAction.', + 'If the action is clear, execute its command or implement the named task directly.', + 'If the action is fuzzy, run the granular nudge or full breakdown, then compress to one target and one command.', + 'Use at most one additional ORP overlay when it clearly reduces friction for the current decision.', + 'Refresh the canonical task list after material progress and continue from the regenerated agentFlow.', + ], + guardrails: [ + 'Do not run paid or remote compute unless the frontier configuration explicitly enables that paid rung.', + 'Prefer local/free compute before opt-in paid compute.', + 'Do not treat bounded search evidence as an all-N proof without a theorem-facing handoff.', + 'Do not run every ORP mode by default.', + 'Persist operationally important changes into canonical artifacts rather than chat-only state.', + ], + writeback: { + refreshCommand: commands.taskListRefresh, + taskListCommand: commands.taskList, + durableArtifactRule: granularBreakdownMode?.durableArtifactRule ?? 'Refresh the canonical task list when the next action changes.', + }, + }; +} + +export function buildProblemTaskList(problem) { + const theoremLoop = buildProblemTheoremLoop(problem); + const claimPass = buildProblemClaimPass(problem); + const formalization = buildProblemFormalization(problem); + const formalizationWork = buildProblemFormalizationWork(problem); + const paths = getProblemTaskListPaths(problem); + const intervalQueuePath = theoremLoop.sources?.packProblemDir ? path.join(theoremLoop.sources.packProblemDir, 'INTERVAL_WORK_QUEUE.yaml') : null; + const intervalQueue = intervalQueuePath ? readYamlIfPresent(intervalQueuePath) : null; + const breakpointScout = getP848ExactBreakpointScout(problem); + const breakpointCertificate = getP848ExactBreakpointCertificate(problem); + const structuralVerifierAudit = getP848ExternalStructuralVerifierAudit(problem); + const baseSideScout = getP848BaseSideScout(problem); + const structuralTwoSideScout = getP848StructuralTwoSideScout(problem); + const mixedBaseFailureScout = getP848MixedBaseFailureScout(problem); + const fullMixedBaseStructuralVerifier = getP848FullMixedBaseStructuralVerifier(problem); + const structuralLiftMiner = getP848StructuralLiftMiner(problem); + const structuralLiftChecklist = getP848StructuralLiftChecklist(problem); + const activeRoute = theoremLoop.activeRoute ?? theoremLoop.currentState?.activeRoute ?? null; + const latestVerifiedInterval = claimPass.currentState?.latestVerifiedInterval + ?? theoremLoop.currentState?.latestVerifiedInterval + ?? null; + const finiteGapStrategy = buildP848FiniteGapStrategy(problem, latestVerifiedInterval, intervalQueue, breakpointCertificate); + const splitCoreAtomizationPlan = buildP848SplitCoreAtomizationPlan(problem, formalizationWork); + const granularBreakdownMode = buildProblemGranularBreakdownMode(problem, formalizationWork); + const orpModeOverlays = buildProblemOrpModeOverlays(problem, granularBreakdownMode); + const currentTasks = buildProblemCurrentTasks(problem, theoremLoop, claimPass, formalization, formalizationWork, intervalQueue); + const completedAnchors = buildProblemCompletedAnchors(formalizationWork); + const nextNeededSteps = buildProblemNextNeededSteps(problem, claimPass, formalizationWork); + const commands = { + problemShow: `erdos problem show ${problem.problemId}`, + problemArtifacts: `erdos problem artifacts ${problem.problemId}`, + taskList: `erdos problem task-list ${problem.problemId}`, + taskListRefresh: `erdos problem task-list-refresh ${problem.problemId}`, + taskListRun: `erdos problem task-list-run ${problem.problemId} --passes 10`, + orpModeList: orpModeOverlays.sourceCommand, + granularBreakdown: granularBreakdownMode.commands.fullBreakdown, + granularNudge: granularBreakdownMode.commands.nudge, + theoremLoop: theoremLoop.commands?.theoremLoop ?? null, + claimPass: claimPass.commands?.claimPass ?? null, + formalization: formalization.commands?.formalization ?? null, + formalizationWork: formalizationWork.commands?.formalizationWork ?? null, + sourceRefresh: theoremLoop.commands?.sourceRefresh ?? null, + }; + const agentFlow = buildProblemAgentFlow(problem, { + currentTasks, + nextNeededSteps, + granularBreakdownMode, + orpModeOverlays, + commands, + }); + + return { + schema: 'erdos.problem_task_list/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + cluster: problem.cluster, + sourceKind: formalizationWork.sourceKind, + taskListMode: formalizationWork.formalizationWorkMode, + currentState: { + activeRoute, + currentClaimSurface: theoremLoop.currentState?.currentClaimSurface ?? null, + routeSummary: theoremLoop.currentState?.routeSummary ?? null, + nextHonestMove: theoremLoop.currentState?.nextHonestMove ?? null, + latestVerifiedInterval, + }, + finiteGapStrategy, + granularBreakdownMode, + orpModeOverlays, + agentFlow, + splitCoreAtomizationPlan, + structuralVerifierAudit: structuralVerifierAudit?.audit + ? { + status: structuralVerifierAudit.audit.status ?? null, + conclusion: structuralVerifierAudit.audit.conclusion ?? null, + summary: structuralVerifierAudit.audit.summary ?? null, + blockerIds: (structuralVerifierAudit.audit.checks ?? []) + .filter((check) => check.status === 'failed' && check.severity === 'blocker') + .map((check) => check.checkId), + nextActions: structuralVerifierAudit.audit.nextActions ?? [], + } + : null, + baseSideScout: baseSideScout?.scout + ? { + status: baseSideScout.scout.status ?? null, + summary: baseSideScout.scout.summary ?? null, + firstNWithSide18MaxExceedingSide7: baseSideScout.scout.firstNWithSide18MaxExceedingSide7 ?? null, + boundary: baseSideScout.scout.boundary ?? null, + } + : null, + structuralTwoSideScout: structuralTwoSideScout?.scout + ? { + status: structuralTwoSideScout.scout.status ?? null, + summary: structuralTwoSideScout.scout.summary ?? null, + firstFailures: structuralTwoSideScout.scout.firstFailures ?? null, + worstRows: structuralTwoSideScout.scout.worstRows ?? null, + boundary: structuralTwoSideScout.scout.boundary ?? null, + } + : null, + mixedBaseFailureScout: mixedBaseFailureScout?.scout + ? { + status: mixedBaseFailureScout.scout.status ?? null, + summary: mixedBaseFailureScout.scout.summary ?? null, + firstMixedFailure: mixedBaseFailureScout.scout.firstMixedFailure ?? null, + worstMixedRow: mixedBaseFailureScout.scout.worstMixedRow ?? null, + boundary: mixedBaseFailureScout.scout.boundary ?? null, + } + : null, + fullMixedBaseStructuralVerifier: fullMixedBaseStructuralVerifier?.verifier + ? { + status: fullMixedBaseStructuralVerifier.verifier.status ?? null, + summary: fullMixedBaseStructuralVerifier.verifier.summary ?? null, + firstMixedFailure: fullMixedBaseStructuralVerifier.verifier.firstMixedFailure ?? null, + worstCertifiedRow: fullMixedBaseStructuralVerifier.verifier.worstCertifiedRow ?? null, + worstExactMixedRow: fullMixedBaseStructuralVerifier.verifier.worstExactMixedRow ?? null, + boundary: fullMixedBaseStructuralVerifier.verifier.boundary ?? null, + } + : null, + structuralLiftMiner: structuralLiftMiner?.miner + ? { + status: structuralLiftMiner.miner.status ?? null, + summary: structuralLiftMiner.miner.summary ?? null, + sourceVerifier: structuralLiftMiner.miner.sourceVerifier ?? null, + liftObligations: structuralLiftMiner.miner.liftObligations ?? [], + recommendedNextSteps: structuralLiftMiner.miner.recommendedNextSteps ?? [], + boundary: structuralLiftMiner.miner.boundary ?? null, + } + : null, + structuralLiftChecklist: structuralLiftChecklist?.checklist + ? { + status: structuralLiftChecklist.checklist.status ?? null, + northStar: structuralLiftChecklist.checklist.northStar ?? null, + currentFocus: structuralLiftChecklist.checklist.currentFocus ?? null, + completionRule: structuralLiftChecklist.checklist.completionRule ?? null, + recommendedNextSteps: structuralLiftChecklist.checklist.recommendedNextSteps ?? [], + boundary: structuralLiftChecklist.checklist.boundary ?? null, + } + : null, + executionRule: buildProblemTaskExecutionRule(problem, granularBreakdownMode), + loopTemplate: buildProblemTaskTemplate(problem, theoremLoop, claimPass, formalizationWork, intervalQueue, granularBreakdownMode), + currentObjective: { + formalizationId: formalization.currentTarget?.formalizationId ?? null, + focusId: formalization.currentTarget?.focusId ?? null, + title: formalization.currentTarget?.title ?? formalizationWork.currentWork?.title ?? null, + activeWorkId: formalizationWork.currentWork?.workId ?? null, + activeWorkTitle: formalizationWork.currentWork?.title ?? null, + activeWorkStatus: formalizationWork.currentWork?.status ?? null, + }, + currentTasks, + completedAnchors, + nextNeededSteps, + commands, + sources: { + packProblemDir: paths.packProblemDir, + taskListJsonPath: paths.taskListJsonPath, + taskListMarkdownPath: paths.taskListMarkdownPath, + theoremLoopJsonPath: theoremLoop.sources?.theoremLoopJsonPath ?? null, + claimPassJsonPath: claimPass.sources?.claimPassJsonPath ?? null, + formalizationJsonPath: formalization.sources?.formalizationJsonPath ?? null, + formalizationWorkJsonPath: formalizationWork.sources?.formalizationWorkJsonPath ?? null, + intervalQueuePath, + exactBreakpointScoutJsonPath: breakpointScout?.path ?? null, + exactBreakpointCertificateJsonPath: breakpointCertificate?.path ?? null, + externalStructuralVerifierAuditJsonPath: structuralVerifierAudit?.path ?? null, + externalStructuralVerifierAuditMarkdownPath: structuralVerifierAudit?.markdownPath ?? null, + baseSideScoutJsonPath: baseSideScout?.path ?? null, + baseSideScoutMarkdownPath: baseSideScout?.markdownPath ?? null, + structuralTwoSideScoutJsonPath: structuralTwoSideScout?.path ?? null, + structuralTwoSideScoutMarkdownPath: structuralTwoSideScout?.markdownPath ?? null, + mixedBaseFailureScoutJsonPath: mixedBaseFailureScout?.path ?? null, + mixedBaseFailureScoutMarkdownPath: mixedBaseFailureScout?.markdownPath ?? null, + fullMixedBaseStructuralVerifierJsonPath: fullMixedBaseStructuralVerifier?.path ?? null, + fullMixedBaseStructuralVerifierMarkdownPath: fullMixedBaseStructuralVerifier?.markdownPath ?? null, + structuralLiftMinerJsonPath: structuralLiftMiner?.path ?? null, + structuralLiftMinerMarkdownPath: structuralLiftMiner?.markdownPath ?? null, + structuralLiftChecklistJsonPath: structuralLiftChecklist?.path ?? null, + structuralLiftChecklistMarkdownPath: structuralLiftChecklist?.markdownPath ?? null, + legacyBridgeJsonPath: theoremLoop.sources?.legacyBridgeJsonPath ?? null, + }, + }; +} + +export function renderProblemTaskListMarkdown(doc) { + const lines = [ + `# ${doc.displayName} Task List`, + '', + 'This task list is the canonical research-loop surface for the problem. It gives one reusable execution rule, one templated loop, the current active tasks, and the next steps discovered from the current theorem/search/verifier state.', + '', + '## Current State', + '', + `- Task list mode: \`${doc.taskListMode}\`.`, + `- Active route: \`${doc.currentState.activeRoute ?? '(none)'}\`.`, + `- Current claim surface: \`${doc.currentState.currentClaimSurface ?? '(none)'}\`.`, + `- Route summary: ${doc.currentState.routeSummary ?? '(none)'}`, + `- Next honest move: ${doc.currentState.nextHonestMove ?? '(none)'}`, + `- Latest verified interval: ${doc.currentState.latestVerifiedInterval ? `\`${doc.currentState.latestVerifiedInterval}\`` : '`(none)`'}`, + '', + '## Execution Rule', + '', + `- Stance: \`${doc.executionRule?.stance ?? 'concrete_execution'}\``, + `- Summary: ${doc.executionRule?.summary ?? '(none)'}`, + ]; + + for (const item of doc.executionRule?.afterEachCompletion ?? []) { + lines.push(`- After each completed step: ${item}`); + } + if (doc.executionRule?.repetitionProtocol) { + lines.push(`- Repetition protocol: ${doc.executionRule.repetitionProtocol}`); + } + if (doc.executionRule?.lowStressLongHorizonNote) { + lines.push(`- Long-horizon note: ${doc.executionRule.lowStressLongHorizonNote}`); + } + + if (doc.granularBreakdownMode) { + lines.push('', '## ORP Granular Breakdown', ''); + lines.push(`- Status: \`${doc.granularBreakdownMode.status}\``); + lines.push(`- Mode id: \`${doc.granularBreakdownMode.modeId}\``); + lines.push(`- Topic: ${doc.granularBreakdownMode.topic}`); + lines.push(`- Activation phrase: ${doc.granularBreakdownMode.activationPhrase}`); + lines.push(`- Invocation rule: ${doc.granularBreakdownMode.invocationRule}`); + lines.push(`- Full breakdown: \`${doc.granularBreakdownMode.commands.fullBreakdown}\``); + lines.push(`- Nudge: \`${doc.granularBreakdownMode.commands.nudge}\``); + for (const item of doc.granularBreakdownMode.loopIntegration ?? []) { + lines.push(`- Loop integration: ${item}`); + } + lines.push(`- Durable artifact rule: ${doc.granularBreakdownMode.durableArtifactRule}`); + } + + if (doc.orpModeOverlays) { + lines.push('', '## ORP Mode Overlay Palette', ''); + lines.push(`- Status: \`${doc.orpModeOverlays.status}\``); + lines.push(`- Source command: \`${doc.orpModeOverlays.sourceCommand}\``); + lines.push(`- Default mode id: \`${doc.orpModeOverlays.defaultModeId}\``); + lines.push(`- Selection rule: ${doc.orpModeOverlays.selectionRule}`); + lines.push(`- Durable when operational: \`${doc.orpModeOverlays.alwaysDurableWhenOperational ? 'yes' : 'no'}\``); + for (const overlay of doc.orpModeOverlays.overlays ?? []) { + lines.push(`- Overlay \`${overlay.modeId}\` (${overlay.role}): ${overlay.useWhen} | placement: ${overlay.loopPlacement} | command: \`${overlay.command}\` | output: ${overlay.outputExpectation}`); + } + } + + if (doc.agentFlow) { + lines.push('', '## Agent Flow', ''); + lines.push(`- Status: \`${doc.agentFlow.status}\``); + lines.push(`- Audience: \`${doc.agentFlow.audience}\``); + lines.push(`- Operating rule: ${doc.agentFlow.operatingRule}`); + if (doc.agentFlow.primaryNextAction) { + lines.push(`- Primary next action: \`${doc.agentFlow.primaryNextAction.stepId}\` [${doc.agentFlow.primaryNextAction.status}] ${doc.agentFlow.primaryNextAction.task}`); + if (doc.agentFlow.primaryNextAction.command) { + lines.push(`- Primary command: \`${doc.agentFlow.primaryNextAction.command}\``); + } + } + lines.push(`- Default agent action: \`${doc.agentFlow.modePolicy?.defaultAction ?? 'execute_primary_next_action'}\``); + lines.push(`- Mode selection: ${doc.agentFlow.modePolicy?.selectionRule ?? 'Use ORP modes only when they reduce friction.'}`); + if (doc.agentFlow.modePolicy?.granularBreakdown?.nudgeCommand) { + lines.push(`- Granular nudge: \`${doc.agentFlow.modePolicy.granularBreakdown.nudgeCommand}\``); + } + for (const overlay of doc.agentFlow.modePolicy?.situationalOverlays ?? []) { + lines.push(`- Situational overlay \`${overlay.modeId}\`: ${overlay.useWhen} | command: \`${overlay.command}\``); + } + for (const guardrail of doc.agentFlow.guardrails ?? []) { + lines.push(`- Agent guardrail: ${guardrail}`); + } + if (doc.agentFlow.writeback?.refreshCommand) { + lines.push(`- Refresh after material progress: \`${doc.agentFlow.writeback.refreshCommand}\``); + } + } + + if (doc.finiteGapStrategy?.status === 'ready') { + lines.push('', '## Finite-Gap Strategy', ''); + lines.push(`- Verdict: \`${doc.finiteGapStrategy.verdict}\``); + lines.push(`- Operational threshold: \`${doc.finiteGapStrategy.operationalThreshold.raw}\` (${doc.finiteGapStrategy.operationalThreshold.trustStatus})`); + lines.push(`- Remaining rows to operational threshold: \`${doc.finiteGapStrategy.remainingRowsToOperationalThresholdLabel}\``); + lines.push(`- Projected endpoint checks to operational threshold: \`${doc.finiteGapStrategy.projectedEndpointChecksToOperationalThresholdLabel}\``); + lines.push(`- Recommended mode: \`${doc.finiteGapStrategy.recommendedMode}\``); + for (const item of doc.finiteGapStrategy.guidance ?? []) { + lines.push(`- Guidance: ${item}`); + } + } + + if (doc.splitCoreAtomizationPlan) { + lines.push('', '## Split-Core Atomization Plan', ''); + lines.push(`- Plan id: \`${doc.splitCoreAtomizationPlan.planId}\``); + lines.push(`- Status: \`${doc.splitCoreAtomizationPlan.status}\``); + lines.push(`- North star: ${doc.splitCoreAtomizationPlan.northStar}`); + lines.push(`- Deterministic rule: ${doc.splitCoreAtomizationPlan.deterministicRule}`); + lines.push(`- Active parent obligation: \`${doc.splitCoreAtomizationPlan.scope?.activeParentObligationId ?? '(unknown)'}\``); + lines.push(`- Target obligation: \`${doc.splitCoreAtomizationPlan.scope?.targetObligationId ?? '(unknown)'}\``); + lines.push(`- Split atoms: \`${doc.splitCoreAtomizationPlan.scope?.splitAtomCount ?? 0}\``); + lines.push(`- D2 split count: \`${doc.splitCoreAtomizationPlan.scope?.d2SplitCount ?? 0}\``); + lines.push(`- D3 split count: \`${doc.splitCoreAtomizationPlan.scope?.d3SplitCount ?? 0}\``); + if (doc.splitCoreAtomizationPlan.packetManifest) { + lines.push(`- Packet directory: \`${doc.splitCoreAtomizationPlan.packetManifest.directoryPath ?? '(none)'}\``); + lines.push(`- Packet manifest JSON: \`${doc.splitCoreAtomizationPlan.packetManifest.manifestJsonPath ?? '(none)'}\``); + lines.push(`- Packet manifest markdown: \`${doc.splitCoreAtomizationPlan.packetManifest.manifestMarkdownPath ?? '(none)'}\``); + lines.push(`- Packet files present: \`${doc.splitCoreAtomizationPlan.packetManifest.allPacketFilesPresent ? 'yes' : 'no'}\``); + lines.push(`- Successor packet count: \`${doc.splitCoreAtomizationPlan.packetManifest.successorPacketCount ?? 0}\``); + lines.push(`- First packet refinement conditions: \`${doc.splitCoreAtomizationPlan.packetManifest.firstPacketRefinementConditionCount ?? 0}\``); + lines.push(`- Verified successor families: \`${doc.splitCoreAtomizationPlan.packetManifest.verifiedSuccessorFamilyCount ?? 0}\``); + lines.push(`- Successor packet files present: \`${doc.splitCoreAtomizationPlan.packetManifest.allSuccessorPacketFilesPresent ? 'yes' : 'no'}\``); + lines.push(`- All materialized successor families verified: \`${doc.splitCoreAtomizationPlan.packetManifest.allMaterializedSuccessorFamiliesVerified ? 'yes' : 'no'}\``); + lines.push(`- First packet edge certificate: \`${doc.splitCoreAtomizationPlan.packetManifest.firstPacketEdgeObstructionCertificateStatus ?? '(none)'}\``); + lines.push(`- First packet edge persistence: \`${doc.splitCoreAtomizationPlan.packetManifest.firstPacketEdgeCongruencePersistenceStatus ?? '(none)'}\``); + lines.push(`- Edge-persistent packet count: \`${doc.splitCoreAtomizationPlan.packetManifest.verifiedEdgeCongruencePacketCount ?? 0}\``); + lines.push(`- First packet matching/K certificate: \`${doc.splitCoreAtomizationPlan.packetManifest.firstPacketMatchingKEnvelopeCertificateStatus ?? '(none)'}\``); + lines.push(`- Matching/K packet count: \`${doc.splitCoreAtomizationPlan.packetManifest.verifiedMatchingKEnvelopePacketCount ?? 0}\``); + lines.push(`- First packet split-discharge readiness: \`${doc.splitCoreAtomizationPlan.packetManifest.firstPacketSplitDischargeReadinessStatus ?? '(none)'}\``); + lines.push(`- Split-discharge ready packet count: \`${doc.splitCoreAtomizationPlan.packetManifest.splitDischargeReadyPacketCount ?? 0}\``); + lines.push(`- P13 row-universe coverage: \`${doc.splitCoreAtomizationPlan.packetManifest.p13RowUniverseCoverageStatus ?? '(none)'}\``); + lines.push(`- P13 row-universe first missing atom: \`${doc.splitCoreAtomizationPlan.packetManifest.p13RowUniverseFirstMissingAtom ?? '(none)'}\``); + lines.push(`- P13 slack-dominance lift: \`${doc.splitCoreAtomizationPlan.packetManifest.p13SlackDominanceLiftStatus ?? '(none)'}\``); + lines.push(`- P13 slack-dominance first lemma: \`${doc.splitCoreAtomizationPlan.packetManifest.p13SlackDominanceFirstOpenLemma ?? '(none)'}\``); + lines.push(`- Side-count floor packet count: \`${doc.splitCoreAtomizationPlan.packetManifest.sideCountFloorPacketCount ?? 0}\``); + lines.push(`- First side-count floor packet: \`${doc.splitCoreAtomizationPlan.packetManifest.firstSideCountFloorPacketToAttack ?? '(none)'}\``); + lines.push(`- First side-count structural margin lemma: \`${doc.splitCoreAtomizationPlan.packetManifest.firstSideCountFloorStructuralMarginLemma ?? '(none)'}\``); + lines.push(`- First side-count moving-term subatom: \`${doc.splitCoreAtomizationPlan.packetManifest.firstSideCountFloorMovingTermSubatom ?? '(none)'}\``); + lines.push(`- Next undischarged p13 packet: \`${doc.splitCoreAtomizationPlan.packetManifest.nextUndischargedP13PacketToAttack ?? '(none)'}\``); + lines.push(`- First packet to attack: \`${doc.splitCoreAtomizationPlan.packetManifest.firstPacketToAttack ?? '(none)'}\``); + lines.push(`- First successor packet to attack: \`${doc.splitCoreAtomizationPlan.packetManifest.firstSuccessorPacketToAttack ?? '(none)'}\``); + lines.push(`- First unverified successor packet to attack: \`${doc.splitCoreAtomizationPlan.packetManifest.firstUnverifiedSuccessorPacketToAttack ?? '(none)'}\``); + } + if (doc.splitCoreAtomizationPlan.rowUniverseCoverage) { + const coverage = doc.splitCoreAtomizationPlan.rowUniverseCoverage; + lines.push(`- Row-universe coverage candidate: \`${coverage.coverageId}\` [${coverage.status}]`); + lines.push(`- Row-universe coverage scope: \`${coverage.currentCoverage?.coverageScope ?? '(none)'}\`, tight witnesses \`${coverage.currentCoverage?.tightWitnessRowCount ?? '(unknown)'}\` / bounded p13 threats \`${coverage.currentCoverage?.threatRowCount ?? '(unknown)'}\``); + if (coverage.boundedStratificationAudit) { + lines.push(`- Bounded p13 row strata: \`${coverage.boundedStratificationAudit.splitStratumCount}\` total, \`${coverage.boundedStratificationAudit.emittedTightSplitCoveredRowCount}\` rows in emitted tight strata, \`${coverage.boundedStratificationAudit.slackDominatedOutsideRowCount}\` / \`${coverage.boundedStratificationAudit.outsideTightSplitRowCount}\` outside rows slack-dominated`); + lines.push(`- Bounded p13 slack floor: tight min \`${coverage.boundedStratificationAudit.minEmittedTightSplitSlack}\`, outside min \`${coverage.boundedStratificationAudit.minOutsideSlack}\`, additional split rows \`${coverage.boundedStratificationAudit.outsideRowsNeedingAdditionalSplitPacket}\``); + } + lines.push(`- Row-universe emitted missing atom: \`${coverage.emittedMissingAtom?.atomId ?? '(none)'}\``); + } + if (doc.splitCoreAtomizationPlan.slackDominanceSymbolicLift) { + const lift = doc.splitCoreAtomizationPlan.slackDominanceSymbolicLift; + lines.push(`- Slack-dominance symbolic lift candidate: \`${lift.candidateId}\` [${lift.status}]`); + lines.push(`- Slack-dominance formula replay: \`${lift.boundedRowCount}\` rows across \`${lift.boundedStratumCount}\` strata, target floor \`${lift.targetNonTightSlackLowerBound}\`, observed min \`${lift.observedMinNonTightSlack}\``); + lines.push(`- Slack-dominance first open lemma: \`${lift.firstOpenSymbolicLemma?.lemmaId ?? '(none)'}\``); + } + lines.push(`- Most confusing question: ${doc.splitCoreAtomizationPlan.mostConfusingPart?.question ?? '(none)'}`); + lines.push(`- Why it matters: ${doc.splitCoreAtomizationPlan.mostConfusingPart?.whyItMatters ?? '(none)'}`); + lines.push(`- First place to attack: \`${doc.splitCoreAtomizationPlan.mostConfusingPart?.firstPlaceToAttack ?? '(none)'}\``); + for (const layer of doc.splitCoreAtomizationPlan.masterLayers ?? []) { + lines.push(`- Layer \`${layer.layerId}\` [${layer.status}]: ${layer.objective} | output: ${layer.deterministicOutput ?? '(none)'}`); + } + for (const atom of doc.splitCoreAtomizationPlan.splitAtoms ?? []) { + lines.push(`- Split atom \`${atom.atomId}\` [${atom.priority}, ${atom.status}]: p=${atom.prime}, split=${atom.splitKey}, witnesses=${atom.witnessCount}, core=${atom.commonMatchingPairCount}, K=${JSON.stringify(atom.requiredMatchingLowerBoundRange)}`); + if (atom.packetArtifact) { + lines.push(`- Split atom packet \`${atom.packetArtifact.packetId}\`: JSON \`${atom.packetArtifact.jsonPath}\`, markdown \`${atom.packetArtifact.markdownPath}\``); + } + } + for (const layer of doc.splitCoreAtomizationPlan.adjacentAtomizedLayers ?? []) { + lines.push(`- Adjacent layer \`${layer.layerId}\` [${layer.status}]: ${layer.reason} | focus: ${layer.focusPlan}`); + } + for (const task of doc.splitCoreAtomizationPlan.recommendedImmediateTasks ?? []) { + lines.push(`- Atomization task \`${task.taskId}\` [${task.status}]: ${task.task} | completion: ${task.completionRule}`); + } + } + + if (doc.structuralVerifierAudit) { + lines.push('', '## Structural Verifier Audit', ''); + lines.push(`- Status: \`${doc.structuralVerifierAudit.status ?? '(unknown)'}\``); + lines.push(`- Conclusion: ${doc.structuralVerifierAudit.conclusion ?? '(none)'}`); + lines.push(`- Blockers: \`${(doc.structuralVerifierAudit.blockerIds ?? []).join(', ') || 'none'}\``); + for (const item of doc.structuralVerifierAudit.nextActions ?? []) { + lines.push(`- Next action: ${item}`); + } + } + + if (doc.baseSideScout) { + lines.push('', '## Base-Side Scout', ''); + lines.push(`- Status: \`${doc.baseSideScout.status ?? '(unknown)'}\``); + lines.push(`- Interval: \`${doc.baseSideScout.summary?.interval ?? '(unknown)'}\``); + lines.push(`- Max side18-minus-side7: \`${doc.baseSideScout.summary?.globalMaxSide18Minus7 ?? '(unknown)'}\``); + lines.push(`- Side18 global exceedance found: \`${doc.baseSideScout.summary?.maxSide18ExceedsSide7 ? 'yes' : 'no'}\``); + if (doc.baseSideScout.firstNWithSide18MaxExceedingSide7) { + lines.push(`- First side18 exceedance: \`${JSON.stringify(doc.baseSideScout.firstNWithSide18MaxExceedingSide7)}\``); + } + lines.push(`- Boundary: ${doc.baseSideScout.boundary?.note ?? '(none)'}`); + } + + if (doc.structuralTwoSideScout) { + lines.push('', '## Two-Sided Structural Scout', ''); + lines.push(`- Status: \`${doc.structuralTwoSideScout.status ?? '(unknown)'}\``); + lines.push(`- Assessed range: \`${doc.structuralTwoSideScout.summary?.assessedRange ?? '(unknown)'}\``); + lines.push(`- Union checks pass: \`${doc.structuralTwoSideScout.summary?.allUnionChecksPass ? 'yes' : 'no'}\``); + lines.push(`- Union failures: \`${doc.structuralTwoSideScout.summary?.unionFailureCount ?? '(unknown)'}\``); + if (doc.structuralTwoSideScout.firstFailures?.union) { + lines.push(`- First union failure: \`${JSON.stringify(doc.structuralTwoSideScout.firstFailures.union)}\``); + } + if (doc.structuralTwoSideScout.worstRows?.union) { + lines.push(`- Worst union row: \`${JSON.stringify(doc.structuralTwoSideScout.worstRows.union)}\``); + } + lines.push(`- Boundary: ${doc.structuralTwoSideScout.boundary?.safety ?? '(none)'}`); + } + + if (doc.mixedBaseFailureScout) { + lines.push('', '## Mixed-Base Failure Scout', ''); + lines.push(`- Status: \`${doc.mixedBaseFailureScout.status ?? '(unknown)'}\``); + lines.push(`- Analyzed rows: \`${doc.mixedBaseFailureScout.summary?.analyzedRowCount ?? '(unknown)'}\``); + lines.push(`- Mixed failures: \`${doc.mixedBaseFailureScout.summary?.mixedFailureCount ?? '(unknown)'}\``); + lines.push(`- All analyzed rows pass mixed bound: \`${doc.mixedBaseFailureScout.summary?.allAnalyzedRowsMixedPass ? 'yes' : 'no'}\``); + lines.push(`- Minimum mixed margin: \`${doc.mixedBaseFailureScout.summary?.minMixedMargin ?? '(unknown)'}\``); + if (doc.mixedBaseFailureScout.worstMixedRow) { + lines.push(`- Worst mixed row: \`${JSON.stringify(doc.mixedBaseFailureScout.worstMixedRow)}\``); + } + lines.push(`- Boundary: ${doc.mixedBaseFailureScout.boundary?.note ?? '(none)'}`); + } + + if (doc.fullMixedBaseStructuralVerifier) { + lines.push('', '## Full Mixed-Base Structural Verifier', ''); + lines.push(`- Status: \`${doc.fullMixedBaseStructuralVerifier.status ?? '(unknown)'}\``); + lines.push(`- Assessed range: \`${doc.fullMixedBaseStructuralVerifier.summary?.assessedRange ?? '(unknown)'}\``); + lines.push(`- All mixed checks pass: \`${doc.fullMixedBaseStructuralVerifier.summary?.allMixedChecksPass ? 'yes' : 'no'}\``); + lines.push(`- Mixed failures: \`${doc.fullMixedBaseStructuralVerifier.summary?.mixedFailureCount ?? '(unknown)'}\``); + lines.push(`- Threatening outsider checks: \`${doc.fullMixedBaseStructuralVerifier.summary?.threateningOutsiderCheckCount ?? '(unknown)'}\``); + lines.push(`- Minimum certified margin: \`${doc.fullMixedBaseStructuralVerifier.summary?.minCertifiedMargin ?? '(unknown)'}\``); + if (doc.fullMixedBaseStructuralVerifier.worstExactMixedRow) { + lines.push(`- Worst exact mixed row: \`${JSON.stringify(doc.fullMixedBaseStructuralVerifier.worstExactMixedRow)}\``); + } + lines.push(`- Boundary: ${doc.fullMixedBaseStructuralVerifier.boundary?.proofObligation ?? '(none)'}`); + } + + if (doc.structuralLiftMiner) { + lines.push('', '## Structural Lift Miner', ''); + lines.push(`- Status: \`${doc.structuralLiftMiner.status ?? '(unknown)'}\``); + lines.push(`- Mined exact rows: \`${doc.structuralLiftMiner.summary?.minedExactRowCount ?? '(unknown)'}\``); + lines.push(`- Coverage complete: \`${doc.structuralLiftMiner.summary?.coverageComplete ? 'yes' : 'no'}\``); + lines.push(`- Primary exact primes: \`${(doc.structuralLiftMiner.summary?.primaryExactPrimes ?? []).join(', ') || '(unknown)'}\``); + lines.push(`- Next theorem lane: \`${doc.structuralLiftMiner.summary?.nextTheoremLane ?? '(unknown)'}\``); + for (const obligation of (doc.structuralLiftMiner.liftObligations ?? []).slice(0, 4)) { + lines.push(`- Obligation \`${obligation.obligationId}\` [${obligation.priority}, ${obligation.status}]: ${obligation.statementTemplate}`); + } + for (const step of (doc.structuralLiftMiner.recommendedNextSteps ?? []).slice(0, 4)) { + lines.push(`- Recommended next: \`${step.stepId}\` [${step.priority}] ${step.why} | command: \`${step.command}\``); + } + lines.push(`- Boundary: ${doc.structuralLiftMiner.boundary?.note ?? '(none)'}`); + } + + if (doc.structuralLiftChecklist) { + lines.push('', '## Structural Lift Reference Backlog', ''); + lines.push(`- Status: \`${doc.structuralLiftChecklist.status ?? '(unknown)'}\``); + lines.push(`- North star: ${doc.structuralLiftChecklist.northStar ?? '(none)'}`); + lines.push(`- Current packet: \`${doc.structuralLiftChecklist.currentFocus?.packetId ?? '(unknown)'}\``); + lines.push(`- First actionable step: \`${doc.structuralLiftChecklist.currentFocus?.firstActionableStepId ?? '(unknown)'}\``); + lines.push(`- Target step: \`${doc.structuralLiftChecklist.currentFocus?.targetStepId ?? '(unknown)'}\``); + lines.push(`- Completion rule: ${doc.structuralLiftChecklist.completionRule ?? '(none)'}`); + for (const step of (doc.structuralLiftChecklist.recommendedNextSteps ?? []).slice(0, 4)) { + lines.push(`- Reference next: \`${step.stepId}\` [${step.priority}] ${step.task} | command: \`${step.command}\``); + } + lines.push(`- Boundary: ${doc.structuralLiftChecklist.boundary?.note ?? '(none)'}`); + } + + lines.push('', '## Template Loop', ''); + for (const step of doc.loopTemplate ?? []) { + lines.push(`- \`${step.stepId}\`: ${step.title} | ${step.task}${step.completionRule ? ` | completion: ${step.completionRule}` : ''}${step.command ? ` | command: \`${step.command}\`` : ''}`); + } + + lines.push('', '## Current Objective', ''); + lines.push(`- Formalization id: \`${doc.currentObjective?.formalizationId ?? '(none)'}\``); + lines.push(`- Focus id: \`${doc.currentObjective?.focusId ?? '(none)'}\``); + lines.push(`- Title: ${doc.currentObjective?.title ?? '(none)'}`); + lines.push(`- Active work id: \`${doc.currentObjective?.activeWorkId ?? '(none)'}\``); + lines.push(`- Active work title: ${doc.currentObjective?.activeWorkTitle ?? '(none)'}`); + lines.push(`- Active work status: \`${doc.currentObjective?.activeWorkStatus ?? '(none)'}\``); + + lines.push('', '## Current Tasks', ''); + for (const task of doc.currentTasks ?? []) { + lines.push(`- \`${task.taskId}\` [${task.status}] ${task.title} | ${task.task}${task.why ? ` | ${task.why}` : ''}${task.completionRule ? ` | completion: ${task.completionRule}` : ''}${task.command ? ` | command: \`${task.command}\`` : ''}`); + } + + lines.push('', '## Completed Anchors', ''); + for (const item of doc.completedAnchors ?? []) { + lines.push(`- \`${item.itemId}\` [${item.status}] ${item.note}`); + } + + lines.push('', '## Next Needed Steps', ''); + for (const item of doc.nextNeededSteps ?? []) { + lines.push(`- \`${item.stepId}\` [${item.status}] ${item.task}${item.source ? ` | source: ${item.source}` : ''}${item.command ? ` | command: \`${item.command}\`` : ''}`); + } + + lines.push('', '## Commands', ''); + lines.push(`- Problem surface: \`${doc.commands.problemShow}\``); + lines.push(`- Problem artifacts: \`${doc.commands.problemArtifacts}\``); + lines.push(`- Task list: \`${doc.commands.taskList}\``); + lines.push(`- Task list refresh: \`${doc.commands.taskListRefresh}\``); + lines.push(`- Task list run: \`${doc.commands.taskListRun}\``); + if (doc.commands.orpModeList) { + lines.push(`- ORP mode list: \`${doc.commands.orpModeList}\``); + } + if (doc.commands.granularBreakdown) { + lines.push(`- ORP granular breakdown: \`${doc.commands.granularBreakdown}\``); + } + if (doc.commands.granularNudge) { + lines.push(`- ORP granular nudge: \`${doc.commands.granularNudge}\``); + } + if (doc.commands.theoremLoop) { + lines.push(`- Theorem loop: \`${doc.commands.theoremLoop}\``); + } + if (doc.commands.claimPass) { + lines.push(`- Claim pass: \`${doc.commands.claimPass}\``); + } + if (doc.commands.formalization) { + lines.push(`- Formalization: \`${doc.commands.formalization}\``); + } + if (doc.commands.formalizationWork) { + lines.push(`- Formalization work: \`${doc.commands.formalizationWork}\``); + } + if (doc.commands.sourceRefresh) { + lines.push(`- Source refresh: \`${doc.commands.sourceRefresh}\``); + } + + lines.push('', '## Sources', ''); + for (const [label, value] of Object.entries(doc.sources ?? {})) { + if (!value) { + continue; + } + lines.push(`- ${label}: \`${value}\``); + } + lines.push(''); + return lines.join('\n'); +} + +export function getProblemTaskListSnapshot(problem) { + const doc = buildProblemTaskList(problem); + const paths = getProblemTaskListPaths(problem); + return { + ...doc, + taskListJsonPath: paths.taskListJsonPath, + taskListMarkdownPath: paths.taskListMarkdownPath, + taskListJsonPresent: Boolean(paths.taskListJsonPath && fs.existsSync(paths.taskListJsonPath)), + taskListMarkdownPresent: Boolean(paths.taskListMarkdownPath && fs.existsSync(paths.taskListMarkdownPath)), + }; +} + +function runSourceRefreshIfNeeded(problem, options = {}) { + const sourceRefresh = getSourceRefreshCommand(problem); + if (!sourceRefresh) { + return { + ok: true, + skipped: true, + command: null, + stdout: null, + stderr: null, + payload: null, + }; + } + + if (!options.refreshSource) { + return { + ok: true, + skipped: true, + command: sourceRefresh.command, + stdout: null, + stderr: null, + payload: null, + }; + } + + try { + const stdout = execFileSync('node', [path.join(repoRoot, 'src', 'cli', 'index.js'), ...sourceRefresh.args], { + cwd: repoRoot, + encoding: 'utf8', + stdio: ['ignore', 'pipe', 'pipe'], + }).trim(); + return { + ok: true, + skipped: false, + command: sourceRefresh.command, + stdout, + stderr: null, + payload: readJsonSafe(stdout), + }; + } catch (error) { + return { + ok: false, + skipped: false, + command: sourceRefresh.command, + stdout: error?.stdout?.toString().trim() || null, + stderr: error?.stderr?.toString().trim() || error?.message || null, + payload: null, + }; + } +} + +function readJsonSafe(text) { + try { + return JSON.parse(text); + } catch { + return null; + } +} + +export function refreshProblemTheoremLoop(problem) { + const sourceRefresh = runSourceRefreshIfNeeded(problem); + if (!sourceRefresh.ok) { + return { + ok: false, + problemId: problem.problemId, + error: sourceRefresh.stderr ?? 'Failed to refresh theorem-loop source state.', + sourceRefresh, + theoremLoop: null, + jsonPath: null, + markdownPath: null, + }; + } + + const theoremLoop = buildProblemTheoremLoop(problem); + const paths = getProblemTheoremLoopPaths(problem); + ensureDir(paths.packProblemDir); + writeJson(paths.theoremLoopJsonPath, theoremLoop); + writeText(paths.theoremLoopMarkdownPath, renderProblemTheoremLoopMarkdown(theoremLoop)); + + return { + ok: true, + problemId: problem.problemId, + theoremLoop, + jsonPath: paths.theoremLoopJsonPath, + markdownPath: paths.theoremLoopMarkdownPath, + sourceRefresh, + }; +} + +export function refreshProblemClaimLoop(problem) { + const theoremRefresh = refreshProblemTheoremLoop(problem); + if (!theoremRefresh.ok) { + return { + ok: false, + problemId: problem.problemId, + error: theoremRefresh.error ?? 'Failed to refresh theorem loop prerequisite for claim loop.', + theoremRefresh, + claimLoop: null, + jsonPath: null, + markdownPath: null, + }; + } + + const claimLoop = buildProblemClaimLoop(problem); + const paths = getProblemClaimLoopPaths(problem); + ensureDir(paths.packProblemDir); + writeJson(paths.claimLoopJsonPath, claimLoop); + writeText(paths.claimLoopMarkdownPath, renderProblemClaimLoopMarkdown(claimLoop)); + + return { + ok: true, + problemId: problem.problemId, + claimLoop, + jsonPath: paths.claimLoopJsonPath, + markdownPath: paths.claimLoopMarkdownPath, + theoremRefresh, + }; +} + +export function refreshProblemClaimPass(problem) { + const claimRefresh = refreshProblemClaimLoop(problem); + if (!claimRefresh.ok) { + return { + ok: false, + problemId: problem.problemId, + error: claimRefresh.error ?? 'Failed to refresh claim loop prerequisite for claim pass.', + claimRefresh, + claimPass: null, + jsonPath: null, + markdownPath: null, + }; + } + + const claimPass = buildProblemClaimPass(problem); + const paths = getProblemClaimPassPaths(problem); + ensureDir(paths.packProblemDir); + writeJson(paths.claimPassJsonPath, claimPass); + writeText(paths.claimPassMarkdownPath, renderProblemClaimPassMarkdown(claimPass)); + + return { + ok: true, + problemId: problem.problemId, + claimPass, + jsonPath: paths.claimPassJsonPath, + markdownPath: paths.claimPassMarkdownPath, + claimRefresh, + }; +} + +export function refreshProblemFormalization(problem) { + const claimPassRefresh = refreshProblemClaimPass(problem); + if (!claimPassRefresh.ok) { + return { + ok: false, + problemId: problem.problemId, + error: claimPassRefresh.error ?? 'Failed to refresh claim pass prerequisite for formalization.', + claimPassRefresh, + formalization: null, + jsonPath: null, + markdownPath: null, + }; + } + + const formalization = buildProblemFormalization(problem); + const paths = getProblemFormalizationPaths(problem); + ensureDir(paths.packProblemDir); + writeJson(paths.formalizationJsonPath, formalization); + writeText(paths.formalizationMarkdownPath, renderProblemFormalizationMarkdown(formalization)); + + return { + ok: true, + problemId: problem.problemId, + formalization, + jsonPath: paths.formalizationJsonPath, + markdownPath: paths.formalizationMarkdownPath, + claimPassRefresh, + }; +} + +export function refreshProblemFormalizationWork(problem) { + const formalizationRefresh = refreshProblemFormalization(problem); + if (!formalizationRefresh.ok) { + return { + ok: false, + problemId: problem.problemId, + error: formalizationRefresh.error ?? 'Failed to refresh formalization prerequisite for formalization work.', + formalizationRefresh, + formalizationWork: null, + jsonPath: null, + markdownPath: null, + }; + } + + const formalizationWork = buildProblemFormalizationWork(problem); + const paths = getProblemFormalizationWorkPaths(problem); + ensureDir(paths.packProblemDir); + writeJson(paths.formalizationWorkJsonPath, formalizationWork); + writeText(paths.formalizationWorkMarkdownPath, renderProblemFormalizationWorkMarkdown(formalizationWork)); + writeText(paths.formalizationWorkSvgPath, renderProblemFormalizationWorkSvg(formalizationWork)); + + return { + ok: true, + problemId: problem.problemId, + formalizationWork, + jsonPath: paths.formalizationWorkJsonPath, + markdownPath: paths.formalizationWorkMarkdownPath, + svgPath: paths.formalizationWorkSvgPath, + formalizationRefresh, + }; +} + +export function refreshProblemTaskList(problem) { + const formalizationWorkRefresh = refreshProblemFormalizationWork(problem); + if (!formalizationWorkRefresh.ok) { + return { + ok: false, + problemId: problem.problemId, + error: formalizationWorkRefresh.error ?? 'Failed to refresh formalization-work prerequisite for task list.', + formalizationWorkRefresh, + taskList: null, + jsonPath: null, + markdownPath: null, + }; + } + + let taskList = buildProblemTaskList(problem); + const splitAtomPacketWrite = writeP848SplitAtomPacketsFromTaskList(problem, taskList); + if (splitAtomPacketWrite?.ok) { + taskList = buildProblemTaskList(problem); + } + const paths = getProblemTaskListPaths(problem); + ensureDir(paths.packProblemDir); + writeJson(paths.taskListJsonPath, taskList); + writeText(paths.taskListMarkdownPath, renderProblemTaskListMarkdown(taskList)); + + return { + ok: true, + problemId: problem.problemId, + taskList, + jsonPath: paths.taskListJsonPath, + markdownPath: paths.taskListMarkdownPath, + formalizationWorkRefresh, + splitAtomPacketWrite, + }; +} + +function buildTaskLoopFingerprint(taskList) { + return JSON.stringify({ + activeRoute: taskList.currentState?.activeRoute ?? null, + currentClaimSurface: taskList.currentState?.currentClaimSurface ?? null, + nextHonestMove: taskList.currentState?.nextHonestMove ?? null, + latestVerifiedInterval: taskList.currentState?.latestVerifiedInterval ?? null, + currentObjective: { + formalizationId: taskList.currentObjective?.formalizationId ?? null, + focusId: taskList.currentObjective?.focusId ?? null, + activeWorkId: taskList.currentObjective?.activeWorkId ?? null, + activeWorkStatus: taskList.currentObjective?.activeWorkStatus ?? null, + }, + currentTasks: (taskList.currentTasks ?? []).slice(0, 8).map((task) => ({ + taskId: task.taskId, + status: task.status, + title: task.title, + task: task.task, + })), + nextNeededSteps: (taskList.nextNeededSteps ?? []).slice(0, 8).map((step) => ({ + stepId: step.stepId, + status: step.status, + task: step.task, + source: step.source, + })), + }); +} + +function pickHighestValueLoopStep(taskList) { + const recommended = (taskList.nextNeededSteps ?? []).find((step) => step.status === 'next' || step.status === 'high'); + if (recommended) { + return { + source: recommended.source ?? 'next_needed_steps', + stepId: recommended.stepId, + task: recommended.task, + command: recommended.command ?? null, + }; + } + + const remainingGap = (taskList.currentTasks ?? []).find((task) => task.taskId === 'discharge_first_remaining_gap'); + if (remainingGap) { + return { + source: 'current_tasks', + stepId: remainingGap.taskId, + task: remainingGap.task, + command: remainingGap.command ?? null, + }; + } + + const currentWork = (taskList.currentTasks ?? []).find((task) => task.taskId === 'execute_current_work_packet'); + if (currentWork) { + return { + source: 'current_tasks', + stepId: currentWork.taskId, + task: currentWork.task, + command: currentWork.command ?? null, + }; + } + + return null; +} + +function renderProblemTaskLoopRunMarkdown(run) { + const lines = [ + `# ${run.displayName} Task Loop Run`, + '', + `- Problem id: \`${run.problemId}\``, + `- Requested passes: \`${run.requestedPasses}\``, + `- Executed passes: \`${run.executedPasses}\``, + `- Stop reason: \`${run.stopReason}\``, + `- Converged: \`${run.converged ? 'yes' : 'no'}\``, + ]; + + if (run.convergedAtPass) { + lines.push(`- Converged at pass: \`${run.convergedAtPass}\``); + } + + if (run.currentState) { + lines.push(`- Active route: \`${run.currentState.activeRoute ?? '(none)'}\``); + lines.push(`- Current claim surface: \`${run.currentState.currentClaimSurface ?? '(none)'}\``); + lines.push(`- Latest verified interval: ${run.currentState.latestVerifiedInterval ? `\`${run.currentState.latestVerifiedInterval}\`` : '`(none)`'}`); + } + + if (run.highestValueStep) { + lines.push(`- Highest-value next step: \`${run.highestValueStep.stepId ?? '(none)'}\` | ${run.highestValueStep.task ?? '(none)'}`); + if (run.highestValueStep.command) { + lines.push(`- Highest-value command: \`${run.highestValueStep.command}\``); + } + } + + lines.push('', '## Passes', ''); + for (const pass of run.passes ?? []) { + lines.push(`- Pass ${pass.passNumber}: changed=\`${pass.changed ? 'yes' : 'no'}\` | active work=\`${pass.activeWorkId ?? '(none)'}\` | next=\`${pass.highestValueStep?.stepId ?? '(none)'}\`${pass.highestValueStep?.task ? ` | ${pass.highestValueStep.task}` : ''}`); + } + + lines.push(''); + return lines.join('\n'); +} + +export function runProblemTaskListLoop(problem, options = {}) { + const requestedPassesRaw = Number.parseInt(String(options.passes ?? 1), 10); + const requestedPasses = Number.isFinite(requestedPassesRaw) && requestedPassesRaw > 0 ? requestedPassesRaw : 1; + const stopOnConvergence = options.stopOnConvergence !== false; + const paths = getProblemTaskLoopRunPaths(problem); + const passes = []; + let previousFingerprint = null; + let finalTaskList = null; + let converged = false; + let convergedAtPass = null; + + for (let passNumber = 1; passNumber <= requestedPasses; passNumber += 1) { + const refresh = refreshProblemTaskList(problem); + if (!refresh.ok) { + return { + ok: false, + problemId: problem.problemId, + requestedPasses, + executedPasses: passes.length, + stopReason: 'refresh_failed', + error: refresh.error ?? 'Failed to refresh canonical task-list surfaces during loop run.', + passes, + jsonPath: null, + markdownPath: null, + }; + } + + finalTaskList = refresh.taskList; + const fingerprint = buildTaskLoopFingerprint(finalTaskList); + const changed = fingerprint !== previousFingerprint; + const highestValueStep = pickHighestValueLoopStep(finalTaskList); + + passes.push({ + passNumber, + changed, + activeRoute: finalTaskList.currentState?.activeRoute ?? null, + latestVerifiedInterval: finalTaskList.currentState?.latestVerifiedInterval ?? null, + currentClaimSurface: finalTaskList.currentState?.currentClaimSurface ?? null, + formalizationId: finalTaskList.currentObjective?.formalizationId ?? null, + focusId: finalTaskList.currentObjective?.focusId ?? null, + activeWorkId: finalTaskList.currentObjective?.activeWorkId ?? null, + activeWorkStatus: finalTaskList.currentObjective?.activeWorkStatus ?? null, + highestValueStep, + fingerprint, + }); + + if (!changed) { + converged = true; + if (convergedAtPass === null) { + convergedAtPass = passNumber; + } + if (stopOnConvergence) { + break; + } + } + + previousFingerprint = fingerprint; + } + + const executedPasses = passes.length; + const stopReason = converged && stopOnConvergence + ? 'converged' + : executedPasses >= requestedPasses + ? 'requested_pass_limit_reached' + : 'completed'; + const highestValueStep = finalTaskList ? pickHighestValueLoopStep(finalTaskList) : null; + const result = { + ok: true, + schema: 'erdos.problem_task_loop_run/1', + generatedAt: new Date().toISOString(), + problemId: problem.problemId, + displayName: problem.displayName, + title: problem.title, + requestedPasses, + executedPasses, + stopOnConvergence, + stopReason, + converged, + convergedAtPass, + currentState: finalTaskList?.currentState ?? null, + currentObjective: finalTaskList?.currentObjective ?? null, + highestValueStep, + passes, + commands: { + taskList: `erdos problem task-list ${problem.problemId}`, + taskListRefresh: `erdos problem task-list-refresh ${problem.problemId}`, + rerun: `erdos problem task-list-run ${problem.problemId} --passes ${requestedPasses}`, + }, + sources: { + taskListJsonPath: finalTaskList?.sources?.taskListJsonPath ?? null, + taskListMarkdownPath: finalTaskList?.sources?.taskListMarkdownPath ?? null, + taskLoopRunJsonPath: paths.taskLoopRunJsonPath, + taskLoopRunMarkdownPath: paths.taskLoopRunMarkdownPath, + }, + }; + + ensureDir(paths.packProblemDir); + writeJson(paths.taskLoopRunJsonPath, result); + writeText(paths.taskLoopRunMarkdownPath, renderProblemTaskLoopRunMarkdown(result)); + + return { + ...result, + jsonPath: paths.taskLoopRunJsonPath, + markdownPath: paths.taskLoopRunMarkdownPath, + }; +} diff --git a/test/p848-endpoint-menu-compiler.test.js b/test/p848-endpoint-menu-compiler.test.js new file mode 100644 index 0000000..f895df1 --- /dev/null +++ b/test/p848-endpoint-menu-compiler.test.js @@ -0,0 +1,163 @@ +import test from 'node:test'; +import assert from 'node:assert/strict'; +import { execFileSync } from 'node:child_process'; +import fs from 'node:fs'; +import os from 'node:os'; +import path from 'node:path'; +import { fileURLToPath } from 'node:url'; + +const repoRoot = path.dirname(path.dirname(fileURLToPath(import.meta.url))); +const compiler = path.join( + repoRoot, + 'packs', + 'number-theory', + 'problems', + '848', + 'compute', + 'problem848_endpoint_menu_compiler.mjs', +); + +function runCompiler(args) { + const tempDir = fs.mkdtempSync(path.join(os.tmpdir(), 'p848-endpoint-menu-')); + const jsonOutput = path.join(tempDir, 'packet.json'); + execFileSync('node', [compiler, ...args, '--json-output', jsonOutput], { + cwd: repoRoot, + encoding: 'utf8', + maxBuffer: 64 * 1024 * 1024, + }); + return JSON.parse(fs.readFileSync(jsonOutput, 'utf8')); +} + +test('problem 848 endpoint menu compiler covers the known q17 seed with the primary menu', () => { + const packet = runCompiler([ + '--primes', + '23,31', + '--fallback-primes', + '37,41,61', + '--start', + '27932207', + '--end', + '27932207', + '--max-square-prime', + '10000', + ]); + + assert.equal(packet.schema, 'erdos.number_theory.p848_endpoint_menu_compiler/1'); + assert.equal(packet.target.residualClass.residue, 5882); + assert.equal(packet.target.residualClass.modulus, 11025); + assert.equal(packet.coverage.primaryCovered, 1); + assert.equal(packet.coverage.primaryMisses, 0); + assert.equal(packet.coverage.allMisses, 0); + assert.equal(packet.claims.provesEndpointFormulas, true); + assert.equal(packet.claims.screensBoundedPrimaryMenuCoverage, true); + assert.equal(packet.claims.provesBoundedPrimaryMenuCoverage, false); + + const selected = packet.seedCheck.firstPrimarySquarefree; + assert.equal(selected.prime, 23); + assert.equal(selected.rightMod25, 18); + assert.equal(selected.compatibilityModPrimeSquare, 0); + assert.equal(selected.withinWindow, true); +}); + +test('problem 848 endpoint menu compiler exposes the p67 repair for the first full-menu parity miss', () => { + const packet = runCompiler([ + '--primes', + '23,31,37,41,61', + '--fallback-primes', + '43,47,53,59,67,71,73,79', + '--start', + '28792157', + '--end', + '28792157', + '--max-square-prime', + '10000', + ]); + + assert.equal(packet.coverage.primaryCovered, 0); + assert.equal(packet.coverage.primaryMisses, 1); + assert.equal(packet.coverage.allCovered, 1); + assert.equal(packet.coverage.allMisses, 0); + + const miss = packet.coverage.firstPrimaryMiss; + assert.equal(miss.left, 28792157); + assert.equal(miss.primaryEndpoints.find((endpoint) => endpoint.prime === 23).squareDivisor, 4); + assert.equal(miss.primaryEndpoints.find((endpoint) => endpoint.prime === 31).squareDivisor, 4); + assert.equal(miss.primaryEndpoints.find((endpoint) => endpoint.prime === 37).squareDivisor, 4); + + const selected = miss.firstAnySquarefree; + assert.equal(selected.prime, 67); + assert.equal(selected.k, 679); + assert.equal(selected.delta, -16989); + assert.equal(selected.right, 28775168); + assert.equal(selected.withinWindow, true); + assert.equal(selected.rightMod25, 18); + assert.equal(selected.compatibilityModPrimeSquare, 0); +}); + +test('problem 848 endpoint menu compiler profiles the p67 window threshold', () => { + const packet = runCompiler([ + '--primes', + '23,31,37,41,61,67', + '--fallback-primes', + '71,73,79,83,89,97,101,103,107,109,113', + '--start', + '34414907', + '--end', + '34414907', + '--window-grid', + '25000,28500,30000', + '--max-square-prime', + '10000', + ]); + + assert.equal(packet.schema, 'erdos.number_theory.p848_endpoint_window_grid/1'); + assert.equal(packet.firstScreenAllCoveredWindow, 28500); + + const summary25000 = packet.summaries.find((summary) => summary.window === 25000); + assert.equal(summary25000.allMisses, 1); + assert.equal(summary25000.firstAllMiss.left, 34414907); + assert.equal(summary25000.firstAllMiss.nearestUsableOutsideWindow[0].prime, 67); + assert.equal(summary25000.firstAllMiss.nearestUsableOutsideWindow[0].delta, -28489); + + const summary28500 = packet.summaries.find((summary) => summary.window === 28500); + assert.equal(summary28500.allMisses, 0); + assert.equal(summary28500.allCovered, 1); +}); + +test('problem 848 endpoint menu compiler emits modular availability thresholds', () => { + const packet = runCompiler([ + '--availability-profile', + '--primes', + '23,31,37,41,61,67', + '--fallback-primes', + '71,73', + '--start', + '34414907', + '--end', + '34414907', + '--window-grid', + '25000,28500', + ]); + + assert.equal(packet.schema, 'erdos.number_theory.p848_endpoint_availability_profile/1'); + + const p23Window25000 = packet.formulasByPrime['23'].availabilityByWindow.find((rule) => rule.window === 25000); + assert.equal(p23Window25000.maxK, 999); + assert.equal(p23Window25000.universallyWithinWindow, true); + + const p37Window25000 = packet.formulasByPrime['37'].availabilityByWindow.find((rule) => rule.window === 25000); + assert.equal(p37Window25000.availableResidueCount, 1000); + assert.equal(p37Window25000.tPeriod, 1369); + assert.equal(p37Window25000.universallyWithinWindow, false); + + const p67Window28500 = packet.formulasByPrime['67'].availabilityByWindow.find((rule) => rule.window === 28500); + assert.equal(p67Window28500.maxK, 1139); + assert.equal(p67Window28500.availableResidueCount, 1140); + assert.equal(p67Window28500.tPeriod, 4489); + + const p67Witness = packet.witnessRows[0].endpoints.find((endpoint) => endpoint.prime === 67); + assert.equal(p67Witness.k, 1139); + assert.equal(p67Witness.delta, -28489); + assert.equal(p67Witness.withinWindows['25000'], false); + assert.equal(p67Witness.withinWindows['28500'], true); +}); From 4de5e92c52626db5d978d4f9c54c898b07232677 Mon Sep 17 00:00:00 2001 From: Cody Mitchell Date: Tue, 14 Apr 2026 11:00:04 -0500 Subject: [PATCH 3/4] Guard npm package contents --- .npmignore | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) create mode 100644 .npmignore diff --git a/.npmignore b/.npmignore new file mode 100644 index 0000000..8b4e1ac --- /dev/null +++ b/.npmignore @@ -0,0 +1,21 @@ +.clawdad/ +.erdos/ +output/ +tmp/ +dist/ +*.tgz +.DS_Store + +# Local/generated frontier-engine run products. Keep source, docs, schemas, and +# compact benchmark profiles in npm; leave raw run bundles in the repo workspace. +research/frontier-engine/artifacts/ +research/frontier-engine/build/ +research/frontier-engine/src/*.egg-info/ +research/frontier-engine/experiments/**/live-frontier-sync/ + +# Exact small-N scan result packets can be very large. The npm package carries +# the scanner and curated proof-facing summaries, not every raw rollout product. +packs/number-theory/problems/848/EXACT_SMALL_N_1_*_RESULTS.json +packs/number-theory/problems/848/EXACT_SMALL_N_1_*_CERTIFICATE.md +!packs/number-theory/problems/848/EXACT_SMALL_N_1_10000_CERTIFICATE.md +packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/ From c54f2f35b10c2407d22ded41ccea055e43051c7b Mon Sep 17 00:00:00 2001 From: Cody Mitchell Date: Tue, 14 Apr 2026 11:10:16 -0500 Subject: [PATCH 4/4] Track p848 split atom fixtures outside npm --- .gitignore | 1 - packs/number-theory/problems/848/.npmignore | 4 + ...ersist_outP2_70_out25_9_smaller_side7.json | 48138 +++++++++++ ..._persist_outP2_70_out25_9_smaller_side7.md | 252 + ...rsist_outP2_99_out25_6_smaller_side18.json | 40955 +++++++++ ...persist_outP2_99_out25_6_smaller_side18.md | 246 + ...rsist_outP2_99_out25_14_smaller_side7.json | 19617 +++++ ...persist_outP2_99_out25_14_smaller_side7.md | 251 + 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 4018914, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 446546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 446546, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 4018914, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 446546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 446546, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 4018914, 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 87436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 21859, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 4284364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1071091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1071091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 87436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 21859, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 807 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V13.left_907", + "side": "side7", + "value": 907, + "residues": { + "value": 907, + "mod25": 7, + "modP": 10, + "modP2": 62 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 4815264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1203816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1203816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 300954, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 4815264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1203816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1203816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 300954, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 4815264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1203816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": 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"D2.1_persist_outP2=70_out25=9_smaller=side7.V14.left_957", + "side": "side7", + "value": 957, + "residues": { + "value": 957, + "mod25": 7, + "modP": 8, + "modP2": 112 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5080714, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5080714, + "hasAnySquareDivisor": true, + 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"productPlusOne": 5213439, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 579271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 579271, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 982 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V16.left_1007", + "side": "side7", + "value": 1007, + "residues": { + "value": 1007, + "mod25": 7, + "modP": 6, + "modP2": 162 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ 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] + }, + "goal": "Prove left core vertex 2007 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V31.left_2032", + "side": "side7", + "value": 2032, + "residues": { + "value": 2032, + "mod25": 7, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 10787889, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220161, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 220161, + 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 17556864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4389216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4389216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1097304, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 274326, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3307 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V50.left_3407", + "side": "side7", + "value": 3407, + "residues": { + "value": 3407, 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] + }, + "goal": "Prove left core vertex 3407 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V51.left_3457", + "side": "side7", + "value": 3457, + "residues": { + "value": 3457, + "mod25": 7, + "modP": 12, + "modP2": 77 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 18353214, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2039246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2039246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 18353214, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2039246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2039246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 18353214, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2039246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2039246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 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5309, + "productPlusOne": 19149564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4787391, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4787391, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 19149564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4787391, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4787391, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3607 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V54.left_3682", + "side": "side7", + "value": 3682, + "residues": { + "value": 3682, + "mod25": 7, + "modP": 3, + "modP2": 133 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 19547739, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2171971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2171971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 19547739, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2171971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2171971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 19547739, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2171971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2171971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 19547739, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 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"quotient": 1230029, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3707 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V56.left_3807", + "side": "side7", + "value": 3807, + "residues": { + "value": 3807, + "mod25": 7, + "modP": 11, + "modP2": 89 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 20211364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 20211364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 20211364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 20211364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 20211364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 20211364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5052841, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3807 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V57.left_3907", + "side": "side7", + "value": 3907, + "residues": { + "value": 3907, + "mod25": 7, + "modP": 7, + "modP2": 20 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 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"square": 4, + "quotient": 5185566, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2304696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 576174, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 20742264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5185566, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185566, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2304696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 576174, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + 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"D2.1_persist_outP2=70_out25=9_smaller=side7.V66.left_4482", + "side": "side7", + "value": 4482, + "residues": { + "value": 4482, + "mod25": 7, + "modP": 10, + "modP2": 88 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 23794939, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 485611, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 485611, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 23794939, + "hasAnySquareDivisor": true, + 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+ }, + "goal": "Prove left core vertex 4582 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V69.left_4607", + "side": "side7", + "value": 4607, + "residues": { + "value": 4607, + "mod25": 7, + "modP": 5, + "modP2": 44 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 24458564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 24458564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 24458564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 24458564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 24458564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 24458564, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6114641, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4607 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V70.left_4707", + "side": "side7", + "value": 4707, + "residues": { + "value": 4707, + "mod25": 7, + "modP": 1, + "modP2": 144 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 24989464, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 24989464, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 24989464, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 24989464, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 24989464, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 24989464, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6247366, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4707 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V71.left_4807", + "side": "side7", + "value": 4807, + "residues": { + "value": 4807, + "mod25": 7, + "modP": 10, + "modP2": 75 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 25520364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2835596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 708899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 25520364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2835596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 708899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 25520364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2835596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 708899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 25520364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2835596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 708899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 25520364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2835596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 708899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 25520364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6380091, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2835596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 708899, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4807 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V72.left_4832", + "side": "side7", + "value": 4832, + "residues": { + "value": 4832, + "mod25": 7, + "modP": 9, + "modP2": 100 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 25653089, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 25653089, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 25653089, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 25653089, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 25653089, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 25653089, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4832 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V73.left_4907", + "side": "side7", + "value": 4907, + "residues": { + "value": 4907, + "mod25": 7, + "modP": 6, + "modP2": 6 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 26051264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628204, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 407051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 26051264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628204, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 407051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 26051264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628204, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 407051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 26051264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628204, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 407051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 26051264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628204, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 407051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 26051264, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6512816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628204, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 407051, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4907 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V74.left_5007", + "side": "side7", + "value": 5007, + "residues": { + "value": 5007, + "mod25": 7, + "modP": 2, + "modP2": 106 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 26582164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 26582164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 26582164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 26582164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 26582164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 26582164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6645541, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5007 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V75.left_5032", + "side": "side7", + "value": 5032, + "residues": { + "value": 5032, + "mod25": 7, + "modP": 1, + "modP2": 131 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 26714889, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 30829364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7707341, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7707341, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 106676, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 34, + "square": 1156, + "quotient": 26669, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 30829364, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7707341, + "stableUnderCurrentSplitModulus": false + }, + 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3499221, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 31492989, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3499221, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3499221, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5932 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V89.left_6007", + "side": "side7", + "value": 6007, + "residues": { + "value": 6007, + "mod25": 7, + "modP": 1, + "modP2": 92 + }, + "status": 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 31891164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7972791, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7972791, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 31891164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7972791, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7972791, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6007 is present 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"stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6932 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V103.left_7007", + "side": "side7", + "value": 7007, + "residues": { + "value": 7007, + "mod25": 7, + "modP": 0, + "modP2": 78 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 37200164, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9300041, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 37731064, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9432766, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9432766, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 37731064, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9432766, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9432766, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7107 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V106.left_7207", + "side": "side7", + "value": 7207, + "residues": { + "value": 7207, + "mod25": 7, + "modP": 5, + "modP2": 109 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 38261964, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9565491, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9565491, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 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"hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9565491, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9565491, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 38261964, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9565491, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9565491, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 38261964, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 38660139, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 38660139, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 38660139, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 38660139, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 38660139, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4295571, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7282 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V108.left_7307", + "side": "side7", + "value": 7307, + "residues": { + "value": 7307, + "mod25": 7, + "modP": 1, + "modP2": 40 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 38792864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2424554, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 38792864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2424554, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 38792864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2424554, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 38792864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2424554, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 38792864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2424554, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 38792864, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9698216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2424554, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7307 is present in the side7 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V109.right_43", + "side": "side18", + "value": 43, + "residues": { + "value": 43, + "mod25": 18, + "modP": 4, + "modP2": 43 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 228288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 3567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 228288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 3567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 228288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 3567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 228288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 3567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 228288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 3567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 228288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 57072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 3567, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 43 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V110.right_118", + "side": "side18", + "value": 118, + "residues": { + "value": 118, + "mod25": 18, + "modP": 1, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 626463, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 626463, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 626463, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 626463, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 626463, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 626463, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 69607, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 118 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V111.right_143", + "side": "side18", + "value": 143, + "residues": { + "value": 143, + "mod25": 18, + "modP": 0, + "modP2": 143 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 759188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 759188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 759188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 759188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 759188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 759188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 189797, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V112.right_243", + "side": "side18", + "value": 243, + "residues": { + "value": 243, + "mod25": 18, + "modP": 9, + "modP2": 74 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 1290088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 1290088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 1290088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 1290088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 1290088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 1290088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 322522, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V113.right_268", + "side": "side18", + "value": 268, + "residues": { + "value": 268, + "mod25": 18, + "modP": 8, + "modP2": 99 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 1422813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 1422813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 1422813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 1422813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 1422813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 1422813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 29037, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 268 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V114.right_343", + "side": "side18", + "value": 343, + "residues": { + "value": 343, + "mod25": 18, + "modP": 5, + "modP2": 5 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 1820988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 202332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 50583, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 1820988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 202332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 50583, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 1820988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 202332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 50583, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 1820988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 202332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 50583, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 1820988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 202332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 50583, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 1820988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 455247, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 202332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 50583, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V115.right_368", + "side": "side18", + "value": 368, + "residues": { + "value": 368, + "mod25": 18, + "modP": 4, + "modP2": 30 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 1953713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 1953713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 1953713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 1953713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 1953713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 1953713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 368 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V116.right_443", + "side": "side18", + "value": 443, + "residues": { + "value": 443, + "mod25": 18, + "modP": 1, + "modP2": 105 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 2351888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146993, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 2351888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146993, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 2351888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146993, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 2351888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146993, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 2351888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146993, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 2351888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 587972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146993, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 443 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V117.right_543", + "side": "side18", + "value": 543, + "residues": { + "value": 543, + "mod25": 18, + "modP": 10, + "modP2": 36 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 2882788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 2882788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 2882788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 2882788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 2882788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 2882788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 720697, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V118.right_568", + "side": "side18", + "value": 568, + "residues": { + "value": 568, + "mod25": 18, + "modP": 9, + "modP2": 61 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 3015513, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 3015513, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 3015513, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 3015513, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 3015513, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 3015513, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 335057, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 568 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V119.right_643", + "side": "side18", + "value": 643, + "residues": { + "value": 643, + "mod25": 18, + "modP": 6, + "modP2": 136 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 3413688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 3413688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 3413688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 3413688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 3413688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 3413688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 853422, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V120.right_718", + "side": "side18", + "value": 718, + "residues": { + "value": 718, + "mod25": 18, + "modP": 3, + "modP2": 42 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 3811863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 3811863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 3811863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 3811863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 3811863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 3811863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 718 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V121.right_743", + "side": "side18", + "value": 743, + "residues": { + "value": 743, + "mod25": 18, + "modP": 2, + "modP2": 67 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 3944588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 3944588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 3944588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 3944588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 3944588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 3944588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 986147, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 743 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V122.right_793", + "side": "side18", + "value": 793, + "residues": { + "value": 793, + "mod25": 18, + "modP": 0, + "modP2": 117 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 4210038, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 4210038, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 4210038, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 4210038, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 4210038, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 4210038, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 467782, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 793 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V123.right_843", + "side": "side18", + "value": 843, + "residues": { + "value": 843, + "mod25": 18, + "modP": 11, + "modP2": 167 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", 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2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 279718, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 4475488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 279718, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 4475488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 279718, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 4475488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 279718, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 4475488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1118872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 279718, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V124.right_943", + "side": "side18", + "value": 943, + "residues": { + "value": 943, + "mod25": 18, + "modP": 7, + "modP2": 98 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5006388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5006388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 5006388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 5006388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 5006388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 5006388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1251597, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V125.right_1018", + "side": "side18", + "value": 1018, + "residues": { + "value": 1018, + "mod25": 18, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5404563, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 66723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5404563, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 66723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 5404563, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 66723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 5404563, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 66723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 5404563, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 66723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 5404563, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 600507, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 66723, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1018 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V126.right_1043", + "side": "side18", + "value": 1043, + "residues": { + "value": 1043, + "mod25": 18, + "modP": 3, + "modP2": 29 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5537288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5537288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 5537288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 5537288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 5537288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 5537288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1384322, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1043 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V127.right_1068", + "side": "side18", + "value": 1068, + "residues": { + "value": 1068, + "mod25": 18, + "modP": 2, + "modP2": 54 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5670013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5670013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 5670013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 5670013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 5670013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 5670013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1068 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V128.right_1143", + "side": "side18", + "value": 1143, + "residues": { + "value": 1143, + "mod25": 18, + "modP": 12, + "modP2": 129 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 6068188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 6068188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 6068188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 6068188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 6068188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 6068188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1517047, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V129.right_1243", + "side": "side18", + "value": 1243, + "residues": { + "value": 1243, + "mod25": 18, + "modP": 8, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 6599088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 733232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 412443, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 183308, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 45827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 6599088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 733232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 412443, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 183308, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 45827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 6599088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 733232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 412443, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 183308, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 45827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 6599088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 733232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 412443, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 183308, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 45827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 6599088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 733232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 412443, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 183308, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 45827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 6599088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1649772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 733232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 412443, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 183308, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 45827, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V130.right_1318", + "side": "side18", + "value": 1318, + "residues": { + "value": 1318, + "mod25": 18, + "modP": 5, + "modP2": 135 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 6997263, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 6997263, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 6997263, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 6997263, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 6997263, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 6997263, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1318 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V131.right_1343", + "side": "side18", + "value": 1343, + "residues": { + "value": 1343, + "mod25": 18, + "modP": 4, + "modP2": 160 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 7129988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 7129988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 7129988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 7129988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 7129988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 7129988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1782497, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V132.right_1443", + "side": "side18", + "value": 1443, + "residues": { + "value": 1443, + "mod25": 18, + "modP": 0, + "modP2": 91 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 7660888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 7660888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 7660888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 7660888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 7660888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1915222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 7660888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 7793613, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 7793613, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 7793613, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 7793613, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 7793613, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 865957, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1468 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V134.right_1493", + "side": "side18", + "value": 1493, + "residues": { + "value": 1493, + "mod25": 18, + "modP": 11, + "modP2": 141 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 7926338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 7926338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 7926338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 7926338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 161762, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1493 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V135.right_1543", + "side": "side18", + "value": 1543, + "residues": { + "value": 1543, + "mod25": 18, + "modP": 9, + "modP2": 22 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 8191788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 8191788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 8191788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 8191788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 8191788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 8191788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2047947, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V136.right_1618", + "side": "side18", + "value": 1618, + "residues": { + "value": 1618, + "mod25": 18, + "modP": 6, + "modP2": 97 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 8589963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 8589963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 8589963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 8589963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 8589963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 8589963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1618 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V137.right_1643", + "side": "side18", + "value": 1643, + "residues": { + "value": 1643, + "mod25": 18, + "modP": 5, + "modP2": 122 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 8722688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 545168, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 136292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 34073, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 8722688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 545168, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 136292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 34073, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 8722688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 545168, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 136292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 34073, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 8722688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 545168, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 136292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 34073, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 8722688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 545168, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 136292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 34073, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 8722688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2180672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 545168, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 136292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 34073, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V138.right_1693", + "side": "side18", + "value": 1693, + "residues": { + "value": 1693, + "mod25": 18, + "modP": 3, + "modP2": 3 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 8988138, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 8988138, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 8988138, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 8988138, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 8988138, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 8988138, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 998682, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1693 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V139.right_1743", + "side": "side18", + "value": 1743, + "residues": { + "value": 1743, + "mod25": 18, + "modP": 1, + "modP2": 53 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 9253588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 9253588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 9253588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 9253588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 9253588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 9253588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2313397, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1743 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V140.right_1843", + "side": "side18", + "value": 1843, + "residues": { + "value": 1843, + "mod25": 18, + "modP": 10, + "modP2": 153 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 9784488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 9784488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 9784488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 9784488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 9784488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 9784488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2446122, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V141.right_1918", + "side": "side18", + "value": 1918, + "residues": { + "value": 1918, + "mod25": 18, + "modP": 7, + "modP2": 59 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 10182663, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 10182663, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 10182663, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 10182663, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 10182663, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 10182663, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131407, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1918 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V142.right_1943", + "side": "side18", + "value": 1943, + "residues": { + "value": 1943, + "mod25": 18, + "modP": 6, + "modP2": 84 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 10315388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 10315388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 10315388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 10315388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 10315388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 10315388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2578847, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V143.right_2043", + "side": "side18", + "value": 2043, + "residues": { + "value": 2043, + "mod25": 18, + "modP": 2, + "modP2": 15 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 10846288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 677893, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 10846288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 677893, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 10846288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 677893, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 10846288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 677893, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 10846288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 677893, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 10846288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2711572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 677893, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2043 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V144.right_2143", + "side": "side18", + "value": 2143, + "residues": { + "value": 2143, + "mod25": 18, + "modP": 11, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 11377188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1264132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 316033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 11377188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1264132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 316033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 11377188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1264132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 316033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 11377188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1264132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 316033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 11377188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1264132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 316033, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 11377188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2844297, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1264132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 316033, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V145.right_2243", + "side": "side18", + "value": 2243, + "residues": { + "value": 2243, + "mod25": 18, + "modP": 7, + "modP2": 46 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 11908088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 11908088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 11908088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 11908088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 11908088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 11908088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2977022, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V146.right_2343", + "side": "side18", + "value": 2343, + "residues": { + "value": 2343, + "mod25": 18, + "modP": 3, + "modP2": 146 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 12438988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 12438988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 12438988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 12438988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 12438988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 12438988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3109747, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V147.right_2368", + "side": "side18", + "value": 2368, + "residues": { + "value": 2368, + "mod25": 18, + "modP": 2, + "modP2": 2 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 12571713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 12571713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 12571713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 12571713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 12571713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 12571713, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1396857, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2368 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V148.right_2443", + "side": "side18", + "value": 2443, + "residues": { + "value": 2443, + "mod25": 18, + "modP": 12, + "modP2": 77 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 12969888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 810618, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 12969888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 810618, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 12969888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 810618, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 12969888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 810618, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 12969888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 810618, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 12969888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3242472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 810618, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2443 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V149.right_2543", + "side": "side18", + "value": 2543, + "residues": { + "value": 2543, + "mod25": 18, + "modP": 8, + "modP2": 8 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 13500788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 13500788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 13500788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 13500788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 13500788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 13500788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3375197, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V150.right_2593", + "side": "side18", + "value": 2593, + "residues": { + "value": 2593, + "mod25": 18, + "modP": 6, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 13766238, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 13766238, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 13766238, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 13766238, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 13766238, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 13766238, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1529582, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2593 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V151.right_2643", + "side": "side18", + "value": 2643, + "residues": { + "value": 2643, + "mod25": 18, + "modP": 4, + "modP2": 108 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 14031688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 14031688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 14031688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 14031688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 14031688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 14031688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3507922, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V152.right_2718", + "side": "side18", + "value": 2718, + "residues": { + "value": 2718, + "mod25": 18, + "modP": 1, + "modP2": 14 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 14429863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 14429863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 14429863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 14429863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 14429863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 14429863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 294487, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2718 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V153.right_2743", + "side": "side18", + "value": 2743, + "residues": { + "value": 2743, + "mod25": 18, + "modP": 0, + "modP2": 39 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 14562588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 14562588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 14562588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 14562588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 14562588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 14562588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3640647, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2743 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V154.right_2818", + "side": "side18", + "value": 2818, + "residues": { + "value": 2818, + "mod25": 18, + "modP": 10, + "modP2": 114 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 14960763, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 14960763, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 14960763, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 14960763, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 14960763, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 14960763, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1662307, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2818 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V155.right_2843", + "side": "side18", + "value": 2843, + "residues": { + "value": 2843, + "mod25": 18, + "modP": 9, + "modP2": 139 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 15093488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 943343, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 15093488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 943343, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 15093488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 943343, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 15093488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 943343, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 15093488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 943343, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 15093488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3773372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 943343, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V156.right_2943", + "side": "side18", + "value": 2943, + "residues": { + "value": 2943, + "mod25": 18, + "modP": 5, + "modP2": 70 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 15624388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 23113, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 15624388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 23113, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 15624388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 23113, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 15624388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 23113, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 15624388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 23113, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 15624388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3906097, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 92452, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 23113, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V157.right_3043", + "side": "side18", + "value": 3043, + "residues": { + "value": 3043, + "mod25": 18, + "modP": 1, + "modP2": 1 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 16155288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1795032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 448758, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 199448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 49862, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 16155288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1795032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 448758, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 199448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 49862, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 16155288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1795032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 448758, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 199448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 49862, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 16155288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1795032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 448758, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 199448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 49862, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 16155288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1795032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 448758, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 199448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 49862, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 16155288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4038822, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1795032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 448758, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 199448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 49862, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3043 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V158.right_3143", + "side": "side18", + "value": 3143, + "residues": { + "value": 3143, + "mod25": 18, + "modP": 10, + "modP2": 101 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 16686188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 16686188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 16686188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 16686188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 16686188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 16686188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4171547, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V159.right_3243", + "side": "side18", + "value": 3243, + "residues": { + "value": 3243, + "mod25": 18, + "modP": 6, + "modP2": 32 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1076068, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 269017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 17217088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1076068, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 269017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 17217088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1076068, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 269017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 17217088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1076068, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 269017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 17217088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4304272, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1076068, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 269017, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V160.right_3268", + "side": "side18", + "value": 3268, + "residues": { + "value": 3268, + "mod25": 18, + "modP": 5, + "modP2": 57 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 17349813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 17349813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 17349813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 17349813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 17349813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 17349813, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1927757, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3268 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V161.right_3343", + "side": "side18", + "value": 3343, + "residues": { + "value": 3343, + "mod25": 18, + "modP": 2, + "modP2": 132 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 17747988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 17747988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 17747988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 17747988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 17747988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 17747988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4436997, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V162.right_3443", + "side": "side18", + "value": 3443, + "residues": { + "value": 3443, + "mod25": 18, + "modP": 11, + "modP2": 63 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 18278888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 37, + "square": 1369, + "quotient": 13352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 74, + "square": 5476, + "quotient": 3338, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 18278888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 37, + "square": 1369, + "quotient": 13352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 74, + "square": 5476, + "quotient": 3338, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 18278888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 37, + "square": 1369, + "quotient": 13352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 74, + "square": 5476, + "quotient": 3338, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 18278888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 37, + "square": 1369, + "quotient": 13352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 74, + "square": 5476, + "quotient": 3338, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 18278888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 37, + "square": 1369, + "quotient": 13352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 74, + "square": 5476, + "quotient": 3338, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 18278888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4569722, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 37, + "square": 1369, + "quotient": 13352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 74, + "square": 5476, + "quotient": 3338, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3443 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V163.right_3493", + "side": "side18", + "value": 3493, + "residues": { + "value": 3493, + "mod25": 18, + "modP": 9, + "modP2": 113 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 18544338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 18544338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 18544338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 18544338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 18544338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 18544338, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2060482, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3493 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V164.right_3543", + "side": "side18", + "value": 3543, + "residues": { + "value": 3543, + "mod25": 18, + "modP": 7, + "modP2": 163 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 18809788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 18809788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 18809788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 18809788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 18809788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 18809788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4702447, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V165.right_3643", + "side": "side18", + "value": 3643, + "residues": { + "value": 3643, + "mod25": 18, + "modP": 3, + "modP2": 94 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 19340688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1208793, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 19340688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1208793, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 19340688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1208793, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 19340688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1208793, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 19340688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1208793, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 19340688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4835172, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1208793, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V166.right_3718", + "side": "side18", + "value": 3718, + "residues": { + "value": 3718, + "mod25": 18, + "modP": 0, + "modP2": 0 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 19738863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 19738863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 19738863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 19738863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 19738863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 19738863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2193207, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3718 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V167.right_3743", + "side": "side18", + "value": 3743, + "residues": { + "value": 3743, + "mod25": 18, + "modP": 12, + "modP2": 25 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 19871588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 164228, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 41057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 19871588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 164228, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 41057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 19871588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 164228, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 41057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 19871588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 164228, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 41057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 19871588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 164228, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 41057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 19871588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4967897, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 164228, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 41057, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3743 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V168.right_3843", + "side": "side18", + "value": 3843, + "residues": { + "value": 3843, + "mod25": 18, + "modP": 8, + "modP2": 125 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 20402488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 20402488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 20402488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 20402488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 20402488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 20402488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5100622, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V169.right_3943", + "side": "side18", + "value": 3943, + "residues": { + "value": 3943, + "mod25": 18, + "modP": 4, + "modP2": 56 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 20933388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2325932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 581483, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 427212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 106803, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 47468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 11867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 20933388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2325932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 581483, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 427212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 106803, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 47468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 11867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 20933388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2325932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 581483, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 427212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 106803, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 47468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 11867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 20933388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2325932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 581483, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 427212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 106803, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 47468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 11867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 20933388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2325932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 581483, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 427212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 106803, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 47468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 11867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 20933388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5233347, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2325932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 581483, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 427212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 106803, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 47468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 11867, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V170.right_4043", + "side": "side18", + "value": 4043, + "residues": { + "value": 4043, + "mod25": 18, + "modP": 0, + "modP2": 156 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 21464288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1341518, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 21464288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1341518, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 21464288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1341518, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 21464288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1341518, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 21464288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1341518, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 21464288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5366072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1341518, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4043 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V171.right_4143", + "side": "side18", + "value": 4143, + "residues": { + "value": 4143, + "mod25": 18, + "modP": 9, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 21995188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 21995188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 21995188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 21995188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 21995188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 21995188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5498797, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V172.right_4168", + "side": "side18", + "value": 4168, + "residues": { + "value": 4168, + "mod25": 18, + "modP": 8, + "modP2": 112 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 22127913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 22127913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 22127913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 22127913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 22127913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 22127913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2458657, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4168 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V173.right_4243", + "side": "side18", + "value": 4243, + "residues": { + "value": 4243, + "mod25": 18, + "modP": 5, + "modP2": 18 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 22526088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 22526088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 22526088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 22526088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 22526088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 22526088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5631522, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V174.right_4343", + "side": "side18", + "value": 4343, + "residues": { + "value": 4343, + "mod25": 18, + "modP": 1, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 23056988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 23056988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 23056988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 23056988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 23056988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 23056988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5764247, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V175.right_4393", + "side": "side18", + "value": 4393, + "residues": { + "value": 4393, + "mod25": 18, + "modP": 12, + "modP2": 168 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 23322438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 23322438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 23322438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 23322438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 23322438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 23322438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2591382, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4393 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V176.right_4443", + "side": "side18", + "value": 4443, + "residues": { + "value": 4443, + "mod25": 18, + "modP": 10, + "modP2": 49 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 23587888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1474243, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 23587888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1474243, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 23587888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1474243, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 23587888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1474243, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 23587888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1474243, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 23587888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5896972, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1474243, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4443 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V177.right_4543", + "side": "side18", + "value": 4543, + "residues": { + "value": 4543, + "mod25": 18, + "modP": 6, + "modP2": 149 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 24118788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 24118788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 24118788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 24118788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 24118788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 24118788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6029697, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V178.right_4618", + "side": "side18", + "value": 4618, + "residues": { + "value": 4618, + "mod25": 18, + "modP": 3, + "modP2": 55 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 24516963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 24516963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 24516963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 24516963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 24516963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 24516963, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2724107, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4618 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V179.right_4643", + "side": "side18", + "value": 4643, + "residues": { + "value": 4643, + "mod25": 18, + "modP": 2, + "modP2": 80 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 24649688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 24649688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 24649688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 24649688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 24649688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 24649688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6162422, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V180.right_4743", + "side": "side18", + "value": 4743, + "residues": { + "value": 4743, + "mod25": 18, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 25180588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 25180588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 25180588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 25180588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 25180588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6295147, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 178552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 44638, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 25711488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2856832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1606968, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 714208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 401742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 178552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 44638, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 25711488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2856832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1606968, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 714208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 401742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 178552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 44638, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 25711488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2856832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1606968, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 714208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 401742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 178552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 44638, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 25711488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2856832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1606968, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 714208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 401742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 178552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 44638, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 25711488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6427872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2856832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1606968, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 714208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 401742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 178552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 44638, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V182.right_4943", + "side": "side18", + "value": 4943, + "residues": { + "value": 4943, + "mod25": 18, + "modP": 3, + "modP2": 42 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 26242388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 26242388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 26242388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 26242388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 26242388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 26242388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6560597, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V183.right_5043", + "side": "side18", + "value": 5043, + "residues": { + "value": 5043, + "mod25": 18, + "modP": 12, + "modP2": 142 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 26773288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 26773288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 26773288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 26773288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 26773288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 26773288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6693322, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5043 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V184.right_5068", + "side": "side18", + "value": 5068, + "residues": { + "value": 5068, + "mod25": 18, + "modP": 11, + "modP2": 167 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 26906013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 332173, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 26906013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 332173, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 26906013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 332173, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 26906013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 332173, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 26906013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 332173, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 26906013, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2989557, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 332173, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5068 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V185.right_5143", + "side": "side18", + "value": 5143, + "residues": { + "value": 5143, + "mod25": 18, + "modP": 8, + "modP2": 73 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 27304188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 27304188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 27304188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 27304188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 27304188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 27304188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6826047, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V186.right_5168", + "side": "side18", + "value": 5168, + "residues": { + "value": 5168, + "mod25": 18, + "modP": 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 559937, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 27436913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 559937, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 559937, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 27436913, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 559937, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 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is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V187.right_5243", + "side": "side18", + "value": 5243, + "residues": { + "value": 5243, + "mod25": 18, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 27835088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1739693, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 27835088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1739693, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 27835088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1739693, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 27835088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1739693, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 27835088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1739693, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 27835088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6958772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1739693, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V188.right_5293", + "side": "side18", + "value": 5293, + "residues": { + "value": 5293, + "mod25": 18, + "modP": 2, + "modP2": 54 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 28100538, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 28100538, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 28100538, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 28100538, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 28100538, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 28100538, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3122282, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5293 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V189.right_5343", + "side": "side18", + "value": 5343, + "residues": { + "value": 5343, + "mod25": 18, + "modP": 0, + "modP2": 104 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 28365988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 28365988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 28365988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 28365988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 28365988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 28365988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7091497, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V190.right_5443", + "side": "side18", + "value": 5443, + "residues": { + "value": 5443, + "mod25": 18, + "modP": 9, + "modP2": 35 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 28896888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 28896888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 28896888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 28896888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 28896888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 28896888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7224222, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5443 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V191.right_5518", + "side": "side18", + "value": 5518, + "residues": { + "value": 5518, + "mod25": 18, + "modP": 6, + "modP2": 110 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 29295063, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 101367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 51, + "square": 2601, + "quotient": 11263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 29295063, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 101367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 51, + "square": 2601, + "quotient": 11263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 29295063, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 101367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 51, + "square": 2601, + "quotient": 11263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 29295063, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 101367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 51, + "square": 2601, + "quotient": 11263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 29295063, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 101367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 51, + "square": 2601, + "quotient": 11263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 29295063, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3255007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 101367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 51, + "square": 2601, + "quotient": 11263, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5518 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V192.right_5543", + "side": "side18", + "value": 5543, + "residues": { + "value": 5543, + "mod25": 18, + "modP": 5, + "modP2": 135 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 29427788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 29427788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 29427788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 29427788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 29427788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 29427788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7356947, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V193.right_5643", + "side": "side18", + "value": 5643, + "residues": { + "value": 5643, + "mod25": 18, + "modP": 1, + "modP2": 66 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 29958688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1872418, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 29958688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1872418, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 29958688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1872418, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 29958688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1872418, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 29958688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1872418, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 29958688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7489672, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1872418, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V194.right_5718", + "side": "side18", + "value": 5718, + "residues": { + "value": 5718, + "mod25": 18, + "modP": 11, + "modP2": 141 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 30356863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 30356863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 30356863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 30356863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 30356863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 30356863, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5718 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V195.right_5743", + "side": "side18", + "value": 5743, + "residues": { + "value": 5743, + "mod25": 18, + "modP": 10, + "modP2": 166 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 30489588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3387732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 846933, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 30489588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3387732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 846933, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 30489588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3387732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 846933, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 30489588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3387732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 846933, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 30489588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3387732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 846933, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 30489588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7622397, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3387732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 846933, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5743 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V196.right_5843", + "side": "side18", + "value": 5843, + "residues": { + "value": 5843, + "mod25": 18, + "modP": 6, + "modP2": 97 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 31020488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 31020488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 31020488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 31020488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 31020488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 31020488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7755122, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V197.right_5943", + "side": "side18", + "value": 5943, + "residues": { + "value": 5943, + "mod25": 18, + "modP": 2, + "modP2": 28 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 31551388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 31551388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 31551388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 31551388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 31551388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 31551388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7887847, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V198.right_5968", + "side": "side18", + "value": 5968, + "residues": { + "value": 5968, + "mod25": 18, + "modP": 1, + "modP2": 53 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 31684113, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 31684113, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 31684113, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 31684113, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 31684113, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 31684113, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3520457, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5968 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V199.right_6043", + "side": "side18", + "value": 6043, + "residues": { + "value": 6043, + "mod25": 18, + "modP": 11, + "modP2": 128 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 32082288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2005143, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 32082288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2005143, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 32082288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2005143, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 32082288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2005143, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 32082288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2005143, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 32082288, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8020572, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2005143, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6043 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V200.right_6143", + "side": "side18", + "value": 6143, + "residues": { + "value": 6143, + "mod25": 18, + "modP": 7, + "modP2": 59 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 32613188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 32613188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 32613188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 32613188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 32613188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 32613188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8153297, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6143 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V201.right_6193", + "side": "side18", + "value": 6193, + "residues": { + "value": 6193, + "mod25": 18, + "modP": 5, + "modP2": 109 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 32878638, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 32878638, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 32878638, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 32878638, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 32878638, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 32878638, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3653182, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6193 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V202.right_6243", + "side": "side18", + "value": 6243, + "residues": { + "value": 6243, + "mod25": 18, + "modP": 3, + "modP2": 159 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 33144088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 33144088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 33144088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 33144088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 33144088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 33144088, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8286022, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6243 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V203.right_6343", + "side": "side18", + "value": 6343, + "residues": { + "value": 6343, + "mod25": 18, + "modP": 12, + "modP2": 90 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 33674988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 33674988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 33674988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 33674988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 33674988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 33674988, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8418747, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6343 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V204.right_6393", + "side": "side18", + "value": 6393, + "residues": { + "value": 6393, + "mod25": 18, + "modP": 10, + "modP2": 140 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 33940438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 33940438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 33940438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 33940438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 33940438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 33940438, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6393 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V205.right_6418", + "side": "side18", + "value": 6418, + "residues": { + "value": 6418, + "mod25": 18, + "modP": 9, + "modP2": 165 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 34073163, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 34073163, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 34073163, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 34073163, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 34073163, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 34073163, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6418 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V206.right_6443", + "side": "side18", + "value": 6443, + "residues": { + "value": 6443, + "mod25": 18, + "modP": 8, + "modP2": 21 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 34205888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2137868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 534467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 34205888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2137868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 534467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 34205888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2137868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 534467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 34205888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2137868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 534467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 34205888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2137868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 534467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 34205888, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8551472, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2137868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 534467, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6443 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V207.right_6543", + "side": "side18", + "value": 6543, + "residues": { + "value": 6543, + "mod25": 18, + "modP": 4, + "modP2": 121 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 34736788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 34736788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 34736788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 34736788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 34736788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 34736788, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8684197, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6543 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V208.right_6643", + "side": "side18", + "value": 6643, + "residues": { + "value": 6643, + "mod25": 18, + "modP": 0, + "modP2": 52 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 35267688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3918632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 979658, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 35267688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3918632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 979658, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 35267688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3918632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 979658, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 35267688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3918632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 979658, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 35267688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3918632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 979658, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 35267688, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8816922, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3918632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 979658, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6643 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V209.right_6743", + "side": "side18", + "value": 6743, + "residues": { + "value": 6743, + "mod25": 18, + "modP": 9, + "modP2": 152 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 35798588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 35798588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 35798588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 35798588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 35798588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 35798588, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8949647, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6743 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V210.right_6768", + "side": "side18", + "value": 6768, + "residues": { + "value": 6768, + "mod25": 18, + "modP": 8, + "modP2": 8 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 35931313, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 35931313, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 35931313, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 35931313, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 35931313, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 35931313, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6768 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V211.right_6843", + "side": "side18", + "value": 6843, + "residues": { + "value": 6843, + "mod25": 18, + "modP": 5, + "modP2": 83 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 36329488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2270593, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 36329488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2270593, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 36329488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2270593, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 36329488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2270593, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 36329488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2270593, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 36329488, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9082372, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2270593, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6843 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V212.right_6868", + "side": "side18", + "value": 6868, + "residues": { + "value": 6868, + "mod25": 18, + "modP": 4, + "modP2": 108 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 36462213, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 36462213, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 36462213, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 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"productPlusOne": 36462213, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6868 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V213.right_6943", + "side": "side18", + "value": 6943, + "residues": { + "value": 6943, + "mod25": 18, + "modP": 1, + "modP2": 14 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + 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"quotient": 9215097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9215097, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 36860388, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9215097, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9215097, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6943 is present in the side18 compatible set for every row in split outP2=70|out25=9|smaller=side7." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V214.right_7043", + "side": "side18", + "value": 7043, + "residues": { + "value": 7043, + "mod25": 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"hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9480547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9480547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 37922188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9480547, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 9480547, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 37922188, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E4.left_207_right_243", + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302, + "checkedSquareRootFloor": 224, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E5.left_307_right_268", + "leftValue": 307, + "rightValue": 268, + "productPlusOne": 82277, + "checkedSquareRootFloor": 286, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E6.left_407_right_343", + "leftValue": 407, + "rightValue": 343, + "productPlusOne": 139602, + "checkedSquareRootFloor": 373, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E7.left_507_right_368", + "leftValue": 507, + "rightValue": 368, + "productPlusOne": 186577, + "checkedSquareRootFloor": 431, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E8.left_532_right_443", + "leftValue": 532, + "rightValue": 443, + "productPlusOne": 235677, + "checkedSquareRootFloor": 485, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E9.left_607_right_543", + "leftValue": 607, + "rightValue": 543, + "productPlusOne": 329602, + "checkedSquareRootFloor": 574, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E10.left_707_right_568", + "leftValue": 707, + "rightValue": 568, + "productPlusOne": 401577, + "checkedSquareRootFloor": 633, + "squareDivisorWitnesses": [], + "isSquarefree": true + } + ], + "failedEdgeAtoms": [], + "proofBoundary": "This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim.", + "nextTheoremAction": "Promote this literal edge-obstruction certificate into A5 congruence-persistence families, or emit a sharper successor atom for any edge whose obstruction is not implied by the split hypotheses." + }, + "edgeCongruencePersistence": { + "schema": "erdos.p848_edge_congruence_persistence/1", + "persistenceId": "D2.1_persist_outP2=70_out25=9_smaller=side7.edge_congruence_persistence", + "status": "literal_constant_edge_persistence_verified", + "proofKind": "constant_pair_squarefree_invariant", + "splitKey": "outP2=70|out25=9|smaller=side7", + "splitModulus": 4225, + "witnessRowCount": 6, + "edgeAtomCount": 108, + "verifiedEdgeAtomCount": 108, + "failedEdgeAtomCount": 0, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "proofFamilies": [ + { + "familyId": "D2.1_persist_outP2=70_out25=9_smaller=side7.edge_constant_squarefree_family", + "status": "congruence_persistence_family_verified", + "proofKind": "constant_pair_squarefree_invariant", + "edgeAtomCount": 108, + "verifiedEdgeAtomCount": 108, + "failedEdgeAtomCount": 0, + "splitKey": "outP2=70|out25=9|smaller=side7", + "splitModulus": 4225, + "statement": "For each exported literal cross pair (l,r), l and r are constants in the packet, so l*r+1 is the same integer for every row satisfying the split hypotheses.", + "proofSteps": [ + "Recompute c = l*r + 1 from the exported literal pair.", + "Check c matches the squarefree certificate attached to the edge atom.", + "Because c has no N or outsider variable, the edge obstruction persists over all rows covered by this literal packet." + ], + "proofBoundary": "This is not yet a parameterized edge-family theorem. 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the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E2.left_82_right_118", + "pairIndex": 1, + "leftValue": 82, + "rightValue": 118, + "productPlusOne": 9677, + "productPlusOneRecomputed": 9677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E3.left_107_right_143", + "pairIndex": 2, + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302, + "productPlusOneRecomputed": 15302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; 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the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E6.left_407_right_343", + "pairIndex": 5, + "leftValue": 407, + "rightValue": 343, + "productPlusOne": 139602, + "productPlusOneRecomputed": 139602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E7.left_507_right_368", + "pairIndex": 6, + "leftValue": 507, + "rightValue": 368, + "productPlusOne": 186577, + "productPlusOneRecomputed": 186577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E8.left_532_right_443", + "pairIndex": 7, + "leftValue": 532, + "rightValue": 443, + "productPlusOne": 235677, + "productPlusOneRecomputed": 235677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E9.left_607_right_543", + "pairIndex": 8, + "leftValue": 607, + "rightValue": 543, + "productPlusOne": 329602, + "productPlusOneRecomputed": 329602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E10.left_707_right_568", + "pairIndex": 9, + "leftValue": 707, + "rightValue": 568, + "productPlusOne": 401577, + "productPlusOneRecomputed": 401577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E11.left_757_right_718", + "pairIndex": 10, + "leftValue": 757, + "rightValue": 718, + "productPlusOne": 543527, + "productPlusOneRecomputed": 543527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E12.left_807_right_643", + "pairIndex": 11, + "leftValue": 807, + "rightValue": 643, + "productPlusOne": 518902, + "productPlusOneRecomputed": 518902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E13.left_907_right_843", + "pairIndex": 12, + "leftValue": 907, + "rightValue": 843, + "productPlusOne": 764602, + "productPlusOneRecomputed": 764602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E14.left_957_right_793", + "pairIndex": 13, + "leftValue": 957, + "rightValue": 793, + "productPlusOne": 758902, + "productPlusOneRecomputed": 758902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E15.left_982_right_743", + "pairIndex": 14, + "leftValue": 982, + "rightValue": 743, + "productPlusOne": 729627, + "productPlusOneRecomputed": 729627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E16.left_1007_right_943", + "pairIndex": 15, + "leftValue": 1007, + "rightValue": 943, + "productPlusOne": 949602, + "productPlusOneRecomputed": 949602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E17.left_1107_right_1018", + "pairIndex": 16, + "leftValue": 1107, + "rightValue": 1018, + "productPlusOne": 1126927, + "productPlusOneRecomputed": 1126927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E18.left_1207_right_1068", + "pairIndex": 17, + "leftValue": 1207, + "rightValue": 1068, + "productPlusOne": 1289077, + "productPlusOneRecomputed": 1289077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E19.left_1307_right_1043", + "pairIndex": 18, + "leftValue": 1307, + "rightValue": 1043, + "productPlusOne": 1363202, + "productPlusOneRecomputed": 1363202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E20.left_1407_right_1143", + "pairIndex": 19, + "leftValue": 1407, + "rightValue": 1143, + "productPlusOne": 1608202, + "productPlusOneRecomputed": 1608202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E21.left_1432_right_1243", + "pairIndex": 20, + "leftValue": 1432, + "rightValue": 1243, + "productPlusOne": 1779977, + "productPlusOneRecomputed": 1779977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E22.left_1507_right_1318", + "pairIndex": 21, + "leftValue": 1507, + "rightValue": 1318, + "productPlusOne": 1986227, + "productPlusOneRecomputed": 1986227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E23.left_1607_right_1343", + "pairIndex": 22, + "leftValue": 1607, + "rightValue": 1343, + "productPlusOne": 2158202, + "productPlusOneRecomputed": 2158202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E24.left_1657_right_1468", + "pairIndex": 23, + "leftValue": 1657, + "rightValue": 1468, + "productPlusOne": 2432477, + "productPlusOneRecomputed": 2432477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E25.left_1707_right_1443", + "pairIndex": 24, + "leftValue": 1707, + "rightValue": 1443, + "productPlusOne": 2463202, + "productPlusOneRecomputed": 2463202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E26.left_1807_right_1543", + "pairIndex": 25, + "leftValue": 1807, + "rightValue": 1543, + "productPlusOne": 2788202, + "productPlusOneRecomputed": 2788202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E27.left_1882_right_1618", + "pairIndex": 26, + "leftValue": 1882, + "rightValue": 1618, + "productPlusOne": 3045077, + "productPlusOneRecomputed": 3045077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E28.left_1907_right_1643", + "pairIndex": 27, + "leftValue": 1907, + "rightValue": 1643, + "productPlusOne": 3133202, + "productPlusOneRecomputed": 3133202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E29.left_1957_right_1493", + "pairIndex": 28, + "leftValue": 1957, + "rightValue": 1493, + "productPlusOne": 2921802, + "productPlusOneRecomputed": 2921802, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E30.left_2007_right_1743", + "pairIndex": 29, + "leftValue": 2007, + "rightValue": 1743, + "productPlusOne": 3498202, + "productPlusOneRecomputed": 3498202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E31.left_2032_right_1693", + "pairIndex": 30, + "leftValue": 2032, + "rightValue": 1693, + "productPlusOne": 3440177, + "productPlusOneRecomputed": 3440177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E32.left_2107_right_1843", + "pairIndex": 31, + "leftValue": 2107, + "rightValue": 1843, + "productPlusOne": 3883202, + "productPlusOneRecomputed": 3883202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E33.left_2207_right_1918", + "pairIndex": 32, + "leftValue": 2207, + "rightValue": 1918, + "productPlusOne": 4233027, + "productPlusOneRecomputed": 4233027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E34.left_2307_right_1943", + "pairIndex": 33, + "leftValue": 2307, + "rightValue": 1943, + "productPlusOne": 4482502, + "productPlusOneRecomputed": 4482502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E35.left_2332_right_2043", + "pairIndex": 34, + "leftValue": 2332, + "rightValue": 2043, + "productPlusOne": 4764277, + "productPlusOneRecomputed": 4764277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E36.left_2407_right_2143", + "pairIndex": 35, + "leftValue": 2407, + "rightValue": 2143, + "productPlusOne": 5158202, + "productPlusOneRecomputed": 5158202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E37.left_2507_right_2243", + "pairIndex": 36, + "leftValue": 2507, + "rightValue": 2243, + "productPlusOne": 5623202, + "productPlusOneRecomputed": 5623202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E38.left_2557_right_2368", + "pairIndex": 37, + "leftValue": 2557, + "rightValue": 2368, + "productPlusOne": 6054977, + "productPlusOneRecomputed": 6054977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E39.left_2607_right_2343", + "pairIndex": 38, + "leftValue": 2607, + "rightValue": 2343, + "productPlusOne": 6108202, + "productPlusOneRecomputed": 6108202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E40.left_2707_right_2443", + "pairIndex": 39, + "leftValue": 2707, + "rightValue": 2443, + "productPlusOne": 6613202, + "productPlusOneRecomputed": 6613202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E41.left_2782_right_2543", + "pairIndex": 40, + "leftValue": 2782, + "rightValue": 2543, + "productPlusOne": 7074627, + "productPlusOneRecomputed": 7074627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E42.left_2807_right_2643", + "pairIndex": 41, + "leftValue": 2807, + "rightValue": 2643, + "productPlusOne": 7418902, + "productPlusOneRecomputed": 7418902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E43.left_2907_right_2718", + "pairIndex": 42, + "leftValue": 2907, + "rightValue": 2718, + "productPlusOne": 7901227, + "productPlusOneRecomputed": 7901227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E44.left_3007_right_2743", + "pairIndex": 43, + "leftValue": 3007, + "rightValue": 2743, + "productPlusOne": 8248202, + "productPlusOneRecomputed": 8248202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E45.left_3107_right_2818", + "pairIndex": 44, + "leftValue": 3107, + "rightValue": 2818, + "productPlusOne": 8755527, + "productPlusOneRecomputed": 8755527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E46.left_3207_right_2843", + "pairIndex": 45, + "leftValue": 3207, + "rightValue": 2843, + "productPlusOne": 9117502, + "productPlusOneRecomputed": 9117502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E47.left_3232_right_2593", + "pairIndex": 46, + "leftValue": 3232, + "rightValue": 2593, + "productPlusOne": 8380577, + "productPlusOneRecomputed": 8380577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E48.left_3257_right_5168", + "pairIndex": 47, + "leftValue": 3257, + "rightValue": 5168, + "productPlusOne": 16832177, + "productPlusOneRecomputed": 16832177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E49.left_3307_right_2943", + "pairIndex": 48, + "leftValue": 3307, + "rightValue": 2943, + "productPlusOne": 9732502, + "productPlusOneRecomputed": 9732502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E50.left_3407_right_3043", + "pairIndex": 49, + "leftValue": 3407, + "rightValue": 3043, + "productPlusOne": 10367502, + "productPlusOneRecomputed": 10367502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E51.left_3457_right_3268", + "pairIndex": 50, + "leftValue": 3457, + "rightValue": 3268, + "productPlusOne": 11297477, + "productPlusOneRecomputed": 11297477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E52.left_3507_right_3143", + "pairIndex": 51, + "leftValue": 3507, + "rightValue": 3143, + "productPlusOne": 11022502, + "productPlusOneRecomputed": 11022502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E53.left_3607_right_3243", + "pairIndex": 52, + "leftValue": 3607, + "rightValue": 3243, + "productPlusOne": 11697502, + "productPlusOneRecomputed": 11697502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E54.left_3682_right_3343", + "pairIndex": 53, + "leftValue": 3682, + "rightValue": 3343, + "productPlusOne": 12308927, + "productPlusOneRecomputed": 12308927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E55.left_3707_right_3443", + "pairIndex": 54, + "leftValue": 3707, + "rightValue": 3443, + "productPlusOne": 12763202, + "productPlusOneRecomputed": 12763202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E56.left_3807_right_3543", + "pairIndex": 55, + "leftValue": 3807, + "rightValue": 3543, + "productPlusOne": 13488202, + "productPlusOneRecomputed": 13488202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E57.left_3907_right_3643", + "pairIndex": 56, + "leftValue": 3907, + "rightValue": 3643, + "productPlusOne": 14233202, + "productPlusOneRecomputed": 14233202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E58.left_3957_right_3493", + "pairIndex": 57, + "leftValue": 3957, + "rightValue": 3493, + "productPlusOne": 13821802, + "productPlusOneRecomputed": 13821802, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E59.left_4007_right_3718", + "pairIndex": 58, + "leftValue": 4007, + "rightValue": 3718, + "productPlusOne": 14898027, + "productPlusOneRecomputed": 14898027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E60.left_4107_right_3743", + "pairIndex": 59, + "leftValue": 4107, + "rightValue": 3743, + "productPlusOne": 15372502, + "productPlusOneRecomputed": 15372502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E61.left_4132_right_3943", + "pairIndex": 60, + "leftValue": 4132, + "rightValue": 3943, + "productPlusOne": 16292477, + "productPlusOneRecomputed": 16292477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E62.left_4207_right_3843", + "pairIndex": 61, + "leftValue": 4207, + "rightValue": 3843, + "productPlusOne": 16167502, + "productPlusOneRecomputed": 16167502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E63.left_4307_right_4043", + "pairIndex": 62, + "leftValue": 4307, + "rightValue": 4043, + "productPlusOne": 17413202, + "productPlusOneRecomputed": 17413202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E64.left_4357_right_4168", + "pairIndex": 63, + "leftValue": 4357, + "rightValue": 4168, + "productPlusOne": 18159977, + "productPlusOneRecomputed": 18159977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E65.left_4407_right_4143", + "pairIndex": 64, + "leftValue": 4407, + "rightValue": 4143, + "productPlusOne": 18258202, + "productPlusOneRecomputed": 18258202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E66.left_4482_right_4243", + "pairIndex": 65, + "leftValue": 4482, + "rightValue": 4243, + "productPlusOne": 19017127, + "productPlusOneRecomputed": 19017127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E67.left_4507_right_4443", + "pairIndex": 66, + "leftValue": 4507, + "rightValue": 4443, + "productPlusOne": 20024602, + "productPlusOneRecomputed": 20024602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E68.left_4582_right_4343", + "pairIndex": 67, + "leftValue": 4582, + "rightValue": 4343, + "productPlusOne": 19899627, + "productPlusOneRecomputed": 19899627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E69.left_4607_right_4543", + "pairIndex": 68, + "leftValue": 4607, + "rightValue": 4543, + "productPlusOne": 20929602, + "productPlusOneRecomputed": 20929602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E70.left_4707_right_4618", + "pairIndex": 69, + "leftValue": 4707, + "rightValue": 4618, + "productPlusOne": 21736927, + "productPlusOneRecomputed": 21736927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E71.left_4807_right_4843", + "pairIndex": 70, + "leftValue": 4807, + "rightValue": 4843, + "productPlusOne": 23280302, + "productPlusOneRecomputed": 23280302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E72.left_4832_right_4643", + "pairIndex": 71, + "leftValue": 4832, + "rightValue": 4643, + "productPlusOne": 22434977, + "productPlusOneRecomputed": 22434977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E73.left_4907_right_4743", + "pairIndex": 72, + "leftValue": 4907, + "rightValue": 4743, + "productPlusOne": 23273902, + "productPlusOneRecomputed": 23273902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E74.left_5007_right_4943", + "pairIndex": 73, + "leftValue": 5007, + "rightValue": 4943, + "productPlusOne": 24749602, + "productPlusOneRecomputed": 24749602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E75.left_5032_right_4393", + "pairIndex": 74, + "leftValue": 5032, + "rightValue": 4393, + "productPlusOne": 22105577, + "productPlusOneRecomputed": 22105577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E76.left_5107_right_5043", + "pairIndex": 75, + "leftValue": 5107, + "rightValue": 5043, + "productPlusOne": 25754602, + "productPlusOneRecomputed": 25754602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E77.left_5207_right_5068", + "pairIndex": 76, + "leftValue": 5207, + "rightValue": 5068, + "productPlusOne": 26389077, + "productPlusOneRecomputed": 26389077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E78.left_5257_right_5518", + "pairIndex": 77, + "leftValue": 5257, + "rightValue": 5518, + "productPlusOne": 29008127, + "productPlusOneRecomputed": 29008127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E79.left_5307_right_5143", + "pairIndex": 78, + "leftValue": 5307, + "rightValue": 5143, + "productPlusOne": 27293902, + "productPlusOneRecomputed": 27293902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E80.left_5407_right_5343", + "pairIndex": 79, + "leftValue": 5407, + "rightValue": 5343, + "productPlusOne": 28889602, + "productPlusOneRecomputed": 28889602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E81.left_5457_right_5293", + "pairIndex": 80, + "leftValue": 5457, + "rightValue": 5293, + "productPlusOne": 28883902, + "productPlusOneRecomputed": 28883902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E82.left_5482_right_5243", + "pairIndex": 81, + "leftValue": 5482, + "rightValue": 5243, + "productPlusOne": 28742127, + "productPlusOneRecomputed": 28742127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E83.left_5507_right_5443", + "pairIndex": 82, + "leftValue": 5507, + "rightValue": 5443, + "productPlusOne": 29974602, + "productPlusOneRecomputed": 29974602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E84.left_5607_right_5543", + "pairIndex": 83, + "leftValue": 5607, + "rightValue": 5543, + "productPlusOne": 31079602, + "productPlusOneRecomputed": 31079602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E85.left_5707_right_5643", + "pairIndex": 84, + "leftValue": 5707, + "rightValue": 5643, + "productPlusOne": 32204602, + "productPlusOneRecomputed": 32204602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E86.left_5807_right_5718", + "pairIndex": 85, + "leftValue": 5807, + "rightValue": 5718, + "productPlusOne": 33204427, + "productPlusOneRecomputed": 33204427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E87.left_5907_right_5743", + "pairIndex": 86, + "leftValue": 5907, + "rightValue": 5743, + "productPlusOne": 33923902, + "productPlusOneRecomputed": 33923902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E88.left_5932_right_5843", + "pairIndex": 87, + "leftValue": 5932, + "rightValue": 5843, + "productPlusOne": 34660677, + "productPlusOneRecomputed": 34660677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E89.left_6007_right_5943", + "pairIndex": 88, + "leftValue": 6007, + "rightValue": 5943, + "productPlusOne": 35699602, + "productPlusOneRecomputed": 35699602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E90.left_6107_right_5968", + "pairIndex": 89, + "leftValue": 6107, + "rightValue": 5968, + "productPlusOne": 36446577, + "productPlusOneRecomputed": 36446577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E91.left_6157_right_6193", + "pairIndex": 90, + "leftValue": 6157, + "rightValue": 6193, + "productPlusOne": 38130302, + "productPlusOneRecomputed": 38130302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E92.left_6207_right_6043", + "pairIndex": 91, + "leftValue": 6207, + "rightValue": 6043, + "productPlusOne": 37508902, + "productPlusOneRecomputed": 37508902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E93.left_6307_right_6243", + "pairIndex": 92, + "leftValue": 6307, + "rightValue": 6243, + "productPlusOne": 39374602, + "productPlusOneRecomputed": 39374602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E94.left_6382_right_6143", + "pairIndex": 93, + "leftValue": 6382, + "rightValue": 6143, + "productPlusOne": 39204627, + "productPlusOneRecomputed": 39204627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E95.left_6407_right_6343", + "pairIndex": 94, + "leftValue": 6407, + "rightValue": 6343, + "productPlusOne": 40639602, + "productPlusOneRecomputed": 40639602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E96.left_6507_right_6418", + "pairIndex": 95, + "leftValue": 6507, + "rightValue": 6418, + "productPlusOne": 41761927, + "productPlusOneRecomputed": 41761927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E97.left_6607_right_6543", + "pairIndex": 96, + "leftValue": 6607, + "rightValue": 6543, + "productPlusOne": 43229602, + "productPlusOneRecomputed": 43229602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E98.left_6707_right_6443", + "pairIndex": 97, + "leftValue": 6707, + "rightValue": 6443, + "productPlusOne": 43213202, + "productPlusOneRecomputed": 43213202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E99.left_6807_right_6643", + "pairIndex": 98, + "leftValue": 6807, + "rightValue": 6643, + "productPlusOne": 45218902, + "productPlusOneRecomputed": 45218902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E100.left_6832_right_6393", + "pairIndex": 99, + "leftValue": 6832, + "rightValue": 6393, + "productPlusOne": 43676977, + "productPlusOneRecomputed": 43676977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E101.left_6907_right_6768", + "pairIndex": 100, + "leftValue": 6907, + "rightValue": 6768, + "productPlusOne": 46746577, + "productPlusOneRecomputed": 46746577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E102.left_6932_right_6743", + "pairIndex": 101, + "leftValue": 6932, + "rightValue": 6743, + "productPlusOne": 46742477, + "productPlusOneRecomputed": 46742477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E103.left_7007_right_6843", + "pairIndex": 102, + "leftValue": 7007, + "rightValue": 6843, + "productPlusOne": 47948902, + "productPlusOneRecomputed": 47948902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E104.left_7057_right_6868", + "pairIndex": 103, + "leftValue": 7057, + "rightValue": 6868, + "productPlusOne": 48467477, + "productPlusOneRecomputed": 48467477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E105.left_7107_right_6943", + "pairIndex": 104, + "leftValue": 7107, + "rightValue": 6943, + "productPlusOne": 49343902, + "productPlusOneRecomputed": 49343902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E106.left_7207_right_7143", + "pairIndex": 105, + "leftValue": 7207, + "rightValue": 7143, + "productPlusOne": 51479602, + "productPlusOneRecomputed": 51479602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E107.left_7282_right_7043", + "pairIndex": 106, + "leftValue": 7282, + "rightValue": 7043, + "productPlusOne": 51287127, + "productPlusOneRecomputed": 51287127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.E108.left_7307_right_7168", + "pairIndex": 107, + "leftValue": 7307, + "rightValue": 7168, + "productPlusOne": 52376577, + "productPlusOneRecomputed": 52376577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + } + ], + "failedChecks": [], + "proofBoundary": "This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions.", + "nextTheoremAction": "After this A5 literal persistence pass, promote matching disjointness and the K-envelope, or lift the edge proof if vertex formulas become parameterized." + }, + "matchingDisjointness": { + "status": "bounded_disjointness_certified", + "leftVertexCount": 108, + "rightVertexCount": 108, + "pairCount": 108, + "reusedLeftValues": [], + "reusedRightValues": [], + "completionRule": "A symbolic packet may promote only if the parameterized left and right vertex families remain pairwise disjoint." + }, + "matchingKEnvelopeCertificate": { + "schema": "erdos.p848_matching_k_envelope_certificate/1", + "certificateId": "D2.1_persist_outP2=70_out25=9_smaller=side7.matching_k_envelope_certificate", + "status": "literal_matching_sampled_k_envelope_verified", + "proofKind": "literal_disjoint_matching_plus_sampled_k_envelope", + "matchingProof": { + "status": "literal_matching_disjointness_verified", + "pairCount": 108, + "leftVertexCount": 108, + "rightVertexCount": 108, + "reusedLeftValues": [], + "reusedRightValues": [], + "proofSteps": [ + "Count the exported literal left vertices.", + "Count the exported literal right vertices.", + "Verify no left value and no right value is reused across the exported pair list." + ], + "proofBoundary": "This proves disjointness for the exported literal pair list. If later work parameterizes vertices, disjointness must be rechecked for the parameterized formulas." + }, + "kEnvelopeProof": { + "status": "sampled_k_envelope_dominated_by_literal_core", + "requiredMatchingLowerBoundRange": [ + 88, + 89 + ], + "commonMatchingPairCount": 108, + "maxRequiredMatchingLowerBound": 89, + "boundedSlackAgainstMaxK": 19, + "inequality": "108 >= 89", + "proofSteps": [ + "Use the exported common-core pair count as the literal matching size.", + "Compare it against the maximum required matching lower bound recorded by the packet.", + "Record the slack and keep the all-N K-formula handoff explicit." + ], + "proofBoundary": "This certifies the K-envelope recorded by the current split packet. It is not by itself a universal K(N,x) formula proof for every future row." + }, + "allLowerLiteralAtomsReady": true, + "proofBoundary": "A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim.", + "nextTheoremAction": "Assemble this with the verified vertex-successor and edge-persistence layers into a split-discharge readiness certificate, or emit the first missing lower atom." + }, + "summary": { + "vertexPresenceAtomCount": 216, + "edgeObstructionAtomCount": 108, + "stableVertexPresenceAtomCount": 3, + "unstableVertexPresenceAtomCount": 213, + "failedVertexPresenceAtomCount": 0, + "allEdgeObstructionsSquarefree": true, + "edgeObstructionCertificateStatus": "literal_edge_obstruction_certificate_verified", + "edgeCongruencePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingDisjointnessStatus": "bounded_disjointness_certified", + "matchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "readyForFirstTheoremPass": true + }, + "nextTheoremActions": [ + "Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N.", + "The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families.", + "Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof.", + "Attack the packet until it either becomes a split lemma or emits a sharper sub-split key." + ], + "splitDischargeReadiness": { + "schema": "erdos.p848_split_discharge_readiness/1", + "readinessId": "D2.1_persist_outP2=70_out25=9_smaller=side7.split_discharge_readiness", + "status": "split_discharge_readiness_candidate", + "proofKind": "lower_atom_assembly_with_explicit_all_n_handoff", + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "splitKey": "outP2=70|out25=9|smaller=side7", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "lowerLayerChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "verified", + "evidence": "11/11 successor vertex-family lemmas verified" + }, + { + "layerId": "A4_edge_obstruction_certificate", + "status": "verified", + "evidence": "literal_edge_obstruction_certificate_verified" + }, + { + "layerId": "A5_edge_congruence_persistence", + "status": "verified", + "evidence": "literal_constant_edge_persistence_verified" + }, + { + "layerId": "A6_matching_disjointness", + "status": "verified", + "evidence": "literal_matching_disjointness_verified" + }, + { + "layerId": "A7_sampled_k_envelope", + "status": "verified_sampled_envelope", + "evidence": "108 >= 89" + } + ], + "blockingChecks": [], + "theoremCandidate": { + "status": "candidate_with_open_all_n_handoff_gaps", + "statement": "For split outP2=70|out25=9|smaller=side7, the exported literal core supplies a disjoint matching of size 108 against the packet K-envelope [88,89].", + "lowerAtomSummary": { + "vertexSuccessorConditionCount": 11, + "verifiedVertexSuccessorCount": 11, + "edgePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingKEnvelopeStatus": "literal_matching_sampled_k_envelope_verified" + } + }, + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "note": "Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "note": "Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "note": "If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families." + } + ], + "proofBoundary": "This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes.", + "nextTheoremAction": "Attack the next p13 split profile or begin the row-universe/symbolic-K handoff once every p13 split has this readiness certificate." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md new file mode 100644 index 0000000..2c7a54d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md @@ -0,0 +1,252 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7 + +This is a theorem-facing split atom packet for Problem 848. It is intentionally atomic: one split profile, one common matching core, one K-envelope, and deterministic sub-atoms for the next proof pass. + +## Summary + +- Packet id: `p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7` +- Parent obligation: `D2_p13_matching_lower_bound` +- Target obligation: `D4_matching_bound_implies_sMaxMixed_bound` +- Prime lane: `13` +- Split key: `outP2=70|out25=9|smaller=side7` +- Priority: `high_p13_active_lane` +- Status: `ready_for_symbolic_persistence_work` +- Witnesses: `6` over `7318..7368` +- Common core size: `108` +- K-envelope: `[88,89]`, slack against max K `19` +- Vertex atoms: `216` +- Vertex atoms stable under current split modulus: `3` +- Vertex atoms needing sharper split or parameterization: `213` +- Edge atoms: `108` +- Edge certificate: `literal_edge_obstruction_certificate_verified` +- Edge congruence persistence: `literal_constant_edge_persistence_verified` +- Disjointness: `bounded_disjointness_certified` +- Matching/K certificate: `literal_matching_sampled_k_envelope_verified` + +## Goal + +Prove that the 108-edge common matching core persists for all p=13 threatening rows in split outP2=70|out25=9|smaller=side7, or replace it with a parameterized extension core. + +## Falsifier Boundary + +A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size. + +## Next Theorem Actions + +- Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N. +- The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families. +- Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof. +- Attack the packet until it either becomes a split lemma or emits a sharper sub-split key. + +## K Envelope + +- Status: `bounded_core_meets_sampled_K_envelope` +- Common core count: `108` +- Max required K: `89` +- Min matching slack: `19` + +## Matching And K-Envelope Certificate + +- Status: `literal_matching_sampled_k_envelope_verified` +- Proof kind: `literal_disjoint_matching_plus_sampled_k_envelope` +- Matching proof: `literal_matching_disjointness_verified` +- K proof: `sampled_k_envelope_dominated_by_literal_core` +- K inequality: `108 >= 89` +- Proof boundary: A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim. + +## Split Discharge Readiness + +- Status: `split_discharge_readiness_candidate` +- Proof kind: `lower_atom_assembly_with_explicit_all_n_handoff` +- Theorem candidate: `candidate_with_open_all_n_handoff_gaps` +- Blocking lower checks: `0` +- Open all-N handoff gaps: `3` +- Proof boundary: This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes. +- Handoff gap `row_universe_split_coverage` [open]: Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile. +- Handoff gap `universal_k_formula_lift` [open]: Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane. +- Handoff gap `literal_to_parameterized_vertex_guard` [open_if_vertices_move]: If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families. + +## Vertex Presence Stability + +- Split modulus: `4225` +- Witness rows: `6` +- Stable under current split modulus: `3` +- Needs sharper split or parametric witness: `213` +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V1.left_7`: side side7, value 7, first square witness {"divisor":2,"square":4,"quotient":9291,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V2.left_82`: side side7, value 82, first square witness {"divisor":3,"square":9,"quotient":48371,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V3.left_107`: side side7, value 107, first square witness {"divisor":2,"square":4,"quotient":142016,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V4.left_207`: side side7, value 207, first square witness {"divisor":2,"square":4,"quotient":274741,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V5.left_307`: side side7, value 307, first square witness {"divisor":2,"square":4,"quotient":407466,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V6.left_407`: side side7, value 407, first square witness {"divisor":2,"square":4,"quotient":540191,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V7.left_507`: side side7, value 507, first square witness {"divisor":2,"square":4,"quotient":672916,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.1_persist_outP2=70_out25=9_smaller=side7.V8.left_532`: side side7, value 532, first square witness {"divisor":3,"square":9,"quotient":313821,"stableUnderCurrentSplitModulus":false} + +## Vertex Presence Refinement + +- Status: `literal_core_requires_sharper_square_witness_split` +- Deterministic move: `emit_successor_atoms_by_square_witness_residue` +- Refinement condition count: `11` +- Covered unstable atoms: `213` +- Uncovered unstable atoms: `0` +- Proof boundary: These square-witness residue classes explain the bounded literal vertex-presence instability; each successor split still needs a theorem-facing persistence proof before it can support an all-N claim. +- Condition `square_4_outsider_1`: out mod 4 = 1, atoms=145, combined modulus=16900, successor=`outP2=70|out25=9|smaller=side7|out4=1` +- Condition `square_9_outsider_8`: out mod 9 = 8, atoms=48, combined modulus=38025, successor=`outP2=70|out25=9|smaller=side7|out9=8` +- Condition `square_49_outsider_17`: out mod 49 = 17, atoms=9, combined modulus=207025, successor=`outP2=70|out25=9|smaller=side7|out49=17` +- Condition `square_121_outsider_106`: out mod 121 = 106, atoms=3, combined modulus=511225, successor=`outP2=70|out25=9|smaller=side7|out121=106` +- Condition `square_361_outsider_255`: out mod 361 = 255, atoms=2, combined modulus=1525225, successor=`outP2=70|out25=9|smaller=side7|out361=255` +- Condition `square_529_outsider_19`: out mod 529 = 19, atoms=1, combined modulus=2235025, successor=`outP2=70|out25=9|smaller=side7|out529=19` +- Condition `square_841_outsider_263`: out mod 841 = 263, atoms=1, combined modulus=3553225, successor=`outP2=70|out25=9|smaller=side7|out841=263` +- Condition `square_961_outsider_504`: out mod 961 = 504, atoms=1, combined modulus=4060225, successor=`outP2=70|out25=9|smaller=side7|out961=504` +- Condition `square_1681_outsider_266`: out mod 1681 = 266, atoms=1, combined modulus=7102225, successor=`outP2=70|out25=9|smaller=side7|out1681=266` +- Condition `square_2809_outsider_2500`: out mod 2809 = 2500, atoms=1, combined modulus=11868025, successor=`outP2=70|out25=9|smaller=side7|out2809=2500` +- Condition `square_11881_outsider_5309`: out mod 11881 = 5309, atoms=1, combined modulus=50197225, successor=`outP2=70|out25=9|smaller=side7|out11881=5309` + +## Edge Obstruction Certificate + +- Status: `literal_edge_obstruction_certificate_verified` +- Proof kind: `literal_product_plus_one_squarefree_missing_edge_certificate` +- Edge atoms: `108` +- Squarefree edge atoms: `108` +- Non-squarefree edge atoms: `0` +- Product-plus-one range: `{"min":302,"max":52376577}` +- Mod 25 classes: `1` +- Prime-residue classes: `82` +- Prime-square fingerprints: `108` +- Proof boundary: This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim. +- Mod25 class `7:18`: edges=108 +- Prime-residue class `4:0:1`: edges=3 +- Prime-residue class `5:6:5`: edges=3 +- Prime-residue class `7:3:9`: edges=3 +- Prime-residue class `0:9:1`: edges=2 +- Prime-residue class `10:7:6`: edges=2 +- Prime-residue class `11:12:3`: edges=2 +- Prime-residue class `11:4:6`: edges=2 +- Prime-residue class `11:7:0`: edges=2 +- Prime-residue class `12:5:9`: edges=2 +- Prime-residue class `2:11:10`: edges=2 +- Prime-residue class `2:3:7`: edges=2 +- Prime-residue class `2:8:4`: edges=2 +- Prime-residue class `3:0:1`: edges=2 + +## Edge Congruence Persistence + +- Status: `literal_constant_edge_persistence_verified` +- Proof kind: `constant_pair_squarefree_invariant` +- Edge atoms: `108` +- Verified edge atoms: `108` +- Failed edge atoms: `0` +- Depends on sampled N: `no` +- Depends on witness outsider: `no` +- Proof boundary: This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions. +- Family `D2.1_persist_outP2=70_out25=9_smaller=side7.edge_constant_squarefree_family`: status=`congruence_persistence_family_verified`, edges=108, proof=constant_pair_squarefree_invariant + +## Matching Core + +- Pair (7, 43); residues mod25 7:18, mod p 7:4, mod p^2 7:43; product+1 mod p^2 133 +- Pair (82, 118); residues mod25 7:18, mod p 4:1, mod p^2 82:118; product+1 mod p^2 44 +- Pair (107, 143); residues mod25 7:18, mod p 3:0, mod p^2 107:143; product+1 mod p^2 92 +- Pair (207, 243); residues mod25 7:18, mod p 12:9, mod p^2 38:74; product+1 mod p^2 109 +- Pair (307, 268); residues mod25 7:18, mod p 8:8, mod p^2 138:99; product+1 mod p^2 143 +- Pair (407, 343); residues mod25 7:18, mod p 4:5, mod p^2 69:5; product+1 mod p^2 8 +- Pair (507, 368); residues mod25 7:18, mod p 0:4, mod p^2 0:30; product+1 mod p^2 1 +- Pair (532, 443); residues mod25 7:18, mod p 12:1, mod p^2 25:105; product+1 mod p^2 91 +- Pair (607, 543); residues mod25 7:18, mod p 9:10, mod p^2 100:36; product+1 mod p^2 52 +- Pair (707, 568); residues mod25 7:18, mod p 5:9, mod p^2 31:61; product+1 mod p^2 33 +- Pair (757, 718); residues mod25 7:18, mod p 3:3, mod p^2 81:42; product+1 mod p^2 23 +- Pair (807, 643); residues mod25 7:18, mod p 1:6, mod p^2 131:136; product+1 mod p^2 72 +- Pair (907, 843); residues mod25 7:18, mod p 10:11, mod p^2 62:167; product+1 mod p^2 46 +- Pair (957, 793); residues mod25 7:18, mod p 8:0, mod p^2 112:117; product+1 mod p^2 92 +- Pair (982, 743); residues mod25 7:18, mod p 7:2, mod p^2 137:67; product+1 mod p^2 54 +- Pair (1007, 943); residues mod25 7:18, mod p 6:7, mod p^2 162:98; product+1 mod p^2 160 +- Pair (1107, 1018); residues mod25 7:18, mod p 2:4, mod p^2 93:4; product+1 mod p^2 35 +- Pair (1207, 1068); residues mod25 7:18, mod p 11:2, mod p^2 24:54; product+1 mod p^2 114 +- Pair (1307, 1043); residues mod25 7:18, mod p 7:3, mod p^2 124:29; product+1 mod p^2 48 +- Pair (1407, 1143); residues mod25 7:18, mod p 3:12, mod p^2 55:129; product+1 mod p^2 167 +- Pair (1432, 1243); residues mod25 7:18, mod p 2:8, mod p^2 80:60; product+1 mod p^2 69 +- Pair (1507, 1318); residues mod25 7:18, mod p 12:5, mod p^2 155:135; product+1 mod p^2 139 +- Pair (1607, 1343); residues mod25 7:18, mod p 8:4, mod p^2 86:160; product+1 mod p^2 72 +- Pair (1657, 1468); residues mod25 7:18, mod p 6:12, mod p^2 136:116; product+1 mod p^2 60 +- Pair (1707, 1443); residues mod25 7:18, mod p 4:0, mod p^2 17:91; product+1 mod p^2 27 +- Pair (1807, 1543); residues mod25 7:18, mod p 0:9, mod p^2 117:22; product+1 mod p^2 40 +- Pair (1882, 1618); residues mod25 7:18, mod p 10:6, mod p^2 23:97; product+1 mod p^2 35 +- Pair (1907, 1643); residues mod25 7:18, mod p 9:5, mod p^2 48:122; product+1 mod p^2 111 +- Pair (1957, 1493); residues mod25 7:18, mod p 7:11, mod p^2 98:141; product+1 mod p^2 130 +- Pair (2007, 1743); residues mod25 7:18, mod p 5:1, mod p^2 148:53; product+1 mod p^2 71 +- Pair (2032, 1693); residues mod25 7:18, mod p 4:3, mod p^2 4:3; product+1 mod p^2 13 +- Pair (2107, 1843); residues mod25 7:18, mod p 1:10, mod p^2 79:153; product+1 mod p^2 89 +- Pair (2207, 1918); residues mod25 7:18, mod p 10:7, mod p^2 10:59; product+1 mod p^2 84 +- Pair (2307, 1943); residues mod25 7:18, mod p 6:6, mod p^2 110:84; product+1 mod p^2 115 +- Pair (2332, 2043); residues mod25 7:18, mod p 5:2, mod p^2 135:15; product+1 mod p^2 167 +- Pair (2407, 2143); residues mod25 7:18, mod p 2:11, mod p^2 41:115; product+1 mod p^2 153 +- Pair (2507, 2243); residues mod25 7:18, mod p 11:7, mod p^2 141:46; product+1 mod p^2 65 +- Pair (2557, 2368); residues mod25 7:18, mod p 9:2, mod p^2 22:2; product+1 mod p^2 45 +- Pair (2607, 2343); residues mod25 7:18, mod p 7:3, mod p^2 72:146; product+1 mod p^2 35 +- Pair (2707, 2443); residues mod25 7:18, mod p 3:12, mod p^2 3:77; product+1 mod p^2 63 +- Pair (2782, 2543); residues mod25 7:18, mod p 0:8, mod p^2 78:8; product+1 mod p^2 118 +- Pair (2807, 2643); residues mod25 7:18, mod p 12:4, mod p^2 103:108; product+1 mod p^2 140 +- Pair (2907, 2718); residues mod25 7:18, mod p 8:1, mod p^2 34:14; product+1 mod p^2 139 +- Pair (3007, 2743); residues mod25 7:18, mod p 4:0, mod p^2 134:39; product+1 mod p^2 157 +- Pair (3107, 2818); residues mod25 7:18, mod p 0:10, mod p^2 65:114; product+1 mod p^2 144 +- Pair (3207, 2843); residues mod25 7:18, mod p 9:9, mod p^2 165:139; product+1 mod p^2 121 +- Pair (3232, 2593); residues mod25 7:18, mod p 8:6, mod p^2 21:58; product+1 mod p^2 36 +- Pair (3257, 5168); residues mod25 7:18, mod p 7:7, mod p^2 46:98; product+1 mod p^2 115 +- Pair (3307, 2943); residues mod25 7:18, mod p 5:5, mod p^2 96:70; product+1 mod p^2 130 +- Pair (3407, 3043); residues mod25 7:18, mod p 1:1, mod p^2 27:1; product+1 mod p^2 28 +- Pair (3457, 3268); residues mod25 7:18, mod p 12:5, mod p^2 77:57; product+1 mod p^2 165 +- Pair (3507, 3143); residues mod25 7:18, mod p 10:10, mod p^2 127:101; product+1 mod p^2 153 +- Pair (3607, 3243); residues mod25 7:18, mod p 6:6, mod p^2 58:32; product+1 mod p^2 167 +- Pair (3682, 3343); residues mod25 7:18, mod p 3:2, mod p^2 133:132; product+1 mod p^2 150 +- Pair (3707, 3443); residues mod25 7:18, mod p 2:11, mod p^2 158:63; product+1 mod p^2 153 +- Pair (3807, 3543); residues mod25 7:18, mod p 11:7, mod p^2 89:163; product+1 mod p^2 143 +- Pair (3907, 3643); residues mod25 7:18, mod p 7:3, mod p^2 20:94; product+1 mod p^2 22 +- Pair (3957, 3493); residues mod25 7:18, mod p 5:9, mod p^2 70:113; product+1 mod p^2 137 +- Pair (4007, 3718); residues mod25 7:18, mod p 3:0, mod p^2 120:0; product+1 mod p^2 1 +- Pair (4107, 3743); residues mod25 7:18, mod p 12:12, mod p^2 51:25; product+1 mod p^2 93 +- Pair (4132, 3943); residues mod25 7:18, mod p 11:4, mod p^2 76:56; product+1 mod p^2 32 +- Pair (4207, 3843); residues mod25 7:18, mod p 8:8, mod p^2 151:125; product+1 mod p^2 117 +- Pair (4307, 4043); residues mod25 7:18, mod p 4:0, mod p^2 82:156; product+1 mod p^2 118 +- Pair (4357, 4168); residues mod25 7:18, mod p 2:8, mod p^2 132:112; product+1 mod p^2 82 +- Pair (4407, 4143); residues mod25 7:18, mod p 0:9, mod p^2 13:87; product+1 mod p^2 118 +- Pair (4482, 4243); residues mod25 7:18, mod p 10:5, mod p^2 88:18; product+1 mod p^2 64 +- Pair (4507, 4443); residues mod25 7:18, mod p 9:10, mod p^2 113:49; product+1 mod p^2 130 +- Pair (4582, 4343); residues mod25 7:18, mod p 6:1, mod p^2 19:118; product+1 mod p^2 46 +- Pair (4607, 4543); residues mod25 7:18, mod p 5:6, mod p^2 44:149; product+1 mod p^2 135 +- Pair (4707, 4618); residues mod25 7:18, mod p 1:3, mod p^2 144:55; product+1 mod p^2 147 +- Pair (4807, 4843); residues mod25 7:18, mod p 10:7, mod p^2 75:111; product+1 mod p^2 45 +- Pair (4832, 4643); residues mod25 7:18, mod p 9:2, mod p^2 100:80; product+1 mod p^2 58 +- Pair (4907, 4743); residues mod25 7:18, mod p 6:11, mod p^2 6:11; product+1 mod p^2 67 +- Pair (5007, 4943); residues mod25 7:18, mod p 2:3, mod p^2 106:42; product+1 mod p^2 59 +- Pair (5032, 4393); residues mod25 7:18, mod p 1:12, mod p^2 131:168; product+1 mod p^2 39 +- Pair (5107, 5043); residues mod25 7:18, mod p 11:12, mod p^2 37:142; product+1 mod p^2 16 +- Pair (5207, 5068); residues mod25 7:18, mod p 7:11, mod p^2 137:167; product+1 mod p^2 65 +- Pair (5257, 5518); residues mod25 7:18, mod p 5:6, mod p^2 18:110; product+1 mod p^2 122 +- Pair (5307, 5143); residues mod25 7:18, mod p 3:8, mod p^2 68:73; product+1 mod p^2 64 +- Pair (5407, 5343); residues mod25 7:18, mod p 12:0, mod p^2 168:104; product+1 mod p^2 66 +- Pair (5457, 5293); residues mod25 7:18, mod p 10:2, mod p^2 49:54; product+1 mod p^2 112 +- Pair (5482, 5243); residues mod25 7:18, mod p 9:4, mod p^2 74:4; product+1 mod p^2 128 +- Pair (5507, 5443); residues mod25 7:18, mod p 8:9, mod p^2 99:35; product+1 mod p^2 86 +- Pair (5607, 5543); residues mod25 7:18, mod p 4:5, mod p^2 30:135; product+1 mod p^2 164 +- Pair (5707, 5643); residues mod25 7:18, mod p 0:1, mod p^2 130:66; product+1 mod p^2 131 +- Pair (5807, 5718); residues mod25 7:18, mod p 9:11, mod p^2 61:141; product+1 mod p^2 152 +- Pair (5907, 5743); residues mod25 7:18, mod p 5:10, mod p^2 161:166; product+1 mod p^2 25 +- Pair (5932, 5843); residues mod25 7:18, mod p 4:6, mod p^2 17:97; product+1 mod p^2 129 +- Pair (6007, 5943); residues mod25 7:18, mod p 1:2, mod p^2 92:28; product+1 mod p^2 42 +- Pair (6107, 5968); residues mod25 7:18, mod p 10:1, mod p^2 23:53; product+1 mod p^2 37 +- Pair (6157, 6193); residues mod25 7:18, mod p 8:5, mod p^2 73:109; product+1 mod p^2 15 +- Pair (6207, 6043); residues mod25 7:18, mod p 6:11, mod p^2 123:128; product+1 mod p^2 28 +- Pair (6307, 6243); residues mod25 7:18, mod p 2:3, mod p^2 54:159; product+1 mod p^2 137 +- Pair (6382, 6143); residues mod25 7:18, mod p 12:7, mod p^2 129:59; product+1 mod p^2 7 +- Pair (6407, 6343); residues mod25 7:18, mod p 11:12, mod p^2 154:90; product+1 mod p^2 3 +- Pair (6507, 6418); residues mod25 7:18, mod p 7:9, mod p^2 85:165; product+1 mod p^2 168 +- Pair (6607, 6543); residues mod25 7:18, mod p 3:4, mod p^2 16:121; product+1 mod p^2 78 +- Pair (6707, 6443); residues mod25 7:18, mod p 12:8, mod p^2 116:21; product+1 mod p^2 71 +- Pair (6807, 6643); residues mod25 7:18, mod p 8:0, mod p^2 47:52; product+1 mod p^2 79 +- Pair (6832, 6393); residues mod25 7:18, mod p 7:10, mod p^2 72:140; product+1 mod p^2 110 +- Pair (6907, 6768); residues mod25 7:18, mod p 4:8, mod p^2 147:8; product+1 mod p^2 163 +- Pair (6932, 6743); residues mod25 7:18, mod p 3:9, mod p^2 3:152; product+1 mod p^2 119 +- Pair (7007, 6843); residues mod25 7:18, mod p 0:5, mod p^2 78:83; product+1 mod p^2 53 +- Pair (7057, 6868); residues mod25 7:18, mod p 11:4, mod p^2 128:108; product+1 mod p^2 136 +- Pair (7107, 6943); residues mod25 7:18, mod p 9:1, mod p^2 9:14; product+1 mod p^2 127 +- Pair (7207, 7143); residues mod25 7:18, mod p 5:6, mod p^2 109:45; product+1 mod p^2 5 +- Pair (7282, 7043); residues mod25 7:18, mod p 2:10, mod p^2 15:114; product+1 mod p^2 21 +- Pair (7307, 7168); residues mod25 7:18, mod p 1:5, mod p^2 40:70; product+1 mod p^2 97 diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json new file mode 100644 index 0000000..308282d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json @@ -0,0 +1,40955 @@ +{ + "schema": "erdos.p848_split_atom_packet/1", + "generatedAt": "2026-04-14T11:46:09.729Z", + "problemId": "848", + "packetId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "sourcePlanId": "p848_split_core_atomization_master_plan_v1", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "prime": 13, + "splitKey": "outP2=99|out25=6|smaller=side18", + "priority": "high_p13_active_lane", + "status": "ready_for_symbolic_persistence_work", + "sourceArtifacts": { + "taskList": "TASK_LIST.json", + "formalizationWork": "FORMALIZATION_WORK.json", + "matchingPatternMiner": "MATCHING_PATTERN_MINER.json" + }, + "inputs": { + "witnessCount": 5, + "nRange": "7307..7357", + "boundedTarget": { + "requiredMatchingLowerBoundRange": [ + 85, + 85 + ], + "commonMatchingPairCount": 105, + "commonMatchingPairExportComplete": true, + "commonMatchingPairs": [ + { + "leftValue": 32, + "rightValue": 68, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 32, + "rightModP2": 68, + "leftModP": 6, + "rightModP": 3, + "productPlusOneModP2": 149 + }, + { + "leftValue": 57, + "rightValue": 93, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 57, + "rightModP2": 93, + "leftModP": 5, + "rightModP": 2, + "productPlusOneModP2": 63 + }, + { + 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 310392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 137952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 77598, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 34488, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 15328, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 8622, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 3832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 36, + "square": 1296, + "quotient": 958, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 1241568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 310392, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 310392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 137952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 77598, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 34488, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 15328, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 8622, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 3832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 36, + "square": 1296, + "quotient": 958, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 1241568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 310392, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 310392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 137952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 77598, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 34488, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 15328, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 8622, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 3832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 36, + "square": 1296, + "quotient": 958, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 257 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V5.left_357", + "side": "side7", + "value": 357, + "residues": { + "value": 357, + "mod25": 7, + "modP": 6, + "modP2": 19 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 1724668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 1724668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 1724668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 1724668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 1724668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 431167, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 357 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V6.left_457", + "side": "side7", + "value": 457, + "residues": { + "value": 457, + "mod25": 7, + "modP": 2, + "modP2": 119 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2207768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2207768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2207768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2207768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2207768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 551942, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 457 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V7.left_482", + "side": "side7", + "value": 482, + "residues": { + "value": 482, + "mod25": 7, + "modP": 1, + "modP2": 144 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2328543, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2328543, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2328543, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2328543, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2328543, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 258727, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 482 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V8.left_557", + "side": "side7", + "value": 557, + "residues": { + "value": 557, + "mod25": 7, + "modP": 11, + "modP2": 50 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2690868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2690868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2690868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2690868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2690868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 672717, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 557 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V9.left_632", + "side": "side7", + "value": 632, + "residues": { + "value": 632, + "mod25": 7, + "modP": 8, + "modP2": 125 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3053193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3053193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3053193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3053193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3053193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 632 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V10.left_657", + "side": "side7", + "value": 657, + "residues": { + "value": 657, + "mod25": 7, + "modP": 7, + "modP2": 150 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3173968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 198373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3173968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 198373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3173968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 198373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3173968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 198373, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3173968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 793492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 198373, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 657 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V11.left_707", + "side": "side7", + "value": 707, + "residues": { + "value": 707, + "mod25": 7, + "modP": 5, + "modP2": 31 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3415518, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3415518, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3415518, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3415518, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3415518, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 379502, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 707 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V12.left_757", + "side": "side7", + "value": 757, + "residues": { + "value": 757, + "mod25": 7, + "modP": 3, + "modP2": 81 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3657068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3657068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3657068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3657068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3657068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 914267, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 757 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V13.left_857", + "side": "side7", + "value": 857, + "residues": { + "value": 857, + "mod25": 7, + "modP": 12, + "modP2": 12 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4140168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4140168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4140168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4140168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4140168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1035042, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V14.left_932", + "side": "side7", + "value": 932, + "residues": { + "value": 932, + "mod25": 7, + "modP": 9, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4502493, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4502493, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4502493, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4502493, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4502493, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 500277, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 932 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V15.left_957", + "side": "side7", + "value": 957, + "residues": { + "value": 957, + "mod25": 7, + "modP": 8, + "modP2": 112 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4623268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4623268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4623268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4623268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4623268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1155817, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V16.left_1007", + "side": "side7", + "value": 1007, + "residues": { + "value": 1007, + "mod25": 7, + "modP": 6, + "modP2": 162 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4864818, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4864818, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4864818, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4864818, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4864818, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1007 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V17.left_1057", + "side": "side7", + "value": 1057, + "residues": { + "value": 1057, + "mod25": 7, + "modP": 4, + "modP2": 43 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 5106368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 319148, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 79787, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 5106368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 319148, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 79787, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 5106368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1276592, 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"hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1276592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 319148, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 79787, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1057 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V18.left_1082", + "side": "side7", + "value": 1082, + "residues": { + "value": 1082, + "mod25": 7, + "modP": 3, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 5227143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 5227143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 5227143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 5227143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 5227143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1082 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V19.left_1157", + "side": "side7", + "value": 1157, + "residues": { + "value": 1157, + "mod25": 7, + "modP": 0, + "modP2": 143 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 621052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 155263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 5589468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 621052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 155263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 5589468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 621052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 155263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 5589468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1397367, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 621052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 155263, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1157 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V20.left_1257", + "side": "side7", + "value": 1257, + "residues": { + "value": 1257, + "mod25": 7, + "modP": 9, + "modP2": 74 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 6072568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1518142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1518142, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 6072568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1518142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1518142, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 6072568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + 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"stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 6193343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 6193343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 6193343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 36647, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7357, + "outsider": 4831, + 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"hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 741827, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 741827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 6676443, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 741827, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 741827, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 6676443, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + 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"squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 741827, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1382 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V24.left_1457", + "side": "side7", + "value": 1457, + "residues": { + "value": 1457, + "mod25": 7, + "modP": 1, + "modP2": 105 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 7038768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1759692, + "stableUnderCurrentSplitModulus": false 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"hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1759692, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1759692, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 439923, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1457 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V25.left_1557", + "side": "side7", + "value": 1557, + "residues": { + "value": 1557, + "mod25": 7, + "modP": 10, + "modP2": 36 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 7521868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 7521868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 7521868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 7521868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1880467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 7521868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": 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"square": 9, + "quotient": 862602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 862602, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 7763418, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 862602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 862602, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 7763418, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 862602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 862602, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1607 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V27.left_1657", + "side": "side7", + "value": 1657, + "residues": { + "value": 1657, + "mod25": 7, + "modP": 6, + "modP2": 136 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 8004968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2001242, + "stableUnderCurrentSplitModulus": false 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"quotient": 2001242, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 8004968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2001242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2001242, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 8004968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2001242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2001242, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1657 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V28.left_1757", + "side": "side7", + "value": 1757, + "residues": { + "value": 1757, + "mod25": 7, + "modP": 2, + "modP2": 67 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 8488068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2122017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2122017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 8488068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2122017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2122017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 8488068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2122017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2122017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 8488068, + "hasAnySquareDivisor": true, + 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"D2.2_persist_outP2=99_out25=6_smaller=side18.V29.left_1832", + "side": "side7", + "value": 1832, + "residues": { + "value": 1832, + "mod25": 7, + "modP": 12, + "modP2": 142 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 8850393, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 983377, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 983377, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 8850393, + "hasAnySquareDivisor": true, + 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"square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 560698, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 8971168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 560698, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 8971168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 560698, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 8971168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2242792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 560698, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V31.left_1957", + "side": "side7", + "value": 1957, + "residues": { + "value": 1957, + "mod25": 7, + "modP": 7, + "modP2": 98 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 9454268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 9454268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 9454268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 9454268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 9454268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2363567, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V32.left_2057", + "side": "side7", + "value": 2057, + "residues": { + "value": 2057, + "mod25": 7, + "modP": 3, + "modP2": 29 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 9937368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1104152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 276038, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 9937368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1104152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 276038, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 9937368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1104152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 276038, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 9937368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1104152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 276038, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 9937368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2484342, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1104152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 276038, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2057 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V33.left_2157", + "side": "side7", + "value": 2157, + "residues": { + "value": 2157, + "mod25": 7, + "modP": 12, + "modP2": 129 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 10420468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 10420468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 10420468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 10420468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 10420468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2605117, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2157 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V34.left_2232", + "side": "side7", + "value": 2232, + "residues": { + "value": 2232, + "mod25": 7, + "modP": 9, + "modP2": 35 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 10782793, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 10782793, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 10782793, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 10782793, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 10782793, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2232 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V35.left_2257", + "side": "side7", + "value": 2257, + "residues": { + "value": 2257, + "mod25": 7, + "modP": 8, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", 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"divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 681473, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 10903568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 681473, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 10903568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 681473, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 10903568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2725892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 681473, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2257 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V36.left_2282", + "side": "side7", + "value": 2282, + "residues": { + "value": 2282, + "mod25": 7, + "modP": 7, + "modP2": 85 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 11024343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 136103, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 11024343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 136103, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 11024343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 136103, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 11024343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 136103, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 11024343, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1224927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 136103, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2282 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V37.left_2357", + "side": "side7", + "value": 2357, + "residues": { + "value": 2357, + "mod25": 7, + "modP": 4, + "modP2": 160 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 11386668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 11386668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 11386668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 11386668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 11386668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2846667, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2357 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V38.left_2457", + "side": "side7", + "value": 2457, + "residues": { + "value": 2457, + "mod25": 7, + "modP": 0, + "modP2": 91 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 11869768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 11869768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 11869768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 11869768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 11869768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2967442, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2457 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V39.left_2507", + "side": "side7", + "value": 2507, + "residues": { + "value": 2507, + "mod25": 7, + "modP": 11, + "modP2": 141 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12111318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12111318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12111318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12111318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12111318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1345702, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2507 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V40.left_2557", + "side": "side7", + "value": 2557, + "residues": { + "value": 2557, + "mod25": 7, + "modP": 9, + "modP2": 22 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12352868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3088217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3088217, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12352868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3088217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3088217, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12352868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3088217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3088217, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12352868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 802248, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 200562, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12835968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3208992, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3208992, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 802248, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 200562, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12835968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3208992, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3208992, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 802248, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 200562, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2657 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V42.left_2732", + "side": "side7", + "value": 2732, + "residues": { + "value": 2732, + "mod25": 7, + "modP": 2, + "modP2": 28 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13198293, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1466477, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1466477, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13198293, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1466477, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, 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"witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13319068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13319068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 13319068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 13319068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 13319068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3329767, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2757 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V44.left_2857", + "side": "side7", + "value": 2857, + "residues": { + "value": 2857, + "mod25": 7, + "modP": 10, + "modP2": 153 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13802168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13802168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 13802168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 13802168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 13802168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3450542, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V45.left_2957", + "side": "side7", + "value": 2957, + "residues": { + "value": 2957, + "mod25": 7, + "modP": 6, + "modP2": 84 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 14285268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1587252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 396813, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 14285268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1587252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 396813, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 14285268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1587252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 396813, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 14285268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1587252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 396813, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 14285268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3571317, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1587252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 396813, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V46.left_3057", + "side": "side7", + "value": 3057, + "residues": { + "value": 3057, + "mod25": 7, + "modP": 2, + "modP2": 15 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 14768368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 923023, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 14768368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 923023, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 14768368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 923023, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 14768368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 923023, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 14768368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3692092, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 923023, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3057 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V47.left_3157", + "side": "side7", + "value": 3157, + "residues": { + "value": 3157, + "mod25": 7, + "modP": 11, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 15251468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 15251468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 15251468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 15251468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 15251468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3812867, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3157 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V48.left_3182", + "side": "side7", + "value": 3182, + "residues": { + "value": 3182, + "mod25": 7, + "modP": 10, + "modP2": 140 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 15372243, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 15372243, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 15372243, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 15372243, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 15372243, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1708027, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3182 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V49.left_3257", + "side": "side7", + "value": 3257, + "residues": { + "value": 3257, + "mod25": 7, + "modP": 7, + "modP2": 46 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 15734568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 15734568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 15734568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 15734568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 15734568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3933642, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3257 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V50.left_3357", + "side": "side7", + "value": 3357, + "residues": { + "value": 3357, + "mod25": 7, + "modP": 3, + "modP2": 146 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 16217668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 16217668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 16217668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 16217668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 16217668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4054417, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3357 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V51.left_3407", + "side": "side7", + "value": 3407, + "residues": { + "value": 3407, + "mod25": 7, + "modP": 1, + "modP2": 27 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 16459218, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 16459218, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 16459218, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 16459218, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 16459218, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1828802, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3407 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V52.left_3457", + "side": "side7", + "value": 3457, + "residues": { + "value": 3457, + "mod25": 7, + "modP": 12, + "modP2": 77 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 16700768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1043798, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 340832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 85208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 21302, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 16700768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1043798, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 340832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 85208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 21302, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 16700768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1043798, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 340832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 85208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 21302, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 16700768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1043798, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 340832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 85208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 21302, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 16700768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4175192, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1043798, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 340832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 85208, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 21302, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3457 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V53.left_3557", + "side": "side7", + "value": 3557, + "residues": { + "value": 3557, + "mod25": 7, + "modP": 8, + "modP2": 8 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 17183868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 17183868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 17183868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 17183868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 17183868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4295967, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3557 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V54.left_3632", + "side": "side7", + "value": 3632, + "residues": { + "value": 3632, + "mod25": 7, + "modP": 5, + "modP2": 83 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 17546193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 17546193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 17546193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 17546193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 17546193, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1949577, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3632 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V55.left_3657", + "side": "side7", + "value": 3657, + "residues": { + "value": 3657, + "mod25": 7, + "modP": 4, + "modP2": 108 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 17666968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 146008, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 36502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 17666968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 146008, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 36502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 17666968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 146008, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 36502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 17666968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 146008, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 36502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 17666968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4416742, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 146008, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 36502, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3657 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V56.left_3757", + "side": "side7", + "value": 3757, + "residues": { + "value": 3757, + "mod25": 7, + "modP": 0, + "modP2": 39 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 18150068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 18150068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 18150068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 18150068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 18150068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4537517, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3757 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V57.left_3807", + "side": "side7", + "value": 3807, + "residues": { + "value": 3807, + "mod25": 7, + "modP": 11, + "modP2": 89 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 18391618, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 18391618, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 18391618, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 18391618, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 18391618, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3807 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V58.left_3857", + "side": "side7", + "value": 3857, + "residues": { + "value": 3857, + "mod25": 7, + "modP": 9, + "modP2": 139 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 18633168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2070352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1164573, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 517588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 129397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 18633168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2070352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1164573, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 517588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 129397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 18633168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2070352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1164573, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 517588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 129397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 18633168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2070352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1164573, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 517588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 129397, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 18633168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4658292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2070352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1164573, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 517588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 129397, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V59.left_3957", + "side": "side7", + "value": 3957, + "residues": { + "value": 3957, + "mod25": 7, + "modP": 5, + "modP2": 70 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 19116268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 19116268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 19116268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 19116268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 19116268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4779067, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V60.left_4057", + "side": "side7", + "value": 4057, + "residues": { + "value": 4057, + "mod25": 7, + "modP": 1, + "modP2": 1 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 19599368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 19599368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 19599368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 19599368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 19599368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4899842, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4057 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V61.left_4082", + "side": "side7", + "value": 4082, + "residues": { + "value": 4082, + "mod25": 7, + "modP": 0, + "modP2": 26 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 19720143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 19720143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 19720143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 19720143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 19720143, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2191127, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4082 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V62.left_4157", + "side": "side7", + "value": 4157, + "residues": { + "value": 4157, + "mod25": 7, + "modP": 10, + "modP2": 101 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20082468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20082468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20082468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20082468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20082468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5020617, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4157 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V63.left_4257", + "side": "side7", + "value": 4257, + "residues": { + "value": 4257, + "mod25": 7, + "modP": 6, + "modP2": 32 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20565568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5141392, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5141392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1285348, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 321337, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20565568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5141392, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5141392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1285348, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 321337, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20565568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5141392, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5141392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1285348, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 321337, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20565568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 321337, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4257 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V64.left_4307", + "side": "side7", + "value": 4307, + "residues": { + "value": 4307, + "mod25": 7, + "modP": 4, + "modP2": 82 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20807118, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 256878, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 27, + "square": 729, + "quotient": 28542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20807118, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 256878, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 27, + "square": 729, + "quotient": 28542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20807118, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 256878, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 27, + "square": 729, + "quotient": 28542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20807118, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 256878, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 27, + "square": 729, + "quotient": 28542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20807118, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2311902, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 256878, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 27, + "square": 729, + "quotient": 28542, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4307 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V65.left_4357", + "side": "side7", + "value": 4357, + "residues": { + "value": 4357, + "mod25": 7, + "modP": 2, + "modP2": 132 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 21048668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 21048668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 21048668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 21048668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 21048668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5262167, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4357 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V66.left_4457", + "side": "side7", + "value": 4457, + "residues": { + "value": 4457, + "mod25": 7, + "modP": 11, + "modP2": 63 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 21531768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 21531768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 21531768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 21531768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 21531768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5382942, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4457 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V67.left_4532", + "side": "side7", + "value": 4532, + "residues": { + "value": 4532, + "mod25": 7, + "modP": 8, + "modP2": 138 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 21894093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 21894093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 21894093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 21894093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2432677, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + 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"needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 22014868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 22014868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22014868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22014868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5503717, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 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"square": 16, + "quotient": 1406123, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22497968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5624492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5624492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1406123, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22497968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5624492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5624492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1406123, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22497968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5624492, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5624492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1406123, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4657 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V70.left_4682", + "side": "side7", + 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"quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22618743, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22618743, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22618743, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4682 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V71.left_4757", + "side": "side7", + "value": 4757, + "residues": { + "value": 4757, + "mod25": 7, + "modP": 12, + "modP2": 25 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + 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"firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5745267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5745267, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2553452, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 638363, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22981068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5745267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5745267, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2553452, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 638363, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22981068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5745267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5745267, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2553452, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 638363, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22981068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { 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"allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 23464168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 23464168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 23464168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 23464168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 23464168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5866042, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V73.left_4957", + "side": "side7", + "value": 4957, + "residues": { + "value": 4957, + "mod25": 7, + "modP": 4, + "modP2": 56 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 23947268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 23947268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 23947268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 23947268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 23947268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5986817, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V74.left_4982", + "side": "side7", + "value": 4982, + "residues": { + "value": 4982, + "mod25": 7, + "modP": 3, + "modP2": 81 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 24068043, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 24068043, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 24068043, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 24068043, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 24068043, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2674227, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4982 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V75.left_5057", + "side": "side7", + "value": 5057, + "residues": { + "value": 5057, + "mod25": 7, + "modP": 0, + "modP2": 156 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 24430368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1526898, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 24430368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1526898, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 24430368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1526898, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 24430368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6107592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1526898, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 24430368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6228367, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5157 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V77.left_5207", + "side": "side7", + "value": 5207, + "residues": { + "value": 5207, + "mod25": 7, + "modP": 7, + "modP2": 137 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25155018, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25155018, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25155018, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25155018, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25155018, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2795002, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5207 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V78.left_5257", + "side": "side7", + "value": 5257, + "residues": { + "value": 5257, + "mod25": 7, + "modP": 5, + "modP2": 18 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25396568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25396568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25396568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25396568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25396568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6349142, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5257 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V79.left_5357", + "side": "side7", + "value": 5357, + "residues": { + "value": 5357, + "mod25": 7, + "modP": 1, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25879668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25879668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25879668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25879668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25879668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6469917, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5357 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V80.left_5432", + "side": "side7", + "value": 5432, + "residues": { + "value": 5432, + "mod25": 7, + "modP": 11, + "modP2": 24 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26241993, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26241993, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26241993, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26241993, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 26241993, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2915777, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5432 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V81.left_5457", + "side": "side7", + "value": 5457, + "residues": { + "value": 5457, + "mod25": 7, + "modP": 10, + "modP2": 49 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26362768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6590692, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6590692, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1647673, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26362768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6590692, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6590692, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1647673, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26362768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6590692, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6590692, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1647673, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26362768, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V82.left_5507", + "side": "side7", + "value": 5507, + "residues": { + "value": 5507, + "mod25": 7, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26604318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26604318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26604318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26604318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 26604318, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 157422, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove left core vertex 5507 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V83.left_5557", + "side": "side7", + "value": 5557, + "residues": { + "value": 5557, + "mod25": 7, + "modP": 6, + "modP2": 149 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26845868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26845868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26845868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26845868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 26845868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6711467, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5557 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V84.left_5657", + "side": "side7", + "value": 5657, + "residues": { + "value": 5657, + "mod25": 7, + "modP": 2, + "modP2": 80 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27328968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3036552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 759138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 27328968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3036552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 759138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 27328968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3036552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 759138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 27328968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3036552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 759138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27328968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6832242, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3036552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 759138, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5657 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V85.left_5757", + "side": "side7", + "value": 5757, + "residues": { + "value": 5757, + "mod25": 7, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27812068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 27812068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 27812068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 27812068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27812068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6953017, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5757 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V86.left_5782", + "side": "side7", + "value": 5782, + "residues": { + "value": 5782, + "mod25": 7, + "modP": 10, + "modP2": 36 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27932843, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 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"firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27932843, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5782 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V87.left_5857", + "side": "side7", + "value": 5857, + "residues": { + "value": 5857, + "mod25": 7, + "modP": 7, + "modP2": 111 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28295168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1768448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 442112, + "stableUnderCurrentSplitModulus": 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"divisor": 8, + "square": 64, + "quotient": 442112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 110528, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 32, + "square": 1024, + "quotient": 27632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 64, + "square": 4096, + "quotient": 6908, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 128, + "square": 16384, + "quotient": 1727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28295168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1768448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 442112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 110528, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 32, + "square": 1024, + "quotient": 27632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 64, + "square": 4096, + "quotient": 6908, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 128, + "square": 16384, + "quotient": 1727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28295168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1768448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 442112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 110528, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 32, + "square": 1024, + "quotient": 27632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 64, + "square": 4096, + "quotient": 6908, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 128, + "square": 16384, + "quotient": 1727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 28295168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7073792, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1768448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 442112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 110528, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 32, + "square": 1024, + "quotient": 27632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 64, + "square": 4096, + "quotient": 6908, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 128, + "square": 16384, + "quotient": 1727, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V88.left_5882", + "side": "side7", + "value": 5882, + "residues": { + "value": 5882, + "mod25": 7, + "modP": 6, + "modP2": 136 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28415943, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3157327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3157327, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 28415943, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3157327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3157327, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28415943, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3157327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3157327, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28415943, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 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+ "modP2": 161 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28536718, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 28536718, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28536718, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28536718, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 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"N": 7337, + "outsider": 4831, + "productPlusOne": 28778268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7194567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7194567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28778268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7194567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7194567, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 28778268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7194567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7194567, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V91.left_6057", + "side": "side7", + "value": 6057, + "residues": { + "value": 6057, + "mod25": 7, + "modP": 12, + "modP2": 142 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + 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"firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7315342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7315342, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 29261368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7315342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7315342, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 29261368, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7315342, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7315342, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6057 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V92.left_6107", + "side": "side7", + "value": 6107, + "residues": { + "value": 6107, + "mod25": 7, + "modP": 10, + "modP2": 23 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 29502918, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3278102, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 29502918, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3278102, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3278102, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 29502918, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3278102, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 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"N": 7343, + "outsider": 4831, + "productPlusOne": 29744468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7436117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7436117, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 29744468, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7436117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7436117, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6157 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V94.left_6257", + "side": "side7", + "value": 6257, + "residues": { + "value": 6257, + "mod25": 7, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 30227568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7556892, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7556892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1889223, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 30227568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7556892, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7556892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1889223, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 30227568, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7556892, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7556892, + 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7556892, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1889223, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6257 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V95.left_6332", + "side": "side7", + "value": 6332, + "residues": { + "value": 6332, + "mod25": 7, + "modP": 1, + "modP2": 79 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 30589893, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3398877, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3398877, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 377653, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 30589893, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3398877, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3398877, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 377653, + "stableUnderCurrentSplitModulus": false + } + ] + }, + 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 30710668, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7677667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7677667, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6357 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V97.left_6457", + "side": "side7", + "value": 6457, + "residues": { + "value": 6457, + "mod25": 7, + "modP": 9, + "modP2": 35 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + 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"hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7798442, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7798442, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6457 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V98.left_6532", + "side": "side7", + "value": 6532, + "residues": { + "value": 6532, + "mod25": 7, + "modP": 6, + "modP2": 110 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 31556093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 31556093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 31556093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 31556093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 31556093, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6532 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V99.left_6557", + "side": "side7", + "value": 6557, + "residues": { + "value": 6557, + "mod25": 7, + "modP": 5, + "modP2": 135 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 31676868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 879913, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 31676868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7919217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7919217, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3519652, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 879913, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 31676868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7919217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7919217, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3519652, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 879913, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 31676868, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7919217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7919217, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3519652, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 879913, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6557 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V100.left_6657", + "side": "side7", + "value": 6657, + "residues": { + "value": 6657, + "mod25": 7, + "modP": 1, + "modP2": 66 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32159968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8039992, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8039992, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2009998, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32159968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8039992, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8039992, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2009998, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 32159968, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32280743, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32280743, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + } + ] + }, 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"productPlusOne": 32643068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32643068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 32643068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 32643068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 32643068, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8160767, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6757 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V103.left_6782", + "side": "side7", + "value": 6782, + "residues": { + "value": 6782, + "mod25": 7, + "modP": 9, + "modP2": 22 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32763843, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3640427, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 32763843, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3640427, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3640427, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 32763843, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3640427, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 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+ "N": 7343, + "outsider": 4831, + "productPlusOne": 33126168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8281542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8281542, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 33126168, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8281542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8281542, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6857 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V105.left_6957", + "side": "side7", + "value": 6957, + "residues": { + "value": 6957, + "mod25": 7, + "modP": 2, + "modP2": 28 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 33609268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 33609268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 33609268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 33609268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 33609268, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8402317, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6957 is present in the side7 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V106.right_68", + "side": "side18", + "value": 68, + "residues": { + "value": 68, + "mod25": 18, + "modP": 3, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 328509, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 621, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 328509, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 621, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 328509, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 621, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 328509, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 621, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 328509, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 36501, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 621, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 68 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V107.right_93", + "side": "side18", + "value": 93, + "residues": { + "value": 93, + "mod25": 18, + "modP": 2, + "modP2": 93 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 449284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 449284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 449284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 449284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 449284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112321, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 93 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V108.right_193", + "side": "side18", + "value": 193, + "residues": { + "value": 193, + "mod25": 18, + "modP": 11, + "modP2": 24 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 932384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 58274, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 932384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 58274, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 932384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 58274, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 932384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 58274, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 932384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 233096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 58274, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V109.right_268", + "side": "side18", + "value": 268, + "residues": { + "value": 268, + "mod25": 18, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 1294709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 1294709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 1294709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 1294709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 1294709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7661, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove right core vertex 268 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V110.right_293", + "side": "side18", + "value": 293, + "residues": { + "value": 293, + "mod25": 18, + "modP": 7, + "modP2": 124 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 1415484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 157276, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 39319, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 1415484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 157276, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 39319, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 1415484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 157276, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 39319, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 1415484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 157276, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 39319, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 1415484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 353871, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 157276, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 39319, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V111.right_393", + "side": "side18", + "value": 393, + "residues": { + "value": 393, + "mod25": 18, + "modP": 3, + "modP2": 55 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 1898584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 1898584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 1898584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 1898584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 1898584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 474646, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V112.right_468", + "side": "side18", + "value": 468, + "residues": { + "value": 468, + "mod25": 18, + "modP": 0, + "modP2": 130 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2260909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2260909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2260909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2260909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2260909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 468 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V113.right_493", + "side": "side18", + "value": 493, + "residues": { + "value": 493, + "mod25": 18, + "modP": 12, + "modP2": 155 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2381684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2381684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2381684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2381684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2381684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 595421, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V114.right_518", + "side": "side18", + "value": 518, + "residues": { + "value": 518, + "mod25": 18, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2502459, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2502459, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2502459, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2502459, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2502459, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 278051, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 518 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V115.right_593", + "side": "side18", + "value": 593, + "residues": { + "value": 593, + "mod25": 18, + "modP": 8, + "modP2": 86 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2864784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 179049, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2864784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 179049, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2864784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 179049, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2864784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 179049, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2864784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 716196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 179049, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V116.right_693", + "side": "side18", + "value": 693, + "residues": { + "value": 693, + "mod25": 18, + "modP": 4, + "modP2": 17 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3347884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3347884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3347884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3347884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3347884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 836971, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V117.right_743", + "side": "side18", + "value": 743, + "residues": { + "value": 743, + "mod25": 18, + "modP": 2, + "modP2": 67 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3589434, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 44314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3589434, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 44314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3589434, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 44314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3589434, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 44314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3589434, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 398826, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 44314, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 743 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V118.right_793", + "side": "side18", + "value": 793, + "residues": { + "value": 793, + "mod25": 18, + "modP": 0, + "modP2": 117 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3830984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 13256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 34, + "square": 1156, + "quotient": 3314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3830984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 13256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 34, + "square": 1156, + "quotient": 3314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3830984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 13256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 34, + "square": 1156, + "quotient": 3314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3830984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 13256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 34, + "square": 1156, + "quotient": 3314, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3830984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 957746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 17, + "square": 289, + "quotient": 13256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 34, + "square": 1156, + "quotient": 3314, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V119.right_893", + "side": "side18", + "value": 893, + "residues": { + "value": 893, + "mod25": 18, + "modP": 9, + "modP2": 48 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4314084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4314084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4314084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4314084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4314084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1078521, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V120.right_968", + "side": "side18", + "value": 968, + "residues": { + "value": 968, + "mod25": 18, + "modP": 6, + "modP2": 123 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4676409, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4676409, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4676409, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4676409, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4676409, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 519601, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 968 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V121.right_993", + "side": "side18", + "value": 993, + "residues": { + "value": 993, + "mod25": 18, + "modP": 5, + "modP2": 148 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4797184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 299824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 74956, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 18739, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4797184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 299824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 74956, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 18739, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4797184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 299824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 74956, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 18739, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4797184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 299824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 74956, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 18739, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4797184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1199296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 299824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 74956, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 18739, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V122.right_1093", + "side": "side18", + "value": 1093, + "residues": { + "value": 1093, + "mod25": 18, + "modP": 1, + "modP2": 79 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 5280284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 5280284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 5280284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 5280284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 5280284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1320071, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V123.right_1193", + "side": "side18", + "value": 1193, + "residues": { + "value": 1193, + "mod25": 18, + "modP": 10, + "modP2": 10 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 5763384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 640376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 160094, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 5763384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 640376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 160094, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 5763384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 640376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 160094, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 5763384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 640376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 160094, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 5763384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1440846, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 640376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 160094, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V124.right_1293", + "side": "side18", + "value": 1293, + "residues": { + "value": 1293, + "mod25": 18, + "modP": 6, + "modP2": 110 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 6246484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 6246484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 6246484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 6246484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 6246484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1561621, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V125.right_1393", + "side": "side18", + "value": 1393, + "residues": { + "value": 1393, + "mod25": 18, + "modP": 2, + "modP2": 41 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 6729584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 420599, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 6729584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 420599, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 6729584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 420599, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 6729584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 420599, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 6729584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1682396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 420599, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V126.right_1418", + "side": "side18", + "value": 1418, + "residues": { + "value": 1418, + "mod25": 18, + "modP": 1, + "modP2": 66 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 6850359, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 6850359, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 6850359, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 6850359, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 6850359, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 761151, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1418 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V127.right_1493", + "side": "side18", + "value": 1493, + "residues": { + "value": 1493, + "mod25": 18, + "modP": 11, + "modP2": 141 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 7212684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 7212684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 7212684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 7212684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 7212684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1803171, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V128.right_1593", + "side": "side18", + "value": 1593, + "residues": { + "value": 1593, + "mod25": 18, + "modP": 7, + "modP2": 72 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 7695784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 7695784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 7695784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 7695784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 7695784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1923946, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V129.right_1643", + "side": "side18", + "value": 1643, + "residues": { + "value": 1643, + "mod25": 18, + "modP": 5, + "modP2": 122 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 7937334, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 7937334, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 7937334, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 7937334, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 7937334, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 881926, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1643 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V130.right_1693", + "side": "side18", + "value": 1693, + "residues": { + "value": 1693, + "mod25": 18, + "modP": 3, + "modP2": 3 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 8178884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 166916, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 41729, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 8178884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 166916, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 41729, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 8178884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 166916, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 41729, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 8178884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 166916, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 41729, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 8178884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2044721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 166916, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 41729, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V131.right_1793", + "side": "side18", + "value": 1793, + "residues": { + "value": 1793, + "mod25": 18, + "modP": 12, + "modP2": 103 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 8661984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 541374, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 8661984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 541374, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 8661984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 541374, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 8661984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 541374, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 8661984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2165496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 541374, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V132.right_1868", + "side": "side18", + "value": 1868, + "residues": { + "value": 1868, + "mod25": 18, + "modP": 9, + "modP2": 9 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 9024309, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 9024309, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 9024309, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 9024309, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 9024309, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1002701, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1868 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V133.right_1893", + "side": "side18", + "value": 1893, + "residues": { + "value": 1893, + "mod25": 18, + "modP": 8, + "modP2": 34 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 9145084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 9145084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 9145084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 9145084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 9145084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2286271, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V134.right_1993", + "side": "side18", + "value": 1993, + "residues": { + "value": 1993, + "mod25": 18, + "modP": 4, + "modP2": 134 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 9628184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 9628184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 9628184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 9628184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 9628184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2407046, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V135.right_2093", + "side": "side18", + "value": 2093, + "residues": { + "value": 2093, + "mod25": 18, + "modP": 0, + "modP2": 65 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 10111284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1123476, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 280869, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 10111284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1123476, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 280869, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 10111284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1123476, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 280869, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 10111284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1123476, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 280869, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 10111284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2527821, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1123476, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 280869, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V136.right_2193", + "side": "side18", + "value": 2193, + "residues": { + "value": 2193, + "mod25": 18, + "modP": 9, + "modP2": 165 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 10594384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 662149, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 10594384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 662149, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 10594384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 662149, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 10594384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 662149, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 10594384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2648596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 662149, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V137.right_2293", + "side": "side18", + "value": 2293, + "residues": { + "value": 2293, + "mod25": 18, + "modP": 5, + "modP2": 96 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 11077484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 11077484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 11077484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 11077484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 11077484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2769371, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V138.right_2318", + "side": "side18", + "value": 2318, + "residues": { + "value": 2318, + "mod25": 18, + "modP": 4, + "modP2": 121 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 11198259, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 11198259, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 11198259, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 11198259, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 11198259, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1244251, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2318 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V139.right_2393", + "side": "side18", + "value": 2393, + "residues": { + "value": 2393, + "mod25": 18, + "modP": 1, + "modP2": 27 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 11560584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 11560584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 11560584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 11560584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 11560584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2890146, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V140.right_2493", + "side": "side18", + "value": 2493, + "residues": { + "value": 2493, + "mod25": 18, + "modP": 10, + "modP2": 127 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12043684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12043684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12043684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12043684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12043684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3010921, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V141.right_2543", + "side": "side18", + "value": 2543, + "residues": { + "value": 2543, + "mod25": 18, + "modP": 8, + "modP2": 8 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12285234, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12285234, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12285234, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12285234, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12285234, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1365026, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2543 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V142.right_2568", + "side": "side18", + "value": 2568, + "residues": { + "value": 2568, + "mod25": 18, + "modP": 7, + "modP2": 33 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12406009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12406009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12406009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12406009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12406009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2568 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V143.right_2593", + "side": "side18", + "value": 2593, + "residues": { + "value": 2593, + "mod25": 18, + "modP": 6, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12526784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 782924, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 195731, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12526784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 782924, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 195731, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12526784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 782924, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 195731, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12526784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 782924, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 195731, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12526784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3131696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 782924, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 195731, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V144.right_2693", + "side": "side18", + "value": 2693, + "residues": { + "value": 2693, + "mod25": 18, + "modP": 2, + "modP2": 158 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13009884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13009884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 13009884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 13009884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 13009884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3252471, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V145.right_2768", + "side": "side18", + "value": 2768, + "residues": { + "value": 2768, + "mod25": 18, + "modP": 12, + "modP2": 64 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13372209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 165089, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13372209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 165089, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 13372209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 165089, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 13372209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 165089, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 13372209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1485801, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 165089, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2768 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V146.right_2793", + "side": "side18", + "value": 2793, + "residues": { + "value": 2793, + "mod25": 18, + "modP": 11, + "modP2": 89 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13492984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13492984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 13492984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 13492984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 13492984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3373246, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V147.right_2893", + "side": "side18", + "value": 2893, + "residues": { + "value": 2893, + "mod25": 18, + "modP": 7, + "modP2": 20 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 13976084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 13976084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 13976084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 13976084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 13976084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3494021, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V148.right_2918", + "side": "side18", + "value": 2918, + "residues": { + "value": 2918, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 14096859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 14096859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 14096859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 14096859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 14096859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2918 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V149.right_2993", + "side": "side18", + "value": 2993, + "residues": { + "value": 2993, + "mod25": 18, + "modP": 3, + "modP2": 120 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 14459184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1606576, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 903699, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 401644, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 100411, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 14459184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1606576, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 903699, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 401644, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 100411, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 14459184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1606576, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 903699, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 401644, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 100411, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 14459184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1606576, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 903699, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 401644, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 100411, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 14459184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3614796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1606576, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 903699, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 401644, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 100411, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V150.right_3093", + "side": "side18", + "value": 3093, + "residues": { + "value": 3093, + "mod25": 18, + "modP": 12, + "modP2": 51 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 14942284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 14942284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 14942284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 14942284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 14942284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3735571, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V151.right_3193", + "side": "side18", + "value": 3193, + "residues": { + "value": 3193, + "mod25": 18, + "modP": 8, + "modP2": 151 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 15425384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 15425384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 15425384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 15425384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 15425384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3856346, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V152.right_3218", + "side": "side18", + "value": 3218, + "residues": { + "value": 3218, + "mod25": 18, + "modP": 7, + "modP2": 7 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 15546159, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 15546159, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 15546159, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 15546159, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 15546159, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1727351, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3218 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V153.right_3293", + "side": "side18", + "value": 3293, + "residues": { + "value": 3293, + "mod25": 18, + "modP": 4, + "modP2": 82 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 15908484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 15908484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 15908484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 15908484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 15908484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3977121, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V154.right_3393", + "side": "side18", + "value": 3393, + "residues": { + "value": 3393, + "mod25": 18, + "modP": 0, + "modP2": 13 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 16391584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1024474, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 16391584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1024474, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 16391584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1024474, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 16391584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1024474, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 16391584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4097896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1024474, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V155.right_3443", + "side": "side18", + "value": 3443, + "residues": { + "value": 3443, + "mod25": 18, + "modP": 11, + "modP2": 63 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 16633134, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 16633134, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 16633134, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 16633134, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 16633134, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1848126, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3443 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V156.right_3493", + "side": "side18", + "value": 3493, + "residues": { + "value": 3493, + "mod25": 18, + "modP": 9, + "modP2": 113 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 16874684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 16874684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 16874684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 16874684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 16874684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4218671, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V157.right_3593", + "side": "side18", + "value": 3593, + "residues": { + "value": 3593, + "mod25": 18, + "modP": 5, + "modP2": 44 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 17357784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 17357784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 17357784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 17357784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 17357784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4339446, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V158.right_3668", + "side": "side18", + "value": 3668, + "residues": { + "value": 3668, + "mod25": 18, + "modP": 2, + "modP2": 119 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 17720109, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 17720109, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 17720109, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 17720109, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 17720109, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1968901, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3668 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V159.right_3693", + "side": "side18", + "value": 3693, + "residues": { + "value": 3693, + "mod25": 18, + "modP": 1, + "modP2": 144 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 17840884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 17840884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 17840884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 17840884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 17840884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4460221, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V160.right_3793", + "side": "side18", + "value": 3793, + "residues": { + "value": 3793, + "mod25": 18, + "modP": 10, + "modP2": 75 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 18323984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1145249, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 59, + "square": 3481, + "quotient": 5264, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 118, + "square": 13924, + "quotient": 1316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 236, + "square": 55696, + "quotient": 329, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 18323984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1145249, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 59, + "square": 3481, + "quotient": 5264, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 118, + "square": 13924, + "quotient": 1316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 236, + "square": 55696, + "quotient": 329, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 18323984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1145249, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 59, + "square": 3481, + "quotient": 5264, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 118, + "square": 13924, + "quotient": 1316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 236, + "square": 55696, + "quotient": 329, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 18323984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1145249, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 59, + "square": 3481, + "quotient": 5264, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 118, + "square": 13924, + "quotient": 1316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 236, + "square": 55696, + "quotient": 329, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 18323984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4580996, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1145249, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 59, + "square": 3481, + "quotient": 5264, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 118, + "square": 13924, + "quotient": 1316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 236, + "square": 55696, + "quotient": 329, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V161.right_3893", + "side": "side18", + "value": 3893, + "residues": { + "value": 3893, + "mod25": 18, + "modP": 6, + "modP2": 6 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 18807084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2089676, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 522419, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 18807084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2089676, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 522419, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 18807084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2089676, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 522419, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 18807084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2089676, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 522419, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 18807084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4701771, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2089676, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 522419, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V162.right_3993", + "side": "side18", + "value": 3993, + "residues": { + "value": 3993, + "mod25": 18, + "modP": 2, + "modP2": 106 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 19290184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 19290184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 19290184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 19290184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 19290184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4822546, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V163.right_4093", + "side": "side18", + "value": 4093, + "residues": { + "value": 4093, + "mod25": 18, + "modP": 11, + "modP2": 37 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 19773284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 19773284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 19773284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 19773284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 19773284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4943321, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V164.right_4118", + "side": "side18", + "value": 4118, + "residues": { + "value": 4118, + "mod25": 18, + "modP": 10, + "modP2": 62 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 19894059, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 19894059, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 19894059, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 19894059, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 19894059, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2210451, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4118 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V165.right_4143", + "side": "side18", + "value": 4143, + "residues": { + "value": 4143, + "mod25": 18, + "modP": 9, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20014834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20014834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20014834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20014834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20014834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4143 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V166.right_4193", + "side": "side18", + "value": 4193, + "residues": { + "value": 4193, + "mod25": 18, + "modP": 7, + "modP2": 137 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20256384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1266024, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 316506, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20256384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1266024, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 316506, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20256384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1266024, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 316506, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20256384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1266024, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 316506, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20256384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5064096, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1266024, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 316506, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V167.right_4293", + "side": "side18", + "value": 4293, + "residues": { + "value": 4293, + "mod25": 18, + "modP": 3, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20739484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20739484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20739484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20739484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20739484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5184871, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V168.right_4343", + "side": "side18", + "value": 4343, + "residues": { + "value": 4343, + "mod25": 18, + "modP": 1, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20981034, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20981034, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20981034, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20981034, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20981034, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2331226, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4343 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V169.right_4393", + "side": "side18", + "value": 4393, + "residues": { + "value": 4393, + "mod25": 18, + "modP": 12, + "modP2": 168 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 21222584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 21222584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 21222584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 21222584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 21222584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5305646, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V170.right_4493", + "side": "side18", + "value": 4493, + "residues": { + "value": 4493, + "mod25": 18, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 21705684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 32109, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 21705684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 32109, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 21705684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 32109, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 21705684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 32109, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 21705684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5426421, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 128436, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 32109, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V171.right_4568", + "side": "side18", + "value": 4568, + "residues": { + "value": 4568, + "mod25": 18, + "modP": 5, + "modP2": 5 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 22068009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 22068009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22068009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22068009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22068009, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2452001, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4568 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V172.right_4593", + "side": "side18", + "value": 4593, + "residues": { + "value": 4593, + "mod25": 18, + "modP": 4, + "modP2": 30 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 22188784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1386799, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 22188784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1386799, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22188784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1386799, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22188784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1386799, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22188784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5547196, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1386799, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V173.right_4693", + "side": "side18", + "value": 4693, + "residues": { + "value": 4693, + "mod25": 18, + "modP": 0, + "modP2": 130 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 22671884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 22671884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22671884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22671884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22671884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5667971, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V174.right_4768", + "side": "side18", + "value": 4768, + "residues": { + "value": 4768, + "mod25": 18, + "modP": 10, + "modP2": 36 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 23034209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 23034209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 23034209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 23034209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 23034209, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4768 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V175.right_4793", + "side": "side18", + "value": 4793, + "residues": { + "value": 4793, + "mod25": 18, + "modP": 9, + "modP2": 61 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 23154984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2572776, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 643194, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 285864, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 71466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 23154984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2572776, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 643194, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 285864, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 71466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 23154984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2572776, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 643194, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 285864, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 71466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 23154984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2572776, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 643194, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 285864, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 71466, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 23154984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5788746, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2572776, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 643194, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 285864, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 71466, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V176.right_4893", + "side": "side18", + "value": 4893, + "residues": { + "value": 4893, + "mod25": 18, + "modP": 5, + "modP2": 161 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 23638084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 23638084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 23638084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 23638084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 23638084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5909521, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V177.right_4993", + "side": "side18", + "value": 4993, + "residues": { + "value": 4993, + "mod25": 18, + "modP": 1, + "modP2": 92 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 24121184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1507574, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 24121184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1507574, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 24121184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1507574, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 24121184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1507574, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 24121184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6030296, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1507574, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V178.right_5018", + "side": "side18", + "value": 5018, + "residues": { + "value": 5018, + "mod25": 18, + "modP": 0, + "modP2": 117 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 24241959, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 24241959, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 24241959, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 24241959, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 24241959, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2693551, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5018 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V179.right_5093", + "side": "side18", + "value": 5093, + "residues": { + "value": 5093, + "mod25": 18, + "modP": 10, + "modP2": 23 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 24604284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 24604284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 24604284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 24604284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 24604284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6151071, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V180.right_5193", + "side": "side18", + "value": 5193, + "residues": { + "value": 5193, + "mod25": 18, + "modP": 6, + "modP2": 123 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25087384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25087384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25087384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25087384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25087384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6271846, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V181.right_5243", + "side": "side18", + "value": 5243, + "residues": { + "value": 5243, + "mod25": 18, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25328934, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25328934, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25328934, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25328934, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25328934, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2814326, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5243 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V182.right_5293", + "side": "side18", + "value": 5293, + "residues": { + "value": 5293, + "mod25": 18, + "modP": 2, + "modP2": 54 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25570484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25570484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25570484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25570484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25570484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6392621, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V183.right_5368", + "side": "side18", + "value": 5368, + "residues": { + "value": 5368, + "mod25": 18, + "modP": 12, + "modP2": 129 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25932809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25932809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25932809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25932809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25932809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5368 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V184.right_5393", + "side": "side18", + "value": 5393, + "residues": { + "value": 5393, + "mod25": 18, + "modP": 11, + "modP2": 154 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26053584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628349, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26053584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628349, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26053584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628349, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26053584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628349, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 26053584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6513396, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1628349, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V185.right_5468", + "side": "side18", + "value": 5468, + "residues": { + "value": 5468, + "mod25": 18, + "modP": 8, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26415909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26415909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26415909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26415909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 26415909, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2935101, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5468 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V186.right_5493", + "side": "side18", + "value": 5493, + "residues": { + "value": 5493, + "mod25": 18, + "modP": 7, + "modP2": 85 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 26536684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 26536684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 26536684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 26536684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 26536684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6634171, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V187.right_5593", + "side": "side18", + "value": 5593, + "residues": { + "value": 5593, + "mod25": 18, + "modP": 3, + "modP2": 16 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27019784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 223304, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 55826, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 27019784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 223304, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 55826, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 27019784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 223304, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 55826, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 27019784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 223304, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 55826, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27019784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6754946, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 223304, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 55826, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V188.right_5693", + "side": "side18", + "value": 5693, + "residues": { + "value": 5693, + "mod25": 18, + "modP": 12, + "modP2": 116 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27502884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3055876, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 763969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 27502884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3055876, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 763969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 27502884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3055876, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 763969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 27502884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3055876, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 763969, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27502884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6875721, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3055876, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 763969, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V189.right_5793", + "side": "side18", + "value": 5793, + "residues": { + "value": 5793, + "mod25": 18, + "modP": 8, + "modP2": 47 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27985984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1749124, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 437281, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 27985984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1749124, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 437281, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 27985984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1749124, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 437281, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 27985984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1749124, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 437281, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27985984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6996496, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1749124, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 437281, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V190.right_5893", + "side": "side18", + "value": 5893, + "residues": { + "value": 5893, + "mod25": 18, + "modP": 4, + "modP2": 147 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28469084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 28469084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28469084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28469084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 28469084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7117271, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V191.right_5918", + "side": "side18", + "value": 5918, + "residues": { + "value": 5918, + "mod25": 18, + "modP": 3, + "modP2": 3 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28589859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 28589859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28589859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28589859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 28589859, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3176651, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5918 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V192.right_5993", + "side": "side18", + "value": 5993, + "residues": { + "value": 5993, + "mod25": 18, + "modP": 0, + "modP2": 78 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28952184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 28952184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28952184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28952184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 28952184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7238046, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V193.right_6093", + "side": "side18", + "value": 6093, + "residues": { + "value": 6093, + "mod25": 18, + "modP": 9, + "modP2": 9 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 29435284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 29435284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 29435284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 29435284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 29435284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7358821, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V194.right_6143", + "side": "side18", + "value": 6143, + "residues": { + "value": 6143, + "mod25": 18, + "modP": 7, + "modP2": 59 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 29676834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 29676834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 29676834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 29676834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 29676834, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3297426, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6143 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V195.right_6193", + "side": "side18", + "value": 6193, + "residues": { + "value": 6193, + "mod25": 18, + "modP": 5, + "modP2": 109 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 29918384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1869899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 29918384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1869899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 29918384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1869899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 29918384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1869899, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 29918384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7479596, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1869899, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V196.right_6293", + "side": "side18", + "value": 6293, + "residues": { + "value": 6293, + "mod25": 18, + "modP": 1, + "modP2": 40 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 30401484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 30401484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 30401484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 30401484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 30401484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7600371, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6293 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V197.right_6368", + "side": "side18", + "value": 6368, + "residues": { + "value": 6368, + "mod25": 18, + "modP": 11, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 30763809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 30763809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 30763809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 30763809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 30763809, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3418201, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6368 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V198.right_6393", + "side": "side18", + "value": 6393, + "residues": { + "value": 6393, + "mod25": 18, + "modP": 10, + "modP2": 140 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 30884584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 30884584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 30884584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 30884584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 30884584, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7721146, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6393 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V199.right_6493", + "side": "side18", + "value": 6493, + "residues": { + "value": 6493, + "mod25": 18, + "modP": 6, + "modP2": 71 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 31367684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 31367684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 31367684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 31367684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 31367684, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7841921, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6493 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V200.right_6593", + "side": "side18", + "value": 6593, + "residues": { + "value": 6593, + "mod25": 18, + "modP": 2, + "modP2": 2 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 31850784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3538976, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1990674, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 884744, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 650016, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 221186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 162504, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 72224, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 40626, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 18056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 84, + "square": 7056, + "quotient": 4514, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 31850784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3538976, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1990674, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 884744, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 650016, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 221186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 162504, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 72224, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 40626, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 18056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 84, + "square": 7056, + "quotient": 4514, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 31850784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3538976, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1990674, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 884744, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 650016, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 221186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 162504, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 72224, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 40626, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 18056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 84, + "square": 7056, + "quotient": 4514, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 31850784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3538976, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1990674, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 884744, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 650016, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 221186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 162504, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 72224, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 40626, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 18056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 84, + "square": 7056, + "quotient": 4514, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 31850784, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7962696, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 3538976, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1990674, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 884744, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 650016, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 221186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 162504, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 72224, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 40626, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 42, + "square": 1764, + "quotient": 18056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 84, + "square": 7056, + "quotient": 4514, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6593 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V201.right_6693", + "side": "side18", + "value": 6693, + "residues": { + "value": 6693, + "mod25": 18, + "modP": 11, + "modP2": 102 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32333884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32333884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 32333884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 32333884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 32333884, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8083471, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6693 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V202.right_6793", + "side": "side18", + "value": 6793, + "residues": { + "value": 6793, + "mod25": 18, + "modP": 7, + "modP2": 33 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32816984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32816984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 32816984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 32816984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 32816984, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8204246, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6793 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V203.right_6818", + "side": "side18", + "value": 6818, + "residues": { + "value": 6818, + "mod25": 18, + "modP": 6, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32937759, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 406639, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32937759, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 406639, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 32937759, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 406639, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 32937759, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 406639, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 32937759, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3659751, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 406639, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6818 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V204.right_6893", + "side": "side18", + "value": 6893, + "residues": { + "value": 6893, + "mod25": 18, + "modP": 3, + "modP2": 133 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 33300084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 19, + "square": 361, + "quotient": 92244, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 38, + "square": 1444, + "quotient": 23061, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 33300084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 19, + "square": 361, + "quotient": 92244, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 38, + "square": 1444, + "quotient": 23061, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 33300084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 19, + "square": 361, + "quotient": 92244, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 38, + "square": 1444, + "quotient": 23061, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 33300084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 19, + "square": 361, + "quotient": 92244, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 38, + "square": 1444, + "quotient": 23061, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 33300084, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8325021, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 19, + "square": 361, + "quotient": 92244, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 38, + "square": 1444, + "quotient": 23061, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6893 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V205.right_6993", + "side": "side18", + "value": 6993, + "residues": { + "value": 6993, + "mod25": 18, + "modP": 12, + "modP2": 64 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 33783184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2111449, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 33783184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2111449, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 33783184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2111449, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 33783184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2111449, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 33783184, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8445796, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 2111449, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6993 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V206.right_7043", + "side": "side18", + "value": 7043, + "residues": { + "value": 7043, + "mod25": 18, + "modP": 10, + "modP2": 114 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 34024734, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 34024734, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 34024734, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 34024734, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 34024734, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3780526, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7043 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V207.right_7093", + "side": "side18", + "value": 7093, + "residues": { + "value": 7093, + "mod25": 18, + "modP": 8, + "modP2": 164 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 34266284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 34266284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 34266284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 34266284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 34266284, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8566571, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7093 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V208.right_7193", + "side": "side18", + "value": 7193, + "residues": { + "value": 7193, + "mod25": 18, + "modP": 4, + "modP2": 95 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 34749384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 34749384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 34749384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 34749384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 34749384, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8687346, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7193 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V209.right_7268", + "side": "side18", + "value": 7268, + "residues": { + "value": 7268, + "mod25": 18, + "modP": 1, + "modP2": 1 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 35111709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 35111709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 35111709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 35111709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 35111709, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3901301, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7268 is present in the side18 compatible set for every row in split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V210.right_7293", + "side": "side18", + "value": 7293, + "residues": { + "value": 7293, + "mod25": 18, + "modP": 0, + "modP2": 26 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 35232484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8808121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8808121, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 35232484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8808121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 8808121, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 35232484, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 8808121, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 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"atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E16.left_1007_right_1418", + "pairIndex": 15, + "pair": { + "leftValue": 1007, + "rightValue": 1418, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 162, + "rightModP2": 66, + "leftModP": 6, + "rightModP": 1, + "productPlusOneModP2": 46 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1427927, + "checkedSquareRootFloor": 1194, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1007, 1418) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E17.left_1057_right_993", + "pairIndex": 16, + "pair": { + "leftValue": 1057, + "rightValue": 993, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 43, + "rightModP2": 148, + "leftModP": 4, + "rightModP": 5, + "productPlusOneModP2": 112 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1049602, + "checkedSquareRootFloor": 1024, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1057, 993) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E18.left_1082_right_1193", + "pairIndex": 17, + "pair": { + "leftValue": 1082, + "rightValue": 1193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 68, + "rightModP2": 10, + "leftModP": 3, + "rightModP": 10, + "productPlusOneModP2": 5 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1290827, + "checkedSquareRootFloor": 1136, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1082, 1193) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E19.left_1157_right_1093", + "pairIndex": 18, + "pair": { + "leftValue": 1157, + "rightValue": 1093, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 143, + "rightModP2": 79, + "leftModP": 0, + "rightModP": 1, + "productPlusOneModP2": 144 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1264602, + "checkedSquareRootFloor": 1124, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1157, 1093) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E20.left_1257_right_1293", + "pairIndex": 19, + "pair": { + "leftValue": 1257, + "rightValue": 1293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 74, + "rightModP2": 110, + "leftModP": 9, + "rightModP": 6, + "productPlusOneModP2": 29 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1625302, + "checkedSquareRootFloor": 1274, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1257, 1293) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E21.left_1282_right_1393", + "pairIndex": 20, + "pair": { + "leftValue": 1282, + "rightValue": 1393, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 99, + "rightModP2": 41, + "leftModP": 8, + "rightModP": 2, + "productPlusOneModP2": 4 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1785827, + "checkedSquareRootFloor": 1336, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1282, 1393) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E22.left_1357_right_1493", + "pairIndex": 21, + "pair": { + "leftValue": 1357, + "rightValue": 1493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 5, + "rightModP2": 141, + "leftModP": 5, + "rightModP": 11, + "productPlusOneModP2": 30 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2026002, + "checkedSquareRootFloor": 1423, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1357, 1493) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E23.left_1382_right_1593", + "pairIndex": 22, + "pair": { + "leftValue": 1382, + "rightValue": 1593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 30, + "rightModP2": 72, + "leftModP": 4, + "rightModP": 7, + "productPlusOneModP2": 133 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2201527, + "checkedSquareRootFloor": 1483, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1382, 1593) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E24.left_1457_right_1868", + "pairIndex": 23, + "pair": { + "leftValue": 1457, + "rightValue": 1868, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 105, + "rightModP2": 9, + "leftModP": 1, + "rightModP": 9, + "productPlusOneModP2": 101 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2721677, + "checkedSquareRootFloor": 1649, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1457, 1868) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, 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"bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2640302, + "checkedSquareRootFloor": 1624, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1607, 1643) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E27.left_1657_right_1793", + "pairIndex": 26, + "pair": { + "leftValue": 1657, + "rightValue": 1793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 136, + "rightModP2": 103, + "leftModP": 6, + "rightModP": 12, + "productPlusOneModP2": 151 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2971002, + "checkedSquareRootFloor": 1723, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1657, 1793) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E28.left_1757_right_1893", + "pairIndex": 27, + "pair": { + "leftValue": 1757, + "rightValue": 1893, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 67, + "rightModP2": 34, + "leftModP": 2, + "rightModP": 8, + "productPlusOneModP2": 82 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 3326002, + "checkedSquareRootFloor": 1823, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1757, 1893) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E29.left_1832_right_1993", + "pairIndex": 28, + "pair": { + "leftValue": 1832, + "rightValue": 1993, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 142, + "rightModP2": 134, + "leftModP": 12, + "rightModP": 4, + "productPlusOneModP2": 101 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 3651177, + "checkedSquareRootFloor": 1910, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1832, 1993) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E30.left_1857_right_2093", + "pairIndex": 29, + "pair": { + "leftValue": 1857, + "rightValue": 2093, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 167, + "rightModP2": 65, + "leftModP": 11, + "rightModP": 0, + "productPlusOneModP2": 40 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 3886702, + "checkedSquareRootFloor": 1971, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1857, 2093) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E31.left_1957_right_2193", + "pairIndex": 30, + "pair": { + "leftValue": 1957, + "rightValue": 2193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 98, + "rightModP2": 165, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 116 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 4291702, + "checkedSquareRootFloor": 2071, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1957, 2193) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E32.left_2057_right_2318", + "pairIndex": 31, + "pair": { + "leftValue": 2057, + "rightValue": 2318, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 29, + "rightModP2": 121, + "leftModP": 3, + "rightModP": 4, + "productPlusOneModP2": 130 + }, + "status": 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}, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E34.left_2232_right_2393", + "pairIndex": 33, + "pair": { + "leftValue": 2232, + "rightValue": 2393, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 35, + "rightModP2": 27, + "leftModP": 9, + "rightModP": 1, + "productPlusOneModP2": 101 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 5341177, + "checkedSquareRootFloor": 2311, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (2232, 2393) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E35.left_2257_right_2493", + "pairIndex": 34, + "pair": { + "leftValue": 2257, + "rightValue": 2493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 60, + "rightModP2": 127, + "leftModP": 8, + "rightModP": 10, + "productPlusOneModP2": 16 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 5626702, + "checkedSquareRootFloor": 2372, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (2257, 2493) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E36.left_2282_right_2543", + "pairIndex": 35, + "pair": { + "leftValue": 2282, + "rightValue": 2543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 85, + "rightModP2": 8, + "leftModP": 7, + "rightModP": 8, + "productPlusOneModP2": 5 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 5803127, + "checkedSquareRootFloor": 2408, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (2282, 2543) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + 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}, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E40.left_2557_right_2693", + "pairIndex": 39, + "pair": { + "leftValue": 2557, + "rightValue": 2693, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 22, + "rightModP2": 158, + "leftModP": 9, + "rightModP": 2, + "productPlusOneModP2": 97 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 6886002, + "checkedSquareRootFloor": 2624, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (2557, 2693) remains a missing cross edge throughout split outP2=99|out25=6|smaller=side18." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E41.left_2657_right_2793", + "pairIndex": 40, + "pair": { + "leftValue": 2657, + "rightValue": 2793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 122, + "rightModP2": 89, + "leftModP": 5, + "rightModP": 11, + "productPlusOneModP2": 43 + }, + "status": 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the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E2.left_57_right_93", + "pairIndex": 1, + "leftValue": 57, + "rightValue": 93, + "productPlusOne": 5302, + "productPlusOneRecomputed": 5302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E3.left_157_right_193", + "pairIndex": 2, + "leftValue": 157, + "rightValue": 193, + "productPlusOne": 30302, + "productPlusOneRecomputed": 30302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E4.left_257_right_293", + "pairIndex": 3, + "leftValue": 257, + "rightValue": 293, + "productPlusOne": 75302, + "productPlusOneRecomputed": 75302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E5.left_357_right_268", + "pairIndex": 4, + "leftValue": 357, + "rightValue": 268, + "productPlusOne": 95677, + "productPlusOneRecomputed": 95677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E6.left_457_right_393", + "pairIndex": 5, + "leftValue": 457, + "rightValue": 393, + "productPlusOne": 179602, + "productPlusOneRecomputed": 179602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E7.left_482_right_468", + "pairIndex": 6, + "leftValue": 482, + "rightValue": 468, + "productPlusOne": 225577, + "productPlusOneRecomputed": 225577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E8.left_557_right_493", + "pairIndex": 7, + "leftValue": 557, + "rightValue": 493, + "productPlusOne": 274602, + "productPlusOneRecomputed": 274602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E9.left_632_right_518", + "pairIndex": 8, + "leftValue": 632, + "rightValue": 518, + "productPlusOne": 327377, + "productPlusOneRecomputed": 327377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E10.left_657_right_593", + "pairIndex": 9, + "leftValue": 657, + "rightValue": 593, + "productPlusOne": 389602, + "productPlusOneRecomputed": 389602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E11.left_707_right_743", + "pairIndex": 10, + "leftValue": 707, + "rightValue": 743, + "productPlusOne": 525302, + "productPlusOneRecomputed": 525302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E12.left_757_right_693", + "pairIndex": 11, + "leftValue": 757, + "rightValue": 693, + "productPlusOne": 524602, + "productPlusOneRecomputed": 524602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E13.left_857_right_793", + "pairIndex": 12, + "leftValue": 857, + "rightValue": 793, + "productPlusOne": 679602, + "productPlusOneRecomputed": 679602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E14.left_932_right_893", + "pairIndex": 13, + "leftValue": 932, + "rightValue": 893, + "productPlusOne": 832277, + "productPlusOneRecomputed": 832277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E15.left_957_right_968", + "pairIndex": 14, + "leftValue": 957, + "rightValue": 968, + "productPlusOne": 926377, + "productPlusOneRecomputed": 926377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E16.left_1007_right_1418", + "pairIndex": 15, + "leftValue": 1007, + "rightValue": 1418, + "productPlusOne": 1427927, + "productPlusOneRecomputed": 1427927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E17.left_1057_right_993", + "pairIndex": 16, + "leftValue": 1057, + "rightValue": 993, + "productPlusOne": 1049602, + "productPlusOneRecomputed": 1049602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E18.left_1082_right_1193", + "pairIndex": 17, + "leftValue": 1082, + "rightValue": 1193, + "productPlusOne": 1290827, + "productPlusOneRecomputed": 1290827, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E19.left_1157_right_1093", + "pairIndex": 18, + "leftValue": 1157, + "rightValue": 1093, + "productPlusOne": 1264602, + "productPlusOneRecomputed": 1264602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E20.left_1257_right_1293", + "pairIndex": 19, + "leftValue": 1257, + "rightValue": 1293, + "productPlusOne": 1625302, + "productPlusOneRecomputed": 1625302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E21.left_1282_right_1393", + "pairIndex": 20, + "leftValue": 1282, + "rightValue": 1393, + "productPlusOne": 1785827, + "productPlusOneRecomputed": 1785827, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E22.left_1357_right_1493", + "pairIndex": 21, + "leftValue": 1357, + "rightValue": 1493, + "productPlusOne": 2026002, + "productPlusOneRecomputed": 2026002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E23.left_1382_right_1593", + "pairIndex": 22, + "leftValue": 1382, + "rightValue": 1593, + "productPlusOne": 2201527, + "productPlusOneRecomputed": 2201527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E24.left_1457_right_1868", + "pairIndex": 23, + "leftValue": 1457, + "rightValue": 1868, + "productPlusOne": 2721677, + "productPlusOneRecomputed": 2721677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E25.left_1557_right_1693", + "pairIndex": 24, + "leftValue": 1557, + "rightValue": 1693, + "productPlusOne": 2636002, + "productPlusOneRecomputed": 2636002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E26.left_1607_right_1643", + "pairIndex": 25, + "leftValue": 1607, + "rightValue": 1643, + "productPlusOne": 2640302, + "productPlusOneRecomputed": 2640302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E27.left_1657_right_1793", + "pairIndex": 26, + "leftValue": 1657, + "rightValue": 1793, + "productPlusOne": 2971002, + "productPlusOneRecomputed": 2971002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E28.left_1757_right_1893", + "pairIndex": 27, + "leftValue": 1757, + "rightValue": 1893, + "productPlusOne": 3326002, + "productPlusOneRecomputed": 3326002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E29.left_1832_right_1993", + "pairIndex": 28, + "leftValue": 1832, + "rightValue": 1993, + "productPlusOne": 3651177, + "productPlusOneRecomputed": 3651177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E30.left_1857_right_2093", + "pairIndex": 29, + "leftValue": 1857, + "rightValue": 2093, + "productPlusOne": 3886702, + "productPlusOneRecomputed": 3886702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E31.left_1957_right_2193", + "pairIndex": 30, + "leftValue": 1957, + "rightValue": 2193, + "productPlusOne": 4291702, + "productPlusOneRecomputed": 4291702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E32.left_2057_right_2318", + "pairIndex": 31, + "leftValue": 2057, + "rightValue": 2318, + "productPlusOne": 4768127, + "productPlusOneRecomputed": 4768127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E33.left_2157_right_2293", + "pairIndex": 32, + "leftValue": 2157, + "rightValue": 2293, + "productPlusOne": 4946002, + "productPlusOneRecomputed": 4946002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E34.left_2232_right_2393", + "pairIndex": 33, + "leftValue": 2232, + "rightValue": 2393, + "productPlusOne": 5341177, + "productPlusOneRecomputed": 5341177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E35.left_2257_right_2493", + "pairIndex": 34, + "leftValue": 2257, + "rightValue": 2493, + "productPlusOne": 5626702, + "productPlusOneRecomputed": 5626702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E36.left_2282_right_2543", + "pairIndex": 35, + "leftValue": 2282, + "rightValue": 2543, + "productPlusOne": 5803127, + "productPlusOneRecomputed": 5803127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E37.left_2357_right_2568", + "pairIndex": 36, + "leftValue": 2357, + "rightValue": 2568, + "productPlusOne": 6052777, + "productPlusOneRecomputed": 6052777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E38.left_2457_right_2593", + "pairIndex": 37, + "leftValue": 2457, + "rightValue": 2593, + "productPlusOne": 6371002, + "productPlusOneRecomputed": 6371002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E39.left_2507_right_2768", + "pairIndex": 38, + "leftValue": 2507, + "rightValue": 2768, + "productPlusOne": 6939377, + "productPlusOneRecomputed": 6939377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E40.left_2557_right_2693", + "pairIndex": 39, + "leftValue": 2557, + "rightValue": 2693, + "productPlusOne": 6886002, + "productPlusOneRecomputed": 6886002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E41.left_2657_right_2793", + "pairIndex": 40, + "leftValue": 2657, + "rightValue": 2793, + "productPlusOne": 7421002, + "productPlusOneRecomputed": 7421002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E42.left_2732_right_2893", + "pairIndex": 41, + "leftValue": 2732, + "rightValue": 2893, + "productPlusOne": 7903677, + "productPlusOneRecomputed": 7903677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E43.left_2757_right_2993", + "pairIndex": 42, + "leftValue": 2757, + "rightValue": 2993, + "productPlusOne": 8251702, + "productPlusOneRecomputed": 8251702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E44.left_2857_right_3093", + "pairIndex": 43, + "leftValue": 2857, + "rightValue": 3093, + "productPlusOne": 8836702, + "productPlusOneRecomputed": 8836702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E45.left_2957_right_2918", + "pairIndex": 44, + "leftValue": 2957, + "rightValue": 2918, + "productPlusOne": 8628527, + "productPlusOneRecomputed": 8628527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E46.left_3057_right_3193", + "pairIndex": 45, + "leftValue": 3057, + "rightValue": 3193, + "productPlusOne": 9761002, + "productPlusOneRecomputed": 9761002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E47.left_3157_right_3293", + "pairIndex": 46, + "leftValue": 3157, + "rightValue": 3293, + "productPlusOne": 10396002, + "productPlusOneRecomputed": 10396002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E48.left_3182_right_3393", + "pairIndex": 47, + "leftValue": 3182, + "rightValue": 3393, + "productPlusOne": 10796527, + "productPlusOneRecomputed": 10796527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E49.left_3257_right_3218", + "pairIndex": 48, + "leftValue": 3257, + "rightValue": 3218, + "productPlusOne": 10481027, + "productPlusOneRecomputed": 10481027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E50.left_3357_right_3593", + "pairIndex": 49, + "leftValue": 3357, + "rightValue": 3593, + "productPlusOne": 12061702, + "productPlusOneRecomputed": 12061702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E51.left_3407_right_3443", + "pairIndex": 50, + "leftValue": 3407, + "rightValue": 3443, + "productPlusOne": 11730302, + "productPlusOneRecomputed": 11730302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E52.left_3457_right_3493", + "pairIndex": 51, + "leftValue": 3457, + "rightValue": 3493, + "productPlusOne": 12075302, + "productPlusOneRecomputed": 12075302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E53.left_3557_right_3668", + "pairIndex": 52, + "leftValue": 3557, + "rightValue": 3668, + "productPlusOne": 13047077, + "productPlusOneRecomputed": 13047077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E54.left_3632_right_3693", + "pairIndex": 53, + "leftValue": 3632, + "rightValue": 3693, + "productPlusOne": 13412977, + "productPlusOneRecomputed": 13412977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E55.left_3657_right_3793", + "pairIndex": 54, + "leftValue": 3657, + "rightValue": 3793, + "productPlusOne": 13871002, + "productPlusOneRecomputed": 13871002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E56.left_3757_right_3893", + "pairIndex": 55, + "leftValue": 3757, + "rightValue": 3893, + "productPlusOne": 14626002, + "productPlusOneRecomputed": 14626002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E57.left_3807_right_4118", + "pairIndex": 56, + "leftValue": 3807, + "rightValue": 4118, + "productPlusOne": 15677227, + "productPlusOneRecomputed": 15677227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E58.left_3857_right_3993", + "pairIndex": 57, + "leftValue": 3857, + "rightValue": 3993, + "productPlusOne": 15401002, + "productPlusOneRecomputed": 15401002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E59.left_3957_right_4093", + "pairIndex": 58, + "leftValue": 3957, + "rightValue": 4093, + "productPlusOne": 16196002, + "productPlusOneRecomputed": 16196002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E60.left_4057_right_4193", + "pairIndex": 59, + "leftValue": 4057, + "rightValue": 4193, + "productPlusOne": 17011002, + "productPlusOneRecomputed": 17011002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E61.left_4082_right_4143", + "pairIndex": 60, + "leftValue": 4082, + "rightValue": 4143, + "productPlusOne": 16911727, + "productPlusOneRecomputed": 16911727, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E62.left_4157_right_4293", + "pairIndex": 61, + "leftValue": 4157, + "rightValue": 4293, + "productPlusOne": 17846002, + "productPlusOneRecomputed": 17846002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E63.left_4257_right_4393", + "pairIndex": 62, + "leftValue": 4257, + "rightValue": 4393, + "productPlusOne": 18701002, + "productPlusOneRecomputed": 18701002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E64.left_4307_right_4343", + "pairIndex": 63, + "leftValue": 4307, + "rightValue": 4343, + "productPlusOne": 18705302, + "productPlusOneRecomputed": 18705302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E65.left_4357_right_4493", + "pairIndex": 64, + "leftValue": 4357, + "rightValue": 4493, + "productPlusOne": 19576002, + "productPlusOneRecomputed": 19576002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E66.left_4457_right_4568", + "pairIndex": 65, + "leftValue": 4457, + "rightValue": 4568, + "productPlusOne": 20359577, + "productPlusOneRecomputed": 20359577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E67.left_4532_right_4593", + "pairIndex": 66, + "leftValue": 4532, + "rightValue": 4593, + "productPlusOne": 20815477, + "productPlusOneRecomputed": 20815477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E68.left_4557_right_4693", + "pairIndex": 67, + "leftValue": 4557, + "rightValue": 4693, + "productPlusOne": 21386002, + "productPlusOneRecomputed": 21386002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E69.left_4657_right_4768", + "pairIndex": 68, + "leftValue": 4657, + "rightValue": 4768, + "productPlusOne": 22204577, + "productPlusOneRecomputed": 22204577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E70.left_4682_right_4793", + "pairIndex": 69, + "leftValue": 4682, + "rightValue": 4793, + "productPlusOne": 22440827, + "productPlusOneRecomputed": 22440827, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E71.left_4757_right_4893", + "pairIndex": 70, + "leftValue": 4757, + "rightValue": 4893, + "productPlusOne": 23276002, + "productPlusOneRecomputed": 23276002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E72.left_4857_right_4993", + "pairIndex": 71, + "leftValue": 4857, + "rightValue": 4993, + "productPlusOne": 24251002, + "productPlusOneRecomputed": 24251002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E73.left_4957_right_5093", + "pairIndex": 72, + "leftValue": 4957, + "rightValue": 5093, + "productPlusOne": 25246002, + "productPlusOneRecomputed": 25246002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E74.left_4982_right_5018", + "pairIndex": 73, + "leftValue": 4982, + "rightValue": 5018, + "productPlusOne": 24999677, + "productPlusOneRecomputed": 24999677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E75.left_5057_right_5193", + "pairIndex": 74, + "leftValue": 5057, + "rightValue": 5193, + "productPlusOne": 26261002, + "productPlusOneRecomputed": 26261002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E76.left_5157_right_5293", + "pairIndex": 75, + "leftValue": 5157, + "rightValue": 5293, + "productPlusOne": 27296002, + "productPlusOneRecomputed": 27296002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E77.left_5207_right_5243", + "pairIndex": 76, + "leftValue": 5207, + "rightValue": 5243, + "productPlusOne": 27300302, + "productPlusOneRecomputed": 27300302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E78.left_5257_right_5368", + "pairIndex": 77, + "leftValue": 5257, + "rightValue": 5368, + "productPlusOne": 28219577, + "productPlusOneRecomputed": 28219577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E79.left_5357_right_5468", + "pairIndex": 78, + "leftValue": 5357, + "rightValue": 5468, + "productPlusOne": 29292077, + "productPlusOneRecomputed": 29292077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E80.left_5432_right_5393", + "pairIndex": 79, + "leftValue": 5432, + "rightValue": 5393, + "productPlusOne": 29294777, + "productPlusOneRecomputed": 29294777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E81.left_5457_right_5493", + "pairIndex": 80, + "leftValue": 5457, + "rightValue": 5493, + "productPlusOne": 29975302, + "productPlusOneRecomputed": 29975302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E82.left_5507_right_5918", + "pairIndex": 81, + "leftValue": 5507, + "rightValue": 5918, + "productPlusOne": 32590427, + "productPlusOneRecomputed": 32590427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E83.left_5557_right_5693", + "pairIndex": 82, + "leftValue": 5557, + "rightValue": 5693, + "productPlusOne": 31636002, + "productPlusOneRecomputed": 31636002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E84.left_5657_right_5593", + "pairIndex": 83, + "leftValue": 5657, + "rightValue": 5593, + "productPlusOne": 31639602, + "productPlusOneRecomputed": 31639602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E85.left_5757_right_5793", + "pairIndex": 84, + "leftValue": 5757, + "rightValue": 5793, + "productPlusOne": 33350302, + "productPlusOneRecomputed": 33350302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E86.left_5782_right_5893", + "pairIndex": 85, + "leftValue": 5782, + "rightValue": 5893, + "productPlusOne": 34073327, + "productPlusOneRecomputed": 34073327, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E87.left_5857_right_5993", + "pairIndex": 86, + "leftValue": 5857, + "rightValue": 5993, + "productPlusOne": 35101002, + "productPlusOneRecomputed": 35101002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E88.left_5882_right_6093", + "pairIndex": 87, + "leftValue": 5882, + "rightValue": 6093, + "productPlusOne": 35839027, + "productPlusOneRecomputed": 35839027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E89.left_5907_right_6143", + "pairIndex": 88, + "leftValue": 5907, + "rightValue": 6143, + "productPlusOne": 36286702, + "productPlusOneRecomputed": 36286702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E90.left_5957_right_6293", + "pairIndex": 89, + "leftValue": 5957, + "rightValue": 6293, + "productPlusOne": 37487402, + "productPlusOneRecomputed": 37487402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E91.left_6057_right_6193", + "pairIndex": 90, + "leftValue": 6057, + "rightValue": 6193, + "productPlusOne": 37511002, + "productPlusOneRecomputed": 37511002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E92.left_6107_right_6368", + "pairIndex": 91, + "leftValue": 6107, + "rightValue": 6368, + "productPlusOne": 38889377, + "productPlusOneRecomputed": 38889377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E93.left_6157_right_6393", + "pairIndex": 92, + "leftValue": 6157, + "rightValue": 6393, + "productPlusOne": 39361702, + "productPlusOneRecomputed": 39361702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E94.left_6257_right_6593", + "pairIndex": 93, + "leftValue": 6257, + "rightValue": 6593, + "productPlusOne": 41252402, + "productPlusOneRecomputed": 41252402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E95.left_6332_right_6493", + "pairIndex": 94, + "leftValue": 6332, + "rightValue": 6493, + "productPlusOne": 41113677, + "productPlusOneRecomputed": 41113677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E96.left_6357_right_6693", + "pairIndex": 95, + "leftValue": 6357, + "rightValue": 6693, + "productPlusOne": 42547402, + "productPlusOneRecomputed": 42547402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E97.left_6457_right_6793", + "pairIndex": 96, + "leftValue": 6457, + "rightValue": 6793, + "productPlusOne": 43862402, + "productPlusOneRecomputed": 43862402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E98.left_6532_right_6893", + "pairIndex": 97, + "leftValue": 6532, + "rightValue": 6893, + "productPlusOne": 45025077, + "productPlusOneRecomputed": 45025077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E99.left_6557_right_6818", + "pairIndex": 98, + "leftValue": 6557, + "rightValue": 6818, + "productPlusOne": 44705627, + "productPlusOneRecomputed": 44705627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E100.left_6657_right_7093", + "pairIndex": 99, + "leftValue": 6657, + "rightValue": 7093, + "productPlusOne": 47218102, + "productPlusOneRecomputed": 47218102, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E101.left_6682_right_6993", + "pairIndex": 100, + "leftValue": 6682, + "rightValue": 6993, + "productPlusOne": 46727227, + "productPlusOneRecomputed": 46727227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E102.left_6757_right_7193", + "pairIndex": 101, + "leftValue": 6757, + "rightValue": 7193, + "productPlusOne": 48603102, + "productPlusOneRecomputed": 48603102, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E103.left_6782_right_7043", + "pairIndex": 102, + "leftValue": 6782, + "rightValue": 7043, + "productPlusOne": 47765627, + "productPlusOneRecomputed": 47765627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E104.left_6857_right_7268", + "pairIndex": 103, + "leftValue": 6857, + "rightValue": 7268, + "productPlusOne": 49836677, + "productPlusOneRecomputed": 49836677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.E105.left_6957_right_7293", + "pairIndex": 104, + "leftValue": 6957, + "rightValue": 7293, + "productPlusOne": 50737402, + "productPlusOneRecomputed": 50737402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + } + ], + "failedChecks": [], + "proofBoundary": "This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions.", + "nextTheoremAction": "After this A5 literal persistence pass, promote matching disjointness and the K-envelope, or lift the edge proof if vertex formulas become parameterized." + }, + "matchingDisjointness": { + "status": "bounded_disjointness_certified", + "leftVertexCount": 105, + "rightVertexCount": 105, + "pairCount": 105, + "reusedLeftValues": [], + "reusedRightValues": [], + "completionRule": "A symbolic packet may promote only if the parameterized left and right vertex families remain pairwise disjoint." + }, + "matchingKEnvelopeCertificate": { + "schema": "erdos.p848_matching_k_envelope_certificate/1", + "certificateId": "D2.2_persist_outP2=99_out25=6_smaller=side18.matching_k_envelope_certificate", + "status": "literal_matching_sampled_k_envelope_verified", + "proofKind": "literal_disjoint_matching_plus_sampled_k_envelope", + "matchingProof": { + "status": "literal_matching_disjointness_verified", + "pairCount": 105, + "leftVertexCount": 105, + "rightVertexCount": 105, + "reusedLeftValues": [], + "reusedRightValues": [], + "proofSteps": [ + "Count the exported literal left vertices.", + "Count the exported literal right vertices.", + "Verify no left value and no right value is reused across the exported pair list." + ], + "proofBoundary": "This proves disjointness for the exported literal pair list. If later work parameterizes vertices, disjointness must be rechecked for the parameterized formulas." + }, + "kEnvelopeProof": { + "status": "sampled_k_envelope_dominated_by_literal_core", + "requiredMatchingLowerBoundRange": [ + 85, + 85 + ], + "commonMatchingPairCount": 105, + "maxRequiredMatchingLowerBound": 85, + "boundedSlackAgainstMaxK": 20, + "inequality": "105 >= 85", + "proofSteps": [ + "Use the exported common-core pair count as the literal matching size.", + "Compare it against the maximum required matching lower bound recorded by the packet.", + "Record the slack and keep the all-N K-formula handoff explicit." + ], + "proofBoundary": "This certifies the K-envelope recorded by the current split packet. It is not by itself a universal K(N,x) formula proof for every future row." + }, + "allLowerLiteralAtomsReady": true, + "proofBoundary": "A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim.", + "nextTheoremAction": "Assemble this with the verified vertex-successor and edge-persistence layers into a split-discharge readiness certificate, or emit the first missing lower atom." + }, + "summary": { + "vertexPresenceAtomCount": 210, + "edgeObstructionAtomCount": 105, + "stableVertexPresenceAtomCount": 4, + "unstableVertexPresenceAtomCount": 206, + "failedVertexPresenceAtomCount": 0, + "allEdgeObstructionsSquarefree": true, + "edgeObstructionCertificateStatus": "literal_edge_obstruction_certificate_verified", + "edgeCongruencePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingDisjointnessStatus": "bounded_disjointness_certified", + "matchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "readyForFirstTheoremPass": true + }, + "nextTheoremActions": [ + "Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N.", + "The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families.", + "Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof.", + "Attack the packet until it either becomes a split lemma or emits a sharper sub-split key." + ], + "splitDischargeReadiness": { + "schema": "erdos.p848_split_discharge_readiness/1", + "readinessId": "D2.2_persist_outP2=99_out25=6_smaller=side18.split_discharge_readiness", + "status": "split_discharge_readiness_candidate", + "proofKind": "lower_atom_assembly_with_explicit_all_n_handoff", + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "splitKey": "outP2=99|out25=6|smaller=side18", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "lowerLayerChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "verified", + "evidence": "8/8 successor vertex-family lemmas verified" + }, + { + "layerId": "A4_edge_obstruction_certificate", + "status": "verified", + "evidence": "literal_edge_obstruction_certificate_verified" + }, + { + "layerId": "A5_edge_congruence_persistence", + "status": "verified", + "evidence": "literal_constant_edge_persistence_verified" + }, + { + "layerId": "A6_matching_disjointness", + "status": "verified", + "evidence": "literal_matching_disjointness_verified" + }, + { + "layerId": "A7_sampled_k_envelope", + "status": "verified_sampled_envelope", + "evidence": "105 >= 85" + } + ], + "blockingChecks": [], + "theoremCandidate": { + "status": "candidate_with_open_all_n_handoff_gaps", + "statement": "For split outP2=99|out25=6|smaller=side18, the exported literal core supplies a disjoint matching of size 105 against the packet K-envelope [85,85].", + "lowerAtomSummary": { + "vertexSuccessorConditionCount": 8, + "verifiedVertexSuccessorCount": 8, + "edgePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingKEnvelopeStatus": "literal_matching_sampled_k_envelope_verified" + } + }, + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "note": "Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "note": "Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "note": "If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families." + } + ], + "proofBoundary": "This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes.", + "nextTheoremAction": "Attack the next p13 split profile or begin the row-universe/symbolic-K handoff once every p13 split has this readiness certificate." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md new file mode 100644 index 0000000..cc4b1bd --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md @@ -0,0 +1,246 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18 + +This is a theorem-facing split atom packet for Problem 848. It is intentionally atomic: one split profile, one common matching core, one K-envelope, and deterministic sub-atoms for the next proof pass. + +## Summary + +- Packet id: `p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18` +- Parent obligation: `D2_p13_matching_lower_bound` +- Target obligation: `D4_matching_bound_implies_sMaxMixed_bound` +- Prime lane: `13` +- Split key: `outP2=99|out25=6|smaller=side18` +- Priority: `high_p13_active_lane` +- Status: `ready_for_symbolic_persistence_work` +- Witnesses: `5` over `7307..7357` +- Common core size: `105` +- K-envelope: `[85,85]`, slack against max K `20` +- Vertex atoms: `210` +- Vertex atoms stable under current split modulus: `4` +- Vertex atoms needing sharper split or parameterization: `206` +- Edge atoms: `105` +- Edge certificate: `literal_edge_obstruction_certificate_verified` +- Edge congruence persistence: `literal_constant_edge_persistence_verified` +- Disjointness: `bounded_disjointness_certified` +- Matching/K certificate: `literal_matching_sampled_k_envelope_verified` + +## Goal + +Prove that the 105-edge common matching core persists for all p=13 threatening rows in split outP2=99|out25=6|smaller=side18, or replace it with a parameterized extension core. + +## Falsifier Boundary + +A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size. + +## Next Theorem Actions + +- Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N. +- The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families. +- Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof. +- Attack the packet until it either becomes a split lemma or emits a sharper sub-split key. + +## K Envelope + +- Status: `bounded_core_meets_sampled_K_envelope` +- Common core count: `105` +- Max required K: `85` +- Min matching slack: `20` + +## Matching And K-Envelope Certificate + +- Status: `literal_matching_sampled_k_envelope_verified` +- Proof kind: `literal_disjoint_matching_plus_sampled_k_envelope` +- Matching proof: `literal_matching_disjointness_verified` +- K proof: `sampled_k_envelope_dominated_by_literal_core` +- K inequality: `105 >= 85` +- Proof boundary: A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim. + +## Split Discharge Readiness + +- Status: `split_discharge_readiness_candidate` +- Proof kind: `lower_atom_assembly_with_explicit_all_n_handoff` +- Theorem candidate: `candidate_with_open_all_n_handoff_gaps` +- Blocking lower checks: `0` +- Open all-N handoff gaps: `3` +- Proof boundary: This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes. +- Handoff gap `row_universe_split_coverage` [open]: Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile. +- Handoff gap `universal_k_formula_lift` [open]: Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane. +- Handoff gap `literal_to_parameterized_vertex_guard` [open_if_vertices_move]: If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families. + +## Vertex Presence Stability + +- Split modulus: `4225` +- Witness rows: `5` +- Stable under current split modulus: `4` +- Needs sharper split or parametric witness: `206` +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V1.left_32`: side side7, value 32, first square witness {"divisor":3,"square":9,"quotient":17177,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V2.left_57`: side side7, value 57, first square witness {"divisor":2,"square":4,"quotient":68842,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V3.left_157`: side side7, value 157, first square witness {"divisor":2,"square":4,"quotient":189617,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V4.left_257`: side side7, value 257, first square witness {"divisor":2,"square":4,"quotient":310392,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V5.left_357`: side side7, value 357, first square witness {"divisor":2,"square":4,"quotient":431167,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V6.left_457`: side side7, value 457, first square witness {"divisor":2,"square":4,"quotient":551942,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V7.left_482`: side side7, value 482, first square witness {"divisor":3,"square":9,"quotient":258727,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.2_persist_outP2=99_out25=6_smaller=side18.V8.left_557`: side side7, value 557, first square witness {"divisor":2,"square":4,"quotient":672717,"stableUnderCurrentSplitModulus":false} + +## Vertex Presence Refinement + +- Status: `literal_core_requires_sharper_square_witness_split` +- Deterministic move: `emit_successor_atoms_by_square_witness_residue` +- Refinement condition count: `8` +- Covered unstable atoms: `206` +- Uncovered unstable atoms: `0` +- Proof boundary: These square-witness residue classes explain the bounded literal vertex-presence instability; each successor split still needs a theorem-facing persistence proof before it can support an all-N claim. +- Condition `square_4_outsider_3`: out mod 4 = 3, atoms=142, combined modulus=16900, successor=`outP2=99|out25=6|smaller=side18|out4=3` +- Condition `square_9_outsider_7`: out mod 9 = 7, atoms=48, combined modulus=38025, successor=`outP2=99|out25=6|smaller=side18|out9=7` +- Condition `square_49_outsider_29`: out mod 49 = 29, atoms=8, combined modulus=207025, successor=`outP2=99|out25=6|smaller=side18|out49=29` +- Condition `square_121_outsider_112`: out mod 121 = 112, atoms=3, combined modulus=511225, successor=`outP2=99|out25=6|smaller=side18|out121=112` +- Condition `square_961_outsider_26`: out mod 961 = 26, atoms=2, combined modulus=4060225, successor=`outP2=99|out25=6|smaller=side18|out961=26` +- Condition `square_289_outsider_207`: out mod 289 = 207, atoms=1, combined modulus=1221025, successor=`outP2=99|out25=6|smaller=side18|out289=207` +- Condition `square_361_outsider_138`: out mod 361 = 138, atoms=1, combined modulus=1525225, successor=`outP2=99|out25=6|smaller=side18|out361=138` +- Condition `square_1849_outsider_1133`: out mod 1849 = 1133, atoms=1, combined modulus=7812025, successor=`outP2=99|out25=6|smaller=side18|out1849=1133` + +## Edge Obstruction Certificate + +- Status: `literal_edge_obstruction_certificate_verified` +- Proof kind: `literal_product_plus_one_squarefree_missing_edge_certificate` +- Edge atoms: `105` +- Squarefree edge atoms: `105` +- Non-squarefree edge atoms: `0` +- Product-plus-one range: `{"min":2177,"max":50737402}` +- Mod 25 classes: `1` +- Prime-residue classes: `75` +- Prime-square fingerprints: `105` +- Proof boundary: This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim. +- Mod25 class `7:18`: edges=105 +- Prime-residue class `0:6:1`: edges=3 +- Prime-residue class `12:5:9`: edges=3 +- Prime-residue class `2:8:4`: edges=3 +- Prime-residue class `5:11:4`: edges=3 +- Prime-residue class `6:12:8`: edges=3 +- Prime-residue class `9:2:6`: edges=3 +- Prime-residue class `1:11:12`: edges=2 +- Prime-residue class `1:8:9`: edges=2 +- Prime-residue class `10:3:5`: edges=2 +- Prime-residue class `10:4:2`: edges=2 +- Prime-residue class `10:7:6`: edges=2 +- Prime-residue class `11:12:3`: edges=2 +- Prime-residue class `2:3:7`: edges=2 + +## Edge Congruence Persistence + +- Status: `literal_constant_edge_persistence_verified` +- Proof kind: `constant_pair_squarefree_invariant` +- Edge atoms: `105` +- Verified edge atoms: `105` +- Failed edge atoms: `0` +- Depends on sampled N: `no` +- Depends on witness outsider: `no` +- Proof boundary: This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions. +- Family `D2.2_persist_outP2=99_out25=6_smaller=side18.edge_constant_squarefree_family`: status=`congruence_persistence_family_verified`, edges=105, proof=constant_pair_squarefree_invariant + +## Matching Core + +- Pair (32, 68); residues mod25 7:18, mod p 6:3, mod p^2 32:68; product+1 mod p^2 149 +- Pair (57, 93); residues mod25 7:18, mod p 5:2, mod p^2 57:93; product+1 mod p^2 63 +- Pair (157, 193); residues mod25 7:18, mod p 1:11, mod p^2 157:24; product+1 mod p^2 51 +- Pair (257, 293); residues mod25 7:18, mod p 10:7, mod p^2 88:124; product+1 mod p^2 97 +- Pair (357, 268); residues mod25 7:18, mod p 6:8, mod p^2 19:99; product+1 mod p^2 23 +- Pair (457, 393); residues mod25 7:18, mod p 2:3, mod p^2 119:55; product+1 mod p^2 124 +- Pair (482, 468); residues mod25 7:18, mod p 1:0, mod p^2 144:130; product+1 mod p^2 131 +- Pair (557, 493); residues mod25 7:18, mod p 11:12, mod p^2 50:155; product+1 mod p^2 146 +- Pair (632, 518); residues mod25 7:18, mod p 8:11, mod p^2 125:11; product+1 mod p^2 24 +- Pair (657, 593); residues mod25 7:18, mod p 7:8, mod p^2 150:86; product+1 mod p^2 57 +- Pair (707, 743); residues mod25 7:18, mod p 5:2, mod p^2 31:67; product+1 mod p^2 50 +- Pair (757, 693); residues mod25 7:18, mod p 3:4, mod p^2 81:17; product+1 mod p^2 26 +- Pair (857, 793); residues mod25 7:18, mod p 12:0, mod p^2 12:117; product+1 mod p^2 53 +- Pair (932, 893); residues mod25 7:18, mod p 9:9, mod p^2 87:48; product+1 mod p^2 121 +- Pair (957, 968); residues mod25 7:18, mod p 8:6, mod p^2 112:123; product+1 mod p^2 88 +- Pair (1007, 1418); residues mod25 7:18, mod p 6:1, mod p^2 162:66; product+1 mod p^2 46 +- Pair (1057, 993); residues mod25 7:18, mod p 4:5, mod p^2 43:148; product+1 mod p^2 112 +- Pair (1082, 1193); residues mod25 7:18, mod p 3:10, mod p^2 68:10; product+1 mod p^2 5 +- Pair (1157, 1093); residues mod25 7:18, mod p 0:1, mod p^2 143:79; product+1 mod p^2 144 +- Pair (1257, 1293); residues mod25 7:18, mod p 9:6, mod p^2 74:110; product+1 mod p^2 29 +- Pair (1282, 1393); residues mod25 7:18, mod p 8:2, mod p^2 99:41; product+1 mod p^2 4 +- Pair (1357, 1493); residues mod25 7:18, mod p 5:11, mod p^2 5:141; product+1 mod p^2 30 +- Pair (1382, 1593); residues mod25 7:18, mod p 4:7, mod p^2 30:72; product+1 mod p^2 133 +- Pair (1457, 1868); residues mod25 7:18, mod p 1:9, mod p^2 105:9; product+1 mod p^2 101 +- Pair (1557, 1693); residues mod25 7:18, mod p 10:3, mod p^2 36:3; product+1 mod p^2 109 +- Pair (1607, 1643); residues mod25 7:18, mod p 8:5, mod p^2 86:122; product+1 mod p^2 15 +- Pair (1657, 1793); residues mod25 7:18, mod p 6:12, mod p^2 136:103; product+1 mod p^2 151 +- Pair (1757, 1893); residues mod25 7:18, mod p 2:8, mod p^2 67:34; product+1 mod p^2 82 +- Pair (1832, 1993); residues mod25 7:18, mod p 12:4, mod p^2 142:134; product+1 mod p^2 101 +- Pair (1857, 2093); residues mod25 7:18, mod p 11:0, mod p^2 167:65; product+1 mod p^2 40 +- Pair (1957, 2193); residues mod25 7:18, mod p 7:9, mod p^2 98:165; product+1 mod p^2 116 +- Pair (2057, 2318); residues mod25 7:18, mod p 3:4, mod p^2 29:121; product+1 mod p^2 130 +- Pair (2157, 2293); residues mod25 7:18, mod p 12:5, mod p^2 129:96; product+1 mod p^2 48 +- Pair (2232, 2393); residues mod25 7:18, mod p 9:1, mod p^2 35:27; product+1 mod p^2 101 +- Pair (2257, 2493); residues mod25 7:18, mod p 8:10, mod p^2 60:127; product+1 mod p^2 16 +- Pair (2282, 2543); residues mod25 7:18, mod p 7:8, mod p^2 85:8; product+1 mod p^2 5 +- Pair (2357, 2568); residues mod25 7:18, mod p 4:7, mod p^2 160:33; product+1 mod p^2 42 +- Pair (2457, 2593); residues mod25 7:18, mod p 0:6, mod p^2 91:58; product+1 mod p^2 40 +- Pair (2507, 2768); residues mod25 7:18, mod p 11:12, mod p^2 141:64; product+1 mod p^2 68 +- Pair (2557, 2693); residues mod25 7:18, mod p 9:2, mod p^2 22:158; product+1 mod p^2 97 +- Pair (2657, 2793); residues mod25 7:18, mod p 5:11, mod p^2 122:89; product+1 mod p^2 43 +- Pair (2732, 2893); residues mod25 7:18, mod p 2:7, mod p^2 28:20; product+1 mod p^2 54 +- Pair (2757, 2993); residues mod25 7:18, mod p 1:3, mod p^2 53:120; product+1 mod p^2 108 +- Pair (2857, 3093); residues mod25 7:18, mod p 10:12, mod p^2 153:51; product+1 mod p^2 30 +- Pair (2957, 2918); residues mod25 7:18, mod p 6:6, mod p^2 84:45; product+1 mod p^2 63 +- Pair (3057, 3193); residues mod25 7:18, mod p 2:8, mod p^2 15:151; product+1 mod p^2 69 +- Pair (3157, 3293); residues mod25 7:18, mod p 11:4, mod p^2 115:82; product+1 mod p^2 136 +- Pair (3182, 3393); residues mod25 7:18, mod p 10:0, mod p^2 140:13; product+1 mod p^2 131 +- Pair (3257, 3218); residues mod25 7:18, mod p 7:7, mod p^2 46:7; product+1 mod p^2 154 +- Pair (3357, 3593); residues mod25 7:18, mod p 3:5, mod p^2 146:44; product+1 mod p^2 3 +- Pair (3407, 3443); residues mod25 7:18, mod p 1:11, mod p^2 27:63; product+1 mod p^2 12 +- Pair (3457, 3493); residues mod25 7:18, mod p 12:9, mod p^2 77:113; product+1 mod p^2 83 +- Pair (3557, 3668); residues mod25 7:18, mod p 8:2, mod p^2 8:119; product+1 mod p^2 108 +- Pair (3632, 3693); residues mod25 7:18, mod p 5:1, mod p^2 83:144; product+1 mod p^2 123 +- Pair (3657, 3793); residues mod25 7:18, mod p 4:10, mod p^2 108:75; product+1 mod p^2 158 +- Pair (3757, 3893); residues mod25 7:18, mod p 0:6, mod p^2 39:6; product+1 mod p^2 66 +- Pair (3807, 4118); residues mod25 7:18, mod p 11:10, mod p^2 89:62; product+1 mod p^2 111 +- Pair (3857, 3993); residues mod25 7:18, mod p 9:2, mod p^2 139:106; product+1 mod p^2 32 +- Pair (3957, 4093); residues mod25 7:18, mod p 5:11, mod p^2 70:37; product+1 mod p^2 56 +- Pair (4057, 4193); residues mod25 7:18, mod p 1:7, mod p^2 1:137; product+1 mod p^2 138 +- Pair (4082, 4143); residues mod25 7:18, mod p 0:9, mod p^2 26:87; product+1 mod p^2 66 +- Pair (4157, 4293); residues mod25 7:18, mod p 10:3, mod p^2 101:68; product+1 mod p^2 109 +- Pair (4257, 4393); residues mod25 7:18, mod p 6:12, mod p^2 32:168; product+1 mod p^2 138 +- Pair (4307, 4343); residues mod25 7:18, mod p 4:1, mod p^2 82:118; product+1 mod p^2 44 +- Pair (4357, 4493); residues mod25 7:18, mod p 2:8, mod p^2 132:99; product+1 mod p^2 56 +- Pair (4457, 4568); residues mod25 7:18, mod p 11:5, mod p^2 63:5; product+1 mod p^2 147 +- Pair (4532, 4593); residues mod25 7:18, mod p 8:4, mod p^2 138:30; product+1 mod p^2 85 +- Pair (4557, 4693); residues mod25 7:18, mod p 7:0, mod p^2 163:130; product+1 mod p^2 66 +- Pair (4657, 4768); residues mod25 7:18, mod p 3:10, mod p^2 94:36; product+1 mod p^2 5 +- Pair (4682, 4793); residues mod25 7:18, mod p 2:9, mod p^2 119:61; product+1 mod p^2 162 +- Pair (4757, 4893); residues mod25 7:18, mod p 12:5, mod p^2 25:161; product+1 mod p^2 139 +- Pair (4857, 4993); residues mod25 7:18, mod p 8:1, mod p^2 125:92; product+1 mod p^2 9 +- Pair (4957, 5093); residues mod25 7:18, mod p 4:10, mod p^2 56:23; product+1 mod p^2 106 +- Pair (4982, 5018); residues mod25 7:18, mod p 3:0, mod p^2 81:117; product+1 mod p^2 14 +- Pair (5057, 5193); residues mod25 7:18, mod p 0:6, mod p^2 156:123; product+1 mod p^2 92 +- Pair (5157, 5293); residues mod25 7:18, mod p 9:2, mod p^2 87:54; product+1 mod p^2 136 +- Pair (5207, 5243); residues mod25 7:18, mod p 7:4, mod p^2 137:4; product+1 mod p^2 42 +- Pair (5257, 5368); residues mod25 7:18, mod p 5:12, mod p^2 18:129; product+1 mod p^2 126 +- Pair (5357, 5468); residues mod25 7:18, mod p 1:8, mod p^2 118:60; product+1 mod p^2 152 +- Pair (5432, 5393); residues mod25 7:18, mod p 11:11, mod p^2 24:154; product+1 mod p^2 148 +- Pair (5457, 5493); residues mod25 7:18, mod p 10:7, mod p^2 49:85; product+1 mod p^2 110 +- Pair (5507, 5918); residues mod25 7:18, mod p 8:3, mod p^2 99:3; product+1 mod p^2 129 +- Pair (5557, 5693); residues mod25 7:18, mod p 6:12, mod p^2 149:116; product+1 mod p^2 47 +- Pair (5657, 5593); residues mod25 7:18, mod p 2:3, mod p^2 80:16; product+1 mod p^2 98 +- Pair (5757, 5793); residues mod25 7:18, mod p 11:8, mod p^2 11:47; product+1 mod p^2 11 +- Pair (5782, 5893); residues mod25 7:18, mod p 10:4, mod p^2 36:147; product+1 mod p^2 54 +- Pair (5857, 5993); residues mod25 7:18, mod p 7:0, mod p^2 111:78; product+1 mod p^2 40 +- Pair (5882, 6093); residues mod25 7:18, mod p 6:9, mod p^2 136:9; product+1 mod p^2 42 +- Pair (5907, 6143); residues mod25 7:18, mod p 5:7, mod p^2 161:59; product+1 mod p^2 36 +- Pair (5957, 6293); residues mod25 7:18, mod p 3:1, mod p^2 42:40; product+1 mod p^2 160 +- Pair (6057, 6193); residues mod25 7:18, mod p 12:5, mod p^2 142:109; product+1 mod p^2 100 +- Pair (6107, 6368); residues mod25 7:18, mod p 10:11, mod p^2 23:115; product+1 mod p^2 111 +- Pair (6157, 6393); residues mod25 7:18, mod p 8:10, mod p^2 73:140; product+1 mod p^2 81 +- Pair (6257, 6593); residues mod25 7:18, mod p 4:2, mod p^2 4:2; product+1 mod p^2 9 +- Pair (6332, 6493); residues mod25 7:18, mod p 1:6, mod p^2 79:71; product+1 mod p^2 33 +- Pair (6357, 6693); residues mod25 7:18, mod p 0:11, mod p^2 104:102; product+1 mod p^2 131 +- Pair (6457, 6793); residues mod25 7:18, mod p 9:7, mod p^2 35:33; product+1 mod p^2 142 +- Pair (6532, 6893); residues mod25 7:18, mod p 6:3, mod p^2 110:133; product+1 mod p^2 97 +- Pair (6557, 6818); residues mod25 7:18, mod p 5:6, mod p^2 135:58; product+1 mod p^2 57 +- Pair (6657, 7093); residues mod25 7:18, mod p 1:8, mod p^2 66:164; product+1 mod p^2 9 +- Pair (6682, 6993); residues mod25 7:18, mod p 0:12, mod p^2 91:64; product+1 mod p^2 79 +- Pair (6757, 7193); residues mod25 7:18, mod p 10:4, mod p^2 166:95; product+1 mod p^2 54 +- Pair (6782, 7043); residues mod25 7:18, mod p 9:10, mod p^2 22:114; product+1 mod p^2 143 +- Pair (6857, 7268); residues mod25 7:18, mod p 6:1, mod p^2 97:1; product+1 mod p^2 98 +- Pair (6957, 7293); residues mod25 7:18, mod p 2:0, mod p^2 28:26; product+1 mod p^2 53 diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json new file mode 100644 index 0000000..112d0d9 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json @@ -0,0 +1,19617 @@ +{ + "schema": "erdos.p848_split_atom_packet/1", + "generatedAt": "2026-04-14T11:46:09.743Z", + "problemId": "848", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "sourcePlanId": "p848_split_core_atomization_master_plan_v1", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "prime": 13, + "splitKey": "outP2=99|out25=14|smaller=side7", + "priority": "highest_singleton_profile", + "status": "ready_for_symbolic_persistence_work", 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"side7", + "value": 407, + "residues": { + "value": 407, + "mod25": 7, + "modP": 4, + "modP2": 69 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 728124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 182031, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 182031, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V8.left_482", + "side": "side7", + "value": 482, + "residues": { + "value": 482, + "mod25": 7, + "modP": 1, + "modP2": 144 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 862299, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 95811, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 95811, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 482 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V9.left_507", + "side": "side7", + "value": 507, + "residues": { + "value": 507, + "mod25": 7, + "modP": 0, + "modP2": 0 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 907024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 226756, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 226756, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 56689, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V10.left_607", + "side": "side7", + "value": 607, + "residues": { + "value": 607, + "mod25": 7, + "modP": 9, + "modP2": 100 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1085924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 271481, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 271481, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V11.left_707", + "side": "side7", + "value": 707, + "residues": { + "value": 707, + "mod25": 7, + "modP": 5, + "modP2": 31 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1264824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 316206, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 316206, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 140536, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 35134, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V12.left_782", + "side": "side7", + "value": 782, + "residues": { + "value": 782, + "mod25": 7, + "modP": 2, + "modP2": 106 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1398999, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 28551, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 28551, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 782 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V13.left_807", + "side": "side7", + "value": 807, + "residues": { + "value": 807, + "mod25": 7, + "modP": 1, + "modP2": 131 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1443724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 360931, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 360931, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V14.left_907", + "side": "side7", + "value": 907, + "residues": { + "value": 907, + "mod25": 7, + "modP": 10, + "modP2": 62 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1622624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 405656, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 405656, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 101414, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V15.left_932", + "side": "side7", + "value": 932, + "residues": { + "value": 932, + "mod25": 7, + "modP": 9, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1667349, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 185261, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 185261, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 932 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V16.left_982", + "side": "side7", + "value": 982, + "residues": { + "value": 982, + "mod25": 7, + "modP": 7, + "modP2": 137 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1756799, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 14519, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 14519, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 982 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V17.left_1007", + "side": "side7", + "value": 1007, + "residues": { + "value": 1007, + "mod25": 7, + "modP": 6, + "modP2": 162 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1801524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 450381, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 450381, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V18.left_1107", + "side": "side7", + "value": 1107, + "residues": { + "value": 1107, + "mod25": 7, + "modP": 2, + "modP2": 93 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1980424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 495106, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 495106, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V19.left_1157", + "side": "side7", + "value": 1157, + "residues": { + "value": 1157, + "mod25": 7, + "modP": 0, + "modP2": 143 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2069874, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 229986, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 229986, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 25554, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1157 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V20.left_1207", + "side": "side7", + "value": 1207, + "residues": { + "value": 1207, + "mod25": 7, + "modP": 11, + "modP2": 24 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2159324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 539831, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 539831, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V21.left_1282", + "side": "side7", + "value": 1282, + "residues": { + "value": 1282, + "mod25": 7, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2293499, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 13571, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 13571, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 13571, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove left core vertex 1282 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V22.left_1307", + "side": "side7", + "value": 1307, + "residues": { + "value": 1307, + "mod25": 7, + "modP": 7, + "modP2": 124 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2338224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 584556, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 584556, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 146139, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V23.left_1382", + "side": "side7", + "value": 1382, + "residues": { + "value": 1382, + "mod25": 7, + "modP": 4, + "modP2": 30 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2472399, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 274711, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 274711, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1382 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V24.left_1407", + "side": "side7", + "value": 1407, + "residues": { + "value": 1407, + "mod25": 7, + "modP": 3, + "modP2": 55 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2517124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 629281, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 629281, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V25.left_1507", + "side": "side7", + "value": 1507, + "residues": { + "value": 1507, + "mod25": 7, + "modP": 12, + "modP2": 155 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2696024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 674006, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 674006, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V26.left_1532", + "side": "side7", + "value": 1532, + "residues": { + "value": 1532, + "mod25": 7, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2740749, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 5181, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 23, + "square": 529, + "quotient": 5181, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1532 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V27.left_1607", + "side": "side7", + "value": 1607, + "residues": { + "value": 1607, + "mod25": 7, + "modP": 8, + "modP2": 86 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2874924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 718731, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 718731, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 319436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 79859, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V28.left_1707", + "side": "side7", + "value": 1707, + "residues": { + "value": 1707, + "mod25": 7, + "modP": 4, + "modP2": 17 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3053824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 763456, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 763456, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 190864, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 47716, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 11929, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V29.left_1807", + "side": "side7", + "value": 1807, + "residues": { + "value": 1807, + "mod25": 7, + "modP": 0, + "modP2": 117 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3232724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 808181, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 808181, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V30.left_1832", + "side": "side7", + "value": 1832, + "residues": { + "value": 1832, + "mod25": 7, + "modP": 12, + "modP2": 142 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3277449, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 364161, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 364161, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1832 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V31.left_1907", + "side": "side7", + "value": 1907, + "residues": { + "value": 1907, + "mod25": 7, + "modP": 9, + "modP2": 48 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3411624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 852906, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 852906, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V32.left_2007", + "side": "side7", + "value": 2007, + "residues": { + "value": 2007, + "mod25": 7, + "modP": 5, + "modP2": 148 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3590524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 897631, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 897631, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 73276, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 18319, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V33.left_2057", + "side": "side7", + "value": 2057, + "residues": { + "value": 2057, + "mod25": 7, + "modP": 3, + "modP2": 29 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3679974, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 408886, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 408886, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2057 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V34.left_2107", + "side": "side7", + "value": 2107, + "residues": { + "value": 2107, + "mod25": 7, + "modP": 1, + "modP2": 79 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3769424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 942356, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 942356, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 235589, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V35.left_2207", + "side": "side7", + "value": 2207, + "residues": { + "value": 2207, + "mod25": 7, + "modP": 10, + "modP2": 10 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3948324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 987081, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 987081, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V36.left_2282", + "side": "side7", + "value": 2282, + "residues": { + "value": 2282, + "mod25": 7, + "modP": 7, + "modP2": 85 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4082499, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 453611, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 453611, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2282 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V37.left_2307", + "side": "side7", + "value": 2307, + "residues": { + "value": 2307, + "mod25": 7, + "modP": 6, + "modP2": 110 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4127224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1031806, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1031806, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V38.left_2407", + "side": "side7", + "value": 2407, + "residues": { + "value": 2407, + "mod25": 7, + "modP": 2, + "modP2": 41 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4306124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1076531, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1076531, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V39.left_2507", + "side": "side7", + "value": 2507, + "residues": { + "value": 2507, + "mod25": 7, + "modP": 11, + "modP2": 141 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4485024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1121256, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1121256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 498336, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 280314, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 124584, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 31146, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V40.left_2607", + "side": "side7", + "value": 2607, + "residues": { + "value": 2607, + "mod25": 7, + "modP": 7, + "modP2": 72 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4663924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1165981, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1165981, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V41.left_2707", + "side": "side7", + "value": 2707, + "residues": { + "value": 2707, + "mod25": 7, + "modP": 3, + "modP2": 3 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4842824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1210706, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1210706, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V42.left_2732", + "side": "side7", + "value": 2732, + "residues": { + "value": 2732, + "mod25": 7, + "modP": 2, + "modP2": 28 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4887549, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 543061, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 543061, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2732 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V43.left_2807", + "side": "side7", + "value": 2807, + "residues": { + "value": 2807, + "mod25": 7, + "modP": 12, + "modP2": 103 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5021724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1255431, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1255431, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V44.left_2907", + "side": "side7", + "value": 2907, + "residues": { + "value": 2907, + "mod25": 7, + "modP": 8, + "modP2": 34 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5200624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1300156, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1300156, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 325039, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V45.left_2957", + "side": "side7", + "value": 2957, + "residues": { + "value": 2957, + "mod25": 7, + "modP": 6, + "modP2": 84 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5290074, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 587786, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 587786, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2957 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V46.left_3007", + "side": "side7", + "value": 3007, + "residues": { + "value": 3007, + "mod25": 7, + "modP": 4, + "modP2": 134 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5379524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1344881, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1344881, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V47.left_3107", + "side": "side7", + "value": 3107, + "residues": { + "value": 3107, + "mod25": 7, + "modP": 0, + "modP2": 65 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5558424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1389606, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1389606, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 31, + "square": 961, + "quotient": 5784, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 62, + "square": 3844, + "quotient": 1446, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V48.left_3182", + "side": "side7", + "value": 3182, + "residues": { + "value": 3182, + "mod25": 7, + "modP": 10, + "modP2": 140 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5692599, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 632511, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 632511, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 70279, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3182 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V49.left_3207", + "side": "side7", + "value": 3207, + "residues": { + "value": 3207, + "mod25": 7, + "modP": 9, + "modP2": 165 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5737324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1434331, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1434331, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V50.left_3232", + "side": "side7", + "value": 3232, + "residues": { + "value": 3232, + "mod25": 7, + "modP": 8, + "modP2": 21 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5782049, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 118001, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 118001, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3232 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V51.left_3307", + "side": "side7", + "value": 3307, + "residues": { + "value": 3307, + "mod25": 7, + "modP": 5, + "modP2": 96 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5916224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1479056, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1479056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 369764, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 92441, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V52.left_3407", + "side": "side7", + "value": 3407, + "residues": { + "value": 3407, + "mod25": 7, + "modP": 1, + "modP2": 27 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6095124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1523781, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1523781, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 677236, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 169309, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 19, + "square": 361, + "quotient": 16884, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 38, + "square": 1444, + "quotient": 4221, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 57, + "square": 3249, + "quotient": 1876, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 114, + "square": 12996, + "quotient": 469, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V53.left_3507", + "side": "side7", + "value": 3507, + "residues": { + "value": 3507, + "mod25": 7, + "modP": 10, + "modP2": 127 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6274024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1568506, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1568506, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V54.left_3607", + "side": "side7", + "value": 3607, + "residues": { + "value": 3607, + "mod25": 7, + "modP": 6, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6452924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1613231, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1613231, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V55.left_3632", + "side": "side7", + "value": 3632, + "residues": { + "value": 3632, + "mod25": 7, + "modP": 5, + "modP2": 83 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6497649, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 721961, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 721961, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3632 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V56.left_3707", + "side": "side7", + "value": 3707, + "residues": { + "value": 3707, + "mod25": 7, + "modP": 2, + "modP2": 158 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6631824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1657956, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1657956, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 414489, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V57.left_3807", + "side": "side7", + "value": 3807, + "residues": { + "value": 3807, + "mod25": 7, + "modP": 11, + "modP2": 89 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6810724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1702681, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1702681, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V58.left_3857", + "side": "side7", + "value": 3857, + "residues": { + "value": 3857, + "mod25": 7, + "modP": 9, + "modP2": 139 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6900174, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 766686, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 766686, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3857 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V59.left_3907", + "side": "side7", + "value": 3907, + "residues": { + "value": 3907, + "mod25": 7, + "modP": 7, + "modP2": 20 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6989624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1747406, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1747406, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V60.left_4007", + "side": "side7", + "value": 4007, + "residues": { + "value": 4007, + "mod25": 7, + "modP": 3, + "modP2": 120 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7168524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1792131, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1792131, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 59244, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 14811, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V61.left_4082", + "side": "side7", + "value": 4082, + "residues": { + "value": 4082, + "mod25": 7, + "modP": 0, + "modP2": 26 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7302699, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 811411, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 811411, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4082 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V62.left_4107", + "side": "side7", + "value": 4107, + "residues": { + "value": 4107, + "mod25": 7, + "modP": 12, + "modP2": 51 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7347424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1836856, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1836856, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 459214, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V63.left_4207", + "side": "side7", + "value": 4207, + "residues": { + "value": 4207, + "mod25": 7, + "modP": 8, + "modP2": 151 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7526324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1881581, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1881581, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V64.left_4307", + "side": "side7", + "value": 4307, + "residues": { + "value": 4307, + "mod25": 7, + "modP": 4, + "modP2": 82 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7705224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1926306, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1926306, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 856136, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 214034, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V65.left_4407", + "side": "side7", + "value": 4407, + "residues": { + "value": 4407, + "mod25": 7, + "modP": 0, + "modP2": 13 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7884124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1971031, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1971031, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 71, + "square": 5041, + "quotient": 1564, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 142, + "square": 20164, + "quotient": 391, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V66.left_4457", + "side": "side7", + "value": 4457, + "residues": { + "value": 4457, + "mod25": 7, + "modP": 11, + "modP2": 63 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7973574, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 162726, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 162726, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4457 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V67.left_4507", + "side": "side7", + "value": 4507, + "residues": { + "value": 4507, + "mod25": 7, + "modP": 9, + "modP2": 113 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8063024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2015756, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2015756, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503939, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V68.left_4532", + "side": "side7", + "value": 4532, + "residues": { + "value": 4532, + "mod25": 7, + "modP": 8, + "modP2": 138 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8107749, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 900861, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 900861, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4532 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V69.left_4607", + "side": "side7", + "value": 4607, + "residues": { + "value": 4607, + "mod25": 7, + "modP": 5, + "modP2": 44 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8241924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2060481, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2060481, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V70.left_4707", + "side": "side7", + "value": 4707, + "residues": { + "value": 4707, + "mod25": 7, + "modP": 1, + "modP2": 144 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8420824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2105206, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2105206, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V71.left_4757", + "side": "side7", + "value": 4757, + "residues": { + "value": 4757, + "mod25": 7, + "modP": 12, + "modP2": 25 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8510274, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 945586, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 945586, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4757 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V72.left_4807", + "side": "side7", + "value": 4807, + "residues": { + "value": 4807, + "mod25": 7, + "modP": 10, + "modP2": 75 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8599724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2149931, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2149931, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V73.left_4907", + "side": "side7", + "value": 4907, + "residues": { + "value": 4907, + "mod25": 7, + "modP": 6, + "modP2": 6 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8778624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2194656, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2194656, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 548664, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 137166, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V74.left_4982", + "side": "side7", + "value": 4982, + "residues": { + "value": 4982, + "mod25": 7, + "modP": 3, + "modP2": 81 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8912799, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 990311, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 990311, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4982 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V75.left_5007", + "side": "side7", + "value": 5007, + "residues": { + "value": 5007, + "mod25": 7, + "modP": 2, + "modP2": 106 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8957524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2239381, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2239381, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V76.left_5107", + "side": "side7", + "value": 5107, + "residues": { + "value": 5107, + "mod25": 7, + "modP": 11, + "modP2": 37 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9136424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2284106, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2284106, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 47, + "square": 2209, + "quotient": 4136, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 94, + "square": 8836, + "quotient": 1034, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V77.left_5207", + "side": "side7", + "value": 5207, + "residues": { + "value": 5207, + "mod25": 7, + "modP": 7, + "modP2": 137 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9315324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2328831, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2328831, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1035036, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 258759, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 115004, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 28751, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V78.left_5307", + "side": "side7", + "value": 5307, + "residues": { + "value": 5307, + "mod25": 7, + "modP": 3, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9494224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2373556, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2373556, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 593389, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V79.left_5407", + "side": "side7", + "value": 5407, + "residues": { + "value": 5407, + "mod25": 7, + "modP": 12, + "modP2": 168 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9673124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2418281, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2418281, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V80.left_5432", + "side": "side7", + "value": 5432, + "residues": { + "value": 5432, + "mod25": 7, + "modP": 11, + "modP2": 24 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9717849, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1079761, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1079761, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5432 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V81.left_5507", + "side": "side7", + "value": 5507, + "residues": { + "value": 5507, + "mod25": 7, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9852024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2463006, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 58296, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2463006, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 58296, + "stableUnderCurrentSplitModulus": true + }, + { + "divisor": 26, + "square": 676, + "quotient": 14574, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V82.left_5607", + "side": "side7", + "value": 5607, + "residues": { + "value": 5607, + "mod25": 7, + "modP": 4, + "modP2": 30 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10030924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2507731, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2507731, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V83.left_5657", + "side": "side7", + "value": 5657, + "residues": { + "value": 5657, + "mod25": 7, + "modP": 2, + "modP2": 80 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10120374, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1124486, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1124486, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5657 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V84.left_5682", + "side": "side7", + "value": 5682, + "residues": { + "value": 5682, + "mod25": 7, + "modP": 1, + "modP2": 105 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10165099, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 207451, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 207451, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5682 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V85.left_5707", + "side": "side7", + "value": 5707, + "residues": { + "value": 5707, + "mod25": 7, + "modP": 0, + "modP2": 130 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10209824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2552456, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2552456, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 638114, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V86.left_5807", + "side": "side7", + "value": 5807, + "residues": { + "value": 5807, + "mod25": 7, + "modP": 9, + "modP2": 61 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10388724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2597181, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2597181, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V87.left_5882", + "side": "side7", + "value": 5882, + "residues": { + "value": 5882, + "mod25": 7, + "modP": 6, + "modP2": 136 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10522899, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1169211, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1169211, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5882 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V88.left_5907", + "side": "side7", + "value": 5907, + "residues": { + "value": 5907, + "mod25": 7, + "modP": 5, + "modP2": 161 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10567624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2641906, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2641906, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V89.left_6007", + "side": "side7", + "value": 6007, + "residues": { + "value": 6007, + "mod25": 7, + "modP": 1, + "modP2": 92 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10746524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2686631, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2686631, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V90.left_6107", + "side": "side7", + "value": 6107, + "residues": { + "value": 6107, + "mod25": 7, + "modP": 10, + "modP2": 23 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10925424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2731356, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2731356, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1213936, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 682839, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 303484, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 75871, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V91.left_6207", + "side": "side7", + "value": 6207, + "residues": { + "value": 6207, + "mod25": 7, + "modP": 6, + "modP2": 123 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11104324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2776081, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2776081, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V92.left_6307", + "side": "side7", + "value": 6307, + "residues": { + "value": 6307, + "mod25": 7, + "modP": 2, + "modP2": 54 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11283224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2820806, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2820806, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V93.left_6332", + "side": "side7", + "value": 6332, + "residues": { + "value": 6332, + "mod25": 7, + "modP": 1, + "modP2": 79 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11327949, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1258661, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1258661, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6332 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V94.left_6407", + "side": "side7", + "value": 6407, + "residues": { + "value": 6407, + "mod25": 7, + "modP": 11, + "modP2": 154 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11462124, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2865531, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2865531, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6407 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V95.left_6507", + "side": "side7", + "value": 6507, + "residues": { + "value": 6507, + "mod25": 7, + "modP": 7, + "modP2": 85 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11641024, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2910256, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2910256, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 727564, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 181891, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6507 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V96.left_6557", + "side": "side7", + "value": 6557, + "residues": { + "value": 6557, + "mod25": 7, + "modP": 5, + "modP2": 135 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11730474, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1303386, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1303386, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6557 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V97.left_6607", + "side": "side7", + "value": 6607, + "residues": { + "value": 6607, + "mod25": 7, + "modP": 3, + "modP2": 16 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11819924, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2954981, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2954981, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6607 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V98.left_6707", + "side": "side7", + "value": 6707, + "residues": { + "value": 6707, + "mod25": 7, + "modP": 12, + "modP2": 116 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11998824, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2999706, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2999706, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6707 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V99.left_6782", + "side": "side7", + "value": 6782, + "residues": { + "value": 6782, + "mod25": 7, + "modP": 9, + "modP2": 22 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12132999, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1348111, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1348111, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6782 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V100.left_6807", + "side": "side7", + "value": 6807, + "residues": { + "value": 6807, + "mod25": 7, + "modP": 8, + "modP2": 47 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12177724, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3044431, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3044431, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6807 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V101.left_6907", + "side": "side7", + "value": 6907, + "residues": { + "value": 6907, + "mod25": 7, + "modP": 4, + "modP2": 147 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12356624, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3089156, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3089156, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 772289, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 252176, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 63044, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 15761, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6907 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V102.left_6957", + "side": "side7", + "value": 6957, + "residues": { + "value": 6957, + "mod25": 7, + "modP": 2, + "modP2": 28 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12446074, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 43066, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 43066, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6957 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V103.left_7007", + "side": "side7", + "value": 7007, + "residues": { + "value": 7007, + "mod25": 7, + "modP": 0, + "modP2": 78 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12535524, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3133881, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3133881, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1392836, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 348209, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7007 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V104.left_7032", + "side": "side7", + "value": 7032, + "residues": { + "value": 7032, + "mod25": 7, + "modP": 12, + "modP2": 103 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12580249, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 103969, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 103969, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7032 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V105.left_7107", + "side": "side7", + "value": 7107, + "residues": { + "value": 7107, + "mod25": 7, + "modP": 9, + "modP2": 9 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12714424, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3178606, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3178606, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7107 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V106.left_7207", + "side": "side7", + "value": 7207, + "residues": { + "value": 7207, + "mod25": 7, + "modP": 5, + "modP2": 109 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12893324, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3223331, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3223331, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7207 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V107.left_7232", + "side": "side7", + "value": 7232, + "residues": { + "value": 7232, + "mod25": 7, + "modP": 4, + "modP2": 134 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12938049, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1437561, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1437561, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 159729, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7232 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V108.left_7307", + "side": "side7", + "value": 7307, + "residues": { + "value": 7307, + "mod25": 7, + "modP": 1, + "modP2": 40 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 13072224, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3268056, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3268056, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 817014, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7307 is present in the side7 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V109.right_43", + "side": "side18", + "value": 43, + "residues": { + "value": 43, + "mod25": 18, + "modP": 4, + "modP2": 43 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 76928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 19232, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 19232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 4808, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 1202, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 43 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V110.right_68", + "side": "side18", + "value": 68, + "residues": { + "value": 68, + "mod25": 18, + "modP": 3, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 121653, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 13517, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 13517, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 68 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V111.right_143", + "side": "side18", + "value": 143, + "residues": { + "value": 143, + "mod25": 18, + "modP": 0, + "modP2": 143 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 255828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 63957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 63957, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V112.right_243", + "side": "side18", + "value": 243, + "residues": { + "value": 243, + "mod25": 18, + "modP": 9, + "modP2": 74 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 434728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 108682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 108682, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 8872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 2218, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V113.right_268", + "side": "side18", + "value": 268, + "residues": { + "value": 268, + "mod25": 18, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 479453, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 2837, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 2837, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 2837, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove right core vertex 268 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V114.right_293", + "side": "side18", + "value": 293, + "residues": { + "value": 293, + "mod25": 18, + "modP": 7, + "modP2": 124 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 524178, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 58242, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 58242, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 293 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V115.right_343", + "side": "side18", + "value": 343, + "residues": { + "value": 343, + "mod25": 18, + "modP": 5, + "modP2": 5 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 613628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 153407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 153407, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V116.right_443", + "side": "side18", + "value": 443, + "residues": { + "value": 443, + "mod25": 18, + "modP": 1, + "modP2": 105 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 792528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 198132, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 198132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 49533, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V117.right_518", + "side": "side18", + "value": 518, + "residues": { + "value": 518, + "mod25": 18, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 926703, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 102967, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 102967, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 518 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V118.right_543", + "side": "side18", + "value": 543, + "residues": { + "value": 543, + "mod25": 18, + "modP": 10, + "modP2": 36 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 971428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 242857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 242857, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V119.right_643", + "side": "side18", + "value": 643, + "residues": { + "value": 643, + "mod25": 18, + "modP": 6, + "modP2": 136 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1150328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 287582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 287582, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V120.right_743", + "side": "side18", + "value": 743, + "residues": { + "value": 743, + "mod25": 18, + "modP": 2, + "modP2": 67 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1329228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 332307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 332307, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 147692, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 36923, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V121.right_843", + "side": "side18", + "value": 843, + "residues": { + "value": 843, + "mod25": 18, + "modP": 11, + "modP2": 167 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1508128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 377032, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 377032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 94258, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V122.right_943", + "side": "side18", + "value": 943, + "residues": { + "value": 943, + "mod25": 18, + "modP": 7, + "modP2": 98 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1687028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 421757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 421757, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V123.right_968", + "side": "side18", + "value": 968, + "residues": { + "value": 968, + "mod25": 18, + "modP": 6, + "modP2": 123 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1731753, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 192417, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 192417, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 968 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V124.right_1043", + "side": "side18", + "value": 1043, + "residues": { + "value": 1043, + "mod25": 18, + "modP": 3, + "modP2": 29 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1865928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 466482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 466482, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V125.right_1143", + "side": "side18", + "value": 1143, + "residues": { + "value": 1143, + "mod25": 18, + "modP": 12, + "modP2": 129 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2044828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 511207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 511207, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V126.right_1193", + "side": "side18", + "value": 1193, + "residues": { + "value": 1193, + "mod25": 18, + "modP": 10, + "modP2": 10 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2134278, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 237142, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 237142, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1193 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V127.right_1243", + "side": "side18", + "value": 1243, + "residues": { + "value": 1243, + "mod25": 18, + "modP": 8, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2223728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 555932, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 555932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 138983, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V128.right_1343", + "side": "side18", + "value": 1343, + "residues": { + "value": 1343, + "mod25": 18, + "modP": 4, + "modP2": 160 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2402628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 600657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 600657, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V129.right_1418", + "side": "side18", + "value": 1418, + "residues": { + "value": 1418, + "mod25": 18, + "modP": 1, + "modP2": 66 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2536803, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 281867, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 281867, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1418 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V130.right_1443", + "side": "side18", + "value": 1443, + "residues": { + "value": 1443, + "mod25": 18, + "modP": 0, + "modP2": 91 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2581528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 645382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 645382, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V131.right_1468", + "side": "side18", + "value": 1468, + "residues": { + "value": 1468, + "mod25": 18, + "modP": 12, + "modP2": 116 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2626253, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 53597, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 53597, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1468 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V132.right_1543", + "side": "side18", + "value": 1543, + "residues": { + "value": 1543, + "mod25": 18, + "modP": 9, + "modP2": 22 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2760428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 690107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 690107, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V133.right_1643", + "side": "side18", + "value": 1643, + "residues": { + "value": 1643, + "mod25": 18, + "modP": 5, + "modP2": 122 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2939328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 734832, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 734832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 326592, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 183708, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 81648, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 45927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 36288, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 20412, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 9072, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 5103, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 27, + "square": 729, + "quotient": 4032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 36, + "square": 1296, + "quotient": 2268, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 54, + "square": 2916, + "quotient": 1008, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 72, + "square": 5184, + "quotient": 567, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 81, + "square": 6561, + "quotient": 448, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 108, + "square": 11664, + "quotient": 252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 162, + "square": 26244, + "quotient": 112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 216, + "square": 46656, + "quotient": 63, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 324, + "square": 104976, + "quotient": 28, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 648, + "square": 419904, + "quotient": 7, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V134.right_1743", + "side": "side18", + "value": 1743, + "residues": { + "value": 1743, + "mod25": 18, + "modP": 1, + "modP2": 53 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3118228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 779557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 779557, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V135.right_1843", + "side": "side18", + "value": 1843, + "residues": { + "value": 1843, + "mod25": 18, + "modP": 10, + "modP2": 153 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3297128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 824282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 824282, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V136.right_1868", + "side": "side18", + "value": 1868, + "residues": { + "value": 1868, + "mod25": 18, + "modP": 9, + "modP2": 9 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3341853, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 371317, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 371317, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1868 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V137.right_1943", + "side": "side18", + "value": 1943, + "residues": { + "value": 1943, + "mod25": 18, + "modP": 6, + "modP2": 84 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3476028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 869007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 869007, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V138.right_2043", + "side": "side18", + "value": 2043, + "residues": { + "value": 2043, + "mod25": 18, + "modP": 2, + "modP2": 15 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3654928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 913732, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 913732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 228433, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V139.right_2093", + "side": "side18", + "value": 2093, + "residues": { + "value": 2093, + "mod25": 18, + "modP": 0, + "modP2": 65 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3744378, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 416042, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 416042, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2093 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V140.right_2143", + "side": "side18", + "value": 2143, + "residues": { + "value": 2143, + "mod25": 18, + "modP": 11, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 3833828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 958457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 958457, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V141.right_2243", + "side": "side18", + "value": 2243, + "residues": { + "value": 2243, + "mod25": 18, + "modP": 7, + "modP2": 46 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4012728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1003182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1003182, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V142.right_2318", + "side": "side18", + "value": 2318, + "residues": { + "value": 2318, + "mod25": 18, + "modP": 4, + "modP2": 121 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4146903, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 460767, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 460767, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2318 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V143.right_2343", + "side": "side18", + "value": 2343, + "residues": { + "value": 2343, + "mod25": 18, + "modP": 3, + "modP2": 146 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4191628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1047907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1047907, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V144.right_2443", + "side": "side18", + "value": 2443, + "residues": { + "value": 2443, + "mod25": 18, + "modP": 12, + "modP2": 77 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4370528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1092632, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1092632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 273158, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V145.right_2543", + "side": "side18", + "value": 2543, + "residues": { + "value": 2543, + "mod25": 18, + "modP": 8, + "modP2": 8 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4549428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1137357, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1137357, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 505492, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 126373, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V146.right_2643", + "side": "side18", + "value": 2643, + "residues": { + "value": 2643, + "mod25": 18, + "modP": 4, + "modP2": 108 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4728328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1182082, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1182082, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V147.right_2693", + "side": "side18", + "value": 2693, + "residues": { + "value": 2693, + "mod25": 18, + "modP": 2, + "modP2": 158 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4817778, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 98322, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 98322, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2693 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V148.right_2743", + "side": "side18", + "value": 2743, + "residues": { + "value": 2743, + "mod25": 18, + "modP": 0, + "modP2": 39 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4907228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1226807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1226807, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V149.right_2768", + "side": "side18", + "value": 2768, + "residues": { + "value": 2768, + "mod25": 18, + "modP": 12, + "modP2": 64 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4951953, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 550217, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 550217, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2768 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V150.right_2843", + "side": "side18", + "value": 2843, + "residues": { + "value": 2843, + "mod25": 18, + "modP": 9, + "modP2": 139 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5086128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1271532, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1271532, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 317883, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V151.right_2918", + "side": "side18", + "value": 2918, + "residues": { + "value": 2918, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5220303, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 43143, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 43143, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2918 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V152.right_2943", + "side": "side18", + "value": 2943, + "residues": { + "value": 2943, + "mod25": 18, + "modP": 5, + "modP2": 70 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5265028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1316257, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1316257, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V153.right_2993", + "side": "side18", + "value": 2993, + "residues": { + "value": 2993, + "mod25": 18, + "modP": 3, + "modP2": 120 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5354478, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 594942, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 594942, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2993 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V154.right_3043", + "side": "side18", + "value": 3043, + "residues": { + "value": 3043, + "mod25": 18, + "modP": 1, + "modP2": 1 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5443928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1360982, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1360982, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V155.right_3143", + "side": "side18", + "value": 3143, + "residues": { + "value": 3143, + "mod25": 18, + "modP": 10, + "modP2": 101 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5622828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1405707, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1405707, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V156.right_3218", + "side": "side18", + "value": 3218, + "residues": { + "value": 3218, + "mod25": 18, + "modP": 7, + "modP2": 7 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5757003, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 639667, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 639667, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3218 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V157.right_3243", + "side": "side18", + "value": 3243, + "residues": { + "value": 3243, + "mod25": 18, + "modP": 6, + "modP2": 32 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5801728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1450432, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1450432, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 362608, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 90652, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 22663, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V158.right_3343", + "side": "side18", + "value": 3343, + "residues": { + "value": 3343, + "mod25": 18, + "modP": 2, + "modP2": 132 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5980628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1495157, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1495157, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V159.right_3443", + "side": "side18", + "value": 3443, + "residues": { + "value": 3443, + "mod25": 18, + "modP": 11, + "modP2": 63 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6159528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1539882, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1539882, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 684392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 171098, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V160.right_3543", + "side": "side18", + "value": 3543, + "residues": { + "value": 3543, + "mod25": 18, + "modP": 7, + "modP2": 163 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6338428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1584607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1584607, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V161.right_3643", + "side": "side18", + "value": 3643, + "residues": { + "value": 3643, + "mod25": 18, + "modP": 3, + "modP2": 94 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6517328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1629332, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1629332, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 407333, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V162.right_3668", + "side": "side18", + "value": 3668, + "residues": { + "value": 3668, + "mod25": 18, + "modP": 2, + "modP2": 119 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6562053, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 729117, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 729117, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 81013, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3668 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V163.right_3743", + "side": "side18", + "value": 3743, + "residues": { + "value": 3743, + "mod25": 18, + "modP": 12, + "modP2": 25 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6696228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1674057, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1674057, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V164.right_3768", + "side": "side18", + "value": 3768, + "residues": { + "value": 3768, + "mod25": 18, + "modP": 11, + "modP2": 50 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6740953, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 18673, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 18673, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3768 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V165.right_3843", + "side": "side18", + "value": 3843, + "residues": { + "value": 3843, + "mod25": 18, + "modP": 8, + "modP2": 125 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6875128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1718782, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1718782, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V166.right_3893", + "side": "side18", + "value": 3893, + "residues": { + "value": 3893, + "mod25": 18, + "modP": 6, + "modP2": 6 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6964578, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 773842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 773842, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3893 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V167.right_3918", + "side": "side18", + "value": 3918, + "residues": { + "value": 3918, + "mod25": 18, + "modP": 5, + "modP2": 31 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7009303, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 143047, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 143047, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3918 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V168.right_3943", + "side": "side18", + "value": 3943, + "residues": { + "value": 3943, + "mod25": 18, + "modP": 4, + "modP2": 56 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7054028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1763507, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1763507, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V169.right_4043", + "side": "side18", + "value": 4043, + "residues": { + "value": 4043, + "mod25": 18, + "modP": 0, + "modP2": 156 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7232928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1808232, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1808232, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 452058, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V170.right_4068", + "side": "side18", + "value": 4068, + "residues": { + "value": 4068, + "mod25": 18, + "modP": 12, + "modP2": 12 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7277653, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 7573, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 7573, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4068 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V171.right_4118", + "side": "side18", + "value": 4118, + "residues": { + "value": 4118, + "mod25": 18, + "modP": 10, + "modP2": 62 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7367103, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 818567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 818567, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4118 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V172.right_4143", + "side": "side18", + "value": 4143, + "residues": { + "value": 4143, + "mod25": 18, + "modP": 9, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7411828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1852957, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1852957, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V173.right_4243", + "side": "side18", + "value": 4243, + "residues": { + "value": 4243, + "mod25": 18, + "modP": 5, + "modP2": 18 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7590728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1897682, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1897682, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V174.right_4343", + "side": "side18", + "value": 4343, + "residues": { + "value": 4343, + "mod25": 18, + "modP": 1, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7769628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1942407, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1942407, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 863292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 215823, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V175.right_4443", + "side": "side18", + "value": 4443, + "residues": { + "value": 4443, + "mod25": 18, + "modP": 10, + "modP2": 49 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7948528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1987132, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1987132, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 496783, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V176.right_4493", + "side": "side18", + "value": 4493, + "residues": { + "value": 4493, + "mod25": 18, + "modP": 8, + "modP2": 99 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8037978, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 47562, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 13, + "square": 169, + "quotient": 47562, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 47562, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove right core vertex 4493 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V177.right_4543", + "side": "side18", + "value": 4543, + "residues": { + "value": 4543, + "mod25": 18, + "modP": 6, + "modP2": 149 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8127428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2031857, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2031857, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V178.right_4568", + "side": "side18", + "value": 4568, + "residues": { + "value": 4568, + "mod25": 18, + "modP": 5, + "modP2": 5 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8172153, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 908017, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 908017, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4568 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V179.right_4618", + "side": "side18", + "value": 4618, + "residues": { + "value": 4618, + "mod25": 18, + "modP": 3, + "modP2": 55 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8261603, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 89, + "square": 7921, + "quotient": 1043, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 89, + "square": 7921, + "quotient": 1043, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4618 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V180.right_4643", + "side": "side18", + "value": 4643, + "residues": { + "value": 4643, + "mod25": 18, + "modP": 2, + "modP2": 80 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8306328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2076582, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2076582, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V181.right_4743", + "side": "side18", + "value": 4743, + "residues": { + "value": 4743, + "mod25": 18, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8485228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2121307, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2121307, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V182.right_4793", + "side": "side18", + "value": 4793, + "residues": { + "value": 4793, + "mod25": 18, + "modP": 9, + "modP2": 61 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8574678, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 952742, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 952742, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4793 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V183.right_4843", + "side": "side18", + "value": 4843, + "residues": { + "value": 4843, + "mod25": 18, + "modP": 7, + "modP2": 111 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8664128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2166032, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2166032, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 541508, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 135377, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V184.right_4943", + "side": "side18", + "value": 4943, + "residues": { + "value": 4943, + "mod25": 18, + "modP": 3, + "modP2": 42 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8843028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2210757, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2210757, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V185.right_5018", + "side": "side18", + "value": 5018, + "residues": { + "value": 5018, + "mod25": 18, + "modP": 0, + "modP2": 117 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8977203, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 997467, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 997467, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5018 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V186.right_5043", + "side": "side18", + "value": 5043, + "residues": { + "value": 5043, + "mod25": 18, + "modP": 12, + "modP2": 142 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9021928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2255482, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2255482, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V187.right_5143", + "side": "side18", + "value": 5143, + "residues": { + "value": 5143, + "mod25": 18, + "modP": 8, + "modP2": 73 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9200828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2300207, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2300207, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 187772, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 46943, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V188.right_5243", + "side": "side18", + "value": 5243, + "residues": { + "value": 5243, + "mod25": 18, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9379728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2344932, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2344932, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1042192, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 586233, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260548, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 65137, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V189.right_5343", + "side": "side18", + "value": 5343, + "residues": { + "value": 5343, + "mod25": 18, + "modP": 0, + "modP2": 104 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9558628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2389657, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2389657, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V190.right_5443", + "side": "side18", + "value": 5443, + "residues": { + "value": 5443, + "mod25": 18, + "modP": 9, + "modP2": 35 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9737528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2434382, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2434382, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V191.right_5468", + "side": "side18", + "value": 5468, + "residues": { + "value": 5468, + "mod25": 18, + "modP": 8, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9782253, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1086917, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1086917, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5468 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V192.right_5543", + "side": "side18", + "value": 5543, + "residues": { + "value": 5543, + "mod25": 18, + "modP": 5, + "modP2": 135 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9916428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2479107, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2479107, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V193.right_5643", + "side": "side18", + "value": 5643, + "residues": { + "value": 5643, + "mod25": 18, + "modP": 1, + "modP2": 66 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10095328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2523832, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2523832, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 630958, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V194.right_5693", + "side": "side18", + "value": 5693, + "residues": { + "value": 5693, + "mod25": 18, + "modP": 12, + "modP2": 116 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10184778, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131642, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1131642, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 125738, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5693 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V195.right_5743", + "side": "side18", + "value": 5743, + "residues": { + "value": 5743, + "mod25": 18, + "modP": 10, + "modP2": 166 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10274228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2568557, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2568557, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V196.right_5843", + "side": "side18", + "value": 5843, + "residues": { + "value": 5843, + "mod25": 18, + "modP": 6, + "modP2": 97 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10453128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2613282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2613282, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V197.right_5918", + "side": "side18", + "value": 5918, + "residues": { + "value": 5918, + "mod25": 18, + "modP": 3, + "modP2": 3 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10587303, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1176367, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1176367, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5918 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V198.right_5943", + "side": "side18", + "value": 5943, + "residues": { + "value": 5943, + "mod25": 18, + "modP": 2, + "modP2": 28 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10632028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2658007, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2658007, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 87868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 21967, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V199.right_6043", + "side": "side18", + "value": 6043, + "residues": { + "value": 6043, + "mod25": 18, + "modP": 11, + "modP2": 128 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10810928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2702732, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2702732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 675683, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V200.right_6143", + "side": "side18", + "value": 6143, + "residues": { + "value": 6143, + "mod25": 18, + "modP": 7, + "modP2": 59 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10989828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2747457, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2747457, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1221092, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 305273, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V201.right_6243", + "side": "side18", + "value": 6243, + "residues": { + "value": 6243, + "mod25": 18, + "modP": 3, + "modP2": 159 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11168728, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2792182, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2792182, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6243 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V202.right_6293", + "side": "side18", + "value": 6293, + "residues": { + "value": 6293, + "mod25": 18, + "modP": 1, + "modP2": 40 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11258178, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 21282, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 23, + "square": 529, + "quotient": 21282, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6293 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V203.right_6343", + "side": "side18", + "value": 6343, + "residues": { + "value": 6343, + "mod25": 18, + "modP": 12, + "modP2": 90 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11347628, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2836907, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2836907, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6343 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V204.right_6368", + "side": "side18", + "value": 6368, + "residues": { + "value": 6368, + "mod25": 18, + "modP": 11, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11392353, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1265817, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1265817, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 232497, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 25833, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6368 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V205.right_6418", + "side": "side18", + "value": 6418, + "residues": { + "value": 6418, + "mod25": 18, + "modP": 9, + "modP2": 165 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11481803, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 37, + "square": 1369, + "quotient": 8387, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 37, + "square": 1369, + "quotient": 8387, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6418 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V206.right_6443", + "side": "side18", + "value": 6443, + "residues": { + "value": 6443, + "mod25": 18, + "modP": 8, + "modP2": 21 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11526528, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2881632, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2881632, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 720408, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 180102, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6443 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V207.right_6543", + "side": "side18", + "value": 6543, + "residues": { + "value": 6543, + "mod25": 18, + "modP": 4, + "modP2": 121 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11705428, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2926357, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2926357, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6543 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V208.right_6593", + "side": "side18", + "value": 6593, + "residues": { + "value": 6593, + "mod25": 18, + "modP": 2, + "modP2": 2 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11794878, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1310542, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1310542, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6593 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V209.right_6643", + "side": "side18", + "value": 6643, + "residues": { + "value": 6643, + "mod25": 18, + "modP": 0, + "modP2": 52 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11884328, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2971082, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2971082, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6643 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V210.right_6668", + "side": "side18", + "value": 6668, + "residues": { + "value": 6668, + "mod25": 18, + "modP": 12, + "modP2": 77 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11929053, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 41277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 41277, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6668 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V211.right_6743", + "side": "side18", + "value": 6743, + "residues": { + "value": 6743, + "mod25": 18, + "modP": 9, + "modP2": 152 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12063228, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3015807, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3015807, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6743 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V212.right_6818", + "side": "side18", + "value": 6818, + "residues": { + "value": 6818, + "mod25": 18, + "modP": 6, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12197403, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1355267, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1355267, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6818 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V213.right_6843", + "side": "side18", + "value": 6843, + "residues": { + "value": 6843, + "mod25": 18, + "modP": 5, + "modP2": 83 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12242128, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3060532, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3060532, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 765133, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6843 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V214.right_6943", + "side": "side18", + "value": 6943, + "residues": { + "value": 6943, + "mod25": 18, + "modP": 1, + "modP2": 14 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12421028, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3105257, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3105257, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6943 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V215.right_7043", + "side": "side18", + "value": 7043, + "residues": { + "value": 7043, + "mod25": 18, + "modP": 10, + "modP2": 114 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12599928, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3149982, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3149982, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1399992, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 349998, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7043 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V216.right_7143", + "side": "side18", + "value": 7143, + "residues": { + "value": 7143, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12778828, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3194707, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3194707, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7143 is present in the side18 compatible set for every row in split outP2=99|out25=14|smaller=side7." + } + ], + "vertexPresenceSummary": { + "splitModulus": 4225, + "witnessRowCount": 1, + "vertexPresenceAtomCount": 216, + "stableUnderCurrentSplitModulusCount": 4, + "needsSharperSplitOrParametricWitnessCount": 212, + "failedVertexPresenceAtomCount": 0, + "refinementStatus": "literal_core_requires_sharper_square_witness_split", + "refinementConditionCount": 10, + "dominantRefinementConditions": [ + { + "conditionId": "square_4_outsider_1", + "square": 4, + "requiredOutsiderResidueModSquare": 1, + "atomCount": 145, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out4=1" + }, + { + "conditionId": "square_9_outsider_7", + "square": 9, + "requiredOutsiderResidueModSquare": 7, + "atomCount": 49, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out9=7" + }, + { + "conditionId": "square_49_outsider_25", + "square": 49, + "requiredOutsiderResidueModSquare": 25, + "atomCount": 7, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out49=25" + }, + { + "conditionId": "square_121_outsider_95", + "square": 121, + "requiredOutsiderResidueModSquare": 95, + "atomCount": 3, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out121=95" + }, + { + "conditionId": "square_289_outsider_55", + "square": 289, + "requiredOutsiderResidueModSquare": 55, + "atomCount": 2, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out289=55" + }, + { + "conditionId": "square_529_outsider_202", + "square": 529, + "requiredOutsiderResidueModSquare": 202, + "atomCount": 2, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out529=202" + }, + { + "conditionId": "square_361_outsider_345", + "square": 361, + "requiredOutsiderResidueModSquare": 345, + "atomCount": 1, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out361=345" + }, + { + "conditionId": "square_961_outsider_828", + "square": 961, + "requiredOutsiderResidueModSquare": 828, + "atomCount": 1, + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out961=828" + } + ], + "firstUnstableAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V1.left_7", + "side": "side7", + "value": 7, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3131, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V2.left_32", + "side": "side7", + "value": 32, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 6361, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V3.left_107", + "side": "side7", + "value": 107, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47856, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V4.left_207", + "side": "side7", + "value": 207, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 92581, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V5.left_257", + "side": "side7", + "value": 257, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 51086, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V6.left_307", + "side": "side7", + "value": 307, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 137306, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V7.left_407", + "side": "side7", + "value": 407, + 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"status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 139602, + "checkedSquareRootFloor": 373, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (407, 343) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E8.left_482_right_443", + "pairIndex": 7, + "pair": { + "leftValue": 482, + "rightValue": 443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 144, + "rightModP2": 105, + "leftModP": 1, + "rightModP": 1, + "productPlusOneModP2": 80 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 213527, + "checkedSquareRootFloor": 462, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (482, 443) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E9.left_507_right_518", + "pairIndex": 8, + "pair": { + "leftValue": 507, + "rightValue": 518, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 0, + "rightModP2": 11, + "leftModP": 0, + "rightModP": 11, + "productPlusOneModP2": 1 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 262627, + "checkedSquareRootFloor": 512, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (507, 518) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E10.left_607_right_543", + "pairIndex": 9, + "pair": { + "leftValue": 607, + "rightValue": 543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 100, + "rightModP2": 36, + "leftModP": 9, + "rightModP": 10, + "productPlusOneModP2": 52 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 329602, + "checkedSquareRootFloor": 574, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (607, 543) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E11.left_707_right_643", + "pairIndex": 10, + "pair": { + "leftValue": 707, + "rightValue": 643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 31, + "rightModP2": 136, + "leftModP": 5, + "rightModP": 6, + "productPlusOneModP2": 161 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 454602, + "checkedSquareRootFloor": 674, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (707, 643) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E12.left_782_right_743", + "pairIndex": 11, + "pair": { + "leftValue": 782, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 106, + "rightModP2": 67, + "leftModP": 2, + "rightModP": 2, + "productPlusOneModP2": 5 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 581027, + "checkedSquareRootFloor": 762, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (782, 743) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E13.left_807_right_843", + "pairIndex": 12, + "pair": { + "leftValue": 807, + "rightValue": 843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 131, + "rightModP2": 167, + "leftModP": 1, + "rightModP": 11, + "productPlusOneModP2": 77 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 680302, + "checkedSquareRootFloor": 824, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (807, 843) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E14.left_907_right_943", + "pairIndex": 13, + "pair": { + "leftValue": 907, + "rightValue": 943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 62, + "rightModP2": 98, + "leftModP": 10, + "rightModP": 7, + "productPlusOneModP2": 162 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 855302, + "checkedSquareRootFloor": 924, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (907, 943) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E15.left_932_right_968", + "pairIndex": 14, + "pair": { + "leftValue": 932, + "rightValue": 968, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 87, + "rightModP2": 123, + "leftModP": 9, + "rightModP": 6, + "productPlusOneModP2": 55 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 902177, + "checkedSquareRootFloor": 949, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (932, 968) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E16.left_982_right_1143", + "pairIndex": 15, + "pair": { + "leftValue": 982, + "rightValue": 1143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 137, + "rightModP2": 129, + "leftModP": 7, + "rightModP": 12, + "productPlusOneModP2": 98 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1122427, + "checkedSquareRootFloor": 1059, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (982, 1143) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E17.left_1007_right_1043", + "pairIndex": 16, + "pair": { + "leftValue": 1007, + "rightValue": 1043, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 162, + "rightModP2": 29, + "leftModP": 6, + "rightModP": 3, + "productPlusOneModP2": 136 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1050302, + "checkedSquareRootFloor": 1024, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1007, 1043) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, 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}, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E21.left_1282_right_1418", + "pairIndex": 20, + "pair": { + "leftValue": 1282, + "rightValue": 1418, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 99, + "rightModP2": 66, + "leftModP": 8, + "rightModP": 1, + "productPlusOneModP2": 113 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1817877, + "checkedSquareRootFloor": 1348, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1282, 1418) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E22.left_1307_right_1443", + "pairIndex": 21, + "pair": { + "leftValue": 1307, + "rightValue": 1443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 124, + "rightModP2": 91, + "leftModP": 7, + "rightModP": 0, + "productPlusOneModP2": 131 + }, + "status": 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}, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E24.left_1407_right_1543", + "pairIndex": 23, + "pair": { + "leftValue": 1407, + "rightValue": 1543, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 55, + "rightModP2": 22, + "leftModP": 3, + "rightModP": 9, + "productPlusOneModP2": 28 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2171002, + "checkedSquareRootFloor": 1473, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1407, 1543) remains a missing cross edge throughout split outP2=99|out25=14|smaller=side7." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E25.left_1507_right_1643", + "pairIndex": 24, + "pair": { + "leftValue": 1507, + "rightValue": 1643, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 155, + "rightModP2": 122, + "leftModP": 12, + "rightModP": 5, + "productPlusOneModP2": 152 + }, + "status": 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"edgeAtomIds": [ + "D2.3_persist_outP2=99_out25=14_smaller=side7.E37.left_2307_right_2543" + ], + "examples": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E37.left_2307_right_2543", + "leftValue": 2307, + "rightValue": 2543, + "productPlusOne": 5866702 + } + ], + "edgeCount": 1 + }, + { + "groupKey": "113:49:130", + "leftModP2": 113, + "rightModP2": 49, + "productPlusOneModP2": 130, + "edgeAtomIds": [ + "D2.3_persist_outP2=99_out25=14_smaller=side7.E67.left_4507_right_4443" + ], + "examples": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E67.left_4507_right_4443", + "leftValue": 4507, + "rightValue": 4443, + "productPlusOne": 20024602 + } + ], + "edgeCount": 1 + }, + { + "groupKey": "116:21:71", + "leftModP2": 116, + "rightModP2": 21, + "productPlusOneModP2": 71, + "edgeAtomIds": [ + "D2.3_persist_outP2=99_out25=14_smaller=side7.E98.left_6707_right_6443" + ], + "examples": [ + { + "atomId": 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"firstEdgeCertificates": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E1.left_7_right_43", + "leftValue": 7, + "rightValue": 43, + "productPlusOne": 302, + "checkedSquareRootFloor": 17, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E2.left_32_right_68", + "leftValue": 32, + "rightValue": 68, + "productPlusOne": 2177, + "checkedSquareRootFloor": 46, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E3.left_107_right_143", + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302, + "checkedSquareRootFloor": 123, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E4.left_207_right_243", + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302, + "checkedSquareRootFloor": 224, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E5.left_257_right_293", + "leftValue": 257, + "rightValue": 293, + "productPlusOne": 75302, + "checkedSquareRootFloor": 274, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E6.left_307_right_268", + "leftValue": 307, + "rightValue": 268, + "productPlusOne": 82277, + "checkedSquareRootFloor": 286, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E7.left_407_right_343", + "leftValue": 407, + "rightValue": 343, + "productPlusOne": 139602, + "checkedSquareRootFloor": 373, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E8.left_482_right_443", + "leftValue": 482, + "rightValue": 443, + "productPlusOne": 213527, + "checkedSquareRootFloor": 462, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E9.left_507_right_518", + "leftValue": 507, + "rightValue": 518, + "productPlusOne": 262627, + "checkedSquareRootFloor": 512, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E10.left_607_right_543", + "leftValue": 607, + "rightValue": 543, + "productPlusOne": 329602, + "checkedSquareRootFloor": 574, + "squareDivisorWitnesses": [], + "isSquarefree": true + } + ], + "failedEdgeAtoms": [], + "proofBoundary": "This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim.", + "nextTheoremAction": "Promote this literal edge-obstruction certificate into A5 congruence-persistence families, or emit a sharper successor atom for any edge whose obstruction is not implied by the split hypotheses." + }, + "edgeCongruencePersistence": { + "schema": "erdos.p848_edge_congruence_persistence/1", + "persistenceId": "D2.3_persist_outP2=99_out25=14_smaller=side7.edge_congruence_persistence", + "status": "literal_constant_edge_persistence_verified", + "proofKind": "constant_pair_squarefree_invariant", + "splitKey": "outP2=99|out25=14|smaller=side7", + "splitModulus": 4225, + "witnessRowCount": 1, + "edgeAtomCount": 108, + "verifiedEdgeAtomCount": 108, + "failedEdgeAtomCount": 0, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "proofFamilies": [ + { + "familyId": "D2.3_persist_outP2=99_out25=14_smaller=side7.edge_constant_squarefree_family", + "status": "congruence_persistence_family_verified", + "proofKind": "constant_pair_squarefree_invariant", + "edgeAtomCount": 108, + "verifiedEdgeAtomCount": 108, + "failedEdgeAtomCount": 0, + "splitKey": "outP2=99|out25=14|smaller=side7", + "splitModulus": 4225, + "statement": "For each exported literal cross pair (l,r), l and r are constants in the packet, so l*r+1 is the same integer for every row satisfying the split hypotheses.", + "proofSteps": [ + "Recompute c = l*r + 1 from the exported literal pair.", + "Check c matches the squarefree certificate attached to the edge atom.", + "Because c has no N or outsider variable, the edge obstruction persists over all rows covered by this literal packet." + ], + "proofBoundary": "This is not yet a parameterized edge-family theorem. If later proof work replaces literal pair constants with formulas in N, this constant-family proof must be lifted or replaced.", + "exampleEdgeAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E1.left_7_right_43", + "leftValue": 7, + "rightValue": 43, + "productPlusOne": 302 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E2.left_32_right_68", + "leftValue": 32, + "rightValue": 68, + "productPlusOne": 2177 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E3.left_107_right_143", + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E4.left_207_right_243", + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E5.left_257_right_293", + "leftValue": 257, + "rightValue": 293, + "productPlusOne": 75302 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E6.left_307_right_268", + "leftValue": 307, + "rightValue": 268, + "productPlusOne": 82277 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E7.left_407_right_343", + "leftValue": 407, + "rightValue": 343, + "productPlusOne": 139602 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E8.left_482_right_443", + "leftValue": 482, + "rightValue": 443, + "productPlusOne": 213527 + } + ] + } + ], + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E1.left_7_right_43", + "pairIndex": 0, + "leftValue": 7, + "rightValue": 43, + "productPlusOne": 302, + "productPlusOneRecomputed": 302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E2.left_32_right_68", + "pairIndex": 1, + "leftValue": 32, + "rightValue": 68, + "productPlusOne": 2177, + "productPlusOneRecomputed": 2177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E3.left_107_right_143", + "pairIndex": 2, + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302, + "productPlusOneRecomputed": 15302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E4.left_207_right_243", + "pairIndex": 3, + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302, + "productPlusOneRecomputed": 50302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E5.left_257_right_293", + "pairIndex": 4, + "leftValue": 257, + "rightValue": 293, + "productPlusOne": 75302, + "productPlusOneRecomputed": 75302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E6.left_307_right_268", + "pairIndex": 5, + "leftValue": 307, + "rightValue": 268, + "productPlusOne": 82277, + "productPlusOneRecomputed": 82277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E7.left_407_right_343", + "pairIndex": 6, + "leftValue": 407, + "rightValue": 343, + "productPlusOne": 139602, + "productPlusOneRecomputed": 139602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E8.left_482_right_443", + "pairIndex": 7, + "leftValue": 482, + "rightValue": 443, + "productPlusOne": 213527, + "productPlusOneRecomputed": 213527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E9.left_507_right_518", + "pairIndex": 8, + "leftValue": 507, + "rightValue": 518, + "productPlusOne": 262627, + "productPlusOneRecomputed": 262627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E10.left_607_right_543", + "pairIndex": 9, + "leftValue": 607, + "rightValue": 543, + "productPlusOne": 329602, + "productPlusOneRecomputed": 329602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E11.left_707_right_643", + "pairIndex": 10, + "leftValue": 707, + "rightValue": 643, + "productPlusOne": 454602, + "productPlusOneRecomputed": 454602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E12.left_782_right_743", + "pairIndex": 11, + "leftValue": 782, + "rightValue": 743, + "productPlusOne": 581027, + "productPlusOneRecomputed": 581027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E13.left_807_right_843", + "pairIndex": 12, + "leftValue": 807, + "rightValue": 843, + "productPlusOne": 680302, + "productPlusOneRecomputed": 680302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E14.left_907_right_943", + "pairIndex": 13, + "leftValue": 907, + "rightValue": 943, + "productPlusOne": 855302, + "productPlusOneRecomputed": 855302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E15.left_932_right_968", + "pairIndex": 14, + "leftValue": 932, + "rightValue": 968, + "productPlusOne": 902177, + "productPlusOneRecomputed": 902177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E16.left_982_right_1143", + "pairIndex": 15, + "leftValue": 982, + "rightValue": 1143, + "productPlusOne": 1122427, + "productPlusOneRecomputed": 1122427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E17.left_1007_right_1043", + "pairIndex": 16, + "leftValue": 1007, + "rightValue": 1043, + "productPlusOne": 1050302, + "productPlusOneRecomputed": 1050302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E18.left_1107_right_1243", + "pairIndex": 17, + "leftValue": 1107, + "rightValue": 1243, + "productPlusOne": 1376002, + "productPlusOneRecomputed": 1376002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E19.left_1157_right_1193", + "pairIndex": 18, + "leftValue": 1157, + "rightValue": 1193, + "productPlusOne": 1380302, + "productPlusOneRecomputed": 1380302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E20.left_1207_right_1343", + "pairIndex": 19, + "leftValue": 1207, + "rightValue": 1343, + "productPlusOne": 1621002, + "productPlusOneRecomputed": 1621002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E21.left_1282_right_1418", + "pairIndex": 20, + "leftValue": 1282, + "rightValue": 1418, + "productPlusOne": 1817877, + "productPlusOneRecomputed": 1817877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E22.left_1307_right_1443", + "pairIndex": 21, + "leftValue": 1307, + "rightValue": 1443, + "productPlusOne": 1886002, + "productPlusOneRecomputed": 1886002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E23.left_1382_right_1468", + "pairIndex": 22, + "leftValue": 1382, + "rightValue": 1468, + "productPlusOne": 2028777, + "productPlusOneRecomputed": 2028777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E24.left_1407_right_1543", + "pairIndex": 23, + "leftValue": 1407, + "rightValue": 1543, + "productPlusOne": 2171002, + "productPlusOneRecomputed": 2171002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E25.left_1507_right_1643", + "pairIndex": 24, + "leftValue": 1507, + "rightValue": 1643, + "productPlusOne": 2476002, + "productPlusOneRecomputed": 2476002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E26.left_1532_right_1743", + "pairIndex": 25, + "leftValue": 1532, + "rightValue": 1743, + "productPlusOne": 2670277, + "productPlusOneRecomputed": 2670277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E27.left_1607_right_1868", + "pairIndex": 26, + "leftValue": 1607, + "rightValue": 1868, + "productPlusOne": 3001877, + "productPlusOneRecomputed": 3001877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E28.left_1707_right_1843", + "pairIndex": 27, + "leftValue": 1707, + "rightValue": 1843, + "productPlusOne": 3146002, + "productPlusOneRecomputed": 3146002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E29.left_1807_right_1943", + "pairIndex": 28, + "leftValue": 1807, + "rightValue": 1943, + "productPlusOne": 3511002, + "productPlusOneRecomputed": 3511002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E30.left_1832_right_2043", + "pairIndex": 29, + "leftValue": 1832, + "rightValue": 2043, + "productPlusOne": 3742777, + "productPlusOneRecomputed": 3742777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E31.left_1907_right_2243", + "pairIndex": 30, + "leftValue": 1907, + "rightValue": 2243, + "productPlusOne": 4277402, + "productPlusOneRecomputed": 4277402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E32.left_2007_right_2143", + "pairIndex": 31, + "leftValue": 2007, + "rightValue": 2143, + "productPlusOne": 4301002, + "productPlusOneRecomputed": 4301002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E33.left_2057_right_2093", + "pairIndex": 32, + "leftValue": 2057, + "rightValue": 2093, + "productPlusOne": 4305302, + "productPlusOneRecomputed": 4305302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E34.left_2107_right_2318", + "pairIndex": 33, + "leftValue": 2107, + "rightValue": 2318, + "productPlusOne": 4884027, + "productPlusOneRecomputed": 4884027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E35.left_2207_right_2343", + "pairIndex": 34, + "leftValue": 2207, + "rightValue": 2343, + "productPlusOne": 5171002, + "productPlusOneRecomputed": 5171002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E36.left_2282_right_2443", + "pairIndex": 35, + "leftValue": 2282, + "rightValue": 2443, + "productPlusOne": 5574927, + "productPlusOneRecomputed": 5574927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E37.left_2307_right_2543", + "pairIndex": 36, + "leftValue": 2307, + "rightValue": 2543, + "productPlusOne": 5866702, + "productPlusOneRecomputed": 5866702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E38.left_2407_right_2643", + "pairIndex": 37, + "leftValue": 2407, + "rightValue": 2643, + "productPlusOne": 6361702, + "productPlusOneRecomputed": 6361702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E39.left_2507_right_2768", + "pairIndex": 38, + "leftValue": 2507, + "rightValue": 2768, + "productPlusOne": 6939377, + "productPlusOneRecomputed": 6939377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E40.left_2607_right_2743", + "pairIndex": 39, + "leftValue": 2607, + "rightValue": 2743, + "productPlusOne": 7151002, + "productPlusOneRecomputed": 7151002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E41.left_2707_right_2843", + "pairIndex": 40, + "leftValue": 2707, + "rightValue": 2843, + "productPlusOne": 7696002, + "productPlusOneRecomputed": 7696002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E42.left_2732_right_2693", + "pairIndex": 41, + "leftValue": 2732, + "rightValue": 2693, + "productPlusOne": 7357277, + "productPlusOneRecomputed": 7357277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E43.left_2807_right_2918", + "pairIndex": 42, + "leftValue": 2807, + "rightValue": 2918, + "productPlusOne": 8190827, + "productPlusOneRecomputed": 8190827, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E44.left_2907_right_3043", + "pairIndex": 43, + "leftValue": 2907, + "rightValue": 3043, + "productPlusOne": 8846002, + "productPlusOneRecomputed": 8846002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E45.left_2957_right_2993", + "pairIndex": 44, + "leftValue": 2957, + "rightValue": 2993, + "productPlusOne": 8850302, + "productPlusOneRecomputed": 8850302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E46.left_3007_right_2943", + "pairIndex": 45, + "leftValue": 3007, + "rightValue": 2943, + "productPlusOne": 8849602, + "productPlusOneRecomputed": 8849602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E47.left_3107_right_3143", + "pairIndex": 46, + "leftValue": 3107, + "rightValue": 3143, + "productPlusOne": 9765302, + "productPlusOneRecomputed": 9765302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E48.left_3182_right_3243", + "pairIndex": 47, + "leftValue": 3182, + "rightValue": 3243, + "productPlusOne": 10319227, + "productPlusOneRecomputed": 10319227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E49.left_3207_right_3218", + "pairIndex": 48, + "leftValue": 3207, + "rightValue": 3218, + "productPlusOne": 10320127, + "productPlusOneRecomputed": 10320127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E50.left_3232_right_3343", + "pairIndex": 49, + "leftValue": 3232, + "rightValue": 3343, + "productPlusOne": 10804577, + "productPlusOneRecomputed": 10804577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E51.left_3307_right_3443", + "pairIndex": 50, + "leftValue": 3307, + "rightValue": 3443, + "productPlusOne": 11386002, + "productPlusOneRecomputed": 11386002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E52.left_3407_right_3543", + "pairIndex": 51, + "leftValue": 3407, + "rightValue": 3543, + "productPlusOne": 12071002, + "productPlusOneRecomputed": 12071002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E53.left_3507_right_3643", + "pairIndex": 52, + "leftValue": 3507, + "rightValue": 3643, + "productPlusOne": 12776002, + "productPlusOneRecomputed": 12776002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E54.left_3607_right_3743", + "pairIndex": 53, + "leftValue": 3607, + "rightValue": 3743, + "productPlusOne": 13501002, + "productPlusOneRecomputed": 13501002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E55.left_3632_right_3668", + "pairIndex": 54, + "leftValue": 3632, + "rightValue": 3668, + "productPlusOne": 13322177, + "productPlusOneRecomputed": 13322177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E56.left_3707_right_3768", + "pairIndex": 55, + "leftValue": 3707, + "rightValue": 3768, + "productPlusOne": 13967977, + "productPlusOneRecomputed": 13967977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E57.left_3807_right_3843", + "pairIndex": 56, + "leftValue": 3807, + "rightValue": 3843, + "productPlusOne": 14630302, + "productPlusOneRecomputed": 14630302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E58.left_3857_right_3893", + "pairIndex": 57, + "leftValue": 3857, + "rightValue": 3893, + "productPlusOne": 15015302, + "productPlusOneRecomputed": 15015302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E59.left_3907_right_3918", + "pairIndex": 58, + "leftValue": 3907, + "rightValue": 3918, + "productPlusOne": 15307627, + "productPlusOneRecomputed": 15307627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E60.left_4007_right_3943", + "pairIndex": 59, + "leftValue": 4007, + "rightValue": 3943, + "productPlusOne": 15799602, + "productPlusOneRecomputed": 15799602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E61.left_4082_right_4043", + "pairIndex": 60, + "leftValue": 4082, + "rightValue": 4043, + "productPlusOne": 16503527, + "productPlusOneRecomputed": 16503527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E62.left_4107_right_4068", + "pairIndex": 61, + "leftValue": 4107, + "rightValue": 4068, + "productPlusOne": 16707277, + "productPlusOneRecomputed": 16707277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E63.left_4207_right_4118", + "pairIndex": 62, + "leftValue": 4207, + "rightValue": 4118, + "productPlusOne": 17324427, + "productPlusOneRecomputed": 17324427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E64.left_4307_right_4143", + "pairIndex": 63, + "leftValue": 4307, + "rightValue": 4143, + "productPlusOne": 17843902, + "productPlusOneRecomputed": 17843902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E65.left_4407_right_4243", + "pairIndex": 64, + "leftValue": 4407, + "rightValue": 4243, + "productPlusOne": 18698902, + "productPlusOneRecomputed": 18698902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E66.left_4457_right_4568", + "pairIndex": 65, + "leftValue": 4457, + "rightValue": 4568, + "productPlusOne": 20359577, + "productPlusOneRecomputed": 20359577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E67.left_4507_right_4443", + "pairIndex": 66, + "leftValue": 4507, + "rightValue": 4443, + "productPlusOne": 20024602, + "productPlusOneRecomputed": 20024602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E68.left_4532_right_4343", + "pairIndex": 67, + "leftValue": 4532, + "rightValue": 4343, + "productPlusOne": 19682477, + "productPlusOneRecomputed": 19682477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E69.left_4607_right_4543", + "pairIndex": 68, + "leftValue": 4607, + "rightValue": 4543, + "productPlusOne": 20929602, + "productPlusOneRecomputed": 20929602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E70.left_4707_right_4618", + "pairIndex": 69, + "leftValue": 4707, + "rightValue": 4618, + "productPlusOne": 21736927, + "productPlusOneRecomputed": 21736927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E71.left_4757_right_4493", + "pairIndex": 70, + "leftValue": 4757, + "rightValue": 4493, + "productPlusOne": 21373202, + "productPlusOneRecomputed": 21373202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E72.left_4807_right_4843", + "pairIndex": 71, + "leftValue": 4807, + "rightValue": 4843, + "productPlusOne": 23280302, + "productPlusOneRecomputed": 23280302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E73.left_4907_right_4643", + "pairIndex": 72, + "leftValue": 4907, + "rightValue": 4643, + "productPlusOne": 22783202, + "productPlusOneRecomputed": 22783202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E74.left_4982_right_4743", + "pairIndex": 73, + "leftValue": 4982, + "rightValue": 4743, + "productPlusOne": 23629627, + "productPlusOneRecomputed": 23629627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E75.left_5007_right_4943", + "pairIndex": 74, + "leftValue": 5007, + "rightValue": 4943, + "productPlusOne": 24749602, + "productPlusOneRecomputed": 24749602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E76.left_5107_right_5018", + "pairIndex": 75, + "leftValue": 5107, + "rightValue": 5018, + "productPlusOne": 25626927, + "productPlusOneRecomputed": 25626927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E77.left_5207_right_5043", + "pairIndex": 76, + "leftValue": 5207, + "rightValue": 5043, + "productPlusOne": 26258902, + "productPlusOneRecomputed": 26258902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E78.left_5307_right_5143", + "pairIndex": 77, + "leftValue": 5307, + "rightValue": 5143, + "productPlusOne": 27293902, + "productPlusOneRecomputed": 27293902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E79.left_5407_right_5343", + "pairIndex": 78, + "leftValue": 5407, + "rightValue": 5343, + "productPlusOne": 28889602, + "productPlusOneRecomputed": 28889602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E80.left_5432_right_4793", + "pairIndex": 79, + "leftValue": 5432, + "rightValue": 4793, + "productPlusOne": 26035577, + "productPlusOneRecomputed": 26035577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E81.left_5507_right_5243", + "pairIndex": 80, + "leftValue": 5507, + "rightValue": 5243, + "productPlusOne": 28873202, + "productPlusOneRecomputed": 28873202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E82.left_5607_right_5443", + "pairIndex": 81, + "leftValue": 5607, + "rightValue": 5443, + "productPlusOne": 30518902, + "productPlusOneRecomputed": 30518902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E83.left_5657_right_5468", + "pairIndex": 82, + "leftValue": 5657, + "rightValue": 5468, + "productPlusOne": 30932477, + "productPlusOneRecomputed": 30932477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E84.left_5682_right_5543", + "pairIndex": 83, + "leftValue": 5682, + "rightValue": 5543, + "productPlusOne": 31495327, + "productPlusOneRecomputed": 31495327, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E85.left_5707_right_5643", + "pairIndex": 84, + "leftValue": 5707, + "rightValue": 5643, + "productPlusOne": 32204602, + "productPlusOneRecomputed": 32204602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E86.left_5807_right_5743", + "pairIndex": 85, + "leftValue": 5807, + "rightValue": 5743, + "productPlusOne": 33349602, + "productPlusOneRecomputed": 33349602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E87.left_5882_right_5693", + "pairIndex": 86, + "leftValue": 5882, + "rightValue": 5693, + "productPlusOne": 33486227, + "productPlusOneRecomputed": 33486227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E88.left_5907_right_5843", + "pairIndex": 87, + "leftValue": 5907, + "rightValue": 5843, + "productPlusOne": 34514602, + "productPlusOneRecomputed": 34514602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E89.left_6007_right_5918", + "pairIndex": 88, + "leftValue": 6007, + "rightValue": 5918, + "productPlusOne": 35549427, + "productPlusOneRecomputed": 35549427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E90.left_6107_right_5943", + "pairIndex": 89, + "leftValue": 6107, + "rightValue": 5943, + "productPlusOne": 36293902, + "productPlusOneRecomputed": 36293902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E91.left_6207_right_6043", + "pairIndex": 90, + "leftValue": 6207, + "rightValue": 6043, + "productPlusOne": 37508902, + "productPlusOneRecomputed": 37508902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E92.left_6307_right_6243", + "pairIndex": 91, + "leftValue": 6307, + "rightValue": 6243, + "productPlusOne": 39374602, + "productPlusOneRecomputed": 39374602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E93.left_6332_right_6143", + "pairIndex": 92, + "leftValue": 6332, + "rightValue": 6143, + "productPlusOne": 38897477, + "productPlusOneRecomputed": 38897477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E94.left_6407_right_6343", + "pairIndex": 93, + "leftValue": 6407, + "rightValue": 6343, + "productPlusOne": 40639602, + "productPlusOneRecomputed": 40639602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E95.left_6507_right_6368", + "pairIndex": 94, + "leftValue": 6507, + "rightValue": 6368, + "productPlusOne": 41436577, + "productPlusOneRecomputed": 41436577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E96.left_6557_right_6293", + "pairIndex": 95, + "leftValue": 6557, + "rightValue": 6293, + "productPlusOne": 41263202, + "productPlusOneRecomputed": 41263202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E97.left_6607_right_6418", + "pairIndex": 96, + "leftValue": 6607, + "rightValue": 6418, + "productPlusOne": 42403727, + "productPlusOneRecomputed": 42403727, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E98.left_6707_right_6443", + "pairIndex": 97, + "leftValue": 6707, + "rightValue": 6443, + "productPlusOne": 43213202, + "productPlusOneRecomputed": 43213202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E99.left_6782_right_6543", + "pairIndex": 98, + "leftValue": 6782, + "rightValue": 6543, + "productPlusOne": 44374627, + "productPlusOneRecomputed": 44374627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E100.left_6807_right_6643", + "pairIndex": 99, + "leftValue": 6807, + "rightValue": 6643, + "productPlusOne": 45218902, + "productPlusOneRecomputed": 45218902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E101.left_6907_right_6668", + "pairIndex": 100, + "leftValue": 6907, + "rightValue": 6668, + "productPlusOne": 46055877, + "productPlusOneRecomputed": 46055877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E102.left_6957_right_6593", + "pairIndex": 101, + "leftValue": 6957, + "rightValue": 6593, + "productPlusOne": 45867502, + "productPlusOneRecomputed": 45867502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E103.left_7007_right_6743", + "pairIndex": 102, + "leftValue": 7007, + "rightValue": 6743, + "productPlusOne": 47248202, + "productPlusOneRecomputed": 47248202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E104.left_7032_right_6818", + "pairIndex": 103, + "leftValue": 7032, + "rightValue": 6818, + "productPlusOne": 47944177, + "productPlusOneRecomputed": 47944177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E105.left_7107_right_6843", + "pairIndex": 104, + "leftValue": 7107, + "rightValue": 6843, + "productPlusOne": 48633202, + "productPlusOneRecomputed": 48633202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E106.left_7207_right_6943", + "pairIndex": 105, + "leftValue": 7207, + "rightValue": 6943, + "productPlusOne": 50038202, + "productPlusOneRecomputed": 50038202, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E107.left_7232_right_7043", + "pairIndex": 106, + "leftValue": 7232, + "rightValue": 7043, + "productPlusOne": 50934977, + "productPlusOneRecomputed": 50934977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.E108.left_7307_right_7143", + "pairIndex": 107, + "leftValue": 7307, + "rightValue": 7143, + "productPlusOne": 52193902, + "productPlusOneRecomputed": 52193902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + } + ], + "failedChecks": [], + "proofBoundary": "This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions.", + "nextTheoremAction": "After this A5 literal persistence pass, promote matching disjointness and the K-envelope, or lift the edge proof if vertex formulas become parameterized." + }, + "matchingDisjointness": { + "status": "bounded_disjointness_certified", + "leftVertexCount": 108, + "rightVertexCount": 108, + "pairCount": 108, + "reusedLeftValues": [], + "reusedRightValues": [], + "completionRule": "A symbolic packet may promote only if the parameterized left and right vertex families remain pairwise disjoint." + }, + "matchingKEnvelopeCertificate": { + "schema": "erdos.p848_matching_k_envelope_certificate/1", + "certificateId": "D2.3_persist_outP2=99_out25=14_smaller=side7.matching_k_envelope_certificate", + "status": "literal_matching_sampled_k_envelope_verified", + "proofKind": "literal_disjoint_matching_plus_sampled_k_envelope", + "matchingProof": { + "status": "literal_matching_disjointness_verified", + "pairCount": 108, + "leftVertexCount": 108, + "rightVertexCount": 108, + "reusedLeftValues": [], + "reusedRightValues": [], + "proofSteps": [ + "Count the exported literal left vertices.", + "Count the exported literal right vertices.", + "Verify no left value and no right value is reused across the exported pair list." + ], + "proofBoundary": "This proves disjointness for the exported literal pair list. If later work parameterizes vertices, disjointness must be rechecked for the parameterized formulas." + }, + "kEnvelopeProof": { + "status": "sampled_k_envelope_dominated_by_literal_core", + "requiredMatchingLowerBoundRange": [ + 88, + 88 + ], + "commonMatchingPairCount": 108, + "maxRequiredMatchingLowerBound": 88, + "boundedSlackAgainstMaxK": 20, + "inequality": "108 >= 88", + "proofSteps": [ + "Use the exported common-core pair count as the literal matching size.", + "Compare it against the maximum required matching lower bound recorded by the packet.", + "Record the slack and keep the all-N K-formula handoff explicit." + ], + "proofBoundary": "This certifies the K-envelope recorded by the current split packet. It is not by itself a universal K(N,x) formula proof for every future row." + }, + "allLowerLiteralAtomsReady": true, + "proofBoundary": "A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim.", + "nextTheoremAction": "Assemble this with the verified vertex-successor and edge-persistence layers into a split-discharge readiness certificate, or emit the first missing lower atom." + }, + "summary": { + "vertexPresenceAtomCount": 216, + "edgeObstructionAtomCount": 108, + "stableVertexPresenceAtomCount": 4, + "unstableVertexPresenceAtomCount": 212, + "failedVertexPresenceAtomCount": 0, + "allEdgeObstructionsSquarefree": true, + "edgeObstructionCertificateStatus": "literal_edge_obstruction_certificate_verified", + "edgeCongruencePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingDisjointnessStatus": "bounded_disjointness_certified", + "matchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "readyForFirstTheoremPass": true + }, + "nextTheoremActions": [ + "Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N.", + "The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families.", + "Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof.", + "Attack the packet until it either becomes a split lemma or emits a sharper sub-split key." + ], + "splitDischargeReadiness": { + "schema": "erdos.p848_split_discharge_readiness/1", + "readinessId": "D2.3_persist_outP2=99_out25=14_smaller=side7.split_discharge_readiness", + "status": "split_discharge_readiness_candidate", + "proofKind": "lower_atom_assembly_with_explicit_all_n_handoff", + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "splitKey": "outP2=99|out25=14|smaller=side7", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "lowerLayerChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "verified", + "evidence": "10/10 successor vertex-family lemmas verified" + }, + { + "layerId": "A4_edge_obstruction_certificate", + "status": "verified", + "evidence": "literal_edge_obstruction_certificate_verified" + }, + { + "layerId": "A5_edge_congruence_persistence", + "status": "verified", + "evidence": "literal_constant_edge_persistence_verified" + }, + { + "layerId": "A6_matching_disjointness", + "status": "verified", + "evidence": "literal_matching_disjointness_verified" + }, + { + "layerId": "A7_sampled_k_envelope", + "status": "verified_sampled_envelope", + "evidence": "108 >= 88" + } + ], + "blockingChecks": [], + "theoremCandidate": { + "status": "candidate_with_open_all_n_handoff_gaps", + "statement": "For split outP2=99|out25=14|smaller=side7, the exported literal core supplies a disjoint matching of size 108 against the packet K-envelope [88,88].", + "lowerAtomSummary": { + "vertexSuccessorConditionCount": 10, + "verifiedVertexSuccessorCount": 10, + "edgePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingKEnvelopeStatus": "literal_matching_sampled_k_envelope_verified" + } + }, + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "note": "Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "note": "Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "note": "If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families." + } + ], + "proofBoundary": "This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes.", + "nextTheoremAction": "Attack the next p13 split profile or begin the row-universe/symbolic-K handoff once every p13 split has this readiness certificate." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md new file mode 100644 index 0000000..ba5896c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md @@ -0,0 +1,251 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7 + +This is a theorem-facing split atom packet for Problem 848. It is intentionally atomic: one split profile, one common matching core, one K-envelope, and deterministic sub-atoms for the next proof pass. + +## Summary + +- Packet id: `p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7` +- Parent obligation: `D2_p13_matching_lower_bound` +- Target obligation: `D4_matching_bound_implies_sMaxMixed_bound` +- Prime lane: `13` +- Split key: `outP2=99|out25=14|smaller=side7` +- Priority: `highest_singleton_profile` +- Status: `ready_for_symbolic_persistence_work` +- Witnesses: `1` over `7343..7343` +- Common core size: `108` +- K-envelope: `[88,88]`, slack against max K `20` +- Vertex atoms: `216` +- Vertex atoms stable under current split modulus: `4` +- Vertex atoms needing sharper split or parameterization: `212` +- Edge atoms: `108` +- Edge certificate: `literal_edge_obstruction_certificate_verified` +- Edge congruence persistence: `literal_constant_edge_persistence_verified` +- Disjointness: `bounded_disjointness_certified` +- Matching/K certificate: `literal_matching_sampled_k_envelope_verified` + +## Goal + +Prove that the 108-edge common matching core persists for all p=13 threatening rows in split outP2=99|out25=14|smaller=side7, or replace it with a parameterized extension core. + +## Falsifier Boundary + +A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size. + +## Next Theorem Actions + +- Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N. +- The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families. +- Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof. +- Attack the packet until it either becomes a split lemma or emits a sharper sub-split key. + +## K Envelope + +- Status: `bounded_core_meets_sampled_K_envelope` +- Common core count: `108` +- Max required K: `88` +- Min matching slack: `20` + +## Matching And K-Envelope Certificate + +- Status: `literal_matching_sampled_k_envelope_verified` +- Proof kind: `literal_disjoint_matching_plus_sampled_k_envelope` +- Matching proof: `literal_matching_disjointness_verified` +- K proof: `sampled_k_envelope_dominated_by_literal_core` +- K inequality: `108 >= 88` +- Proof boundary: A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim. + +## Split Discharge Readiness + +- Status: `split_discharge_readiness_candidate` +- Proof kind: `lower_atom_assembly_with_explicit_all_n_handoff` +- Theorem candidate: `candidate_with_open_all_n_handoff_gaps` +- Blocking lower checks: `0` +- Open all-N handoff gaps: `3` +- Proof boundary: This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes. +- Handoff gap `row_universe_split_coverage` [open]: Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile. +- Handoff gap `universal_k_formula_lift` [open]: Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane. +- Handoff gap `literal_to_parameterized_vertex_guard` [open_if_vertices_move]: If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families. + +## Vertex Presence Stability + +- Split modulus: `4225` +- Witness rows: `1` +- Stable under current split modulus: `4` +- Needs sharper split or parametric witness: `212` +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V1.left_7`: side side7, value 7, first square witness {"divisor":2,"square":4,"quotient":3131,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V2.left_32`: side side7, value 32, first square witness {"divisor":3,"square":9,"quotient":6361,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V3.left_107`: side side7, value 107, first square witness {"divisor":2,"square":4,"quotient":47856,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V4.left_207`: side side7, value 207, first square witness {"divisor":2,"square":4,"quotient":92581,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V5.left_257`: side side7, value 257, first square witness {"divisor":3,"square":9,"quotient":51086,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V6.left_307`: side side7, value 307, first square witness {"divisor":2,"square":4,"quotient":137306,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V7.left_407`: side side7, value 407, first square witness {"divisor":2,"square":4,"quotient":182031,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D2.3_persist_outP2=99_out25=14_smaller=side7.V8.left_482`: side side7, value 482, first square witness {"divisor":3,"square":9,"quotient":95811,"stableUnderCurrentSplitModulus":false} + +## Vertex Presence Refinement + +- Status: `literal_core_requires_sharper_square_witness_split` +- Deterministic move: `emit_successor_atoms_by_square_witness_residue` +- Refinement condition count: `10` +- Covered unstable atoms: `212` +- Uncovered unstable atoms: `0` +- Proof boundary: These square-witness residue classes explain the bounded literal vertex-presence instability; each successor split still needs a theorem-facing persistence proof before it can support an all-N claim. +- Condition `square_4_outsider_1`: out mod 4 = 1, atoms=145, combined modulus=16900, successor=`outP2=99|out25=14|smaller=side7|out4=1` +- Condition `square_9_outsider_7`: out mod 9 = 7, atoms=49, combined modulus=38025, successor=`outP2=99|out25=14|smaller=side7|out9=7` +- Condition `square_49_outsider_25`: out mod 49 = 25, atoms=7, combined modulus=207025, successor=`outP2=99|out25=14|smaller=side7|out49=25` +- Condition `square_121_outsider_95`: out mod 121 = 95, atoms=3, combined modulus=511225, successor=`outP2=99|out25=14|smaller=side7|out121=95` +- Condition `square_289_outsider_55`: out mod 289 = 55, atoms=2, combined modulus=1221025, successor=`outP2=99|out25=14|smaller=side7|out289=55` +- Condition `square_529_outsider_202`: out mod 529 = 202, atoms=2, combined modulus=2235025, successor=`outP2=99|out25=14|smaller=side7|out529=202` +- Condition `square_361_outsider_345`: out mod 361 = 345, atoms=1, combined modulus=1525225, successor=`outP2=99|out25=14|smaller=side7|out361=345` +- Condition `square_961_outsider_828`: out mod 961 = 828, atoms=1, combined modulus=4060225, successor=`outP2=99|out25=14|smaller=side7|out961=828` +- Condition `square_1369_outsider_420`: out mod 1369 = 420, atoms=1, combined modulus=5784025, successor=`outP2=99|out25=14|smaller=side7|out1369=420` +- Condition `square_7921_outsider_1789`: out mod 7921 = 1789, atoms=1, combined modulus=33466225, successor=`outP2=99|out25=14|smaller=side7|out7921=1789` + +## Edge Obstruction Certificate + +- Status: `literal_edge_obstruction_certificate_verified` +- Proof kind: `literal_product_plus_one_squarefree_missing_edge_certificate` +- Edge atoms: `108` +- Squarefree edge atoms: `108` +- Non-squarefree edge atoms: `0` +- Product-plus-one range: `{"min":302,"max":52193902}` +- Mod 25 classes: `1` +- Prime-residue classes: `72` +- Prime-square fingerprints: `108` +- Proof boundary: This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim. +- Mod25 class `7:18`: edges=108 +- Prime-residue class `10:7:6`: edges=3 +- Prime-residue class `2:2:5`: edges=3 +- Prime-residue class `3:9:2`: edges=3 +- Prime-residue class `5:6:5`: edges=3 +- Prime-residue class `6:3:6`: edges=3 +- Prime-residue class `7:12:7`: edges=3 +- Prime-residue class `8:1:9`: edges=3 +- Prime-residue class `9:10:0`: edges=3 +- Prime-residue class `0:10:1`: edges=2 +- Prime-residue class `1:3:4`: edges=2 +- Prime-residue class `1:7:8`: edges=2 +- Prime-residue class `10:3:5`: edges=2 +- Prime-residue class `11:12:3`: edges=2 + +## Edge Congruence Persistence + +- Status: `literal_constant_edge_persistence_verified` +- Proof kind: `constant_pair_squarefree_invariant` +- Edge atoms: `108` +- Verified edge atoms: `108` +- Failed edge atoms: `0` +- Depends on sampled N: `no` +- Depends on witness outsider: `no` +- Proof boundary: This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions. +- Family `D2.3_persist_outP2=99_out25=14_smaller=side7.edge_constant_squarefree_family`: status=`congruence_persistence_family_verified`, edges=108, proof=constant_pair_squarefree_invariant + +## Matching Core + +- Pair (7, 43); residues mod25 7:18, mod p 7:4, mod p^2 7:43; product+1 mod p^2 133 +- Pair (32, 68); residues mod25 7:18, mod p 6:3, mod p^2 32:68; product+1 mod p^2 149 +- Pair (107, 143); residues mod25 7:18, mod p 3:0, mod p^2 107:143; product+1 mod p^2 92 +- Pair (207, 243); residues mod25 7:18, mod p 12:9, mod p^2 38:74; product+1 mod p^2 109 +- Pair (257, 293); residues mod25 7:18, mod p 10:7, mod p^2 88:124; product+1 mod p^2 97 +- Pair (307, 268); residues mod25 7:18, mod p 8:8, mod p^2 138:99; product+1 mod p^2 143 +- Pair (407, 343); residues mod25 7:18, mod p 4:5, mod p^2 69:5; product+1 mod p^2 8 +- Pair (482, 443); residues mod25 7:18, mod p 1:1, mod p^2 144:105; product+1 mod p^2 80 +- Pair (507, 518); residues mod25 7:18, mod p 0:11, mod p^2 0:11; product+1 mod p^2 1 +- Pair (607, 543); residues mod25 7:18, mod p 9:10, mod p^2 100:36; product+1 mod p^2 52 +- Pair (707, 643); residues mod25 7:18, mod p 5:6, mod p^2 31:136; product+1 mod p^2 161 +- Pair (782, 743); residues mod25 7:18, mod p 2:2, mod p^2 106:67; product+1 mod p^2 5 +- Pair (807, 843); residues mod25 7:18, mod p 1:11, mod p^2 131:167; product+1 mod p^2 77 +- Pair (907, 943); residues mod25 7:18, mod p 10:7, mod p^2 62:98; product+1 mod p^2 162 +- Pair (932, 968); residues mod25 7:18, mod p 9:6, mod p^2 87:123; product+1 mod p^2 55 +- Pair (982, 1143); residues mod25 7:18, mod p 7:12, mod p^2 137:129; product+1 mod p^2 98 +- Pair (1007, 1043); residues mod25 7:18, mod p 6:3, mod p^2 162:29; product+1 mod p^2 136 +- Pair (1107, 1243); residues mod25 7:18, mod p 2:8, mod p^2 93:60; product+1 mod p^2 4 +- Pair (1157, 1193); residues mod25 7:18, mod p 0:10, mod p^2 143:10; product+1 mod p^2 79 +- Pair (1207, 1343); residues mod25 7:18, mod p 11:4, mod p^2 24:160; product+1 mod p^2 123 +- Pair (1282, 1418); residues mod25 7:18, mod p 8:1, mod p^2 99:66; product+1 mod p^2 113 +- Pair (1307, 1443); residues mod25 7:18, mod p 7:0, mod p^2 124:91; product+1 mod p^2 131 +- Pair (1382, 1468); residues mod25 7:18, mod p 4:12, mod p^2 30:116; product+1 mod p^2 101 +- Pair (1407, 1543); residues mod25 7:18, mod p 3:9, mod p^2 55:22; product+1 mod p^2 28 +- Pair (1507, 1643); residues mod25 7:18, mod p 12:5, mod p^2 155:122; product+1 mod p^2 152 +- Pair (1532, 1743); residues mod25 7:18, mod p 11:1, mod p^2 11:53; product+1 mod p^2 77 +- Pair (1607, 1868); residues mod25 7:18, mod p 8:9, mod p^2 86:9; product+1 mod p^2 99 +- Pair (1707, 1843); residues mod25 7:18, mod p 4:10, mod p^2 17:153; product+1 mod p^2 67 +- Pair (1807, 1943); residues mod25 7:18, mod p 0:6, mod p^2 117:84; product+1 mod p^2 27 +- Pair (1832, 2043); residues mod25 7:18, mod p 12:2, mod p^2 142:15; product+1 mod p^2 103 +- Pair (1907, 2243); residues mod25 7:18, mod p 9:7, mod p^2 48:46; product+1 mod p^2 12 +- Pair (2007, 2143); residues mod25 7:18, mod p 5:11, mod p^2 148:115; product+1 mod p^2 121 +- Pair (2057, 2093); residues mod25 7:18, mod p 3:0, mod p^2 29:65; product+1 mod p^2 27 +- Pair (2107, 2318); residues mod25 7:18, mod p 1:4, mod p^2 79:121; product+1 mod p^2 96 +- Pair (2207, 2343); residues mod25 7:18, mod p 10:3, mod p^2 10:146; product+1 mod p^2 109 +- Pair (2282, 2443); residues mod25 7:18, mod p 7:12, mod p^2 85:77; product+1 mod p^2 124 +- Pair (2307, 2543); residues mod25 7:18, mod p 6:8, mod p^2 110:8; product+1 mod p^2 36 +- Pair (2407, 2643); residues mod25 7:18, mod p 2:4, mod p^2 41:108; product+1 mod p^2 35 +- Pair (2507, 2768); residues mod25 7:18, mod p 11:12, mod p^2 141:64; product+1 mod p^2 68 +- Pair (2607, 2743); residues mod25 7:18, mod p 7:0, mod p^2 72:39; product+1 mod p^2 105 +- Pair (2707, 2843); residues mod25 7:18, mod p 3:9, mod p^2 3:139; product+1 mod p^2 80 +- Pair (2732, 2693); residues mod25 7:18, mod p 2:2, mod p^2 28:158; product+1 mod p^2 31 +- Pair (2807, 2918); residues mod25 7:18, mod p 12:6, mod p^2 103:45; product+1 mod p^2 73 +- Pair (2907, 3043); residues mod25 7:18, mod p 8:1, mod p^2 34:1; product+1 mod p^2 35 +- Pair (2957, 2993); residues mod25 7:18, mod p 6:3, mod p^2 84:120; product+1 mod p^2 110 +- Pair (3007, 2943); residues mod25 7:18, mod p 4:5, mod p^2 134:70; product+1 mod p^2 86 +- Pair (3107, 3143); residues mod25 7:18, mod p 0:10, mod p^2 65:101; product+1 mod p^2 144 +- Pair (3182, 3243); residues mod25 7:18, mod p 10:6, mod p^2 140:32; product+1 mod p^2 87 +- Pair (3207, 3218); residues mod25 7:18, mod p 9:7, mod p^2 165:7; product+1 mod p^2 142 +- Pair (3232, 3343); residues mod25 7:18, mod p 8:2, mod p^2 21:132; product+1 mod p^2 69 +- Pair (3307, 3443); residues mod25 7:18, mod p 5:11, mod p^2 96:63; product+1 mod p^2 134 +- Pair (3407, 3543); residues mod25 7:18, mod p 1:7, mod p^2 27:163; product+1 mod p^2 8 +- Pair (3507, 3643); residues mod25 7:18, mod p 10:3, mod p^2 127:94; product+1 mod p^2 109 +- Pair (3607, 3743); residues mod25 7:18, mod p 6:12, mod p^2 58:25; product+1 mod p^2 99 +- Pair (3632, 3668); residues mod25 7:18, mod p 5:2, mod p^2 83:119; product+1 mod p^2 76 +- Pair (3707, 3768); residues mod25 7:18, mod p 2:11, mod p^2 158:50; product+1 mod p^2 127 +- Pair (3807, 3843); residues mod25 7:18, mod p 11:8, mod p^2 89:125; product+1 mod p^2 141 +- Pair (3857, 3893); residues mod25 7:18, mod p 9:6, mod p^2 139:6; product+1 mod p^2 159 +- Pair (3907, 3918); residues mod25 7:18, mod p 7:5, mod p^2 20:31; product+1 mod p^2 114 +- Pair (4007, 3943); residues mod25 7:18, mod p 3:4, mod p^2 120:56; product+1 mod p^2 130 +- Pair (4082, 4043); residues mod25 7:18, mod p 0:0, mod p^2 26:156; product+1 mod p^2 1 +- Pair (4107, 4068); residues mod25 7:18, mod p 12:12, mod p^2 51:12; product+1 mod p^2 106 +- Pair (4207, 4118); residues mod25 7:18, mod p 8:10, mod p^2 151:62; product+1 mod p^2 68 +- Pair (4307, 4143); residues mod25 7:18, mod p 4:9, mod p^2 82:87; product+1 mod p^2 37 +- Pair (4407, 4243); residues mod25 7:18, mod p 0:5, mod p^2 13:18; product+1 mod p^2 66 +- Pair (4457, 4568); residues mod25 7:18, mod p 11:5, mod p^2 63:5; product+1 mod p^2 147 +- Pair (4507, 4443); residues mod25 7:18, mod p 9:10, mod p^2 113:49; product+1 mod p^2 130 +- Pair (4532, 4343); residues mod25 7:18, mod p 8:1, mod p^2 138:118; product+1 mod p^2 61 +- Pair (4607, 4543); residues mod25 7:18, mod p 5:6, mod p^2 44:149; product+1 mod p^2 135 +- Pair (4707, 4618); residues mod25 7:18, mod p 1:3, mod p^2 144:55; product+1 mod p^2 147 +- Pair (4757, 4493); residues mod25 7:18, mod p 12:8, mod p^2 25:99; product+1 mod p^2 110 +- Pair (4807, 4843); residues mod25 7:18, mod p 10:7, mod p^2 75:111; product+1 mod p^2 45 +- Pair (4907, 4643); residues mod25 7:18, mod p 6:2, mod p^2 6:80; product+1 mod p^2 143 +- Pair (4982, 4743); residues mod25 7:18, mod p 3:11, mod p^2 81:11; product+1 mod p^2 47 +- Pair (5007, 4943); residues mod25 7:18, mod p 2:3, mod p^2 106:42; product+1 mod p^2 59 +- Pair (5107, 5018); residues mod25 7:18, mod p 11:0, mod p^2 37:117; product+1 mod p^2 105 +- Pair (5207, 5043); residues mod25 7:18, mod p 7:12, mod p^2 137:142; product+1 mod p^2 20 +- Pair (5307, 5143); residues mod25 7:18, mod p 3:8, mod p^2 68:73; product+1 mod p^2 64 +- Pair (5407, 5343); residues mod25 7:18, mod p 12:0, mod p^2 168:104; product+1 mod p^2 66 +- Pair (5432, 4793); residues mod25 7:18, mod p 11:9, mod p^2 24:61; product+1 mod p^2 113 +- Pair (5507, 5243); residues mod25 7:18, mod p 8:4, mod p^2 99:4; product+1 mod p^2 59 +- Pair (5607, 5443); residues mod25 7:18, mod p 4:9, mod p^2 30:35; product+1 mod p^2 37 +- Pair (5657, 5468); residues mod25 7:18, mod p 2:8, mod p^2 80:60; product+1 mod p^2 69 +- Pair (5682, 5543); residues mod25 7:18, mod p 1:5, mod p^2 105:135; product+1 mod p^2 149 +- Pair (5707, 5643); residues mod25 7:18, mod p 0:1, mod p^2 130:66; product+1 mod p^2 131 +- Pair (5807, 5743); residues mod25 7:18, mod p 9:10, mod p^2 61:166; product+1 mod p^2 156 +- Pair (5882, 5693); residues mod25 7:18, mod p 6:12, mod p^2 136:116; product+1 mod p^2 60 +- Pair (5907, 5843); residues mod25 7:18, mod p 5:6, mod p^2 161:97; product+1 mod p^2 70 +- Pair (6007, 5918); residues mod25 7:18, mod p 1:3, mod p^2 92:3; product+1 mod p^2 108 +- Pair (6107, 5943); residues mod25 7:18, mod p 10:2, mod p^2 23:28; product+1 mod p^2 138 +- Pair (6207, 6043); residues mod25 7:18, mod p 6:11, mod p^2 123:128; product+1 mod p^2 28 +- Pair (6307, 6243); residues mod25 7:18, mod p 2:3, mod p^2 54:159; product+1 mod p^2 137 +- Pair (6332, 6143); residues mod25 7:18, mod p 1:7, mod p^2 79:59; product+1 mod p^2 99 +- Pair (6407, 6343); residues mod25 7:18, mod p 11:12, mod p^2 154:90; product+1 mod p^2 3 +- Pair (6507, 6368); residues mod25 7:18, mod p 7:11, mod p^2 85:115; product+1 mod p^2 143 +- Pair (6557, 6293); residues mod25 7:18, mod p 5:1, mod p^2 135:40; product+1 mod p^2 162 +- Pair (6607, 6418); residues mod25 7:18, mod p 3:9, mod p^2 16:165; product+1 mod p^2 106 +- Pair (6707, 6443); residues mod25 7:18, mod p 12:8, mod p^2 116:21; product+1 mod p^2 71 +- Pair (6782, 6543); residues mod25 7:18, mod p 9:4, mod p^2 22:121; product+1 mod p^2 128 +- Pair (6807, 6643); residues mod25 7:18, mod p 8:0, mod p^2 47:52; product+1 mod p^2 79 +- Pair (6907, 6668); residues mod25 7:18, mod p 4:12, mod p^2 147:77; product+1 mod p^2 166 +- Pair (6957, 6593); residues mod25 7:18, mod p 2:2, mod p^2 28:2; product+1 mod p^2 57 +- Pair (7007, 6743); residues mod25 7:18, mod p 0:9, mod p^2 78:152; product+1 mod p^2 27 +- Pair (7032, 6818); residues mod25 7:18, mod p 12:6, mod p^2 103:58; product+1 mod p^2 60 +- Pair (7107, 6843); residues mod25 7:18, mod p 9:5, mod p^2 9:83; product+1 mod p^2 72 +- Pair (7207, 6943); residues mod25 7:18, mod p 5:1, mod p^2 109:14; product+1 mod p^2 6 +- Pair (7232, 7043); residues mod25 7:18, mod p 4:10, mod p^2 134:114; product+1 mod p^2 67 +- Pair (7307, 7143); residues mod25 7:18, mod p 1:6, mod p^2 40:45; product+1 mod p^2 111 diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.json new file mode 100644 index 0000000..c522063 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.json @@ -0,0 +1,70641 @@ +{ + "schema": "erdos.p848_split_atom_packet/1", + "generatedAt": "2026-04-14T11:46:09.813Z", + "problemId": "848", + "packetId": "p848_split_atom_packet_D3_1_persist_outP2_38_out25_23_smaller_side7", + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7", + "sourcePlanId": "p848_split_core_atomization_master_plan_v1", + "parentObligationId": "D3_p17_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "prime": 17, + "splitKey": "outP2=38|out25=23|smaller=side7", + "priority": "supporting_p17_companion_lane", + "status": "ready_for_symbolic_persistence_work", + "sourceArtifacts": { + "taskList": "TASK_LIST.json", + "formalizationWork": "FORMALIZATION_WORK.json", + "matchingPatternMiner": "MATCHING_PATTERN_MINER_P17.json" + }, + "inputs": { + "witnessCount": 10, + "nRange": "7307..7393", + "boundedTarget": { + "requiredMatchingLowerBoundRange": [ + 12, + 14 + ], + "commonMatchingPairCount": 109, + "commonMatchingPairExportComplete": true, + "commonMatchingPairs": [ + { + "leftValue": 7, + "rightValue": 43, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 7, + "rightModP2": 43, + "leftModP": 7, + "rightModP": 9, + "productPlusOneModP2": 13 + }, + { + "leftValue": 82, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 82, + "rightModP2": 118, + "leftModP": 14, + "rightModP": 16, + "productPlusOneModP2": 140 + }, + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1133093, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 10197837, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1133093, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1133093, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 10197837, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1133093, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5692553, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 22770212, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5692553, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5692553, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 22770212, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5692553, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 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"N": 7332, + "outsider": 4373, + "productPlusOne": 22988862, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2554318, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2554318, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 22988862, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2554318, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2554318, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 22988862, + "hasAnySquareDivisor": true, + 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"productPlusOne": 31953512, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7988378, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7988378, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 31953512, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7988378, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7988378, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 31953512, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7988378, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7988378, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7307 is present in the side7 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V110.right_43", + "side": "side18", + "value": 43, + "residues": { + "value": 43, + "mod25": 18, + "modP": 9, + "modP2": 43 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 188040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47010, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 43 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V111.right_118", + "side": "side18", + "value": 118, + "residues": { + "value": 118, + "mod25": 18, + "modP": 16, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 516015, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 57335, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 118 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V112.right_143", + "side": "side18", + "value": 143, + "residues": { + "value": 143, + "mod25": 18, + "modP": 7, + "modP2": 143 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 625340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156335, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V113.right_243", + "side": "side18", + "value": 243, + "residues": { + "value": 243, + "mod25": 18, + "modP": 5, + "modP2": 243 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 1062640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 265660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 66415, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 243 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V114.right_343", + "side": "side18", + "value": 343, + "residues": { + "value": 343, + "mod25": 18, + "modP": 3, + "modP2": 54 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 1499940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 374985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 166660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 41665, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 343 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V115.right_443", + "side": "side18", + "value": 443, + "residues": { + "value": 443, + "mod25": 18, + "modP": 1, + "modP2": 154 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 1937240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 484310, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 443 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V116.right_543", + "side": "side18", + "value": 543, + "residues": { + "value": 543, + "mod25": 18, + "modP": 16, + "modP2": 254 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 2374540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 593635, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 48460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 12115, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 543 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V117.right_568", + "side": "side18", + "value": 568, + "residues": { + "value": 568, + "mod25": 18, + "modP": 7, + "modP2": 279 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 2483865, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 30665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 2483865, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 30665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 2483865, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 30665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 2483865, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 30665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 2483865, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 275985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, 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"goal": "Prove right core vertex 568 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V118.right_643", + "side": "side18", + "value": 643, + "residues": { + "value": 643, + "mod25": 18, + "modP": 14, + "modP2": 65 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 2811840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 702960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 702960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 175740, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 43935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 2811840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 702960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 702960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 175740, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 43935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 2811840, + 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}, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 2921165, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 17285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 17285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 2921165, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 17285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 17285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 2921165, + "hasAnySquareDivisor": true, + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 3249140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 3249140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 3249140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 3249140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 3249140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 812285, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 743 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V121.right_793", + "side": "side18", + "value": 793, + "residues": { + "value": 793, + "mod25": 18, + "modP": 11, + "modP2": 215 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 3467790, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 385310, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 793 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V122.right_843", + "side": "side18", + "value": 843, + "residues": { + "value": 843, + "mod25": 18, + "modP": 10, + "modP2": 265 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 3686440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 921610, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 843 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V123.right_943", + "side": "side18", + "value": 943, + "residues": { + "value": 943, + "mod25": 18, + "modP": 8, + "modP2": 76 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 4123740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1030935, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 943 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V124.right_1018", + "side": "side18", + "value": 1018, + "residues": { + "value": 1018, + "mod25": 18, + "modP": 15, + "modP2": 151 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 4451715, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 494635, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1018 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V125.right_1043", + "side": "side18", + "value": 1043, + "residues": { + "value": 1043, + "mod25": 18, + "modP": 6, + "modP2": 176 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 4561040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1140260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 285065, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V126.right_1143", + "side": "side18", + "value": 1143, + "residues": { + "value": 1143, + "mod25": 18, + "modP": 4, + "modP2": 276 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 4998340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1249585, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V127.right_1243", + "side": "side18", + "value": 1243, + "residues": { + "value": 1243, + "mod25": 18, + "modP": 2, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 150990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 5435640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1358910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 603960, + "stableUnderCurrentSplitModulus": 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"firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1468235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1468235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 5872940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1468235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1468235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 5872940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1468235, + 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7184840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 7184840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 7184840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 7184840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 7184840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 7184840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1796210, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1643 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V133.right_1693", + "side": "side18", + "value": 1693, + "residues": { + "value": 1693, + "mod25": 18, + "modP": 10, + "modP2": 248 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 7403490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 822610, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1693 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V134.right_1743", + "side": "side18", + "value": 1743, + "residues": { + "value": 1743, 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 7622140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 1905535, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1743 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V135.right_1768", + "side": "side18", + "value": 1768, + "residues": { + "value": 1768, + "mod25": 18, + "modP": 0, + "modP2": 34 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 7731465, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 157785, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1768 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V136.right_1843", + "side": "side18", + "value": 1843, + "residues": { + "value": 1843, + "mod25": 18, + "modP": 7, + "modP2": 109 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 8059440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2014860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 503715, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1843 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V137.right_1918", + "side": "side18", + "value": 1918, + "residues": { + "value": 1918, + "mod25": 18, + "modP": 14, + "modP2": 184 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 8387415, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 931935, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1918 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V138.right_1943", + "side": "side18", + "value": 1943, + "residues": { + "value": 1943, + "mod25": 18, + "modP": 5, + "modP2": 209 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 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"productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 8496740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2124185, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1943 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V139.right_2043", + "side": "side18", + "value": 2043, + "residues": { + "value": 2043, + "mod25": 18, + "modP": 3, + "modP2": 20 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 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"productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 8934040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2233510, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V140.right_2143", + "side": "side18", + "value": 2143, + "residues": { + "value": 2143, + "mod25": 18, + "modP": 1, + "modP2": 120 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 9371340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2342835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1041260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 260315, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V141.right_2243", + "side": "side18", + "value": 2243, + "residues": { + "value": 2243, + "mod25": 18, + "modP": 16, + "modP2": 220 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 9808640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2452160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 613040, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 153260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 38315, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2243 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V142.right_2343", + "side": "side18", + "value": 2343, + "residues": { + "value": 2343, + "mod25": 18, + "modP": 14, + "modP2": 31 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 10245940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2561485, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2343 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V143.right_2368", + "side": "side18", + "value": 2368, + "residues": { + "value": 2368, + "mod25": 18, + "modP": 5, + "modP2": 56 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 10355265, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1150585, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2368 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V144.right_2443", + "side": "side18", + "value": 2443, + "residues": { + "value": 2443, + "mod25": 18, + "modP": 12, + "modP2": 131 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 10683240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2670810, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2443 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V145.right_2543", + "side": "side18", + "value": 2543, + "residues": { + "value": 2543, + "mod25": 18, + "modP": 10, + "modP2": 231 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2780135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 11120540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 139990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 11339190, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 139990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 11339190, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 139990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 11339190, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 139990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 11339190, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 139990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 11339190, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1259910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 139990, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2593 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V147.right_2643", + "side": "side18", + "value": 2643, + "residues": { + "value": 2643, + "mod25": 18, + "modP": 8, + "modP2": 42 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 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"square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 11557840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2889460, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 722365, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2643 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V148.right_2743", + "side": "side18", + "value": 2743, + "residues": { + "value": 2743, + "mod25": 18, + "modP": 6, + "modP2": 142 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 11995140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 2998785, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2743 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V149.right_2818", + "side": "side18", + "value": 2818, + "residues": { + "value": 2818, + "mod25": 18, + "modP": 13, + "modP2": 217 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 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"divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 12323115, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1369235, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2818 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V150.right_2843", + "side": "side18", + "value": 2843, + 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"hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3108110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3108110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 12432440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3108110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3108110, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2843 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": 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"quotient": 3326760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3326760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1478560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 831690, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 369640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 92410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 13307040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3326760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3326760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1478560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 831690, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 369640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 92410, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V155.right_3093", + "side": "side18", + "value": 3093, + "residues": { + "value": 3093, + "mod25": 18, + "modP": 16, + "modP2": 203 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 13525690, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 1163, + "square": 1352569, + "quotient": 10, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3093 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V156.right_3143", + "side": "side18", + "value": 3143, + "residues": { + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 13744340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3436085, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V157.right_3243", + "side": "side18", + "value": 3243, + "residues": { + "value": 3243, + "mod25": 18, + "modP": 13, + "modP2": 64 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 14181640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3545410, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3243 is present 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"N": 7343, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 14290965, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1587885, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3268 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V159.right_3293", + "side": "side18", + "value": 3293, + "residues": { + "value": 3293, + "mod25": 18, + "modP": 12, + "modP2": 114 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 14400290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 39890, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3293 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V160.right_3343", + "side": "side18", + "value": 3343, + "residues": { + "value": 3343, + "mod25": 18, + "modP": 11, + "modP2": 164 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3654735, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 14618940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 15056240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3764060, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 941015, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 53, + "square": 2809, + "quotient": 5360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 106, + "square": 11236, + "quotient": 1340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 212, + "square": 44944, + "quotient": 335, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3443 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V162.right_3493", + "side": "side18", + "value": 3493, + "residues": { + "value": 3493, + "mod25": 18, + "modP": 8, 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 15274890, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 15274890, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 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"productPlusOne": 15274890, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 15274890, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 15274890, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 15274890, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1697210, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3493 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V163.right_3543", + "side": 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"square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 15493540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 15493540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 15493540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 15493540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 15493540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 15493540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3873385, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 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"D3.1_persist_outP2=38_out25=23_smaller=side7.V164.right_3643", + "side": "side18", + "value": 3643, + "residues": { + "value": 3643, + "mod25": 18, + "modP": 5, + "modP2": 175 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 15930840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 15930840, + "hasAnySquareDivisor": true, + 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 15930840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 15930840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 15930840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 15930840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3982710, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3643 is present 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+ "divisor": 3, + "square": 9, + "quotient": 1806535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1806535, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 30735, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 3415, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 16258815, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1806535, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 1806535, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 30735, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 69, + "square": 4761, + "quotient": 3415, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3718 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V166.right_3743", + "side": "side18", + "value": 3743, + "residues": { + "value": 3743, + "mod25": 18, + "modP": 3, + "modP2": 275 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4092035, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 16368140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 16805440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4201360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1050340, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 262585, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3843 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V168.right_3943", + "side": "side18", + "value": 3943, + "residues": { + "value": 3943, + "mod25": 18, + "modP": 16, + "modP2": 186 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 17242740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4310685, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 1915860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 478965, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3943 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V169.right_4043", + "side": "side18", + "value": 4043, + "residues": { + "value": 4043, + "mod25": 18, + "modP": 14, + "modP2": 286 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 17680040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4420010, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V170.right_4143", + "side": "side18", + "value": 4143, + "residues": { + "value": 4143, + "mod25": 18, + "modP": 12, + "modP2": 97 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 18117340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4529335, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V171.right_4168", + "side": "side18", + "value": 4168, + "residues": { + "value": 4168, + "mod25": 18, + "modP": 3, + "modP2": 122 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 18226665, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2025185, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4168 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V172.right_4218", + "side": "side18", + "value": 4218, + "residues": { + "value": 4218, + "mod25": 18, + "modP": 2, + "modP2": 172 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 18445315, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 376435, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4218 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V173.right_4243", + "side": "side18", + "value": 4243, + "residues": { + "value": 4243, + "mod25": 18, + "modP": 10, + "modP2": 197 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 18554640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4638660, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1159665, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4243 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V174.right_4343", + "side": "side18", + "value": 4343, + "residues": { + "value": 4343, + "mod25": 18, + "modP": 8, + "modP2": 8 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 18991940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4747985, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4343 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V175.right_4393", + "side": "side18", + "value": 4393, + "residues": { + "value": 4393, + "mod25": 18, + "modP": 7, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 19210590, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2134510, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4393 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V176.right_4443", + "side": "side18", + "value": 4443, + "residues": { + "value": 4443, + "mod25": 18, + "modP": 6, + "modP2": 108 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 19429240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4857310, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4443 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V177.right_4543", + "side": "side18", + "value": 4543, + "residues": { + "value": 4543, + "mod25": 18, + "modP": 4, + "modP2": 208 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 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"firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 19866540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 4966635, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4543 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V178.right_4618", + "side": "side18", + "value": 4618, + "residues": { + "value": 4618, + "mod25": 18, + "modP": 11, + "modP2": 283 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + 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"hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 20194515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2243835, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 249315, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4618 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V179.right_4643", + "side": "side18", + "value": 4643, + "residues": { + "value": 4643, + "mod25": 18, + "modP": 2, + "modP2": 19 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 20303840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 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"square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 20303840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 20303840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 20303840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 20303840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 20303840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5075960, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1268990, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4643 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V180.right_4743", + "side": "side18", + "value": 4743, + "residues": { + "value": 4743, + "mod25": 18, + "modP": 0, + "modP2": 119 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 20741140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 20741140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 20741140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 20741140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 20741140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5185285, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4743 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V181.right_4843", + "side": "side18", + "value": 4843, + "residues": { + "value": 4843, + "mod25": 18, + "modP": 15, + "modP2": 219 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 21178440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": 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"outsider": 4373, + "productPlusOne": 21178440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2353160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 588290, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 21178440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, 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"hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 2353160, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 588290, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 21178440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5294610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5294610, + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 126610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 21397090, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 126610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 126610, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 21397090, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 126610, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 22053040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 22053040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 22053040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 22053040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 22053040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 22053040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5513260, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1378315, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V185.right_5068", + "side": "side18", + "value": 5068, + "residues": { + "value": 5068, + "mod25": 18, + "modP": 2, + "modP2": 155 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 22162365, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2462485, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5068 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V186.right_5143", + "side": "side18", + "value": 5143, + "residues": { + "value": 5143, + "mod25": 18, + "modP": 9, + "modP2": 230 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 22490340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5622585, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V187.right_5243", + "side": "side18", + "value": 5243, + "residues": { + "value": 5243, + "mod25": 18, + "modP": 7, + "modP2": 41 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 22927640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5731910, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5243 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V188.right_5293", + "side": "side18", + "value": 5293, + "residues": { + "value": 5293, + "mod25": 18, + "modP": 6, + "modP2": 91 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 23146290, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2571810, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5293 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V189.right_5343", + "side": "side18", + "value": 5343, + "residues": { + "value": 5343, + "mod25": 18, + "modP": 5, + "modP2": 141 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 23364940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5841235, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5343 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V190.right_5443", + "side": "side18", + "value": 5443, + "residues": { + "value": 5443, + "mod25": 18, + "modP": 3, + "modP2": 241 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 23802240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5950560, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1487640, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 485760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 371910, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 121440, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 30360, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 56, + "square": 3136, + "quotient": 7590, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5443 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V191.right_5518", + "side": "side18", + "value": 5518, + "residues": { + "value": 5518, + "mod25": 18, + "modP": 10, + "modP2": 27 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 24130215, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2681135, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5518 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V192.right_5543", + "side": "side18", + "value": 5543, + "residues": { + "value": 5543, + "mod25": 18, + "modP": 1, + "modP2": 52 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 24239540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6059885, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5543 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V193.right_5643", + "side": "side18", + "value": 5643, + "residues": { + "value": 5643, + "mod25": 18, + "modP": 16, + "modP2": 152 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 24676840, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6169210, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5643 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V194.right_5693", + "side": "side18", + "value": 5693, + "residues": { + "value": 5693, + "mod25": 18, + "modP": 15, + "modP2": 202 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 157, + "square": 24649, + "quotient": 1010, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 24895490, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + 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"hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1596965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 25551440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1596965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 25551440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1596965, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 25551440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6387860, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1596965, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5843 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V198.right_5943", + "side": "side18", + "value": 5943, + "residues": { + "value": 5943, + "mod25": 18, + "modP": 10, + "modP2": 163 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 25988740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6497185, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5943 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V199.right_5968", + "side": "side18", + "value": 5968, + "residues": { + "value": 5968, + "mod25": 18, + "modP": 1, + "modP2": 188 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 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"productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 26098065, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2899785, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5968 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V200.right_5993", + "side": "side18", + "value": 5993, + "residues": { + "value": 5993, + "mod25": 18, + "modP": 9, + "modP2": 213 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 121, + "square": 14641, + "quotient": 1790, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 121, + "square": 14641, + "quotient": 1790, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 121, + "square": 14641, + "quotient": 1790, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 121, + "square": 14641, + "quotient": 1790, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 121, + "square": 14641, + "quotient": 1790, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + 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"outsider": 4373, + "productPlusOne": 26207390, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 216590, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 121, + "square": 14641, + "quotient": 1790, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5993 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V201.right_6043", + "side": "side18", + "value": 6043, + "residues": { + "value": 6043, + "mod25": 18, + "modP": 8, + "modP2": 263 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": 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"stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 26426040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 26426040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 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"firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 26426040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6606510, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V202.right_6143", + "side": "side18", + "value": 6143, + "residues": { + "value": 6143, + "mod25": 18, + "modP": 6, + "modP2": 74 + }, + "status": 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] + }, + "goal": "Prove right core vertex 6243 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V205.right_6343", + "side": "side18", + "value": 6343, + "residues": { + "value": 6343, + "mod25": 18, + "modP": 2, + "modP2": 274 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 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"divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 27737940, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 6934485, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6343 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V206.right_6418", + "side": "side18", + "value": 6418, + "residues": { + "value": 6418, + "mod25": 18, + "modP": 9, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 28065915, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3118435, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6418 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V207.right_6443", + "side": "side18", + "value": 6443, + "residues": { + "value": 6443, + "mod25": 18, + "modP": 0, + "modP2": 85 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 28175240, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7043810, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6443 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V208.right_6543", + "side": "side18", + "value": 6543, + "residues": { + "value": 6543, + "mod25": 18, + "modP": 15, + "modP2": 185 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 28612540, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7153135, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6543 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V209.right_6618", + "side": "side18", + "value": 6618, + "residues": { + "value": 6618, + "mod25": 18, + "modP": 5, + "modP2": 260 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 28940515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 28940515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 28940515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + 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"stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 28940515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 28940515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": 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] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 28940515, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 31, + "square": 961, + "quotient": 30115, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6618 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V210.right_6643", + "side": "side18", + "value": 6643, + "residues": { + "value": 6643, + "mod25": 18, + "modP": 13, + "modP2": 285 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 29487140, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7371785, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6743 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V213.right_6843", + "side": "side18", + "value": 6843, + "residues": { + "value": 6843, + "mod25": 18, + "modP": 9, + "modP2": 196 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 29924440, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7481110, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 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"hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 30033765, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 30033765, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 30033765, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 30033765, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 30033765, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3337085, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6868 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V215.right_6943", + "side": "side18", + "value": 6943, + "residues": { + "value": 6943, + "mod25": 18, + "modP": 7, + "modP2": 7 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + 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"N": 7307, + "outsider": 4373, + "productPlusOne": 30361740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 30361740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 30361740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 30361740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 30361740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 30361740, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7590435, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6943 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V216.right_7043", + "side": "side18", + "value": 7043, + "residues": { + "value": 7043, + "mod25": 18, + "modP": 5, + "modP2": 107 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 30799040, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7699760, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1924940, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 481235, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7043 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V217.right_7143", + "side": "side18", + "value": 7143, + "residues": { + "value": 7143, + "mod25": 18, + "modP": 3, + "modP2": 207 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7366, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7368, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 31236340, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7809085, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7143 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.V218.right_7243", + "side": "side18", + "value": 7243, + "residues": { + "value": 7243, + "mod25": 18, + "modP": 1, + "modP2": 18 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7343, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7332, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7337, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7357, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 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"squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7382, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7393, + "outsider": 4373, + "productPlusOne": 31673640, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 7918410, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7243 is present in the side18 compatible set for every row in split outP2=38|out25=23|smaller=side7." + } + ], + "vertexPresenceSummary": { + "splitModulus": 7225, + "witnessRowCount": 10, + "vertexPresenceAtomCount": 218, + "stableUnderCurrentSplitModulusCount": 2, + "needsSharperSplitOrParametricWitnessCount": 216, + "failedVertexPresenceAtomCount": 0, + "refinementStatus": "literal_core_requires_sharper_square_witness_split", + "refinementConditionCount": 9, + "dominantRefinementConditions": [ + { + "conditionId": "square_4_outsider_1", + "square": 4, + "requiredOutsiderResidueModSquare": 1, + "atomCount": 146, + "successorSplitKey": "outP2=38|out25=23|smaller=side7|out4=1" + }, + { + "conditionId": "square_9_outsider_8", + "square": 9, + "requiredOutsiderResidueModSquare": 8, + "atomCount": 48, + "successorSplitKey": "outP2=38|out25=23|smaller=side7|out9=8" + }, + { + "conditionId": 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missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E12.left_807_right_743", + "pairIndex": 11, + "pair": { + "leftValue": 807, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 229, + "rightModP2": 165, + "leftModP": 8, + "rightModP": 12, + "productPlusOneModP2": 216 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 599602, + "checkedSquareRootFloor": 774, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (807, 743) remains a missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E13.left_907_right_843", + "pairIndex": 12, + "pair": { + "leftValue": 907, + "rightValue": 843, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 40, + "rightModP2": 265, + "leftModP": 6, + "rightModP": 10, + "productPlusOneModP2": 197 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 764602, + "checkedSquareRootFloor": 874, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (907, 843) remains a missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E14.left_982_right_943", + "pairIndex": 13, + "pair": { + "leftValue": 982, + "rightValue": 943, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 115, + "rightModP2": 76, + "leftModP": 13, + "rightModP": 8, + "productPlusOneModP2": 71 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 926027, + "checkedSquareRootFloor": 962, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (982, 943) remains a missing cross edge throughout split 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"productPlusOneModP2": 62 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1050577, + "checkedSquareRootFloor": 1024, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1032, 1018) remains a missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E17.left_1082_right_1143", + "pairIndex": 16, + "pair": { + "leftValue": 1082, + "rightValue": 1143, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 215, + "rightModP2": 276, + "leftModP": 11, + "rightModP": 4, + "productPlusOneModP2": 96 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1236727, + "checkedSquareRootFloor": 1112, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1082, 1143) remains a missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E18.left_1107_right_1243", + "pairIndex": 17, + "pair": { + "leftValue": 1107, + "rightValue": 1243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 240, + "rightModP2": 87, + "leftModP": 2, + "rightModP": 2, + "productPlusOneModP2": 73 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1376002, + "checkedSquareRootFloor": 1173, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1107, 1243) remains a missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E19.left_1207_right_1343", + "pairIndex": 18, + "pair": { + "leftValue": 1207, + "rightValue": 1343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 51, + "rightModP2": 187, + "leftModP": 0, + "rightModP": 0, + "productPlusOneModP2": 1 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1621002, + "checkedSquareRootFloor": 1273, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1207, 1343) remains a missing cross edge throughout split outP2=38|out25=23|smaller=side7." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E20.left_1307_right_1443", + "pairIndex": 19, + "pair": { + "leftValue": 1307, + "rightValue": 1443, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 151, + "rightModP2": 287, + "leftModP": 15, + "rightModP": 15, + "productPlusOneModP2": 277 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1886002, + "checkedSquareRootFloor": 1373, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1307, 1443) remains a missing cross edge 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"D3.1_persist_outP2=38_out25=23_smaller=side7.E10.left_707_right_668", + "leftValue": 707, + "rightValue": 668, + "productPlusOne": 472277 + } + ], + "edgeCount": 1 + }, + { + "groupKey": "133:269:231", + "leftModP2": 133, + "rightModP2": 269, + "productPlusOneModP2": 231, + "edgeAtomIds": [ + "D3.1_persist_outP2=38_out25=23_smaller=side7.E71.left_4757_right_4893" + ], + "examples": [ + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E71.left_4757_right_4893", + "leftValue": 4757, + "rightValue": 4893, + "productPlusOne": 23276002 + } + ], + "edgeCount": 1 + }, + { + "groupKey": "138:74:98", + "leftModP2": 138, + "rightModP2": 74, + "productPlusOneModP2": 98, + "edgeAtomIds": [ + "D3.1_persist_outP2=38_out25=23_smaller=side7.E93.left_6207_right_6143" + ], + "examples": [ + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E93.left_6207_right_6143", + "leftValue": 6207, + "rightValue": 6143, + "productPlusOne": 38129602 + } + ], + "edgeCount": 1 + }, + { + "groupKey": "139:175:50", + "leftModP2": 139, + "rightModP2": 175, + "productPlusOneModP2": 50, + "edgeAtomIds": [ + "D3.1_persist_outP2=38_out25=23_smaller=side7.E54.left_3607_right_3643" + ], + "examples": [ + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E54.left_3607_right_3643", + "leftValue": 3607, + "rightValue": 3643, + "productPlusOne": 13140302 + } + ], + "edgeCount": 1 + } + ], + "firstEdgeCertificates": [ + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E1.left_7_right_43", + "leftValue": 7, + "rightValue": 43, + "productPlusOne": 302, + "checkedSquareRootFloor": 17, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E2.left_82_right_118", + "leftValue": 82, + "rightValue": 118, + "productPlusOne": 9677, + "checkedSquareRootFloor": 98, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E3.left_107_right_143", + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302, + "checkedSquareRootFloor": 123, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E4.left_207_right_243", + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302, + "checkedSquareRootFloor": 224, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E5.left_307_right_343", + "leftValue": 307, + "rightValue": 343, + "productPlusOne": 105302, + "checkedSquareRootFloor": 324, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E6.left_407_right_443", + "leftValue": 407, + "rightValue": 443, + "productPlusOne": 180302, + "checkedSquareRootFloor": 424, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E7.left_507_right_543", + "leftValue": 507, + "rightValue": 543, + "productPlusOne": 275302, + "checkedSquareRootFloor": 524, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E8.left_532_right_568", + "leftValue": 532, + "rightValue": 568, + "productPlusOne": 302177, + "checkedSquareRootFloor": 549, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E9.left_607_right_643", + "leftValue": 607, + "rightValue": 643, + "productPlusOne": 390302, + "checkedSquareRootFloor": 624, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E10.left_707_right_668", + "leftValue": 707, + "rightValue": 668, + "productPlusOne": 472277, + "checkedSquareRootFloor": 687, + "squareDivisorWitnesses": [], + "isSquarefree": true + } + ], + "failedEdgeAtoms": [], + "proofBoundary": "This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim.", + "nextTheoremAction": "Promote this literal edge-obstruction certificate into A5 congruence-persistence families, or emit a sharper successor atom for any edge whose obstruction is not implied by the split hypotheses." + }, + "edgeCongruencePersistence": { + "schema": "erdos.p848_edge_congruence_persistence/1", + "persistenceId": "D3.1_persist_outP2=38_out25=23_smaller=side7.edge_congruence_persistence", + "status": "literal_constant_edge_persistence_verified", + "proofKind": "constant_pair_squarefree_invariant", + "splitKey": "outP2=38|out25=23|smaller=side7", + "splitModulus": 7225, + "witnessRowCount": 10, + "edgeAtomCount": 109, + "verifiedEdgeAtomCount": 109, + "failedEdgeAtomCount": 0, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "proofFamilies": [ + { + "familyId": "D3.1_persist_outP2=38_out25=23_smaller=side7.edge_constant_squarefree_family", + "status": "congruence_persistence_family_verified", + "proofKind": "constant_pair_squarefree_invariant", + "edgeAtomCount": 109, + "verifiedEdgeAtomCount": 109, + "failedEdgeAtomCount": 0, + "splitKey": "outP2=38|out25=23|smaller=side7", + "splitModulus": 7225, + "statement": "For each exported literal cross pair (l,r), l and r are constants in the packet, so l*r+1 is the same integer for every row satisfying the split hypotheses.", + "proofSteps": [ + "Recompute c = l*r + 1 from the exported literal pair.", + "Check c matches the squarefree certificate attached to the edge atom.", + "Because c has no N or outsider variable, the edge obstruction persists over all rows covered by this literal packet." + ], + "proofBoundary": "This is not yet a parameterized edge-family theorem. If later proof work replaces literal pair constants with formulas in N, this constant-family proof must be lifted or replaced.", + "exampleEdgeAtoms": [ + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E1.left_7_right_43", + "leftValue": 7, + "rightValue": 43, + "productPlusOne": 302 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E2.left_82_right_118", + "leftValue": 82, + "rightValue": 118, + "productPlusOne": 9677 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E3.left_107_right_143", + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E4.left_207_right_243", + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E5.left_307_right_343", + "leftValue": 307, + "rightValue": 343, + "productPlusOne": 105302 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E6.left_407_right_443", + "leftValue": 407, + "rightValue": 443, + "productPlusOne": 180302 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E7.left_507_right_543", + "leftValue": 507, + "rightValue": 543, + "productPlusOne": 275302 + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E8.left_532_right_568", + "leftValue": 532, + "rightValue": 568, + "productPlusOne": 302177 + } + ] + } + ], + "checks": [ + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E1.left_7_right_43", + "pairIndex": 0, + "leftValue": 7, + "rightValue": 43, + "productPlusOne": 302, + "productPlusOneRecomputed": 302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E2.left_82_right_118", + "pairIndex": 1, + "leftValue": 82, + "rightValue": 118, + "productPlusOne": 9677, + "productPlusOneRecomputed": 9677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E3.left_107_right_143", + "pairIndex": 2, + "leftValue": 107, + "rightValue": 143, + "productPlusOne": 15302, + "productPlusOneRecomputed": 15302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E4.left_207_right_243", + "pairIndex": 3, + "leftValue": 207, + "rightValue": 243, + "productPlusOne": 50302, + "productPlusOneRecomputed": 50302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E5.left_307_right_343", + "pairIndex": 4, + "leftValue": 307, + "rightValue": 343, + "productPlusOne": 105302, + "productPlusOneRecomputed": 105302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E6.left_407_right_443", + "pairIndex": 5, + "leftValue": 407, + "rightValue": 443, + "productPlusOne": 180302, + "productPlusOneRecomputed": 180302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E7.left_507_right_543", + "pairIndex": 6, + "leftValue": 507, + "rightValue": 543, + "productPlusOne": 275302, + "productPlusOneRecomputed": 275302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E8.left_532_right_568", + "pairIndex": 7, + "leftValue": 532, + "rightValue": 568, + "productPlusOne": 302177, + "productPlusOneRecomputed": 302177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E9.left_607_right_643", + "pairIndex": 8, + "leftValue": 607, + "rightValue": 643, + "productPlusOne": 390302, + "productPlusOneRecomputed": 390302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E10.left_707_right_668", + "pairIndex": 9, + "leftValue": 707, + "rightValue": 668, + "productPlusOne": 472277, + "productPlusOneRecomputed": 472277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E11.left_757_right_793", + "pairIndex": 10, + "leftValue": 757, + "rightValue": 793, + "productPlusOne": 600302, + "productPlusOneRecomputed": 600302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E12.left_807_right_743", + "pairIndex": 11, + "leftValue": 807, + "rightValue": 743, + "productPlusOne": 599602, + "productPlusOneRecomputed": 599602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E13.left_907_right_843", + "pairIndex": 12, + "leftValue": 907, + "rightValue": 843, + "productPlusOne": 764602, + "productPlusOneRecomputed": 764602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E14.left_982_right_943", + "pairIndex": 13, + "leftValue": 982, + "rightValue": 943, + "productPlusOne": 926027, + "productPlusOneRecomputed": 926027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E15.left_1007_right_1043", + "pairIndex": 14, + "leftValue": 1007, + "rightValue": 1043, + "productPlusOne": 1050302, + "productPlusOneRecomputed": 1050302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E16.left_1032_right_1018", + "pairIndex": 15, + "leftValue": 1032, + "rightValue": 1018, + "productPlusOne": 1050577, + "productPlusOneRecomputed": 1050577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E17.left_1082_right_1143", + "pairIndex": 16, + "leftValue": 1082, + "rightValue": 1143, + "productPlusOne": 1236727, + "productPlusOneRecomputed": 1236727, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E18.left_1107_right_1243", + "pairIndex": 17, + "leftValue": 1107, + "rightValue": 1243, + "productPlusOne": 1376002, + "productPlusOneRecomputed": 1376002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E19.left_1207_right_1343", + "pairIndex": 18, + "leftValue": 1207, + "rightValue": 1343, + "productPlusOne": 1621002, + "productPlusOneRecomputed": 1621002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E20.left_1307_right_1443", + "pairIndex": 19, + "leftValue": 1307, + "rightValue": 1443, + "productPlusOne": 1886002, + "productPlusOneRecomputed": 1886002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E21.left_1407_right_1468", + "pairIndex": 20, + "leftValue": 1407, + "rightValue": 1468, + "productPlusOne": 2065477, + "productPlusOneRecomputed": 2065477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E22.left_1432_right_1543", + "pairIndex": 21, + "leftValue": 1432, + "rightValue": 1543, + "productPlusOne": 2209577, + "productPlusOneRecomputed": 2209577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E23.left_1507_right_1643", + "pairIndex": 22, + "leftValue": 1507, + "rightValue": 1643, + "productPlusOne": 2476002, + "productPlusOneRecomputed": 2476002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E24.left_1607_right_1743", + "pairIndex": 23, + "leftValue": 1607, + "rightValue": 1743, + "productPlusOne": 2801002, + "productPlusOneRecomputed": 2801002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E25.left_1657_right_1693", + "pairIndex": 24, + "leftValue": 1657, + "rightValue": 1693, + "productPlusOne": 2805302, + "productPlusOneRecomputed": 2805302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E26.left_1682_right_1768", + "pairIndex": 25, + "leftValue": 1682, + "rightValue": 1768, + "productPlusOne": 2973777, + "productPlusOneRecomputed": 2973777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E27.left_1707_right_1843", + "pairIndex": 26, + "leftValue": 1707, + "rightValue": 1843, + "productPlusOne": 3146002, + "productPlusOneRecomputed": 3146002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E28.left_1807_right_1918", + "pairIndex": 27, + "leftValue": 1807, + "rightValue": 1918, + "productPlusOne": 3465827, + "productPlusOneRecomputed": 3465827, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E29.left_1882_right_2043", + "pairIndex": 28, + "leftValue": 1882, + "rightValue": 2043, + "productPlusOne": 3844927, + "productPlusOneRecomputed": 3844927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E30.left_1907_right_1943", + "pairIndex": 29, + "leftValue": 1907, + "rightValue": 1943, + "productPlusOne": 3705302, + "productPlusOneRecomputed": 3705302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E31.left_2007_right_2143", + "pairIndex": 30, + "leftValue": 2007, + "rightValue": 2143, + "productPlusOne": 4301002, + "productPlusOneRecomputed": 4301002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E32.left_2107_right_2243", + "pairIndex": 31, + "leftValue": 2107, + "rightValue": 2243, + "productPlusOne": 4726002, + "productPlusOneRecomputed": 4726002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E33.left_2207_right_2343", + "pairIndex": 32, + "leftValue": 2207, + "rightValue": 2343, + "productPlusOne": 5171002, + "productPlusOneRecomputed": 5171002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E34.left_2307_right_2443", + "pairIndex": 33, + "leftValue": 2307, + "rightValue": 2443, + "productPlusOne": 5636002, + "productPlusOneRecomputed": 5636002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E35.left_2332_right_2368", + "pairIndex": 34, + "leftValue": 2332, + "rightValue": 2368, + "productPlusOne": 5522177, + "productPlusOneRecomputed": 5522177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E36.left_2407_right_2543", + "pairIndex": 35, + "leftValue": 2407, + "rightValue": 2543, + "productPlusOne": 6121002, + "productPlusOneRecomputed": 6121002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E37.left_2507_right_2643", + "pairIndex": 36, + "leftValue": 2507, + "rightValue": 2643, + "productPlusOne": 6626002, + "productPlusOneRecomputed": 6626002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E38.left_2557_right_2593", + "pairIndex": 37, + "leftValue": 2557, + "rightValue": 2593, + "productPlusOne": 6630302, + "productPlusOneRecomputed": 6630302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E39.left_2607_right_2743", + "pairIndex": 38, + "leftValue": 2607, + "rightValue": 2743, + "productPlusOne": 7151002, + "productPlusOneRecomputed": 7151002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E40.left_2707_right_2818", + "pairIndex": 39, + "leftValue": 2707, + "rightValue": 2818, + "productPlusOne": 7628327, + "productPlusOneRecomputed": 7628327, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E41.left_2782_right_2943", + "pairIndex": 40, + "leftValue": 2782, + "rightValue": 2943, + "productPlusOne": 8187427, + "productPlusOneRecomputed": 8187427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E42.left_2807_right_2843", + "pairIndex": 41, + "leftValue": 2807, + "rightValue": 2843, + "productPlusOne": 7980302, + "productPlusOneRecomputed": 7980302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E43.left_2907_right_2968", + "pairIndex": 42, + "leftValue": 2907, + "rightValue": 2968, + "productPlusOne": 8627977, + "productPlusOneRecomputed": 8627977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E44.left_2932_right_3043", + "pairIndex": 43, + "leftValue": 2932, + "rightValue": 3043, + "productPlusOne": 8922077, + "productPlusOneRecomputed": 8922077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E45.left_3007_right_3143", + "pairIndex": 44, + "leftValue": 3007, + "rightValue": 3143, + "productPlusOne": 9451002, + "productPlusOneRecomputed": 9451002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E46.left_3107_right_3243", + "pairIndex": 45, + "leftValue": 3107, + "rightValue": 3243, + "productPlusOne": 10076002, + "productPlusOneRecomputed": 10076002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E47.left_3207_right_3268", + "pairIndex": 46, + "leftValue": 3207, + "rightValue": 3268, + "productPlusOne": 10480477, + "productPlusOneRecomputed": 10480477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E48.left_3232_right_2993", + "pairIndex": 47, + "leftValue": 3232, + "rightValue": 2993, + "productPlusOne": 9673377, + "productPlusOneRecomputed": 9673377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E49.left_3307_right_3343", + "pairIndex": 48, + "leftValue": 3307, + "rightValue": 3343, + "productPlusOne": 11055302, + "productPlusOneRecomputed": 11055302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E50.left_3407_right_3443", + "pairIndex": 49, + "leftValue": 3407, + "rightValue": 3443, + "productPlusOne": 11730302, + "productPlusOneRecomputed": 11730302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E51.left_3457_right_3093", + "pairIndex": 50, + "leftValue": 3457, + "rightValue": 3093, + "productPlusOne": 10692502, + "productPlusOneRecomputed": 10692502, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E52.left_3507_right_3543", + "pairIndex": 51, + "leftValue": 3507, + "rightValue": 3543, + "productPlusOne": 12425302, + "productPlusOneRecomputed": 12425302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E53.left_3532_right_3293", + "pairIndex": 52, + "leftValue": 3532, + "rightValue": 3293, + "productPlusOne": 11630877, + "productPlusOneRecomputed": 11630877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E54.left_3607_right_3643", + "pairIndex": 53, + "leftValue": 3607, + "rightValue": 3643, + "productPlusOne": 13140302, + "productPlusOneRecomputed": 13140302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E55.left_3682_right_3493", + "pairIndex": 54, + "leftValue": 3682, + "rightValue": 3493, + "productPlusOne": 12861227, + "productPlusOneRecomputed": 12861227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E56.left_3707_right_3743", + "pairIndex": 55, + "leftValue": 3707, + "rightValue": 3743, + "productPlusOne": 13875302, + "productPlusOneRecomputed": 13875302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E57.left_3807_right_3718", + "pairIndex": 56, + "leftValue": 3807, + "rightValue": 3718, + "productPlusOne": 14154427, + "productPlusOneRecomputed": 14154427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E58.left_3907_right_3843", + "pairIndex": 57, + "leftValue": 3907, + "rightValue": 3843, + "productPlusOne": 15014602, + "productPlusOneRecomputed": 15014602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E59.left_4007_right_3943", + "pairIndex": 58, + "leftValue": 4007, + "rightValue": 3943, + "productPlusOne": 15799602, + "productPlusOneRecomputed": 15799602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E60.left_4057_right_4168", + "pairIndex": 59, + "leftValue": 4057, + "rightValue": 4168, + "productPlusOne": 16909577, + "productPlusOneRecomputed": 16909577, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E61.left_4107_right_4043", + "pairIndex": 60, + "leftValue": 4107, + "rightValue": 4043, + "productPlusOne": 16604602, + "productPlusOneRecomputed": 16604602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E62.left_4132_right_4143", + "pairIndex": 61, + "leftValue": 4132, + "rightValue": 4143, + "productPlusOne": 17118877, + "productPlusOneRecomputed": 17118877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E63.left_4207_right_4218", + "pairIndex": 62, + "leftValue": 4207, + "rightValue": 4218, + "productPlusOne": 17745127, + "productPlusOneRecomputed": 17745127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E64.left_4307_right_4243", + "pairIndex": 63, + "leftValue": 4307, + "rightValue": 4243, + "productPlusOne": 18274602, + "productPlusOneRecomputed": 18274602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E65.left_4357_right_4393", + "pairIndex": 64, + "leftValue": 4357, + "rightValue": 4393, + "productPlusOne": 19140302, + "productPlusOneRecomputed": 19140302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E66.left_4407_right_4343", + "pairIndex": 65, + "leftValue": 4407, + "rightValue": 4343, + "productPlusOne": 19139602, + "productPlusOneRecomputed": 19139602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E67.left_4507_right_4443", + "pairIndex": 66, + "leftValue": 4507, + "rightValue": 4443, + "productPlusOne": 20024602, + "productPlusOneRecomputed": 20024602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E68.left_4582_right_4543", + "pairIndex": 67, + "leftValue": 4582, + "rightValue": 4543, + "productPlusOne": 20816027, + "productPlusOneRecomputed": 20816027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E69.left_4607_right_4643", + "pairIndex": 68, + "leftValue": 4607, + "rightValue": 4643, + "productPlusOne": 21390302, + "productPlusOneRecomputed": 21390302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E70.left_4707_right_4618", + "pairIndex": 69, + "leftValue": 4707, + "rightValue": 4618, + "productPlusOne": 21736927, + "productPlusOneRecomputed": 21736927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E71.left_4757_right_4893", + "pairIndex": 70, + "leftValue": 4757, + "rightValue": 4893, + "productPlusOne": 23276002, + "productPlusOneRecomputed": 23276002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E72.left_4807_right_4843", + "pairIndex": 71, + "leftValue": 4807, + "rightValue": 4843, + "productPlusOne": 23280302, + "productPlusOneRecomputed": 23280302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E73.left_4907_right_4743", + "pairIndex": 72, + "leftValue": 4907, + "rightValue": 4743, + "productPlusOne": 23273902, + "productPlusOneRecomputed": 23273902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E74.left_5007_right_4943", + "pairIndex": 73, + "leftValue": 5007, + "rightValue": 4943, + "productPlusOne": 24749602, + "productPlusOneRecomputed": 24749602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E75.left_5032_right_5043", + "pairIndex": 74, + "leftValue": 5032, + "rightValue": 5043, + "productPlusOne": 25376377, + "productPlusOneRecomputed": 25376377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E76.left_5107_right_5068", + "pairIndex": 75, + "leftValue": 5107, + "rightValue": 5068, + "productPlusOne": 25882277, + "productPlusOneRecomputed": 25882277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E77.left_5207_right_5143", + "pairIndex": 76, + "leftValue": 5207, + "rightValue": 5143, + "productPlusOne": 26779602, + "productPlusOneRecomputed": 26779602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E78.left_5257_right_5518", + "pairIndex": 77, + "leftValue": 5257, + "rightValue": 5518, + "productPlusOne": 29008127, + "productPlusOneRecomputed": 29008127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E79.left_5307_right_5243", + "pairIndex": 78, + "leftValue": 5307, + "rightValue": 5243, + "productPlusOne": 27824602, + "productPlusOneRecomputed": 27824602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E80.left_5407_right_5343", + "pairIndex": 79, + "leftValue": 5407, + "rightValue": 5343, + "productPlusOne": 28889602, + "productPlusOneRecomputed": 28889602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E81.left_5482_right_5293", + "pairIndex": 80, + "leftValue": 5482, + "rightValue": 5293, + "productPlusOne": 29016227, + "productPlusOneRecomputed": 29016227, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E82.left_5507_right_5443", + "pairIndex": 81, + "leftValue": 5507, + "rightValue": 5443, + "productPlusOne": 29974602, + "productPlusOneRecomputed": 29974602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E83.left_5607_right_5543", + "pairIndex": 82, + "leftValue": 5607, + "rightValue": 5543, + "productPlusOne": 31079602, + "productPlusOneRecomputed": 31079602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E84.left_5657_right_5693", + "pairIndex": 83, + "leftValue": 5657, + "rightValue": 5693, + "productPlusOne": 32205302, + "productPlusOneRecomputed": 32205302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E85.left_5707_right_5643", + "pairIndex": 84, + "leftValue": 5707, + "rightValue": 5643, + "productPlusOne": 32204602, + "productPlusOneRecomputed": 32204602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E86.left_5807_right_5743", + "pairIndex": 85, + "leftValue": 5807, + "rightValue": 5743, + "productPlusOne": 33349602, + "productPlusOneRecomputed": 33349602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E87.left_5907_right_5818", + "pairIndex": 86, + "leftValue": 5907, + "rightValue": 5818, + "productPlusOne": 34366927, + "productPlusOneRecomputed": 34366927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E88.left_5932_right_5843", + "pairIndex": 87, + "leftValue": 5932, + "rightValue": 5843, + "productPlusOne": 34660677, + "productPlusOneRecomputed": 34660677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E89.left_5982_right_5943", + "pairIndex": 88, + "leftValue": 5982, + "rightValue": 5943, + "productPlusOne": 35551027, + "productPlusOneRecomputed": 35551027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E90.left_6007_right_5968", + "pairIndex": 89, + "leftValue": 6007, + "rightValue": 5968, + "productPlusOne": 35849777, + "productPlusOneRecomputed": 35849777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E91.left_6107_right_6043", + "pairIndex": 90, + "leftValue": 6107, + "rightValue": 6043, + "productPlusOne": 36904602, + "productPlusOneRecomputed": 36904602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E92.left_6157_right_6193", + "pairIndex": 91, + "leftValue": 6157, + "rightValue": 6193, + "productPlusOne": 38130302, + "productPlusOneRecomputed": 38130302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E93.left_6207_right_6143", + "pairIndex": 92, + "leftValue": 6207, + "rightValue": 6143, + "productPlusOne": 38129602, + "productPlusOneRecomputed": 38129602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E94.left_6307_right_6243", + "pairIndex": 93, + "leftValue": 6307, + "rightValue": 6243, + "productPlusOne": 39374602, + "productPlusOneRecomputed": 39374602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E95.left_6382_right_6343", + "pairIndex": 94, + "leftValue": 6382, + "rightValue": 6343, + "productPlusOne": 40481027, + "productPlusOneRecomputed": 40481027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E96.left_6407_right_6443", + "pairIndex": 95, + "leftValue": 6407, + "rightValue": 6443, + "productPlusOne": 41280302, + "productPlusOneRecomputed": 41280302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E97.left_6507_right_6418", + "pairIndex": 96, + "leftValue": 6507, + "rightValue": 6418, + "productPlusOne": 41761927, + "productPlusOneRecomputed": 41761927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E98.left_6607_right_6543", + "pairIndex": 97, + "leftValue": 6607, + "rightValue": 6543, + "productPlusOne": 43229602, + "productPlusOneRecomputed": 43229602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E99.left_6707_right_6618", + "pairIndex": 98, + "leftValue": 6707, + "rightValue": 6618, + "productPlusOne": 44386927, + "productPlusOneRecomputed": 44386927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E100.left_6807_right_6643", + "pairIndex": 99, + "leftValue": 6807, + "rightValue": 6643, + "productPlusOne": 45218902, + "productPlusOneRecomputed": 45218902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E101.left_6832_right_6743", + "pairIndex": 100, + "leftValue": 6832, + "rightValue": 6743, + "productPlusOne": 46068177, + "productPlusOneRecomputed": 46068177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E102.left_6907_right_6668", + "pairIndex": 101, + "leftValue": 6907, + "rightValue": 6668, + "productPlusOne": 46055877, + "productPlusOneRecomputed": 46055877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E103.left_7007_right_6843", + "pairIndex": 102, + "leftValue": 7007, + "rightValue": 6843, + "productPlusOne": 47948902, + "productPlusOneRecomputed": 47948902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E104.left_7057_right_6868", + "pairIndex": 103, + "leftValue": 7057, + "rightValue": 6868, + "productPlusOne": 48467477, + "productPlusOneRecomputed": 48467477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E105.left_7082_right_5993", + "pairIndex": 104, + "leftValue": 7082, + "rightValue": 5993, + "productPlusOne": 42442427, + "productPlusOneRecomputed": 42442427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E106.left_7107_right_6943", + "pairIndex": 105, + "leftValue": 7107, + "rightValue": 6943, + "productPlusOne": 49343902, + "productPlusOneRecomputed": 49343902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E107.left_7207_right_7143", + "pairIndex": 106, + "leftValue": 7207, + "rightValue": 7143, + "productPlusOne": 51479602, + "productPlusOneRecomputed": 51479602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E108.left_7282_right_7043", + "pairIndex": 107, + "leftValue": 7282, + "rightValue": 7043, + "productPlusOne": 51287127, + "productPlusOneRecomputed": 51287127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7.E109.left_7307_right_7243", + "pairIndex": 108, + "leftValue": 7307, + "rightValue": 7243, + "productPlusOne": 52924602, + "productPlusOneRecomputed": 52924602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + } + ], + "failedChecks": [], + "proofBoundary": "This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions.", + "nextTheoremAction": "After this A5 literal persistence pass, promote matching disjointness and the K-envelope, or lift the edge proof if vertex formulas become parameterized." + }, + "matchingDisjointness": { + "status": "bounded_disjointness_certified", + "leftVertexCount": 109, + "rightVertexCount": 109, + "pairCount": 109, + "reusedLeftValues": [], + "reusedRightValues": [], + "completionRule": "A symbolic packet may promote only if the parameterized left and right vertex families remain pairwise disjoint." + }, + "matchingKEnvelopeCertificate": { + "schema": "erdos.p848_matching_k_envelope_certificate/1", + "certificateId": "D3.1_persist_outP2=38_out25=23_smaller=side7.matching_k_envelope_certificate", + "status": "literal_matching_sampled_k_envelope_verified", + "proofKind": "literal_disjoint_matching_plus_sampled_k_envelope", + "matchingProof": { + "status": "literal_matching_disjointness_verified", + "pairCount": 109, + "leftVertexCount": 109, + "rightVertexCount": 109, + "reusedLeftValues": [], + "reusedRightValues": [], + "proofSteps": [ + "Count the exported literal left vertices.", + "Count the exported literal right vertices.", + "Verify no left value and no right value is reused across the exported pair list." + ], + "proofBoundary": "This proves disjointness for the exported literal pair list. If later work parameterizes vertices, disjointness must be rechecked for the parameterized formulas." + }, + "kEnvelopeProof": { + "status": "sampled_k_envelope_dominated_by_literal_core", + "requiredMatchingLowerBoundRange": [ + 12, + 14 + ], + "commonMatchingPairCount": 109, + "maxRequiredMatchingLowerBound": 14, + "boundedSlackAgainstMaxK": 95, + "inequality": "109 >= 14", + "proofSteps": [ + "Use the exported common-core pair count as the literal matching size.", + "Compare it against the maximum required matching lower bound recorded by the packet.", + "Record the slack and keep the all-N K-formula handoff explicit." + ], + "proofBoundary": "This certifies the K-envelope recorded by the current split packet. It is not by itself a universal K(N,x) formula proof for every future row." + }, + "allLowerLiteralAtomsReady": true, + "proofBoundary": "A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim.", + "nextTheoremAction": "Assemble this with the verified vertex-successor and edge-persistence layers into a split-discharge readiness certificate, or emit the first missing lower atom." + }, + "summary": { + "vertexPresenceAtomCount": 218, + "edgeObstructionAtomCount": 109, + "stableVertexPresenceAtomCount": 2, + "unstableVertexPresenceAtomCount": 216, + "failedVertexPresenceAtomCount": 0, + "allEdgeObstructionsSquarefree": true, + "edgeObstructionCertificateStatus": "literal_edge_obstruction_certificate_verified", + "edgeCongruencePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingDisjointnessStatus": "bounded_disjointness_certified", + "matchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "readyForFirstTheoremPass": true + }, + "nextTheoremActions": [ + "Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N.", + "The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families.", + "Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof.", + "Attack the packet until it either becomes a split lemma or emits a sharper sub-split key." + ], + "splitDischargeReadiness": { + "schema": "erdos.p848_split_discharge_readiness/1", + "readinessId": "D3.1_persist_outP2=38_out25=23_smaller=side7.split_discharge_readiness", + "status": "split_discharge_readiness_blocked", + "proofKind": "lower_atom_assembly_with_explicit_all_n_handoff", + "atomId": "D3.1_persist_outP2=38_out25=23_smaller=side7", + "splitKey": "outP2=38|out25=23|smaller=side7", + "parentObligationId": "D3_p17_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "lowerLayerChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "blocked", + "evidence": "0/9 successor vertex-family lemmas verified" + }, + { + "layerId": "A4_edge_obstruction_certificate", + "status": "verified", + "evidence": "literal_edge_obstruction_certificate_verified" + }, + { + "layerId": "A5_edge_congruence_persistence", + "status": "verified", + "evidence": "literal_constant_edge_persistence_verified" + }, + { + "layerId": "A6_matching_disjointness", + "status": "verified", + "evidence": "literal_matching_disjointness_verified" + }, + { + "layerId": "A7_sampled_k_envelope", + "status": "verified_sampled_envelope", + "evidence": "109 >= 14" + } + ], + "blockingChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "blocked", + "evidence": "0/9 successor vertex-family lemmas verified" + } + ], + "theoremCandidate": { + "status": "blocked_by_lower_atom", + "statement": "For split outP2=38|out25=23|smaller=side7, the exported literal core supplies a disjoint matching of size 109 against the packet K-envelope [12,14].", + "lowerAtomSummary": { + "vertexSuccessorConditionCount": 9, + "verifiedVertexSuccessorCount": 0, + "edgePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingKEnvelopeStatus": "literal_matching_sampled_k_envelope_verified" + } + }, + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "note": "Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "note": "Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "note": "If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families." + } + ], + "proofBoundary": "This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes.", + "nextTheoremAction": "Discharge the first blocked lower atom before promoting this split." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.md new file mode 100644 index 0000000..fe5dd2f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.md @@ -0,0 +1,251 @@ +# D3.1_persist_outP2=38_out25=23_smaller=side7 + +This is a theorem-facing split atom packet for Problem 848. It is intentionally atomic: one split profile, one common matching core, one K-envelope, and deterministic sub-atoms for the next proof pass. + +## Summary + +- Packet id: `p848_split_atom_packet_D3_1_persist_outP2_38_out25_23_smaller_side7` +- Parent obligation: `D3_p17_matching_lower_bound` +- Target obligation: `D4_matching_bound_implies_sMaxMixed_bound` +- Prime lane: `17` +- Split key: `outP2=38|out25=23|smaller=side7` +- Priority: `supporting_p17_companion_lane` +- Status: `ready_for_symbolic_persistence_work` +- Witnesses: `10` over `7307..7393` +- Common core size: `109` +- K-envelope: `[12,14]`, slack against max K `95` +- Vertex atoms: `218` +- Vertex atoms stable under current split modulus: `2` +- Vertex atoms needing sharper split or parameterization: `216` +- Edge atoms: `109` +- Edge certificate: `literal_edge_obstruction_certificate_verified` +- Edge congruence persistence: `literal_constant_edge_persistence_verified` +- Disjointness: `bounded_disjointness_certified` +- Matching/K certificate: `literal_matching_sampled_k_envelope_verified` + +## Goal + +Prove that the 109-edge common matching core persists for all p=17 threatening rows in split outP2=38|out25=23|smaller=side7, or replace it with a parameterized extension core. + +## Falsifier Boundary + +A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size. + +## Next Theorem Actions + +- Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N. +- The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families. +- Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof. +- Attack the packet until it either becomes a split lemma or emits a sharper sub-split key. + +## K Envelope + +- Status: `bounded_core_meets_sampled_K_envelope` +- Common core count: `109` +- Max required K: `14` +- Min matching slack: `95` + +## Matching And K-Envelope Certificate + +- Status: `literal_matching_sampled_k_envelope_verified` +- Proof kind: `literal_disjoint_matching_plus_sampled_k_envelope` +- Matching proof: `literal_matching_disjointness_verified` +- K proof: `sampled_k_envelope_dominated_by_literal_core` +- K inequality: `109 >= 14` +- Proof boundary: A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim. + +## Split Discharge Readiness + +- Status: `split_discharge_readiness_blocked` +- Proof kind: `lower_atom_assembly_with_explicit_all_n_handoff` +- Theorem candidate: `blocked_by_lower_atom` +- Blocking lower checks: `1` +- Open all-N handoff gaps: `3` +- Proof boundary: This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes. +- Handoff gap `row_universe_split_coverage` [open]: Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile. +- Handoff gap `universal_k_formula_lift` [open]: Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane. +- Handoff gap `literal_to_parameterized_vertex_guard` [open_if_vertices_move]: If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families. + +## Vertex Presence Stability + +- Split modulus: `7225` +- Witness rows: `10` +- Stable under current split modulus: `2` +- Needs sharper split or parametric witness: `216` +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V1.left_7`: side side7, value 7, first square witness {"divisor":2,"square":4,"quotient":7653,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V2.left_82`: side side7, value 82, first square witness {"divisor":3,"square":9,"quotient":39843,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V3.left_107`: side side7, value 107, first square witness {"divisor":2,"square":4,"quotient":116978,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V4.left_207`: side side7, value 207, first square witness {"divisor":2,"square":4,"quotient":226303,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V5.left_307`: side side7, value 307, first square witness {"divisor":2,"square":4,"quotient":335628,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V6.left_407`: side side7, value 407, first square witness {"divisor":2,"square":4,"quotient":444953,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V7.left_507`: side side7, value 507, first square witness {"divisor":2,"square":4,"quotient":554278,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.1_persist_outP2=38_out25=23_smaller=side7.V8.left_532`: side side7, value 532, first square witness {"divisor":3,"square":9,"quotient":258493,"stableUnderCurrentSplitModulus":false} + +## Vertex Presence Refinement + +- Status: `literal_core_requires_sharper_square_witness_split` +- Deterministic move: `emit_successor_atoms_by_square_witness_residue` +- Refinement condition count: `9` +- Covered unstable atoms: `216` +- Uncovered unstable atoms: `0` +- Proof boundary: These square-witness residue classes explain the bounded literal vertex-presence instability; each successor split still needs a theorem-facing persistence proof before it can support an all-N claim. +- Condition `square_4_outsider_1`: out mod 4 = 1, atoms=146, combined modulus=28900, successor=`outP2=38|out25=23|smaller=side7|out4=1` +- Condition `square_9_outsider_8`: out mod 9 = 8, atoms=48, combined modulus=65025, successor=`outP2=38|out25=23|smaller=side7|out9=8` +- Condition `square_49_outsider_12`: out mod 49 = 12, atoms=8, combined modulus=354025, successor=`outP2=38|out25=23|smaller=side7|out49=12` +- Condition `square_121_outsider_17`: out mod 121 = 17, atoms=5, combined modulus=874225, successor=`outP2=38|out25=23|smaller=side7|out121=17` +- Condition `square_169_outsider_148`: out mod 169 = 148, atoms=3, combined modulus=1221025, successor=`outP2=38|out25=23|smaller=side7|out169=148` +- Condition `square_361_outsider_41`: out mod 361 = 41, atoms=2, combined modulus=2608225, successor=`outP2=38|out25=23|smaller=side7|out361=41` +- Condition `square_961_outsider_529`: out mod 961 = 529, atoms=2, combined modulus=6943225, successor=`outP2=38|out25=23|smaller=side7|out961=529` +- Condition `square_24649_outsider_4373`: out mod 24649 = 4373, atoms=1, combined modulus=178089025, successor=`outP2=38|out25=23|smaller=side7|out24649=4373` +- Condition `square_1352569_outsider_4373`: out mod 1352569 = 4373, atoms=1, combined modulus=9772311025, successor=`outP2=38|out25=23|smaller=side7|out1352569=4373` + +## Edge Obstruction Certificate + +- Status: `literal_edge_obstruction_certificate_verified` +- Proof kind: `literal_product_plus_one_squarefree_missing_edge_certificate` +- Edge atoms: `109` +- Squarefree edge atoms: `109` +- Non-squarefree edge atoms: `0` +- Product-plus-one range: `{"min":302,"max":52924602}` +- Mod 25 classes: `1` +- Prime-residue classes: `81` +- Prime-square fingerprints: `109` +- Proof boundary: This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim. +- Mod25 class `7:18`: edges=109 +- Prime-residue class `3:5:16`: edges=5 +- Prime-residue class `5:7:2`: edges=4 +- Prime-residue class `14:1:15`: edges=3 +- Prime-residue class `7:9:13`: edges=3 +- Prime-residue class `1:3:4`: edges=2 +- Prime-residue class `10:14:5`: edges=2 +- Prime-residue class `11:4:11`: edges=2 +- Prime-residue class `12:16:6`: edges=2 +- Prime-residue class `13:15:9`: edges=2 +- Prime-residue class `14:14:10`: edges=2 +- Prime-residue class `14:16:4`: edges=2 +- Prime-residue class `15:11:13`: edges=2 +- Prime-residue class `15:15:5`: edges=2 + +## Edge Congruence Persistence + +- Status: `literal_constant_edge_persistence_verified` +- Proof kind: `constant_pair_squarefree_invariant` +- Edge atoms: `109` +- Verified edge atoms: `109` +- Failed edge atoms: `0` +- Depends on sampled N: `no` +- Depends on witness outsider: `no` +- Proof boundary: This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions. +- Family `D3.1_persist_outP2=38_out25=23_smaller=side7.edge_constant_squarefree_family`: status=`congruence_persistence_family_verified`, edges=109, proof=constant_pair_squarefree_invariant + +## Matching Core + +- Pair (7, 43); residues mod25 7:18, mod p 7:9, mod p^2 7:43; product+1 mod p^2 13 +- Pair (82, 118); residues mod25 7:18, mod p 14:16, mod p^2 82:118; product+1 mod p^2 140 +- Pair (107, 143); residues mod25 7:18, mod p 5:7, mod p^2 107:143; product+1 mod p^2 274 +- Pair (207, 243); residues mod25 7:18, mod p 3:5, mod p^2 207:243; product+1 mod p^2 16 +- Pair (307, 343); residues mod25 7:18, mod p 1:3, mod p^2 18:54; product+1 mod p^2 106 +- Pair (407, 443); residues mod25 7:18, mod p 16:1, mod p^2 118:154; product+1 mod p^2 255 +- Pair (507, 543); residues mod25 7:18, mod p 14:16, mod p^2 218:254; product+1 mod p^2 174 +- Pair (532, 568); residues mod25 7:18, mod p 5:7, mod p^2 243:279; product+1 mod p^2 172 +- Pair (607, 643); residues mod25 7:18, mod p 12:14, mod p^2 29:65; product+1 mod p^2 152 +- Pair (707, 668); residues mod25 7:18, mod p 10:5, mod p^2 129:90; product+1 mod p^2 51 +- Pair (757, 793); residues mod25 7:18, mod p 9:11, mod p^2 179:215; product+1 mod p^2 49 +- Pair (807, 743); residues mod25 7:18, mod p 8:12, mod p^2 229:165; product+1 mod p^2 216 +- Pair (907, 843); residues mod25 7:18, mod p 6:10, mod p^2 40:265; product+1 mod p^2 197 +- Pair (982, 943); residues mod25 7:18, mod p 13:8, mod p^2 115:76; product+1 mod p^2 71 +- Pair (1007, 1043); residues mod25 7:18, mod p 4:6, mod p^2 140:176; product+1 mod p^2 76 +- Pair (1032, 1018); residues mod25 7:18, mod p 12:15, mod p^2 165:151; product+1 mod p^2 62 +- Pair (1082, 1143); residues mod25 7:18, mod p 11:4, mod p^2 215:276; product+1 mod p^2 96 +- Pair (1107, 1243); residues mod25 7:18, mod p 2:2, mod p^2 240:87; product+1 mod p^2 73 +- Pair (1207, 1343); residues mod25 7:18, mod p 0:0, mod p^2 51:187; product+1 mod p^2 1 +- Pair (1307, 1443); residues mod25 7:18, mod p 15:15, mod p^2 151:287; product+1 mod p^2 277 +- Pair (1407, 1468); residues mod25 7:18, mod p 13:6, mod p^2 251:23; product+1 mod p^2 283 +- Pair (1432, 1543); residues mod25 7:18, mod p 4:13, mod p^2 276:98; product+1 mod p^2 172 +- Pair (1507, 1643); residues mod25 7:18, mod p 11:11, mod p^2 62:198; product+1 mod p^2 139 +- Pair (1607, 1743); residues mod25 7:18, mod p 9:9, mod p^2 162:9; product+1 mod p^2 14 +- Pair (1657, 1693); residues mod25 7:18, mod p 8:10, mod p^2 212:248; product+1 mod p^2 268 +- Pair (1682, 1768); residues mod25 7:18, mod p 16:0, mod p^2 237:34; product+1 mod p^2 256 +- Pair (1707, 1843); residues mod25 7:18, mod p 7:7, mod p^2 262:109; product+1 mod p^2 237 +- Pair (1807, 1918); residues mod25 7:18, mod p 5:14, mod p^2 73:184; product+1 mod p^2 139 +- Pair (1882, 2043); residues mod25 7:18, mod p 12:3, mod p^2 148:20; product+1 mod p^2 71 +- Pair (1907, 1943); residues mod25 7:18, mod p 3:5, mod p^2 173:209; product+1 mod p^2 33 +- Pair (2007, 2143); residues mod25 7:18, mod p 1:1, mod p^2 273:120; product+1 mod p^2 104 +- Pair (2107, 2243); residues mod25 7:18, mod p 16:16, mod p^2 84:220; product+1 mod p^2 274 +- Pair (2207, 2343); residues mod25 7:18, mod p 14:14, mod p^2 184:31; product+1 mod p^2 214 +- Pair (2307, 2443); residues mod25 7:18, mod p 12:12, mod p^2 284:131; product+1 mod p^2 213 +- Pair (2332, 2368); residues mod25 7:18, mod p 3:5, mod p^2 20:56; product+1 mod p^2 254 +- Pair (2407, 2543); residues mod25 7:18, mod p 10:10, mod p^2 95:231; product+1 mod p^2 271 +- Pair (2507, 2643); residues mod25 7:18, mod p 8:8, mod p^2 195:42; product+1 mod p^2 99 +- Pair (2557, 2593); residues mod25 7:18, mod p 7:9, mod p^2 245:281; product+1 mod p^2 64 +- Pair (2607, 2743); residues mod25 7:18, mod p 6:6, mod p^2 6:142; product+1 mod p^2 275 +- Pair (2707, 2818); residues mod25 7:18, mod p 4:13, mod p^2 106:217; product+1 mod p^2 172 +- Pair (2782, 2943); residues mod25 7:18, mod p 11:2, mod p^2 181:53; product+1 mod p^2 57 +- Pair (2807, 2843); residues mod25 7:18, mod p 2:4, mod p^2 206:242; product+1 mod p^2 145 +- Pair (2907, 2968); residues mod25 7:18, mod p 0:10, mod p^2 17:78; product+1 mod p^2 171 +- Pair (2932, 3043); residues mod25 7:18, mod p 8:0, mod p^2 42:153; product+1 mod p^2 69 +- Pair (3007, 3143); residues mod25 7:18, mod p 15:15, mod p^2 117:253; product+1 mod p^2 124 +- Pair (3107, 3243); residues mod25 7:18, mod p 13:13, mod p^2 217:64; product+1 mod p^2 17 +- Pair (3207, 3268); residues mod25 7:18, mod p 11:4, mod p^2 28:89; product+1 mod p^2 181 +- Pair (3232, 2993); residues mod25 7:18, mod p 2:1, mod p^2 53:103; product+1 mod p^2 258 +- Pair (3307, 3343); residues mod25 7:18, mod p 9:11, mod p^2 128:164; product+1 mod p^2 185 +- Pair (3407, 3443); residues mod25 7:18, mod p 7:9, mod p^2 228:264; product+1 mod p^2 81 +- Pair (3457, 3093); residues mod25 7:18, mod p 6:16, mod p^2 278:203; product+1 mod p^2 80 +- Pair (3507, 3543); residues mod25 7:18, mod p 5:7, mod p^2 39:75; product+1 mod p^2 36 +- Pair (3532, 3293); residues mod25 7:18, mod p 13:12, mod p^2 64:114; product+1 mod p^2 72 +- Pair (3607, 3643); residues mod25 7:18, mod p 3:5, mod p^2 139:175; product+1 mod p^2 50 +- Pair (3682, 3493); residues mod25 7:18, mod p 10:8, mod p^2 214:25; product+1 mod p^2 149 +- Pair (3707, 3743); residues mod25 7:18, mod p 1:3, mod p^2 239:275; product+1 mod p^2 123 +- Pair (3807, 3718); residues mod25 7:18, mod p 16:12, mod p^2 50:250; product+1 mod p^2 74 +- Pair (3907, 3843); residues mod25 7:18, mod p 14:1, mod p^2 150:86; product+1 mod p^2 185 +- Pair (4007, 3943); residues mod25 7:18, mod p 12:16, mod p^2 250:186; product+1 mod p^2 261 +- Pair (4057, 4168); residues mod25 7:18, mod p 11:3, mod p^2 11:122; product+1 mod p^2 187 +- Pair (4107, 4043); residues mod25 7:18, mod p 10:14, mod p^2 61:286; product+1 mod p^2 107 +- Pair (4132, 4143); residues mod25 7:18, mod p 1:12, mod p^2 86:97; product+1 mod p^2 251 +- Pair (4207, 4218); residues mod25 7:18, mod p 8:2, mod p^2 161:172; product+1 mod p^2 238 +- Pair (4307, 4243); residues mod25 7:18, mod p 6:10, mod p^2 261:197; product+1 mod p^2 265 +- Pair (4357, 4393); residues mod25 7:18, mod p 5:7, mod p^2 22:58; product+1 mod p^2 121 +- Pair (4407, 4343); residues mod25 7:18, mod p 4:8, mod p^2 72:8; product+1 mod p^2 288 +- Pair (4507, 4443); residues mod25 7:18, mod p 2:6, mod p^2 172:108; product+1 mod p^2 81 +- Pair (4582, 4543); residues mod25 7:18, mod p 9:4, mod p^2 247:208; product+1 mod p^2 224 +- Pair (4607, 4643); residues mod25 7:18, mod p 0:2, mod p^2 272:19; product+1 mod p^2 256 +- Pair (4707, 4618); residues mod25 7:18, mod p 15:11, mod p^2 83:283; product+1 mod p^2 81 +- Pair (4757, 4893); residues mod25 7:18, mod p 14:14, mod p^2 133:269; product+1 mod p^2 231 +- Pair (4807, 4843); residues mod25 7:18, mod p 13:15, mod p^2 183:219; product+1 mod p^2 196 +- Pair (4907, 4743); residues mod25 7:18, mod p 11:0, mod p^2 283:119; product+1 mod p^2 154 +- Pair (5007, 4943); residues mod25 7:18, mod p 9:13, mod p^2 94:30; product+1 mod p^2 220 +- Pair (5032, 5043); residues mod25 7:18, mod p 0:11, mod p^2 119:130; product+1 mod p^2 154 +- Pair (5107, 5068); residues mod25 7:18, mod p 7:2, mod p^2 194:155; product+1 mod p^2 15 +- Pair (5207, 5143); residues mod25 7:18, mod p 5:9, mod p^2 5:230; product+1 mod p^2 284 +- Pair (5257, 5518); residues mod25 7:18, mod p 4:10, mod p^2 55:27; product+1 mod p^2 41 +- Pair (5307, 5243); residues mod25 7:18, mod p 3:7, mod p^2 105:41; product+1 mod p^2 260 +- Pair (5407, 5343); residues mod25 7:18, mod p 1:5, mod p^2 205:141; product+1 mod p^2 6 +- Pair (5482, 5293); residues mod25 7:18, mod p 8:6, mod p^2 280:91; product+1 mod p^2 49 +- Pair (5507, 5443); residues mod25 7:18, mod p 16:3, mod p^2 16:241; product+1 mod p^2 100 +- Pair (5607, 5543); residues mod25 7:18, mod p 14:1, mod p^2 116:52; product+1 mod p^2 253 +- Pair (5657, 5693); residues mod25 7:18, mod p 13:15, mod p^2 166:202; product+1 mod p^2 9 +- Pair (5707, 5643); residues mod25 7:18, mod p 12:16, mod p^2 216:152; product+1 mod p^2 176 +- Pair (5807, 5743); residues mod25 7:18, mod p 10:14, mod p^2 27:252; product+1 mod p^2 158 +- Pair (5907, 5818); residues mod25 7:18, mod p 8:4, mod p^2 127:38; product+1 mod p^2 203 +- Pair (5932, 5843); residues mod25 7:18, mod p 16:12, mod p^2 152:63; product+1 mod p^2 40 +- Pair (5982, 5943); residues mod25 7:18, mod p 15:10, mod p^2 202:163; product+1 mod p^2 270 +- Pair (6007, 5968); residues mod25 7:18, mod p 6:1, mod p^2 227:188; product+1 mod p^2 194 +- Pair (6107, 6043); residues mod25 7:18, mod p 4:8, mod p^2 38:263; product+1 mod p^2 169 +- Pair (6157, 6193); residues mod25 7:18, mod p 3:5, mod p^2 88:124; product+1 mod p^2 220 +- Pair (6207, 6143); residues mod25 7:18, mod p 2:6, mod p^2 138:74; product+1 mod p^2 98 +- Pair (6307, 6243); residues mod25 7:18, mod p 0:4, mod p^2 238:174; product+1 mod p^2 86 +- Pair (6382, 6343); residues mod25 7:18, mod p 7:2, mod p^2 24:274; product+1 mod p^2 219 +- Pair (6407, 6443); residues mod25 7:18, mod p 15:0, mod p^2 49:85; product+1 mod p^2 120 +- Pair (6507, 6418); residues mod25 7:18, mod p 13:9, mod p^2 149:60; product+1 mod p^2 271 +- Pair (6607, 6543); residues mod25 7:18, mod p 11:15, mod p^2 249:185; product+1 mod p^2 115 +- Pair (6707, 6618); residues mod25 7:18, mod p 9:5, mod p^2 60:260; product+1 mod p^2 284 +- Pair (6807, 6643); residues mod25 7:18, mod p 7:13, mod p^2 160:285; product+1 mod p^2 228 +- Pair (6832, 6743); residues mod25 7:18, mod p 15:11, mod p^2 185:96; product+1 mod p^2 132 +- Pair (6907, 6668); residues mod25 7:18, mod p 5:4, mod p^2 260:21; product+1 mod p^2 259 +- Pair (7007, 6843); residues mod25 7:18, mod p 3:9, mod p^2 71:196; product+1 mod p^2 45 +- Pair (7057, 6868); residues mod25 7:18, mod p 2:0, mod p^2 121:221; product+1 mod p^2 154 +- Pair (7082, 5993); residues mod25 7:18, mod p 10:9, mod p^2 146:213; product+1 mod p^2 176 +- Pair (7107, 6943); residues mod25 7:18, mod p 1:7, mod p^2 171:7; product+1 mod p^2 42 +- Pair (7207, 7143); residues mod25 7:18, mod p 16:3, mod p^2 271:207; product+1 mod p^2 32 +- Pair (7282, 7043); residues mod25 7:18, mod p 6:5, mod p^2 57:107; product+1 mod p^2 31 +- Pair (7307, 7243); residues mod25 7:18, mod p 14:1, mod p^2 82:18; product+1 mod p^2 32 diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.json new file mode 100644 index 0000000..96c99ab --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.json @@ -0,0 +1,24863 @@ +{ + "schema": "erdos.p848_split_atom_packet/1", + "generatedAt": "2026-04-14T11:46:09.829Z", + "problemId": "848", + "packetId": "p848_split_atom_packet_D3_2_persist_outP2_251_out25_1_smaller_side18", + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18", + "sourcePlanId": "p848_split_core_atomization_master_plan_v1", + "parentObligationId": "D3_p17_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "prime": 17, + "splitKey": "outP2=251|out25=1|smaller=side18", + "priority": "supporting_p17_companion_lane", + "status": "ready_for_symbolic_persistence_work", + "sourceArtifacts": { + "taskList": "TASK_LIST.json", + "formalizationWork": "FORMALIZATION_WORK.json", + "matchingPatternMiner": "MATCHING_PATTERN_MINER_P17.json" + }, + "inputs": { + "witnessCount": 2, + "nRange": "7307..7318", + "boundedTarget": { + "requiredMatchingLowerBoundRange": [ + 10, + 11 + ], + "commonMatchingPairCount": 106, + "commonMatchingPairExportComplete": true, + "commonMatchingPairs": [ + { + "leftValue": 57, + "rightValue": 68, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 57, + 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"needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 14308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3577, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 73, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 14308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 3577, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 292, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 73, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 57 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V2.left_82", + "side": "side7", + "value": 82, + "residues": { + "value": 82, + "mod25": 7, + "modP": 14, + "modP2": 82 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 20583, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2287, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2287, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 20583, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 2287, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 2287, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 82 is present in the 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"needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 64508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 16127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 16127, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 64508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 16127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 16127, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 257 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V5.left_307", + "side": "side7", + "value": 307, + "residues": { + "value": 307, + "mod25": 7, + "modP": 1, + "modP2": 18 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 77058, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 8562, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 8562, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 77058, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 8562, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 8562, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 307 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V6.left_357", + "side": "side7", + "value": 357, + "residues": { + "value": 357, + "mod25": 7, + "modP": 0, + "modP2": 68 + }, + "status": 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"stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 457 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V8.left_532", + "side": "side7", + "value": 532, + "residues": { + "value": 532, + "mod25": 7, + "modP": 5, + "modP2": 243 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 133533, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 14837, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 14837, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 133533, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 14837, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 14837, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 532 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V9.left_557", + "side": "side7", + "value": 557, + "residues": { + "value": 557, + "mod25": 7, + "modP": 13, + "modP2": 268 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 139808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 34952, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 34952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 8738, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 139808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 34952, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 34952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 8738, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 557 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V10.left_657", + "side": "side7", + "value": 657, + "residues": { + "value": 657, + "mod25": 7, + "modP": 11, + "modP2": 79 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 164908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": 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"value": 757, + "mod25": 7, + "modP": 9, + "modP2": 179 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 190008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47502, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 21112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 5278, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 190008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 47502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 47502, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 21112, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 5278, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 757 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V12.left_857", + "side": "side7", + "value": 857, + "residues": { + "value": 857, + "mod25": 7, + "modP": 7, + "modP2": 279 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 215108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 53777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 53777, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 215108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 53777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 53777, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 857 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V13.left_957", + "side": "side7", + "value": 957, + "residues": { + "value": 957, + "mod25": 7, + "modP": 5, + "modP2": 90 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 240208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 60052, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 60052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 15013, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 240208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 60052, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 60052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 15013, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 957 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V14.left_982", + "side": "side7", + "value": 982, + "residues": { + "value": 982, + "mod25": 7, + "modP": 13, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 246483, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 27387, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 27387, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 3043, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 246483, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 27387, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 27387, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 3043, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 982 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V15.left_1057", + "side": "side7", + "value": 1057, + "residues": { + "value": 1057, + "mod25": 7, + "modP": 3, + "modP2": 190 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 265308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 66327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 66327, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 265308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 66327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 66327, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1057 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V16.left_1082", + "side": "side7", + "value": 1082, + "residues": { + "value": 1082, + "mod25": 7, + "modP": 11, + "modP2": 215 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 271583, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 1607, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + 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"needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 290408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 72602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 72602, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 290408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 72602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 72602, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1157 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V18.left_1207", + "side": "side7", + "value": 1207, + "residues": { + "value": 1207, + "mod25": 7, + "modP": 0, + "modP2": 51 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 302958, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 33662, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, 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"needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 315508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 78877, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 78877, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 315508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 78877, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 78877, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1257 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V20.left_1282", + "side": "side7", + "value": 1282, + "residues": { + "value": 1282, + "mod25": 7, + "modP": 7, + "modP2": 126 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 321783, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 6567, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 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"needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 340608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 85152, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 85152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 21288, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 5322, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 340608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 85152, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 85152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 21288, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 5322, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1357 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V22.left_1407", + "side": "side7", + "value": 1407, + "residues": { + "value": 1407, + "mod25": 7, + "modP": 13, + "modP2": 251 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 353158, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 1222, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 17, + "square": 289, + "quotient": 1222, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 1222, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 353158, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 1222, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 17, + "square": 289, + "quotient": 1222, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 1222, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove left core vertex 1407 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V23.left_1432", + "side": "side7", + "value": 1432, + "residues": { + "value": 1432, + "mod25": 7, + "modP": 4, + "modP2": 276 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 359433, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 39937, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 39937, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 359433, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 39937, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 39937, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1432 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V24.left_1457", + "side": "side7", + "value": 1457, + "residues": { + "value": 1457, + "mod25": 7, + "modP": 12, + "modP2": 12 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 365708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 91427, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 91427, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 365708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 91427, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 91427, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1457 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V25.left_1557", + "side": "side7", + "value": 1557, + "residues": { + "value": 1557, + "mod25": 7, + "modP": 10, + "modP2": 112 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 390808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 97702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 97702, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 390808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 97702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 97702, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1557 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V26.left_1657", + "side": "side7", + "value": 1657, + "residues": { + "value": 1657, + "mod25": 7, + "modP": 8, + "modP2": 212 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 415908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 103977, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 103977, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 46212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 11553, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 415908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 103977, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 103977, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 46212, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 11553, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1657 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V27.left_1757", + "side": "side7", + "value": 1757, + "residues": { + "value": 1757, + "mod25": 7, + "modP": 6, + "modP2": 23 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 441008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 110252, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 110252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 27563, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 441008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 110252, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 110252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 27563, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1757 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V28.left_1857", + "side": "side7", + "value": 1857, + "residues": { + "value": 1857, + "mod25": 7, + "modP": 4, + "modP2": 123 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 466108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 116527, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 116527, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 466108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 116527, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 116527, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1857 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V29.left_1882", + "side": "side7", + "value": 1882, + "residues": { + "value": 1882, + "mod25": 7, + "modP": 12, + "modP2": 148 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 472383, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 52487, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 52487, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 472383, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 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"divisor": 2, + "square": 4, + "quotient": 122802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 122802, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 491208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 122802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 122802, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 1957 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V31.left_2057", + "side": "side7", + "value": 2057, + "residues": { + "value": 2057, + "mod25": 7, + "modP": 0, + "modP2": 34 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 516308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 129077, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 129077, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 516308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 129077, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 129077, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2057 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V32.left_2107", + "side": "side7", + "value": 2107, + "residues": { + "value": 2107, + "mod25": 7, + "modP": 16, + "modP2": 84 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 528858, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 58762, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 58762, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 528858, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 58762, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 58762, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2107 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V33.left_2157", + "side": "side7", + "value": 2157, + "residues": { + "value": 2157, + "mod25": 7, + "modP": 15, + "modP2": 134 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 541408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 135352, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 135352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 33838, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 541408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 135352, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 135352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 33838, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2157 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V34.left_2257", + "side": "side7", + "value": 2257, + "residues": { + "value": 2257, + "mod25": 7, + "modP": 13, + "modP2": 234 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 566508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 141627, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 141627, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 566508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 141627, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 141627, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2257 is present in the side7 compatible set for every row in 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"outsider": 251, + "productPlusOne": 591608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 147902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 147902, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 591608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 147902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 147902, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2357 is present in the side7 compatible set for every row in split 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"hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 154177, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 154177, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2457 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V38.left_2507", + "side": "side7", + "value": 2507, + "residues": { + "value": 2507, + "mod25": 7, + "modP": 8, + "modP2": 195 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 629258, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 12842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 12842, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 629258, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 12842, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 12842, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 2507 is present in the side7 compatible set for every row in split 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"stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 40113, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 17828, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 4457, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 641808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 160452, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 160452, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 71312, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 40113, + "stableUnderCurrentSplitModulus": false + 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every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V52.left_3457", + "side": "side7", + "value": 3457, + "residues": { + "value": 3457, + "mod25": 7, + "modP": 6, + "modP2": 278 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 867708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 216927, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 216927, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 96412, 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"goal": "Prove left core vertex 3907 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V61.left_3957", + "side": "side7", + "value": 3957, + "residues": { + "value": 3957, + "mod25": 7, + "modP": 13, + "modP2": 200 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 993208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 248302, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 248302, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 993208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 248302, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 248302, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 3957 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V62.left_4057", + "side": "side7", + "value": 4057, + "residues": { + "value": 4057, + "mod25": 7, + "modP": 11, + "modP2": 11 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1018308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 254577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 254577, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1018308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 254577, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 254577, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4057 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V63.left_4132", + "side": "side7", + "value": 4132, + "residues": { + "value": 4132, + "mod25": 7, + "modP": 1, + "modP2": 86 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1037133, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 115237, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 115237, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1037133, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 115237, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 115237, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4132 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V64.left_4157", + "side": "side7", + "value": 4157, + "residues": { + "value": 4157, + "mod25": 7, + "modP": 9, + "modP2": 111 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1043408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 260852, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 260852, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 65213, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1043408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 260852, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 260852, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 65213, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4157 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V65.left_4257", + "side": "side7", + "value": 4257, + "residues": { + "value": 4257, + "mod25": 7, + "modP": 7, + "modP2": 211 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1068508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 267127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 267127, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1068508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 267127, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 267127, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4257 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V66.left_4357", + "side": "side7", + "value": 4357, + "residues": { + "value": 4357, + "mod25": 7, + "modP": 5, + "modP2": 22 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1093608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 273402, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 273402, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 121512, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 30378, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1093608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 273402, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 273402, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 121512, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 30378, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4357 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V67.left_4457", + "side": "side7", + "value": 4457, + "residues": { + "value": 4457, + "mod25": 7, + "modP": 3, + "modP2": 122 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1118708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 279677, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 279677, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1118708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 279677, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 279677, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4457 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V68.left_4557", + "side": "side7", + "value": 4557, + "residues": { + "value": 4557, + "mod25": 7, + "modP": 1, + "modP2": 222 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1143808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 285952, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 285952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 71488, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 17872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 4468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 32, + "square": 1024, + "quotient": 1117, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1143808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 285952, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 285952, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 71488, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 17872, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 4468, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 32, + "square": 1024, + "quotient": 1117, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4557 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V69.left_4582", + "side": "side7", + "value": 4582, + "residues": { + "value": 4582, + "mod25": 7, + "modP": 9, + "modP2": 247 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1150083, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 127787, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 127787, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1150083, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 127787, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 127787, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4582 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V70.left_4657", + "side": "side7", + "value": 4657, + "residues": { + "value": 4657, + "mod25": 7, + "modP": 16, + "modP2": 33 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1168908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 292227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 292227, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1168908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 292227, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 292227, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4657 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V71.left_4757", + "side": "side7", + "value": 4757, + "residues": { + "value": 4757, + "mod25": 7, + "modP": 14, + "modP2": 133 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1194008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 298502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 298502, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1194008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 298502, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 298502, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4757 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V72.left_4807", + "side": "side7", + "value": 4807, + "residues": { + "value": 4807, + "mod25": 7, + "modP": 13, + "modP2": 183 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1206558, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 134062, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 134062, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1206558, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 134062, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 134062, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4807 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V73.left_4857", + "side": "side7", + "value": 4857, + "residues": { + "value": 4857, + "mod25": 7, + "modP": 12, + "modP2": 233 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1219108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 304777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 304777, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1219108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 304777, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 304777, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4857 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V74.left_4957", + "side": "side7", + "value": 4957, + "residues": { + "value": 4957, + "mod25": 7, + "modP": 10, + "modP2": 44 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1244208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 311052, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 311052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 77763, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 25392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 6348, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 2352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 1587, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 46, + "square": 2116, + "quotient": 588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 92, + "square": 8464, + "quotient": 147, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 161, + "square": 25921, + "quotient": 48, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 322, + "square": 103684, + "quotient": 12, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 644, + "square": 414736, + "quotient": 3, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1244208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 311052, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 311052, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 77763, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 25392, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 6348, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 23, + "square": 529, + "quotient": 2352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 28, + "square": 784, + "quotient": 1587, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 46, + "square": 2116, + "quotient": 588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 92, + "square": 8464, + "quotient": 147, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 161, + "square": 25921, + "quotient": 48, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 322, + "square": 103684, + "quotient": 12, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 644, + "square": 414736, + "quotient": 3, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 4957 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V75.left_5032", + "side": "side7", + "value": 5032, + "residues": { + "value": 5032, + "mod25": 7, + "modP": 0, + "modP2": 119 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1263033, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 140337, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 140337, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 15593, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1263033, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 140337, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 140337, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 15593, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5032 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V76.left_5057", + "side": "side7", + "value": 5057, + "residues": { + "value": 5057, + "mod25": 7, + "modP": 8, + "modP2": 144 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1269308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 317327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 317327, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1269308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 317327, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 317327, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5057 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V77.left_5157", + "side": "side7", + "value": 5157, + "residues": { + "value": 5157, + "mod25": 7, + "modP": 6, + "modP2": 244 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1294408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 323602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 323602, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1294408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 323602, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 323602, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5157 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V78.left_5182", + "side": "side7", + "value": 5182, + "residues": { + "value": 5182, + "mod25": 7, + "modP": 14, + "modP2": 269 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1300683, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 3603, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 3603, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1300683, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 3603, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 3603, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5182 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V79.left_5257", + "side": "side7", + "value": 5257, + "residues": { + "value": 5257, + "mod25": 7, + "modP": 4, + "modP2": 55 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1319508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 329877, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 329877, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 146612, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 36653, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1319508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 329877, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 329877, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 146612, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 36653, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5257 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V80.left_5282", + "side": "side7", + "value": 5282, + "residues": { + "value": 5282, + "mod25": 7, + "modP": 12, + "modP2": 80 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1325783, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 71, + "square": 5041, + "quotient": 263, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 71, + "square": 5041, + "quotient": 263, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1325783, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 71, + "square": 5041, + "quotient": 263, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 71, + "square": 5041, + "quotient": 263, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5282 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V81.left_5307", + "side": "side7", + "value": 5307, + "residues": { + "value": 5307, + "mod25": 7, + "modP": 3, + "modP2": 105 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1332058, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7882, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7882, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1332058, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 7882, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 7882, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5307 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V82.left_5357", + "side": "side7", + "value": 5357, + "residues": { + "value": 5357, + "mod25": 7, + "modP": 2, + "modP2": 155 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1344608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 336152, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 336152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 84038, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1344608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 336152, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 336152, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 84038, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5357 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V83.left_5457", + "side": "side7", + "value": 5457, + "residues": { + "value": 5457, + "mod25": 7, + "modP": 0, + "modP2": 255 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1369708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 342427, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 342427, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1369708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 342427, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 342427, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5457 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V84.left_5482", + "side": "side7", + "value": 5482, + "residues": { + "value": 5482, + "mod25": 7, + "modP": 8, + "modP2": 280 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1375983, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 152887, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 152887, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1375983, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 152887, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 152887, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5482 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V85.left_5557", + "side": "side7", + "value": 5557, + "residues": { + "value": 5557, + "mod25": 7, + "modP": 15, + "modP2": 66 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1394808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 348702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 348702, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1394808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 348702, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 348702, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5557 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V86.left_5657", + "side": "side7", + "value": 5657, + "residues": { + "value": 5657, + "mod25": 7, + "modP": 13, + "modP2": 166 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1419908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 354977, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 354977, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1419908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 354977, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 354977, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5657 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V87.left_5707", + "side": "side7", + "value": 5707, + "residues": { + "value": 5707, + "mod25": 7, + "modP": 12, + "modP2": 216 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1432458, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 159162, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 159162, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1432458, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 159162, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 159162, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5707 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V88.left_5757", + "side": "side7", + "value": 5757, + "residues": { + "value": 5757, + "mod25": 7, + "modP": 11, + "modP2": 266 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1445008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 361252, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 361252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 90313, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1445008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 361252, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 361252, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 90313, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5757 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V89.left_5857", + "side": "side7", + "value": 5857, + "residues": { + "value": 5857, + "mod25": 7, + "modP": 9, + "modP2": 77 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1470108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 367527, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 367527, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1470108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 367527, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 367527, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5857 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V90.left_5932", + "side": "side7", + "value": 5932, + "residues": { + "value": 5932, + "mod25": 7, + "modP": 16, + "modP2": 152 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1488933, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 165437, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 165437, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1488933, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 165437, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 165437, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5932 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V91.left_5957", + "side": "side7", + "value": 5957, + "residues": { + "value": 5957, + "mod25": 7, + "modP": 7, + "modP2": 177 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1495208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 373802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 373802, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1495208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 373802, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 373802, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 5957 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V92.left_6057", + "side": "side7", + "value": 6057, + "residues": { + "value": 6057, + "mod25": 7, + "modP": 5, + "modP2": 277 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1520308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 380077, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 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"needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1545408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 386352, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 386352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 171712, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 96588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 42928, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 24147, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 10732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 2683, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1545408, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 386352, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 386352, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 171712, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 96588, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 42928, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 24147, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 10732, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 24, + "square": 576, + "quotient": 2683, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6157 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V94.left_6182", + "side": "side7", + "value": 6182, + "residues": { + "value": 6182, + "mod25": 7, + "modP": 11, + "modP2": 113 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1551683, + "hasAnySquareDivisor": true, 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"D3.2_persist_outP2=251_out25=1_smaller=side18.V95.left_6257", + "side": "side7", + "value": 6257, + "residues": { + "value": 6257, + "mod25": 7, + "modP": 1, + "modP2": 188 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1570508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 392627, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 392627, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1570508, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 392627, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 392627, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6257 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V96.left_6357", + "side": "side7", + "value": 6357, + "residues": { + "value": 6357, + "mod25": 7, + "modP": 16, + "modP2": 288 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1595608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 398902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 398902, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1595608, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 398902, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 398902, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6357 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V97.left_6382", + "side": "side7", + "value": 6382, + "residues": { + "value": 6382, + "mod25": 7, + "modP": 7, + "modP2": 24 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1601883, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 177987, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 177987, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1601883, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 177987, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 177987, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6382 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V98.left_6457", + "side": "side7", + "value": 6457, + "residues": { + "value": 6457, + "mod25": 7, + "modP": 14, + "modP2": 99 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1620708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 405177, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 405177, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1620708, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 405177, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 405177, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6457 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V99.left_6507", + "side": "side7", + "value": 6507, + "residues": { + "value": 6507, + "mod25": 7, + "modP": 13, + "modP2": 149 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1633258, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 13498, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 13498, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1633258, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 13498, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 13498, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6507 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V100.left_6557", + "side": "side7", + "value": 6557, + "residues": { + "value": 6557, + "mod25": 7, + "modP": 12, + "modP2": 199 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1645808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 411452, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 411452, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 102863, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1645808, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 411452, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 411452, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 102863, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6557 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V101.left_6657", + "side": "side7", + "value": 6657, + "residues": { + "value": 6657, + "mod25": 7, + "modP": 10, + "modP2": 10 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1670908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 417727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 417727, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1670908, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 417727, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 417727, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6657 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V102.left_6757", + "side": "side7", + "value": 6757, + "residues": { + "value": 6757, + "mod25": 7, + "modP": 8, + "modP2": 110 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1696008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 424002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 424002, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1696008, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 424002, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 424002, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6757 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V103.left_6832", + "side": "side7", + "value": 6832, + "residues": { + "value": 6832, + "mod25": 7, + "modP": 15, + "modP2": 185 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1714833, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 190537, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 190537, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1714833, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 190537, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 190537, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6832 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V104.left_6857", + "side": "side7", + "value": 6857, + "residues": { + "value": 6857, + "mod25": 7, + "modP": 6, + "modP2": 210 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1721108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 430277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 430277, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1721108, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 430277, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 430277, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6857 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V105.left_6957", + "side": "side7", + "value": 6957, + "residues": { + "value": 6957, + "mod25": 7, + "modP": 4, + "modP2": 21 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1746208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 436552, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 436552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 109138, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1746208, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 436552, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 436552, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 109138, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 6957 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V106.left_7057", + "side": "side7", + "value": 7057, + "residues": { + "value": 7057, + "mod25": 7, + "modP": 2, + "modP2": 121 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1771308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 442827, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 442827, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 196812, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 49203, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 21868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 5467, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1771308, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 442827, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 442827, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 196812, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 49203, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 21868, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 5467, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove left core vertex 7057 is present in the side7 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V107.right_68", + "side": "side18", + "value": 68, + "residues": { + "value": 68, + "mod25": 18, + "modP": 0, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 17069, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 101, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 17069, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 13, + "square": 169, + "quotient": 101, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 13, + "square": 169, + "quotient": 101, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 68 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V108.right_93", + "side": "side18", + "value": 93, + "residues": { + "value": 93, + "mod25": 18, + "modP": 8, + "modP2": 93 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 23344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5836, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5836, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1459, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 23344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 5836, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 5836, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 1459, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 93 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V109.right_118", + "side": "side18", + "value": 118, + "residues": { + "value": 118, + "mod25": 18, + "modP": 16, + "modP2": 118 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 29619, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3291, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3291, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 29619, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3291, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 3291, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 118 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V110.right_193", + "side": "side18", + "value": 193, + "residues": { + "value": 193, + "mod25": 18, + "modP": 6, + "modP2": 193 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 48444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 12111, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 12111, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 48444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 12111, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 12111, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V111.right_293", + "side": "side18", + "value": 293, + "residues": { + "value": 293, + "mod25": 18, + "modP": 4, + "modP2": 4 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 73544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 18386, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 18386, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 73544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 18386, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 18386, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V112.right_343", + "side": "side18", + "value": 343, + "residues": { + "value": 343, + "mod25": 18, + "modP": 3, + "modP2": 54 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 86094, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 9566, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 9566, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 86094, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 9566, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 9566, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 343 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V113.right_393", + "side": "side18", + "value": 393, + "residues": { + "value": 393, + "mod25": 18, + "modP": 2, + "modP2": 104 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 98644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 24661, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 24661, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 98644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 24661, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 24661, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V114.right_493", + "side": "side18", + "value": 493, + "residues": { + "value": 493, + "mod25": 18, + "modP": 0, + "modP2": 204 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 123744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 30936, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 30936, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 7734, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 123744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 30936, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 30936, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 7734, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V115.right_568", + "side": "side18", + "value": 568, + "residues": { + "value": 568, + "mod25": 18, + "modP": 7, + "modP2": 279 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 142569, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 15841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 15841, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 142569, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 15841, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 15841, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 568 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V116.right_593", + "side": "side18", + "value": 593, + "residues": { + "value": 593, + "mod25": 18, + "modP": 15, + "modP2": 15 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 148844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 37211, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 37211, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 148844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 37211, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 37211, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V117.right_693", + "side": "side18", + "value": 693, + "residues": { + "value": 693, + "mod25": 18, + "modP": 13, + "modP2": 115 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 173944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 43486, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 43486, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 173944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 43486, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 43486, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V118.right_743", + "side": "side18", + "value": 743, + "residues": { + "value": 743, + "mod25": 18, + "modP": 12, + "modP2": 165 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 186494, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 3806, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 3806, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 186494, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 3806, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 3806, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 743 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V119.right_793", + "side": "side18", + "value": 793, + "residues": { + "value": 793, + "mod25": 18, + "modP": 11, + "modP2": 215 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 199044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 49761, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 49761, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 22116, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 5529, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 199044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 49761, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 49761, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 22116, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 5529, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V120.right_893", + "side": "side18", + "value": 893, + "residues": { + "value": 893, + "mod25": 18, + "modP": 9, + "modP2": 26 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 224144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 56036, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 56036, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14009, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 224144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 56036, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 56036, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 14009, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V121.right_993", + "side": "side18", + "value": 993, + "residues": { + "value": 993, + "mod25": 18, + "modP": 7, + "modP2": 126 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 249244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 62311, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 62311, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 249244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 62311, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 62311, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V122.right_1018", + "side": "side18", + "value": 1018, + "residues": { + "value": 1018, + "mod25": 18, + "modP": 15, + "modP2": 151 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 255519, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 28391, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 28391, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 255519, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 28391, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 28391, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1018 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V123.right_1093", + "side": "side18", + "value": 1093, + "residues": { + "value": 1093, + "mod25": 18, + "modP": 5, + "modP2": 226 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 274344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 68586, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 68586, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 274344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 68586, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 68586, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V124.right_1118", + "side": "side18", + "value": 1118, + "residues": { + "value": 1118, + "mod25": 18, + "modP": 13, + "modP2": 251 + }, + "status": "bounded_presence_supported_by_current_split_modulus", + "presenceCheck": { + "status": "bounded_presence_supported_by_current_split_modulus", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": true, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 280619, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 971, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 17, + "square": 289, + "quotient": 971, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 971, + "stableUnderCurrentSplitModulus": true + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 280619, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": true, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 971, + "stableUnderCurrentSplitModulus": true + }, + "firstStableSplitWitness": { + "divisor": 17, + "square": 289, + "quotient": 971, + "stableUnderCurrentSplitModulus": true + }, + "squareDivisorWitnesses": [ + { + "divisor": 17, + "square": 289, + "quotient": 971, + "stableUnderCurrentSplitModulus": true + } + ] + } + ] + }, + "goal": "Prove right core vertex 1118 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V125.right_1193", + "side": "side18", + "value": 1193, + "residues": { + "value": 1193, + "mod25": 18, + "modP": 3, + "modP2": 37 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 299444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 74861, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 74861, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 299444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 74861, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 74861, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V126.right_1243", + "side": "side18", + "value": 1243, + "residues": { + "value": 1243, + "mod25": 18, + "modP": 2, + "modP2": 87 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 311994, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 34666, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 34666, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 311994, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 34666, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 34666, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1243 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V127.right_1293", + "side": "side18", + "value": 1293, + "residues": { + "value": 1293, + "mod25": 18, + "modP": 1, + "modP2": 137 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 324544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 81136, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 81136, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 20284, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 5071, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 324544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 81136, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 81136, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 20284, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 5071, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V128.right_1393", + "side": "side18", + "value": 1393, + "residues": { + "value": 1393, + "mod25": 18, + "modP": 16, + "modP2": 237 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 349644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 87411, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 87411, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 349644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 87411, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 87411, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V129.right_1468", + "side": "side18", + "value": 1468, + "residues": { + "value": 1468, + "mod25": 18, + "modP": 6, + "modP2": 23 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 368469, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 40941, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 40941, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 4549, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 368469, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 40941, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 40941, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 4549, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1468 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V130.right_1493", + "side": "side18", + "value": 1493, + "residues": { + "value": 1493, + "mod25": 18, + "modP": 14, + "modP2": 48 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 374744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 93686, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 93686, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 374744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 93686, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 93686, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V131.right_1593", + "side": "side18", + "value": 1593, + "residues": { + "value": 1593, + "mod25": 18, + "modP": 12, + "modP2": 148 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 399844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 99961, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 99961, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 399844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 99961, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 99961, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V132.right_1693", + "side": "side18", + "value": 1693, + "residues": { + "value": 1693, + "mod25": 18, + "modP": 10, + "modP2": 248 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 424944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 106236, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 106236, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 47216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 26559, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 11804, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 2951, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 424944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 106236, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 106236, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 47216, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 26559, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 11804, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 2951, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V133.right_1793", + "side": "side18", + "value": 1793, + "residues": { + "value": 1793, + "mod25": 18, + "modP": 8, + "modP2": 59 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 450044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112511, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112511, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 450044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 112511, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 112511, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V134.right_1893", + "side": "side18", + "value": 1893, + "residues": { + "value": 1893, + "mod25": 18, + "modP": 6, + "modP2": 159 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 475144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 118786, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 118786, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 475144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 118786, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 118786, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V135.right_1918", + "side": "side18", + "value": 1918, + "residues": { + "value": 1918, + "mod25": 18, + "modP": 14, + "modP2": 184 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 481419, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 53491, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 53491, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 481419, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 53491, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 53491, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1918 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V136.right_1968", + "side": "side18", + "value": 1968, + "residues": { + "value": 1968, + "mod25": 18, + "modP": 13, + "modP2": 234 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 493969, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 10081, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 10081, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 493969, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 10081, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 10081, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1968 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V137.right_1993", + "side": "side18", + "value": 1993, + "residues": { + "value": 1993, + "mod25": 18, + "modP": 4, + "modP2": 259 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 500244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 125061, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 125061, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 500244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 125061, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 125061, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 1993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V138.right_2093", + "side": "side18", + "value": 2093, + "residues": { + "value": 2093, + "mod25": 18, + "modP": 2, + "modP2": 70 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 525344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 131336, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 131336, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 32834, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 525344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 131336, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 131336, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 32834, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V139.right_2143", + "side": "side18", + "value": 2143, + "residues": { + "value": 2143, + "mod25": 18, + "modP": 1, + "modP2": 120 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 537894, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 59766, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 59766, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 537894, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 59766, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 59766, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2143 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V140.right_2193", + "side": "side18", + "value": 2193, + "residues": { + "value": 2193, + "mod25": 18, + "modP": 0, + "modP2": 170 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 550444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 137611, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 137611, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 550444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 137611, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 137611, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V141.right_2293", + "side": "side18", + "value": 2293, + "residues": { + "value": 2293, + "mod25": 18, + "modP": 15, + "modP2": 270 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 575544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 143886, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 143886, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 575544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 143886, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 143886, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V142.right_2368", + "side": "side18", + "value": 2368, + "residues": { + "value": 2368, + "mod25": 18, + "modP": 5, + "modP2": 56 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 594369, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 66041, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 66041, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 594369, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 66041, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 66041, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2368 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V143.right_2393", + "side": "side18", + "value": 2393, + "residues": { + "value": 2393, + "mod25": 18, + "modP": 13, + "modP2": 81 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 600644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 150161, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 150161, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 4964, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 1241, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 600644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 150161, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 150161, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 11, + "square": 121, + "quotient": 4964, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 22, + "square": 484, + "quotient": 1241, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V144.right_2493", + "side": "side18", + "value": 2493, + "residues": { + "value": 2493, + "mod25": 18, + "modP": 11, + "modP2": 181 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 625744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156436, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 39109, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 625744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 156436, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 156436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 39109, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V145.right_2593", + "side": "side18", + "value": 2593, + "residues": { + "value": 2593, + "mod25": 18, + "modP": 9, + "modP2": 281 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 650844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 162711, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 162711, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 72316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 18079, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 650844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 162711, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 162711, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 72316, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 18079, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V146.right_2693", + "side": "side18", + "value": 2693, + "residues": { + "value": 2693, + "mod25": 18, + "modP": 7, + "modP2": 92 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 675944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 168986, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 168986, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 675944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 168986, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 168986, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V147.right_2793", + "side": "side18", + "value": 2793, + "residues": { + "value": 2793, + "mod25": 18, + "modP": 5, + "modP2": 192 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 701044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 175261, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 175261, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 701044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 175261, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 175261, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V148.right_2818", + "side": "side18", + "value": 2818, + "residues": { + "value": 2818, + "mod25": 18, + "modP": 13, + "modP2": 217 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 707319, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 78591, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 78591, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 707319, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 78591, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 78591, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2818 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V149.right_2893", + "side": "side18", + "value": 2893, + "residues": { + "value": 2893, + "mod25": 18, + "modP": 3, + "modP2": 3 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 726144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 181536, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 181536, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 45384, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 11346, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 726144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 181536, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 181536, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 45384, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 11346, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V150.right_2993", + "side": "side18", + "value": 2993, + "residues": { + "value": 2993, + "mod25": 18, + "modP": 1, + "modP2": 103 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 751244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 187811, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 187811, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 751244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 187811, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 187811, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 2993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V151.right_3043", + "side": "side18", + "value": 3043, + "residues": { + "value": 3043, + "mod25": 18, + "modP": 0, + "modP2": 153 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 763794, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 84866, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 84866, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 763794, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 84866, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 84866, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3043 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V152.right_3093", + "side": "side18", + "value": 3093, + "residues": { + "value": 3093, + "mod25": 18, + "modP": 16, + "modP2": 203 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 776344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 194086, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 194086, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 776344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 194086, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 194086, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V153.right_3193", + "side": "side18", + "value": 3193, + "residues": { + "value": 3193, + "mod25": 18, + "modP": 14, + "modP2": 14 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 801444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 200361, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 200361, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 16356, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 4089, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 801444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 200361, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 200361, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 16356, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 14, + "square": 196, + "quotient": 4089, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V154.right_3268", + "side": "side18", + "value": 3268, + "residues": { + "value": 3268, + "mod25": 18, + "modP": 4, + "modP2": 89 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 820269, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 91141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 91141, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 820269, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 91141, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 91141, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3268 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V155.right_3293", + "side": "side18", + "value": 3293, + "residues": { + "value": 3293, + "mod25": 18, + "modP": 12, + "modP2": 114 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 826544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 206636, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 206636, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 51659, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 826544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 206636, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 206636, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 51659, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V156.right_3393", + "side": "side18", + "value": 3393, + "residues": { + "value": 3393, + "mod25": 18, + "modP": 10, + "modP2": 214 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 851644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 212911, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 212911, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 851644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 212911, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 212911, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V157.right_3493", + "side": "side18", + "value": 3493, + "residues": { + "value": 3493, + "mod25": 18, + "modP": 8, + "modP2": 25 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 876744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 219186, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 219186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 97416, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 24354, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 10824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 2706, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 876744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 219186, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 219186, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 97416, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 24354, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 10824, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 18, + "square": 324, + "quotient": 2706, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V158.right_3593", + "side": "side18", + "value": 3593, + "residues": { + "value": 3593, + "mod25": 18, + "modP": 6, + "modP2": 125 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 901844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 225461, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 225461, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 901844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 225461, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 225461, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V159.right_3693", + "side": "side18", + "value": 3693, + "residues": { + "value": 3693, + "mod25": 18, + "modP": 4, + "modP2": 225 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 926944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 231736, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 231736, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 57934, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 926944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 231736, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 231736, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 57934, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V160.right_3718", + "side": "side18", + "value": 3718, + "residues": { + "value": 3718, + "mod25": 18, + "modP": 12, + "modP2": 250 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 933219, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 103691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 103691, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 933219, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 103691, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 103691, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3718 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V161.right_3793", + "side": "side18", + "value": 3793, + "residues": { + "value": 3793, + "mod25": 18, + "modP": 2, + "modP2": 36 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 952044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 238011, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 238011, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 952044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 238011, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 238011, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V162.right_3893", + "side": "side18", + "value": 3893, + "residues": { + "value": 3893, + "mod25": 18, + "modP": 0, + "modP2": 136 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 977144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 244286, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 244286, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 977144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 244286, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 244286, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V163.right_3943", + "side": "side18", + "value": 3943, + "residues": { + "value": 3943, + "mod25": 18, + "modP": 16, + "modP2": 186 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 989694, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 109966, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 109966, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 989694, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 109966, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 109966, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3943 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V164.right_3993", + "side": "side18", + "value": 3993, + "residues": { + "value": 3993, + "mod25": 18, + "modP": 15, + "modP2": 236 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1002244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 250561, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 250561, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1002244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 250561, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 250561, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 3993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V165.right_4093", + "side": "side18", + "value": 4093, + "residues": { + "value": 4093, + "mod25": 18, + "modP": 13, + "modP2": 47 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1027344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 256836, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 256836, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 64209, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1027344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 256836, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 256836, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 64209, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V166.right_4168", + "side": "side18", + "value": 4168, + "residues": { + "value": 4168, + "mod25": 18, + "modP": 3, + "modP2": 122 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1046169, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 116241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 116241, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1046169, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 116241, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 116241, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4168 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V167.right_4193", + "side": "side18", + "value": 4193, + "residues": { + "value": 4193, + "mod25": 18, + "modP": 11, + "modP2": 147 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1052444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 263111, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 263111, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1052444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 263111, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 263111, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V168.right_4293", + "side": "side18", + "value": 4293, + "residues": { + "value": 4293, + "mod25": 18, + "modP": 9, + "modP2": 247 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1077544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 269386, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 269386, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 6376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 26, + "square": 676, + "quotient": 1594, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1077544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 269386, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 269386, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 13, + "square": 169, + "quotient": 6376, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 26, + "square": 676, + "quotient": 1594, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V169.right_4393", + "side": "side18", + "value": 4393, + "residues": { + "value": 4393, + "mod25": 18, + "modP": 7, + "modP2": 58 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1102644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 275661, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 275661, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 122516, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 30629, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1102644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 275661, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 275661, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 122516, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 30629, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V170.right_4418", + "side": "side18", + "value": 4418, + "residues": { + "value": 4418, + "mod25": 18, + "modP": 15, + "modP2": 83 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1108919, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 22631, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 22631, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1108919, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 22631, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 22631, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4418 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V171.right_4493", + "side": "side18", + "value": 4493, + "residues": { + "value": 4493, + "mod25": 18, + "modP": 5, + "modP2": 158 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1127744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 281936, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 281936, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 70484, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 17621, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1127744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 281936, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 281936, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 70484, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 17621, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V172.right_4593", + "side": "side18", + "value": 4593, + "residues": { + "value": 4593, + "mod25": 18, + "modP": 3, + "modP2": 258 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1152844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 288211, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 288211, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1152844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 288211, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 288211, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V173.right_4618", + "side": "side18", + "value": 4618, + "residues": { + "value": 4618, + "mod25": 18, + "modP": 11, + "modP2": 283 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1159119, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 128791, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 128791, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1159119, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 128791, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 128791, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4618 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V174.right_4693", + "side": "side18", + "value": 4693, + "residues": { + "value": 4693, + "mod25": 18, + "modP": 1, + "modP2": 69 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1177944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 294486, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 294486, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1177944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 294486, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 294486, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V175.right_4793", + "side": "side18", + "value": 4793, + "residues": { + "value": 4793, + "mod25": 18, + "modP": 16, + "modP2": 169 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1203044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 300761, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 300761, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1203044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 300761, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 300761, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V176.right_4843", + "side": "side18", + "value": 4843, + "residues": { + "value": 4843, + "mod25": 18, + "modP": 15, + "modP2": 219 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1215594, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 135066, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 135066, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1215594, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 135066, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 135066, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4843 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V177.right_4893", + "side": "side18", + "value": 4893, + "residues": { + "value": 4893, + "mod25": 18, + "modP": 14, + "modP2": 269 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1228144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 307036, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 307036, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 76759, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1228144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 307036, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 307036, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 76759, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V178.right_4993", + "side": "side18", + "value": 4993, + "residues": { + "value": 4993, + "mod25": 18, + "modP": 12, + "modP2": 80 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1253244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 313311, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 313311, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1253244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 313311, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 313311, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 4993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V179.right_5068", + "side": "side18", + "value": 5068, + "residues": { + "value": 5068, + "mod25": 18, + "modP": 2, + "modP2": 155 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1272069, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 141341, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 141341, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1272069, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 141341, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 141341, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5068 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V180.right_5093", + "side": "side18", + "value": 5093, + "residues": { + "value": 5093, + "mod25": 18, + "modP": 10, + "modP2": 180 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1278344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 319586, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 319586, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1278344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 319586, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 319586, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V181.right_5193", + "side": "side18", + "value": 5193, + "residues": { + "value": 5193, + "mod25": 18, + "modP": 8, + "modP2": 280 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1303444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 325861, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 325861, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1303444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 325861, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 325861, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V182.right_5293", + "side": "side18", + "value": 5293, + "residues": { + "value": 5293, + "mod25": 18, + "modP": 6, + "modP2": 91 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1328544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 332136, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 332136, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 147616, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 83034, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 36904, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 9226, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1328544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 332136, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 332136, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 147616, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 83034, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 36904, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 12, + "square": 144, + "quotient": 9226, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V183.right_5393", + "side": "side18", + "value": 5393, + "residues": { + "value": 5393, + "mod25": 18, + "modP": 4, + "modP2": 191 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1353644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 338411, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 338411, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1353644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 338411, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 338411, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V184.right_5418", + "side": "side18", + "value": 5418, + "residues": { + "value": 5418, + "mod25": 18, + "modP": 12, + "modP2": 216 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1359919, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 11239, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 11239, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1359919, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 11239, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 11, + "square": 121, + "quotient": 11239, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5418 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V185.right_5493", + "side": "side18", + "value": 5493, + "residues": { + "value": 5493, + "mod25": 18, + "modP": 2, + "modP2": 2 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1378744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 344686, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 344686, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1378744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 344686, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 344686, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V186.right_5518", + "side": "side18", + "value": 5518, + "residues": { + "value": 5518, + "mod25": 18, + "modP": 10, + "modP2": 27 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1385019, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 153891, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 153891, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 17099, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1385019, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 153891, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 153891, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 9, + "square": 81, + "quotient": 17099, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5518 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V187.right_5543", + "side": "side18", + "value": 5543, + "residues": { + "value": 5543, + "mod25": 18, + "modP": 1, + "modP2": 52 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1391294, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 3854, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 3854, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1391294, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 3854, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 19, + "square": 361, + "quotient": 3854, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5543 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V188.right_5593", + "side": "side18", + "value": 5593, + "residues": { + "value": 5593, + "mod25": 18, + "modP": 0, + "modP2": 102 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1403844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 350961, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 350961, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1403844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 350961, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 350961, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V189.right_5643", + "side": "side18", + "value": 5643, + "residues": { + "value": 5643, + "mod25": 18, + "modP": 16, + "modP2": 152 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1416394, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 28906, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 28906, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1416394, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 28906, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 7, + "square": 49, + "quotient": 28906, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5643 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V190.right_5693", + "side": "side18", + "value": 5693, + "residues": { + "value": 5693, + "mod25": 18, + "modP": 15, + "modP2": 202 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1428944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 357236, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 357236, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 89309, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1428944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 357236, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 357236, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 89309, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V191.right_5743", + "side": "side18", + "value": 5743, + "residues": { + "value": 5743, + "mod25": 18, + "modP": 14, + "modP2": 252 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1441494, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 160166, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 160166, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1441494, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 160166, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 160166, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5743 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V192.right_5793", + "side": "side18", + "value": 5793, + "residues": { + "value": 5793, + "mod25": 18, + "modP": 13, + "modP2": 13 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1454044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 363511, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 363511, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1454044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 363511, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 363511, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V193.right_5893", + "side": "side18", + "value": 5893, + "residues": { + "value": 5893, + "mod25": 18, + "modP": 11, + "modP2": 113 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1479144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 369786, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 369786, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1479144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 369786, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 369786, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V194.right_5968", + "side": "side18", + "value": 5968, + "residues": { + "value": 5968, + "mod25": 18, + "modP": 1, + "modP2": 188 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1497969, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 166441, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 166441, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1497969, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 166441, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 166441, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5968 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V195.right_5993", + "side": "side18", + "value": 5993, + "residues": { + "value": 5993, + "mod25": 18, + "modP": 9, + "modP2": 213 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1504244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 376061, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 376061, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1504244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 376061, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 376061, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 5993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V196.right_6093", + "side": "side18", + "value": 6093, + "residues": { + "value": 6093, + "mod25": 18, + "modP": 7, + "modP2": 24 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1529344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 382336, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 382336, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 95584, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 23896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 5974, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1529344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 382336, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 382336, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 95584, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 8, + "square": 64, + "quotient": 23896, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 16, + "square": 256, + "quotient": 5974, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V197.right_6193", + "side": "side18", + "value": 6193, + "residues": { + "value": 6193, + "mod25": 18, + "modP": 5, + "modP2": 124 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1554444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 388611, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 388611, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 172716, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 43179, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1554444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 388611, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 388611, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 172716, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 43179, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V198.right_6268", + "side": "side18", + "value": 6268, + "residues": { + "value": 6268, + "mod25": 18, + "modP": 12, + "modP2": 199 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1573269, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 151, + "square": 22801, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 151, + "square": 22801, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1573269, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 151, + "square": 22801, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 151, + "square": 22801, + "quotient": 69, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6268 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V199.right_6293", + "side": "side18", + "value": 6293, + "residues": { + "value": 6293, + "mod25": 18, + "modP": 3, + "modP2": 224 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1579544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 394886, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 394886, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1579544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 394886, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 394886, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V200.right_6393", + "side": "side18", + "value": 6393, + "residues": { + "value": 6393, + "mod25": 18, + "modP": 1, + "modP2": 35 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1604644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 401161, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 401161, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1604644, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 401161, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 401161, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6393 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V201.right_6418", + "side": "side18", + "value": 6418, + "residues": { + "value": 6418, + "mod25": 18, + "modP": 9, + "modP2": 60 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1610919, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 178991, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 178991, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1610919, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 178991, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 178991, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6418 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V202.right_6493", + "side": "side18", + "value": 6493, + "residues": { + "value": 6493, + "mod25": 18, + "modP": 16, + "modP2": 135 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1629744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 407436, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 407436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 101859, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1629744, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 407436, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 407436, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 101859, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6493 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V203.right_6593", + "side": "side18", + "value": 6593, + "residues": { + "value": 6593, + "mod25": 18, + "modP": 14, + "modP2": 235 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1654844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 413711, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 413711, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1654844, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 413711, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 413711, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6593 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V204.right_6643", + "side": "side18", + "value": 6643, + "residues": { + "value": 6643, + "mod25": 18, + "modP": 13, + "modP2": 285 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1667394, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 185266, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 185266, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1667394, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 185266, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 185266, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6643 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V205.right_6693", + "side": "side18", + "value": 6693, + "residues": { + "value": 6693, + "mod25": 18, + "modP": 12, + "modP2": 46 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1679944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 419986, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 419986, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1679944, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 419986, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 419986, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6693 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V206.right_6793", + "side": "side18", + "value": 6793, + "residues": { + "value": 6793, + "mod25": 18, + "modP": 10, + "modP2": 146 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1705044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 426261, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 426261, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1705044, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 426261, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 426261, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6793 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V207.right_6868", + "side": "side18", + "value": 6868, + "residues": { + "value": 6868, + "mod25": 18, + "modP": 0, + "modP2": 221 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1723869, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 191541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 191541, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 35181, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 3909, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1723869, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 191541, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 3, + "square": 9, + "quotient": 191541, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 7, + "square": 49, + "quotient": 35181, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 21, + "square": 441, + "quotient": 3909, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6868 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V208.right_6893", + "side": "side18", + "value": 6893, + "residues": { + "value": 6893, + "mod25": 18, + "modP": 8, + "modP2": 246 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1730144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 432536, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 432536, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 108134, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1730144, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 432536, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 432536, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 108134, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6893 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V209.right_6993", + "side": "side18", + "value": 6993, + "residues": { + "value": 6993, + "mod25": 18, + "modP": 6, + "modP2": 57 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1755244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 438811, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 438811, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1755244, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 438811, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 438811, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 6993 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V210.right_7093", + "side": "side18", + "value": 7093, + "residues": { + "value": 7093, + "mod25": 18, + "modP": 4, + "modP2": 157 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1780344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 445086, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 445086, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 197816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 49454, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1780344, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 445086, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 445086, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 3, + "square": 9, + "quotient": 197816, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 6, + "square": 36, + "quotient": 49454, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7093 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V211.right_7193", + "side": "side18", + "value": 7193, + "residues": { + "value": 7193, + "mod25": 18, + "modP": 2, + "modP2": 257 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1805444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 451361, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 451361, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1805444, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 451361, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 451361, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7193 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V212.right_7293", + "side": "side18", + "value": 7293, + "residues": { + "value": 7293, + "mod25": 18, + "modP": 0, + "modP2": 68 + }, + "status": "needs_sharper_split_or_parametric_presence_witness", + "presenceCheck": { + "status": "needs_sharper_split_or_parametric_presence_witness", + "allWitnessRowsCompatible": true, + "allWitnessRowsHaveStableSplitWitness": false, + "witnessChecks": [ + { + "N": 7318, + "outsider": 251, + "productPlusOne": 1830544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 457636, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 457636, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 114409, + "stableUnderCurrentSplitModulus": false + } + ] + }, + { + "N": 7307, + "outsider": 251, + "productPlusOne": 1830544, + "hasAnySquareDivisor": true, + "hasStableSplitWitness": false, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 457636, + "stableUnderCurrentSplitModulus": false + }, + "firstStableSplitWitness": null, + "squareDivisorWitnesses": [ + { + "divisor": 2, + "square": 4, + "quotient": 457636, + "stableUnderCurrentSplitModulus": false + }, + { + "divisor": 4, + "square": 16, + "quotient": 114409, + "stableUnderCurrentSplitModulus": false + } + ] + } + ] + }, + "goal": "Prove right core vertex 7293 is present in the side18 compatible set for every row in split outP2=251|out25=1|smaller=side18." + } + ], + "vertexPresenceSummary": { + "splitModulus": 7225, + "witnessRowCount": 2, + "vertexPresenceAtomCount": 212, + "stableUnderCurrentSplitModulusCount": 2, + "needsSharperSplitOrParametricWitnessCount": 210, + "failedVertexPresenceAtomCount": 0, + "refinementStatus": "literal_core_requires_sharper_square_witness_split", + "refinementConditionCount": 9, + "dominantRefinementConditions": [ 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"square_361_outsider_251", + "square": 361, + "requiredOutsiderResidueModSquare": 251, + "atomCount": 2, + "successorSplitKey": "outP2=251|out25=1|smaller=side18|out361=251" + }, + { + "conditionId": "square_1681_outsider_251", + "square": 1681, + "requiredOutsiderResidueModSquare": 251, + "atomCount": 1, + "successorSplitKey": "outP2=251|out25=1|smaller=side18|out1681=251" + }, + { + "conditionId": "square_5041_outsider_251", + "square": 5041, + "requiredOutsiderResidueModSquare": 251, + "atomCount": 1, + "successorSplitKey": "outP2=251|out25=1|smaller=side18|out5041=251" + } + ], + "firstUnstableAtoms": [ + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V1.left_57", + "side": "side7", + "value": 57, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3577, + "stableUnderCurrentSplitModulus": false + } + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.V2.left_82", + "side": "side7", + "value": 82, + "firstSquareDivisorWitness": 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"bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 7627, + "checkedSquareRootFloor": 87, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (82, 93) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E3.left_157_right_118", + "pairIndex": 2, + "pair": { + "leftValue": 157, + "rightValue": 118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 157, + "rightModP2": 118, + "leftModP": 4, + "rightModP": 16, + "productPlusOneModP2": 31 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 18527, + "checkedSquareRootFloor": 136, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (157, 118) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E4.left_257_right_193", + "pairIndex": 3, + "pair": { + "leftValue": 257, + "rightValue": 193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 257, + "rightModP2": 193, + "leftModP": 2, + "rightModP": 6, + "productPlusOneModP2": 183 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 49602, + "checkedSquareRootFloor": 222, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (257, 193) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E5.left_307_right_343", + "pairIndex": 4, + "pair": { + "leftValue": 307, + "rightValue": 343, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 18, + "rightModP2": 54, + "leftModP": 1, + "rightModP": 3, + "productPlusOneModP2": 106 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 105302, + "checkedSquareRootFloor": 324, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (307, 343) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E6.left_357_right_293", + "pairIndex": 5, + "pair": { + "leftValue": 357, + "rightValue": 293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 68, + "rightModP2": 4, + "leftModP": 0, + "rightModP": 4, + "productPlusOneModP2": 273 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 104602, + "checkedSquareRootFloor": 323, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (357, 293) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E7.left_457_right_393", + "pairIndex": 6, + "pair": { + "leftValue": 457, + "rightValue": 393, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 168, + "rightModP2": 104, + "leftModP": 15, + "rightModP": 2, + "productPlusOneModP2": 133 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 179602, + "checkedSquareRootFloor": 423, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (457, 393) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E8.left_532_right_493", + "pairIndex": 7, + "pair": { + "leftValue": 532, + "rightValue": 493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 243, + "rightModP2": 204, + "leftModP": 5, + "rightModP": 0, + "productPlusOneModP2": 154 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 262277, + "checkedSquareRootFloor": 512, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (532, 493) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E9.left_557_right_593", + "pairIndex": 8, + "pair": { + "leftValue": 557, + "rightValue": 593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 268, + "rightModP2": 15, + "leftModP": 13, + "rightModP": 15, + "productPlusOneModP2": 264 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 330302, + "checkedSquareRootFloor": 574, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (557, 593) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E10.left_657_right_568", + "pairIndex": 9, + "pair": { + "leftValue": 657, + "rightValue": 568, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 79, + "rightModP2": 279, + "leftModP": 11, + "rightModP": 7, + "productPlusOneModP2": 78 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 373177, + "checkedSquareRootFloor": 610, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (657, 568) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E11.left_757_right_693", + "pairIndex": 10, + "pair": { + "leftValue": 757, + "rightValue": 693, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 179, + "rightModP2": 115, + "leftModP": 9, + "rightModP": 13, + "productPlusOneModP2": 67 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 524602, + "checkedSquareRootFloor": 724, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (757, 693) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E12.left_857_right_793", + "pairIndex": 11, + "pair": { + "leftValue": 857, + "rightValue": 793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 279, + "rightModP2": 215, + "leftModP": 7, + "rightModP": 11, + "productPlusOneModP2": 163 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 679602, + "checkedSquareRootFloor": 824, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (857, 793) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E13.left_957_right_893", + "pairIndex": 12, + "pair": { + "leftValue": 957, + "rightValue": 893, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 90, + "rightModP2": 26, + "leftModP": 5, + "rightModP": 9, + "productPlusOneModP2": 29 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 854602, + "checkedSquareRootFloor": 924, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (957, 893) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E14.left_982_right_743", + "pairIndex": 13, + "pair": { + "leftValue": 982, + "rightValue": 743, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 115, + "rightModP2": 165, + "leftModP": 13, + "rightModP": 12, + "productPlusOneModP2": 191 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 729627, + "checkedSquareRootFloor": 854, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (982, 743) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E15.left_1057_right_993", + "pairIndex": 14, + "pair": { + "leftValue": 1057, + "rightValue": 993, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 190, + "rightModP2": 126, + "leftModP": 3, + "rightModP": 7, + "productPlusOneModP2": 243 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1049602, + "checkedSquareRootFloor": 1024, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1057, 993) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E16.left_1082_right_1018", + "pairIndex": 15, + "pair": { + "leftValue": 1082, + "rightValue": 1018, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 215, + "rightModP2": 151, + "leftModP": 11, + "rightModP": 15, + "productPlusOneModP2": 98 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1101477, + "checkedSquareRootFloor": 1049, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1082, 1018) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E17.left_1157_right_1093", + "pairIndex": 16, + "pair": { + "leftValue": 1157, + "rightValue": 1093, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 1, + "rightModP2": 226, + "leftModP": 1, + "rightModP": 5, + "productPlusOneModP2": 227 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1264602, + "checkedSquareRootFloor": 1124, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1157, 1093) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E18.left_1207_right_1118", + "pairIndex": 17, + "pair": { + "leftValue": 1207, + "rightValue": 1118, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 51, + "rightModP2": 251, + "leftModP": 0, + "rightModP": 13, + "productPlusOneModP2": 86 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1349427, + "checkedSquareRootFloor": 1161, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1207, 1118) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E19.left_1257_right_1193", + "pairIndex": 18, + "pair": { + "leftValue": 1257, + "rightValue": 1193, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 101, + "rightModP2": 37, + "leftModP": 16, + "rightModP": 3, + "productPlusOneModP2": 270 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1499602, + "checkedSquareRootFloor": 1224, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1257, 1193) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E20.left_1282_right_1243", + "pairIndex": 19, + "pair": { + "leftValue": 1282, + "rightValue": 1243, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 126, + "rightModP2": 87, + "leftModP": 7, + "rightModP": 2, + "productPlusOneModP2": 270 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1593527, + "checkedSquareRootFloor": 1262, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1282, 1243) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E21.left_1357_right_1293", + "pairIndex": 20, + "pair": { + "leftValue": 1357, + "rightValue": 1293, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 201, + "rightModP2": 137, + "leftModP": 14, + "rightModP": 1, + "productPlusOneModP2": 83 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1754602, + "checkedSquareRootFloor": 1324, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1357, 1293) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E22.left_1407_right_1468", + "pairIndex": 21, + "pair": { + "leftValue": 1407, + "rightValue": 1468, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 251, + "rightModP2": 23, + "leftModP": 13, + "rightModP": 6, + "productPlusOneModP2": 283 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2065477, + "checkedSquareRootFloor": 1437, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1407, 1468) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E23.left_1432_right_1393", + "pairIndex": 22, + "pair": { + "leftValue": 1432, + "rightValue": 1393, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 276, + "rightModP2": 237, + "leftModP": 4, + "rightModP": 16, + "productPlusOneModP2": 99 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 1994777, + "checkedSquareRootFloor": 1412, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1432, 1393) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E24.left_1457_right_1493", + "pairIndex": 23, + "pair": { + "leftValue": 1457, + "rightValue": 1493, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 12, + "rightModP2": 48, + "leftModP": 12, + "rightModP": 14, + "productPlusOneModP2": 288 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2175302, + "checkedSquareRootFloor": 1474, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1457, 1493) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E25.left_1557_right_1593", + "pairIndex": 24, + "pair": { + "leftValue": 1557, + "rightValue": 1593, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 112, + "rightModP2": 148, + "leftModP": 10, + "rightModP": 12, + "productPlusOneModP2": 104 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2480302, + "checkedSquareRootFloor": 1574, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1557, 1593) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E26.left_1657_right_1693", + "pairIndex": 25, + "pair": { + "leftValue": 1657, + "rightValue": 1693, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 212, + "rightModP2": 248, + "leftModP": 8, + "rightModP": 10, + "productPlusOneModP2": 268 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 2805302, + "checkedSquareRootFloor": 1674, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1657, 1693) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E27.left_1757_right_1793", + "pairIndex": 26, + "pair": { + "leftValue": 1757, + "rightValue": 1793, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 23, + "rightModP2": 59, + "leftModP": 6, + "rightModP": 8, + "productPlusOneModP2": 202 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 3150302, + "checkedSquareRootFloor": 1774, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1757, 1793) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + 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"bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 3609677, + "checkedSquareRootFloor": 1899, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1882, 1918) remains a missing cross edge throughout split outP2=251|out25=1|smaller=side18." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E30.left_1957_right_1968", + "pairIndex": 29, + "pair": { + "leftValue": 1957, + "rightValue": 1968, + "leftMod25": 7, + "rightMod25": 18, + "leftModP2": 223, + "rightModP2": 234, + "leftModP": 2, + "rightModP": 13, + "productPlusOneModP2": 163 + }, + "status": "bounded_missing_cross_edge_certified_by_squarefree_product_plus_one", + "squarefreeCheck": { + "productPlusOne": 3851377, + "checkedSquareRootFloor": 1962, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + "goal": "Normalize why (1957, 1968) remains a missing cross edge throughout split 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"productPlusOneModP2": 137, + "edgeAtomIds": [ + "D3.2_persist_outP2=251_out25=1_smaller=side18.E106.left_7057_right_7293" + ], + "examples": [ + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E106.left_7057_right_7293", + "leftValue": 7057, + "rightValue": 7293, + "productPlusOne": 51466702 + } + ], + "edgeCount": 1 + } + ], + "firstEdgeCertificates": [ + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E1.left_57_right_68", + "leftValue": 57, + "rightValue": 68, + "productPlusOne": 3877, + "checkedSquareRootFloor": 62, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E2.left_82_right_93", + "leftValue": 82, + "rightValue": 93, + "productPlusOne": 7627, + "checkedSquareRootFloor": 87, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E3.left_157_right_118", + "leftValue": 157, + "rightValue": 118, + "productPlusOne": 18527, + "checkedSquareRootFloor": 136, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E4.left_257_right_193", + "leftValue": 257, + "rightValue": 193, + "productPlusOne": 49602, + "checkedSquareRootFloor": 222, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E5.left_307_right_343", + "leftValue": 307, + "rightValue": 343, + "productPlusOne": 105302, + "checkedSquareRootFloor": 324, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E6.left_357_right_293", + "leftValue": 357, + "rightValue": 293, + "productPlusOne": 104602, + "checkedSquareRootFloor": 323, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E7.left_457_right_393", + "leftValue": 457, + "rightValue": 393, + "productPlusOne": 179602, + "checkedSquareRootFloor": 423, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E8.left_532_right_493", + "leftValue": 532, + "rightValue": 493, + "productPlusOne": 262277, + "checkedSquareRootFloor": 512, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E9.left_557_right_593", + "leftValue": 557, + "rightValue": 593, + "productPlusOne": 330302, + "checkedSquareRootFloor": 574, + "squareDivisorWitnesses": [], + "isSquarefree": true + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E10.left_657_right_568", + "leftValue": 657, + "rightValue": 568, + "productPlusOne": 373177, + "checkedSquareRootFloor": 610, + "squareDivisorWitnesses": [], + "isSquarefree": true + } + ], + "failedEdgeAtoms": [], + "proofBoundary": "This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim.", + "nextTheoremAction": "Promote this literal edge-obstruction certificate into A5 congruence-persistence families, or emit a sharper successor atom for any edge whose obstruction is not implied by the split hypotheses." + }, + "edgeCongruencePersistence": { + "schema": "erdos.p848_edge_congruence_persistence/1", + "persistenceId": "D3.2_persist_outP2=251_out25=1_smaller=side18.edge_congruence_persistence", + "status": "literal_constant_edge_persistence_verified", + "proofKind": "constant_pair_squarefree_invariant", + "splitKey": "outP2=251|out25=1|smaller=side18", + "splitModulus": 7225, + "witnessRowCount": 2, + "edgeAtomCount": 106, + "verifiedEdgeAtomCount": 106, + "failedEdgeAtomCount": 0, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "proofFamilies": [ + { + "familyId": "D3.2_persist_outP2=251_out25=1_smaller=side18.edge_constant_squarefree_family", + "status": "congruence_persistence_family_verified", + "proofKind": "constant_pair_squarefree_invariant", + "edgeAtomCount": 106, + "verifiedEdgeAtomCount": 106, + "failedEdgeAtomCount": 0, + "splitKey": "outP2=251|out25=1|smaller=side18", + "splitModulus": 7225, + "statement": "For each exported literal cross pair (l,r), l and r are constants in the packet, so l*r+1 is the same integer for every row satisfying the split hypotheses.", + "proofSteps": [ + "Recompute c = l*r + 1 from the exported literal pair.", + "Check c matches the squarefree certificate attached to the edge atom.", + "Because c has no N or outsider variable, the edge obstruction persists over all rows covered by this literal packet." + ], + "proofBoundary": "This is not yet a parameterized edge-family theorem. If later proof work replaces literal pair constants with formulas in N, this constant-family proof must be lifted or replaced.", + "exampleEdgeAtoms": [ + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E1.left_57_right_68", + "leftValue": 57, + "rightValue": 68, + "productPlusOne": 3877 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E2.left_82_right_93", + "leftValue": 82, + "rightValue": 93, + "productPlusOne": 7627 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E3.left_157_right_118", + "leftValue": 157, + "rightValue": 118, + "productPlusOne": 18527 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E4.left_257_right_193", + "leftValue": 257, + "rightValue": 193, + "productPlusOne": 49602 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E5.left_307_right_343", + "leftValue": 307, + "rightValue": 343, + "productPlusOne": 105302 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E6.left_357_right_293", + "leftValue": 357, + "rightValue": 293, + "productPlusOne": 104602 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E7.left_457_right_393", + "leftValue": 457, + "rightValue": 393, + "productPlusOne": 179602 + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E8.left_532_right_493", + "leftValue": 532, + "rightValue": 493, + "productPlusOne": 262277 + } + ] + } + ], + "checks": [ + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E1.left_57_right_68", + "pairIndex": 0, + "leftValue": 57, + "rightValue": 68, + "productPlusOne": 3877, + "productPlusOneRecomputed": 3877, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E2.left_82_right_93", + "pairIndex": 1, + "leftValue": 82, + "rightValue": 93, + "productPlusOne": 7627, + "productPlusOneRecomputed": 7627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E3.left_157_right_118", + "pairIndex": 2, + "leftValue": 157, + "rightValue": 118, + "productPlusOne": 18527, + "productPlusOneRecomputed": 18527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E4.left_257_right_193", + "pairIndex": 3, + "leftValue": 257, + "rightValue": 193, + "productPlusOne": 49602, + "productPlusOneRecomputed": 49602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E5.left_307_right_343", + "pairIndex": 4, + "leftValue": 307, + "rightValue": 343, + "productPlusOne": 105302, + "productPlusOneRecomputed": 105302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E6.left_357_right_293", + "pairIndex": 5, + "leftValue": 357, + "rightValue": 293, + "productPlusOne": 104602, + "productPlusOneRecomputed": 104602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E7.left_457_right_393", + "pairIndex": 6, + "leftValue": 457, + "rightValue": 393, + "productPlusOne": 179602, + "productPlusOneRecomputed": 179602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E8.left_532_right_493", + "pairIndex": 7, + "leftValue": 532, + "rightValue": 493, + "productPlusOne": 262277, + "productPlusOneRecomputed": 262277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E9.left_557_right_593", + "pairIndex": 8, + "leftValue": 557, + "rightValue": 593, + "productPlusOne": 330302, + "productPlusOneRecomputed": 330302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E10.left_657_right_568", + "pairIndex": 9, + "leftValue": 657, + "rightValue": 568, + "productPlusOne": 373177, + "productPlusOneRecomputed": 373177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E11.left_757_right_693", + "pairIndex": 10, + "leftValue": 757, + "rightValue": 693, + "productPlusOne": 524602, + "productPlusOneRecomputed": 524602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E12.left_857_right_793", + "pairIndex": 11, + "leftValue": 857, + "rightValue": 793, + "productPlusOne": 679602, + "productPlusOneRecomputed": 679602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E13.left_957_right_893", + "pairIndex": 12, + "leftValue": 957, + "rightValue": 893, + "productPlusOne": 854602, + "productPlusOneRecomputed": 854602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E14.left_982_right_743", + "pairIndex": 13, + "leftValue": 982, + "rightValue": 743, + "productPlusOne": 729627, + "productPlusOneRecomputed": 729627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E15.left_1057_right_993", + "pairIndex": 14, + "leftValue": 1057, + "rightValue": 993, + "productPlusOne": 1049602, + "productPlusOneRecomputed": 1049602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E16.left_1082_right_1018", + "pairIndex": 15, + "leftValue": 1082, + "rightValue": 1018, + "productPlusOne": 1101477, + "productPlusOneRecomputed": 1101477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E17.left_1157_right_1093", + "pairIndex": 16, + "leftValue": 1157, + "rightValue": 1093, + "productPlusOne": 1264602, + "productPlusOneRecomputed": 1264602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E18.left_1207_right_1118", + "pairIndex": 17, + "leftValue": 1207, + "rightValue": 1118, + "productPlusOne": 1349427, + "productPlusOneRecomputed": 1349427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E19.left_1257_right_1193", + "pairIndex": 18, + "leftValue": 1257, + "rightValue": 1193, + "productPlusOne": 1499602, + "productPlusOneRecomputed": 1499602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E20.left_1282_right_1243", + "pairIndex": 19, + "leftValue": 1282, + "rightValue": 1243, + "productPlusOne": 1593527, + "productPlusOneRecomputed": 1593527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E21.left_1357_right_1293", + "pairIndex": 20, + "leftValue": 1357, + "rightValue": 1293, + "productPlusOne": 1754602, + "productPlusOneRecomputed": 1754602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E22.left_1407_right_1468", + "pairIndex": 21, + "leftValue": 1407, + "rightValue": 1468, + "productPlusOne": 2065477, + "productPlusOneRecomputed": 2065477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E23.left_1432_right_1393", + "pairIndex": 22, + "leftValue": 1432, + "rightValue": 1393, + "productPlusOne": 1994777, + "productPlusOneRecomputed": 1994777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E24.left_1457_right_1493", + "pairIndex": 23, + "leftValue": 1457, + "rightValue": 1493, + "productPlusOne": 2175302, + "productPlusOneRecomputed": 2175302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E25.left_1557_right_1593", + "pairIndex": 24, + "leftValue": 1557, + "rightValue": 1593, + "productPlusOne": 2480302, + "productPlusOneRecomputed": 2480302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E26.left_1657_right_1693", + "pairIndex": 25, + "leftValue": 1657, + "rightValue": 1693, + "productPlusOne": 2805302, + "productPlusOneRecomputed": 2805302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E27.left_1757_right_1793", + "pairIndex": 26, + "leftValue": 1757, + "rightValue": 1793, + "productPlusOne": 3150302, + "productPlusOneRecomputed": 3150302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E28.left_1857_right_1893", + "pairIndex": 27, + "leftValue": 1857, + "rightValue": 1893, + "productPlusOne": 3515302, + "productPlusOneRecomputed": 3515302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E29.left_1882_right_1918", + "pairIndex": 28, + "leftValue": 1882, + "rightValue": 1918, + "productPlusOne": 3609677, + "productPlusOneRecomputed": 3609677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E30.left_1957_right_1968", + "pairIndex": 29, + "leftValue": 1957, + "rightValue": 1968, + "productPlusOne": 3851377, + "productPlusOneRecomputed": 3851377, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E31.left_2057_right_2093", + "pairIndex": 30, + "leftValue": 2057, + "rightValue": 2093, + "productPlusOne": 4305302, + "productPlusOneRecomputed": 4305302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E32.left_2107_right_2143", + "pairIndex": 31, + "leftValue": 2107, + "rightValue": 2143, + "productPlusOne": 4515302, + "productPlusOneRecomputed": 4515302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E33.left_2157_right_1993", + "pairIndex": 32, + "leftValue": 2157, + "rightValue": 1993, + "productPlusOne": 4298902, + "productPlusOneRecomputed": 4298902, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E34.left_2257_right_2193", + "pairIndex": 33, + "leftValue": 2257, + "rightValue": 2193, + "productPlusOne": 4949602, + "productPlusOneRecomputed": 4949602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E35.left_2332_right_2293", + "pairIndex": 34, + "leftValue": 2332, + "rightValue": 2293, + "productPlusOne": 5347277, + "productPlusOneRecomputed": 5347277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E36.left_2357_right_2393", + "pairIndex": 35, + "leftValue": 2357, + "rightValue": 2393, + "productPlusOne": 5640302, + "productPlusOneRecomputed": 5640302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E37.left_2457_right_2368", + "pairIndex": 36, + "leftValue": 2457, + "rightValue": 2368, + "productPlusOne": 5818177, + "productPlusOneRecomputed": 5818177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E38.left_2507_right_2818", + "pairIndex": 37, + "leftValue": 2507, + "rightValue": 2818, + "productPlusOne": 7064727, + "productPlusOneRecomputed": 7064727, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E39.left_2557_right_2493", + "pairIndex": 38, + "leftValue": 2557, + "rightValue": 2493, + "productPlusOne": 6374602, + "productPlusOneRecomputed": 6374602, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E40.left_2632_right_2593", + "pairIndex": 39, + "leftValue": 2632, + "rightValue": 2593, + "productPlusOne": 6824777, + "productPlusOneRecomputed": 6824777, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E41.left_2657_right_2693", + "pairIndex": 40, + "leftValue": 2657, + "rightValue": 2693, + "productPlusOne": 7155302, + "productPlusOneRecomputed": 7155302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E42.left_2757_right_2793", + "pairIndex": 41, + "leftValue": 2757, + "rightValue": 2793, + "productPlusOne": 7700302, + "productPlusOneRecomputed": 7700302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E43.left_2782_right_2893", + "pairIndex": 42, + "leftValue": 2782, + "rightValue": 2893, + "productPlusOne": 8048327, + "productPlusOneRecomputed": 8048327, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E44.left_2857_right_2993", + "pairIndex": 43, + "leftValue": 2857, + "rightValue": 2993, + "productPlusOne": 8551002, + "productPlusOneRecomputed": 8551002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E45.left_2957_right_3093", + "pairIndex": 44, + "leftValue": 2957, + "rightValue": 3093, + "productPlusOne": 9146002, + "productPlusOneRecomputed": 9146002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E46.left_3007_right_3043", + "pairIndex": 45, + "leftValue": 3007, + "rightValue": 3043, + "productPlusOne": 9150302, + "productPlusOneRecomputed": 9150302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E47.left_3057_right_3193", + "pairIndex": 46, + "leftValue": 3057, + "rightValue": 3193, + "productPlusOne": 9761002, + "productPlusOneRecomputed": 9761002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E48.left_3157_right_3268", + "pairIndex": 47, + "leftValue": 3157, + "rightValue": 3268, + "productPlusOne": 10317077, + "productPlusOneRecomputed": 10317077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E49.left_3232_right_3393", + "pairIndex": 48, + "leftValue": 3232, + "rightValue": 3393, + "productPlusOne": 10966177, + "productPlusOneRecomputed": 10966177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E50.left_3257_right_3293", + "pairIndex": 49, + "leftValue": 3257, + "rightValue": 3293, + "productPlusOne": 10725302, + "productPlusOneRecomputed": 10725302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E51.left_3357_right_3593", + "pairIndex": 50, + "leftValue": 3357, + "rightValue": 3593, + "productPlusOne": 12061702, + "productPlusOneRecomputed": 12061702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E52.left_3457_right_3493", + "pairIndex": 51, + "leftValue": 3457, + "rightValue": 3493, + "productPlusOne": 12075302, + "productPlusOneRecomputed": 12075302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E53.left_3482_right_3693", + "pairIndex": 52, + "leftValue": 3482, + "rightValue": 3693, + "productPlusOne": 12859027, + "productPlusOneRecomputed": 12859027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E54.left_3557_right_3718", + "pairIndex": 53, + "leftValue": 3557, + "rightValue": 3718, + "productPlusOne": 13224927, + "productPlusOneRecomputed": 13224927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E55.left_3657_right_3793", + "pairIndex": 54, + "leftValue": 3657, + "rightValue": 3793, + "productPlusOne": 13871002, + "productPlusOneRecomputed": 13871002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E56.left_3682_right_3893", + "pairIndex": 55, + "leftValue": 3682, + "rightValue": 3893, + "productPlusOne": 14334027, + "productPlusOneRecomputed": 14334027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E57.left_3732_right_3943", + "pairIndex": 56, + "leftValue": 3732, + "rightValue": 3943, + "productPlusOne": 14715277, + "productPlusOneRecomputed": 14715277, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E58.left_3757_right_3993", + "pairIndex": 57, + "leftValue": 3757, + "rightValue": 3993, + "productPlusOne": 15001702, + "productPlusOneRecomputed": 15001702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E59.left_3857_right_4168", + "pairIndex": 58, + "leftValue": 3857, + "rightValue": 4168, + "productPlusOne": 16075977, + "productPlusOneRecomputed": 16075977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E60.left_3907_right_4618", + "pairIndex": 59, + "leftValue": 3907, + "rightValue": 4618, + "productPlusOne": 18042527, + "productPlusOneRecomputed": 18042527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E61.left_3957_right_4093", + "pairIndex": 60, + "leftValue": 3957, + "rightValue": 4093, + "productPlusOne": 16196002, + "productPlusOneRecomputed": 16196002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E62.left_4057_right_4193", + "pairIndex": 61, + "leftValue": 4057, + "rightValue": 4193, + "productPlusOne": 17011002, + "productPlusOneRecomputed": 17011002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E63.left_4132_right_4293", + "pairIndex": 62, + "leftValue": 4132, + "rightValue": 4293, + "productPlusOne": 17738677, + "productPlusOneRecomputed": 17738677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E64.left_4157_right_4418", + "pairIndex": 63, + "leftValue": 4157, + "rightValue": 4418, + "productPlusOne": 18365627, + "productPlusOneRecomputed": 18365627, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E65.left_4257_right_4393", + "pairIndex": 64, + "leftValue": 4257, + "rightValue": 4393, + "productPlusOne": 18701002, + "productPlusOneRecomputed": 18701002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E66.left_4357_right_4493", + "pairIndex": 65, + "leftValue": 4357, + "rightValue": 4493, + "productPlusOne": 19576002, + "productPlusOneRecomputed": 19576002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E67.left_4457_right_4593", + "pairIndex": 66, + "leftValue": 4457, + "rightValue": 4593, + "productPlusOne": 20471002, + "productPlusOneRecomputed": 20471002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E68.left_4557_right_4693", + "pairIndex": 67, + "leftValue": 4557, + "rightValue": 4693, + "productPlusOne": 21386002, + "productPlusOneRecomputed": 21386002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E69.left_4582_right_4793", + "pairIndex": 68, + "leftValue": 4582, + "rightValue": 4793, + "productPlusOne": 21961527, + "productPlusOneRecomputed": 21961527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E70.left_4657_right_4893", + "pairIndex": 69, + "leftValue": 4657, + "rightValue": 4893, + "productPlusOne": 22786702, + "productPlusOneRecomputed": 22786702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E71.left_4757_right_5068", + "pairIndex": 70, + "leftValue": 4757, + "rightValue": 5068, + "productPlusOne": 24108477, + "productPlusOneRecomputed": 24108477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E72.left_4807_right_4843", + "pairIndex": 71, + "leftValue": 4807, + "rightValue": 4843, + "productPlusOne": 23280302, + "productPlusOneRecomputed": 23280302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E73.left_4857_right_4993", + "pairIndex": 72, + "leftValue": 4857, + "rightValue": 4993, + "productPlusOne": 24251002, + "productPlusOneRecomputed": 24251002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E74.left_4957_right_5093", + "pairIndex": 73, + "leftValue": 4957, + "rightValue": 5093, + "productPlusOne": 25246002, + "productPlusOneRecomputed": 25246002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E75.left_5032_right_5193", + "pairIndex": 74, + "leftValue": 5032, + "rightValue": 5193, + "productPlusOne": 26131177, + "productPlusOneRecomputed": 26131177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E76.left_5057_right_5393", + "pairIndex": 75, + "leftValue": 5057, + "rightValue": 5393, + "productPlusOne": 27272402, + "productPlusOneRecomputed": 27272402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E77.left_5157_right_5293", + "pairIndex": 76, + "leftValue": 5157, + "rightValue": 5293, + "productPlusOne": 27296002, + "productPlusOneRecomputed": 27296002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E78.left_5182_right_5418", + "pairIndex": 77, + "leftValue": 5182, + "rightValue": 5418, + "productPlusOne": 28076077, + "productPlusOneRecomputed": 28076077, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E79.left_5257_right_5493", + "pairIndex": 78, + "leftValue": 5257, + "rightValue": 5493, + "productPlusOne": 28876702, + "productPlusOneRecomputed": 28876702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E80.left_5282_right_5543", + "pairIndex": 79, + "leftValue": 5282, + "rightValue": 5543, + "productPlusOne": 29278127, + "productPlusOneRecomputed": 29278127, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E81.left_5307_right_5518", + "pairIndex": 80, + "leftValue": 5307, + "rightValue": 5518, + "productPlusOne": 29284027, + "productPlusOneRecomputed": 29284027, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E82.left_5357_right_5793", + "pairIndex": 81, + "leftValue": 5357, + "rightValue": 5793, + "productPlusOne": 31033102, + "productPlusOneRecomputed": 31033102, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E83.left_5457_right_5593", + "pairIndex": 82, + "leftValue": 5457, + "rightValue": 5593, + "productPlusOne": 30521002, + "productPlusOneRecomputed": 30521002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E84.left_5482_right_5643", + "pairIndex": 83, + "leftValue": 5482, + "rightValue": 5643, + "productPlusOne": 30934927, + "productPlusOneRecomputed": 30934927, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E85.left_5557_right_5693", + "pairIndex": 84, + "leftValue": 5557, + "rightValue": 5693, + "productPlusOne": 31636002, + "productPlusOneRecomputed": 31636002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E86.left_5657_right_5968", + "pairIndex": 85, + "leftValue": 5657, + "rightValue": 5968, + "productPlusOne": 33760977, + "productPlusOneRecomputed": 33760977, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E87.left_5707_right_5743", + "pairIndex": 86, + "leftValue": 5707, + "rightValue": 5743, + "productPlusOne": 32775302, + "productPlusOneRecomputed": 32775302, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E88.left_5757_right_5893", + "pairIndex": 87, + "leftValue": 5757, + "rightValue": 5893, + "productPlusOne": 33926002, + "productPlusOneRecomputed": 33926002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E89.left_5857_right_5993", + "pairIndex": 88, + "leftValue": 5857, + "rightValue": 5993, + "productPlusOne": 35101002, + "productPlusOneRecomputed": 35101002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E90.left_5932_right_6093", + "pairIndex": 89, + "leftValue": 5932, + "rightValue": 6093, + "productPlusOne": 36143677, + "productPlusOneRecomputed": 36143677, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E91.left_5957_right_6268", + "pairIndex": 90, + "leftValue": 5957, + "rightValue": 6268, + "productPlusOne": 37338477, + "productPlusOneRecomputed": 37338477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E92.left_6057_right_6193", + "pairIndex": 91, + "leftValue": 6057, + "rightValue": 6193, + "productPlusOne": 37511002, + "productPlusOneRecomputed": 37511002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E93.left_6157_right_6293", + "pairIndex": 92, + "leftValue": 6157, + "rightValue": 6293, + "productPlusOne": 38746002, + "productPlusOneRecomputed": 38746002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E94.left_6182_right_6393", + "pairIndex": 93, + "leftValue": 6182, + "rightValue": 6393, + "productPlusOne": 39521527, + "productPlusOneRecomputed": 39521527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E95.left_6257_right_6418", + "pairIndex": 94, + "leftValue": 6257, + "rightValue": 6418, + "productPlusOne": 40157427, + "productPlusOneRecomputed": 40157427, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E96.left_6357_right_6493", + "pairIndex": 95, + "leftValue": 6357, + "rightValue": 6493, + "productPlusOne": 41276002, + "productPlusOneRecomputed": 41276002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E97.left_6382_right_6593", + "pairIndex": 96, + "leftValue": 6382, + "rightValue": 6593, + "productPlusOne": 42076527, + "productPlusOneRecomputed": 42076527, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E98.left_6457_right_6693", + "pairIndex": 97, + "leftValue": 6457, + "rightValue": 6693, + "productPlusOne": 43216702, + "productPlusOneRecomputed": 43216702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E99.left_6507_right_6643", + "pairIndex": 98, + "leftValue": 6507, + "rightValue": 6643, + "productPlusOne": 43226002, + "productPlusOneRecomputed": 43226002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E100.left_6557_right_6868", + "pairIndex": 99, + "leftValue": 6557, + "rightValue": 6868, + "productPlusOne": 45033477, + "productPlusOneRecomputed": 45033477, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E101.left_6657_right_6793", + "pairIndex": 100, + "leftValue": 6657, + "rightValue": 6793, + "productPlusOne": 45221002, + "productPlusOneRecomputed": 45221002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E102.left_6757_right_6893", + "pairIndex": 101, + "leftValue": 6757, + "rightValue": 6893, + "productPlusOne": 46576002, + "productPlusOneRecomputed": 46576002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E103.left_6832_right_6993", + "pairIndex": 102, + "leftValue": 6832, + "rightValue": 6993, + "productPlusOne": 47776177, + "productPlusOneRecomputed": 47776177, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E104.left_6857_right_7193", + "pairIndex": 103, + "leftValue": 6857, + "rightValue": 7193, + "productPlusOne": 49322402, + "productPlusOneRecomputed": 49322402, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E105.left_6957_right_7093", + "pairIndex": 104, + "leftValue": 6957, + "rightValue": 7093, + "productPlusOne": 49346002, + "productPlusOneRecomputed": 49346002, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + }, + { + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18.E106.left_7057_right_7293", + "pairIndex": 105, + "leftValue": 7057, + "rightValue": 7293, + "productPlusOne": 51466702, + "productPlusOneRecomputed": 51466702, + "productPlusOneConstantMatchesCertificate": true, + "squarefreeCertificateVerified": true, + "dependsOnSampledN": false, + "dependsOnWitnessOutsider": false, + "impliedBySplitHypotheses": true, + "proofReason": "The exported pair uses literal constants, so left*right+1 is invariant across every row in the split; the squarefree certificate therefore persists without an additional sampled-N congruence." + } + ], + "failedChecks": [], + "proofBoundary": "This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions.", + "nextTheoremAction": "After this A5 literal persistence pass, promote matching disjointness and the K-envelope, or lift the edge proof if vertex formulas become parameterized." + }, + "matchingDisjointness": { + "status": "bounded_disjointness_certified", + "leftVertexCount": 106, + "rightVertexCount": 106, + "pairCount": 106, + "reusedLeftValues": [], + "reusedRightValues": [], + "completionRule": "A symbolic packet may promote only if the parameterized left and right vertex families remain pairwise disjoint." + }, + "matchingKEnvelopeCertificate": { + "schema": "erdos.p848_matching_k_envelope_certificate/1", + "certificateId": "D3.2_persist_outP2=251_out25=1_smaller=side18.matching_k_envelope_certificate", + "status": "literal_matching_sampled_k_envelope_verified", + "proofKind": "literal_disjoint_matching_plus_sampled_k_envelope", + "matchingProof": { + "status": "literal_matching_disjointness_verified", + "pairCount": 106, + "leftVertexCount": 106, + "rightVertexCount": 106, + "reusedLeftValues": [], + "reusedRightValues": [], + "proofSteps": [ + "Count the exported literal left vertices.", + "Count the exported literal right vertices.", + "Verify no left value and no right value is reused across the exported pair list." + ], + "proofBoundary": "This proves disjointness for the exported literal pair list. If later work parameterizes vertices, disjointness must be rechecked for the parameterized formulas." + }, + "kEnvelopeProof": { + "status": "sampled_k_envelope_dominated_by_literal_core", + "requiredMatchingLowerBoundRange": [ + 10, + 11 + ], + "commonMatchingPairCount": 106, + "maxRequiredMatchingLowerBound": 11, + "boundedSlackAgainstMaxK": 95, + "inequality": "106 >= 11", + "proofSteps": [ + "Use the exported common-core pair count as the literal matching size.", + "Compare it against the maximum required matching lower bound recorded by the packet.", + "Record the slack and keep the all-N K-formula handoff explicit." + ], + "proofBoundary": "This certifies the K-envelope recorded by the current split packet. It is not by itself a universal K(N,x) formula proof for every future row." + }, + "allLowerLiteralAtomsReady": true, + "proofBoundary": "A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim.", + "nextTheoremAction": "Assemble this with the verified vertex-successor and edge-persistence layers into a split-discharge readiness certificate, or emit the first missing lower atom." + }, + "summary": { + "vertexPresenceAtomCount": 212, + "edgeObstructionAtomCount": 106, + "stableVertexPresenceAtomCount": 2, + "unstableVertexPresenceAtomCount": 210, + "failedVertexPresenceAtomCount": 0, + "allEdgeObstructionsSquarefree": true, + "edgeObstructionCertificateStatus": "literal_edge_obstruction_certificate_verified", + "edgeCongruencePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingDisjointnessStatus": "bounded_disjointness_certified", + "matchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "readyForFirstTheoremPass": true + }, + "nextTheoremActions": [ + "Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N.", + "The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families.", + "Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof.", + "Attack the packet until it either becomes a split lemma or emits a sharper sub-split key." + ], + "splitDischargeReadiness": { + "schema": "erdos.p848_split_discharge_readiness/1", + "readinessId": "D3.2_persist_outP2=251_out25=1_smaller=side18.split_discharge_readiness", + "status": "split_discharge_readiness_blocked", + "proofKind": "lower_atom_assembly_with_explicit_all_n_handoff", + "atomId": "D3.2_persist_outP2=251_out25=1_smaller=side18", + "splitKey": "outP2=251|out25=1|smaller=side18", + "parentObligationId": "D3_p17_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "lowerLayerChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "blocked", + "evidence": "0/9 successor vertex-family lemmas verified" + }, + { + "layerId": "A4_edge_obstruction_certificate", + "status": "verified", + "evidence": "literal_edge_obstruction_certificate_verified" + }, + { + "layerId": "A5_edge_congruence_persistence", + "status": "verified", + "evidence": "literal_constant_edge_persistence_verified" + }, + { + "layerId": "A6_matching_disjointness", + "status": "verified", + "evidence": "literal_matching_disjointness_verified" + }, + { + "layerId": "A7_sampled_k_envelope", + "status": "verified_sampled_envelope", + "evidence": "106 >= 11" + } + ], + "blockingChecks": [ + { + "layerId": "A3_vertex_presence_successors", + "status": "blocked", + "evidence": "0/9 successor vertex-family lemmas verified" + } + ], + "theoremCandidate": { + "status": "blocked_by_lower_atom", + "statement": "For split outP2=251|out25=1|smaller=side18, the exported literal core supplies a disjoint matching of size 106 against the packet K-envelope [10,11].", + "lowerAtomSummary": { + "vertexSuccessorConditionCount": 9, + "verifiedVertexSuccessorCount": 0, + "edgePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingKEnvelopeStatus": "literal_matching_sampled_k_envelope_verified" + } + }, + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "note": "Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "note": "Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "note": "If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families." + } + ], + "proofBoundary": "This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes.", + "nextTheoremAction": "Discharge the first blocked lower atom before promoting this split." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.md new file mode 100644 index 0000000..b8acb49 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.md @@ -0,0 +1,248 @@ +# D3.2_persist_outP2=251_out25=1_smaller=side18 + +This is a theorem-facing split atom packet for Problem 848. It is intentionally atomic: one split profile, one common matching core, one K-envelope, and deterministic sub-atoms for the next proof pass. + +## Summary + +- Packet id: `p848_split_atom_packet_D3_2_persist_outP2_251_out25_1_smaller_side18` +- Parent obligation: `D3_p17_matching_lower_bound` +- Target obligation: `D4_matching_bound_implies_sMaxMixed_bound` +- Prime lane: `17` +- Split key: `outP2=251|out25=1|smaller=side18` +- Priority: `supporting_p17_companion_lane` +- Status: `ready_for_symbolic_persistence_work` +- Witnesses: `2` over `7307..7318` +- Common core size: `106` +- K-envelope: `[10,11]`, slack against max K `95` +- Vertex atoms: `212` +- Vertex atoms stable under current split modulus: `2` +- Vertex atoms needing sharper split or parameterization: `210` +- Edge atoms: `106` +- Edge certificate: `literal_edge_obstruction_certificate_verified` +- Edge congruence persistence: `literal_constant_edge_persistence_verified` +- Disjointness: `bounded_disjointness_certified` +- Matching/K certificate: `literal_matching_sampled_k_envelope_verified` + +## Goal + +Prove that the 106-edge common matching core persists for all p=17 threatening rows in split outP2=251|out25=1|smaller=side18, or replace it with a parameterized extension core. + +## Falsifier Boundary + +A row in this split loses one of the common-core missing-cross edges before a replacement edge is proved, or its K(N,x) exceeds the symbolic core size. + +## Next Theorem Actions + +- Promote the literal vertex-presence checks into residue-family vertex formulas if the vertices move with N. +- The current split modulus does not stabilize every vertex compatibility witness; either sharpen the split by the missing square-witness residues or replace literal vertices with parameterized families. +- Group edge obstruction atoms by residue pattern and product-plus-one squarefree check before attempting a symbolic persistence proof. +- Attack the packet until it either becomes a split lemma or emits a sharper sub-split key. + +## K Envelope + +- Status: `bounded_core_meets_sampled_K_envelope` +- Common core count: `106` +- Max required K: `11` +- Min matching slack: `96` + +## Matching And K-Envelope Certificate + +- Status: `literal_matching_sampled_k_envelope_verified` +- Proof kind: `literal_disjoint_matching_plus_sampled_k_envelope` +- Matching proof: `literal_matching_disjointness_verified` +- K proof: `sampled_k_envelope_dominated_by_literal_core` +- K inequality: `106 >= 11` +- Proof boundary: A6/A7 are certified for this literal packet. Split discharge still needs the vertex-successor proofs, edge persistence, and row-universe coverage to be assembled without bounded-only overclaim. + +## Split Discharge Readiness + +- Status: `split_discharge_readiness_blocked` +- Proof kind: `lower_atom_assembly_with_explicit_all_n_handoff` +- Theorem candidate: `blocked_by_lower_atom` +- Blocking lower checks: `1` +- Open all-N handoff gaps: `3` +- Proof boundary: This is readiness for a theorem-facing split lemma candidate, not a final all-N proof. The listed all-N handoff gaps must stay visible until discharged by the row-universe and symbolic K-formula lanes. +- Handoff gap `row_universe_split_coverage` [open]: Prove every future threatening row in the parent lane is covered by an emitted and discharged split profile. +- Handoff gap `universal_k_formula_lift` [open]: Replace the sampled packet K-envelope with the symbolic K(N,x) inequality used by the all-N D2/D3 lane. +- Handoff gap `literal_to_parameterized_vertex_guard` [open_if_vertices_move]: If later rows require moving vertex formulas instead of literal constants, re-run vertex, edge, and disjointness checks on the parameterized families. + +## Vertex Presence Stability + +- Split modulus: `7225` +- Witness rows: `2` +- Stable under current split modulus: `2` +- Needs sharper split or parametric witness: `210` +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V1.left_57`: side side7, value 57, first square witness {"divisor":2,"square":4,"quotient":3577,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V2.left_82`: side side7, value 82, first square witness {"divisor":3,"square":9,"quotient":2287,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V3.left_157`: side side7, value 157, first square witness {"divisor":2,"square":4,"quotient":9852,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V4.left_257`: side side7, value 257, first square witness {"divisor":2,"square":4,"quotient":16127,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V5.left_307`: side side7, value 307, first square witness {"divisor":3,"square":9,"quotient":8562,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V6.left_357`: side side7, value 357, first square witness {"divisor":2,"square":4,"quotient":22402,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V7.left_457`: side side7, value 457, first square witness {"divisor":2,"square":4,"quotient":28677,"stableUnderCurrentSplitModulus":false} +- First unstable vertex atom `D3.2_persist_outP2=251_out25=1_smaller=side18.V8.left_532`: side side7, value 532, first square witness {"divisor":3,"square":9,"quotient":14837,"stableUnderCurrentSplitModulus":false} + +## Vertex Presence Refinement + +- Status: `literal_core_requires_sharper_square_witness_split` +- Deterministic move: `emit_successor_atoms_by_square_witness_residue` +- Refinement condition count: `9` +- Covered unstable atoms: `210` +- Uncovered unstable atoms: `0` +- Proof boundary: These square-witness residue classes explain the bounded literal vertex-presence instability; each successor split still needs a theorem-facing persistence proof before it can support an all-N claim. +- Condition `square_4_outsider_3`: out mod 4 = 3, atoms=144, combined modulus=28900, successor=`outP2=251|out25=1|smaller=side18|out4=3` +- Condition `square_9_outsider_8`: out mod 9 = 8, atoms=47, combined modulus=65025, successor=`outP2=251|out25=1|smaller=side18|out9=8` +- Condition `square_49_outsider_6`: out mod 49 = 6, atoms=8, combined modulus=354025, successor=`outP2=251|out25=1|smaller=side18|out49=6` +- Condition `square_121_outsider_9`: out mod 121 = 9, atoms=3, combined modulus=874225, successor=`outP2=251|out25=1|smaller=side18|out121=9` +- Condition `square_169_outsider_82`: out mod 169 = 82, atoms=3, combined modulus=1221025, successor=`outP2=251|out25=1|smaller=side18|out169=82` +- Condition `square_361_outsider_251`: out mod 361 = 251, atoms=2, combined modulus=2608225, successor=`outP2=251|out25=1|smaller=side18|out361=251` +- Condition `square_1681_outsider_251`: out mod 1681 = 251, atoms=1, combined modulus=12145225, successor=`outP2=251|out25=1|smaller=side18|out1681=251` +- Condition `square_5041_outsider_251`: out mod 5041 = 251, atoms=1, combined modulus=36421225, successor=`outP2=251|out25=1|smaller=side18|out5041=251` +- Condition `square_22801_outsider_251`: out mod 22801 = 251, atoms=1, combined modulus=164737225, successor=`outP2=251|out25=1|smaller=side18|out22801=251` + +## Edge Obstruction Certificate + +- Status: `literal_edge_obstruction_certificate_verified` +- Proof kind: `literal_product_plus_one_squarefree_missing_edge_certificate` +- Edge atoms: `106` +- Squarefree edge atoms: `106` +- Non-squarefree edge atoms: `0` +- Product-plus-one range: `{"min":3877,"max":51466702}` +- Mod 25 classes: `1` +- Prime-residue classes: `88` +- Prime-square fingerprints: `106` +- Proof boundary: This certifies only the exported literal edge-obstruction atoms for the current split packet. If a later proof replaces literal vertices with moving vertex families, this certificate must be lifted into a symbolic residue-family obstruction proof before it can support an all-N claim. +- Mod25 class `7:18`: edges=106 +- Prime-residue class `12:14:16`: edges=3 +- Prime-residue class `1:1:2`: edges=2 +- Prime-residue class `1:9:10`: edges=2 +- Prime-residue class `10:10:16`: edges=2 +- Prime-residue class `10:12:2`: edges=2 +- Prime-residue class `11:11:3`: edges=2 +- Prime-residue class `13:13:0`: edges=2 +- Prime-residue class `13:15:9`: edges=2 +- Prime-residue class `14:12:16`: edges=2 +- Prime-residue class `16:16:2`: edges=2 +- Prime-residue class `2:13:10`: edges=2 +- Prime-residue class `3:3:10`: edges=2 +- Prime-residue class `4:16:14`: edges=2 + +## Edge Congruence Persistence + +- Status: `literal_constant_edge_persistence_verified` +- Proof kind: `constant_pair_squarefree_invariant` +- Edge atoms: `106` +- Verified edge atoms: `106` +- Failed edge atoms: `0` +- Depends on sampled N: `no` +- Depends on witness outsider: `no` +- Proof boundary: This verifies A5 congruence persistence only for the exported literal matching core. It does not prove that future parameterized vertex families preserve the same squarefree edge obstructions. +- Family `D3.2_persist_outP2=251_out25=1_smaller=side18.edge_constant_squarefree_family`: status=`congruence_persistence_family_verified`, edges=106, proof=constant_pair_squarefree_invariant + +## Matching Core + +- Pair (57, 68); residues mod25 7:18, mod p 6:0, mod p^2 57:68; product+1 mod p^2 120 +- Pair (82, 93); residues mod25 7:18, mod p 14:8, mod p^2 82:93; product+1 mod p^2 113 +- Pair (157, 118); residues mod25 7:18, mod p 4:16, mod p^2 157:118; product+1 mod p^2 31 +- Pair (257, 193); residues mod25 7:18, mod p 2:6, mod p^2 257:193; product+1 mod p^2 183 +- Pair (307, 343); residues mod25 7:18, mod p 1:3, mod p^2 18:54; product+1 mod p^2 106 +- Pair (357, 293); residues mod25 7:18, mod p 0:4, mod p^2 68:4; product+1 mod p^2 273 +- Pair (457, 393); residues mod25 7:18, mod p 15:2, mod p^2 168:104; product+1 mod p^2 133 +- Pair (532, 493); residues mod25 7:18, mod p 5:0, mod p^2 243:204; product+1 mod p^2 154 +- Pair (557, 593); residues mod25 7:18, mod p 13:15, mod p^2 268:15; product+1 mod p^2 264 +- Pair (657, 568); residues mod25 7:18, mod p 11:7, mod p^2 79:279; product+1 mod p^2 78 +- Pair (757, 693); residues mod25 7:18, mod p 9:13, mod p^2 179:115; product+1 mod p^2 67 +- Pair (857, 793); residues mod25 7:18, mod p 7:11, mod p^2 279:215; product+1 mod p^2 163 +- Pair (957, 893); residues mod25 7:18, mod p 5:9, mod p^2 90:26; product+1 mod p^2 29 +- Pair (982, 743); residues mod25 7:18, mod p 13:12, mod p^2 115:165; product+1 mod p^2 191 +- Pair (1057, 993); residues mod25 7:18, mod p 3:7, mod p^2 190:126; product+1 mod p^2 243 +- Pair (1082, 1018); residues mod25 7:18, mod p 11:15, mod p^2 215:151; product+1 mod p^2 98 +- Pair (1157, 1093); residues mod25 7:18, mod p 1:5, mod p^2 1:226; product+1 mod p^2 227 +- Pair (1207, 1118); residues mod25 7:18, mod p 0:13, mod p^2 51:251; product+1 mod p^2 86 +- Pair (1257, 1193); residues mod25 7:18, mod p 16:3, mod p^2 101:37; product+1 mod p^2 270 +- Pair (1282, 1243); residues mod25 7:18, mod p 7:2, mod p^2 126:87; product+1 mod p^2 270 +- Pair (1357, 1293); residues mod25 7:18, mod p 14:1, mod p^2 201:137; product+1 mod p^2 83 +- Pair (1407, 1468); residues mod25 7:18, mod p 13:6, mod p^2 251:23; product+1 mod p^2 283 +- Pair (1432, 1393); residues mod25 7:18, mod p 4:16, mod p^2 276:237; product+1 mod p^2 99 +- Pair (1457, 1493); residues mod25 7:18, mod p 12:14, mod p^2 12:48; product+1 mod p^2 288 +- Pair (1557, 1593); residues mod25 7:18, mod p 10:12, mod p^2 112:148; product+1 mod p^2 104 +- Pair (1657, 1693); residues mod25 7:18, mod p 8:10, mod p^2 212:248; product+1 mod p^2 268 +- Pair (1757, 1793); residues mod25 7:18, mod p 6:8, mod p^2 23:59; product+1 mod p^2 202 +- Pair (1857, 1893); residues mod25 7:18, mod p 4:6, mod p^2 123:159; product+1 mod p^2 195 +- Pair (1882, 1918); residues mod25 7:18, mod p 12:14, mod p^2 148:184; product+1 mod p^2 67 +- Pair (1957, 1968); residues mod25 7:18, mod p 2:13, mod p^2 223:234; product+1 mod p^2 163 +- Pair (2057, 2093); residues mod25 7:18, mod p 0:2, mod p^2 34:70; product+1 mod p^2 69 +- Pair (2107, 2143); residues mod25 7:18, mod p 16:1, mod p^2 84:120; product+1 mod p^2 255 +- Pair (2157, 1993); residues mod25 7:18, mod p 15:4, mod p^2 134:259; product+1 mod p^2 27 +- Pair (2257, 2193); residues mod25 7:18, mod p 13:0, mod p^2 234:170; product+1 mod p^2 188 +- Pair (2332, 2293); residues mod25 7:18, mod p 3:15, mod p^2 20:270; product+1 mod p^2 199 +- Pair (2357, 2393); residues mod25 7:18, mod p 11:13, mod p^2 45:81; product+1 mod p^2 178 +- Pair (2457, 2368); residues mod25 7:18, mod p 9:5, mod p^2 145:56; product+1 mod p^2 29 +- Pair (2507, 2818); residues mod25 7:18, mod p 8:13, mod p^2 195:217; product+1 mod p^2 122 +- Pair (2557, 2493); residues mod25 7:18, mod p 7:11, mod p^2 245:181; product+1 mod p^2 129 +- Pair (2632, 2593); residues mod25 7:18, mod p 14:9, mod p^2 31:281; product+1 mod p^2 42 +- Pair (2657, 2693); residues mod25 7:18, mod p 5:7, mod p^2 56:92; product+1 mod p^2 240 +- Pair (2757, 2793); residues mod25 7:18, mod p 3:5, mod p^2 156:192; product+1 mod p^2 186 +- Pair (2782, 2893); residues mod25 7:18, mod p 11:3, mod p^2 181:3; product+1 mod p^2 255 +- Pair (2857, 2993); residues mod25 7:18, mod p 1:1, mod p^2 256:103; product+1 mod p^2 70 +- Pair (2957, 3093); residues mod25 7:18, mod p 16:16, mod p^2 67:203; product+1 mod p^2 19 +- Pair (3007, 3043); residues mod25 7:18, mod p 15:0, mod p^2 117:153; product+1 mod p^2 273 +- Pair (3057, 3193); residues mod25 7:18, mod p 14:14, mod p^2 167:14; product+1 mod p^2 27 +- Pair (3157, 3268); residues mod25 7:18, mod p 12:4, mod p^2 267:89; product+1 mod p^2 66 +- Pair (3232, 3393); residues mod25 7:18, mod p 2:10, mod p^2 53:214; product+1 mod p^2 72 +- Pair (3257, 3293); residues mod25 7:18, mod p 10:12, mod p^2 78:114; product+1 mod p^2 223 +- Pair (3357, 3593); residues mod25 7:18, mod p 8:6, mod p^2 178:125; product+1 mod p^2 287 +- Pair (3457, 3493); residues mod25 7:18, mod p 6:8, mod p^2 278:25; product+1 mod p^2 15 +- Pair (3482, 3693); residues mod25 7:18, mod p 14:4, mod p^2 14:225; product+1 mod p^2 261 +- Pair (3557, 3718); residues mod25 7:18, mod p 4:12, mod p^2 89:250; product+1 mod p^2 287 +- Pair (3657, 3793); residues mod25 7:18, mod p 2:2, mod p^2 189:36; product+1 mod p^2 158 +- Pair (3682, 3893); residues mod25 7:18, mod p 10:0, mod p^2 214:136; product+1 mod p^2 205 +- Pair (3732, 3943); residues mod25 7:18, mod p 9:16, mod p^2 264:186; product+1 mod p^2 264 +- Pair (3757, 3993); residues mod25 7:18, mod p 0:15, mod p^2 0:236; product+1 mod p^2 1 +- Pair (3857, 4168); residues mod25 7:18, mod p 15:3, mod p^2 100:122; product+1 mod p^2 63 +- Pair (3907, 4618); residues mod25 7:18, mod p 14:11, mod p^2 150:283; product+1 mod p^2 257 +- Pair (3957, 4093); residues mod25 7:18, mod p 13:13, mod p^2 200:47; product+1 mod p^2 153 +- Pair (4057, 4193); residues mod25 7:18, mod p 11:11, mod p^2 11:147; product+1 mod p^2 173 +- Pair (4132, 4293); residues mod25 7:18, mod p 1:9, mod p^2 86:247; product+1 mod p^2 146 +- Pair (4157, 4418); residues mod25 7:18, mod p 9:15, mod p^2 111:83; product+1 mod p^2 255 +- Pair (4257, 4393); residues mod25 7:18, mod p 7:7, mod p^2 211:58; product+1 mod p^2 101 +- Pair (4357, 4493); residues mod25 7:18, mod p 5:5, mod p^2 22:158; product+1 mod p^2 9 +- Pair (4457, 4593); residues mod25 7:18, mod p 3:3, mod p^2 122:258; product+1 mod p^2 265 +- Pair (4557, 4693); residues mod25 7:18, mod p 1:1, mod p^2 222:69; product+1 mod p^2 2 +- Pair (4582, 4793); residues mod25 7:18, mod p 9:16, mod p^2 247:169; product+1 mod p^2 128 +- Pair (4657, 4893); residues mod25 7:18, mod p 16:14, mod p^2 33:269; product+1 mod p^2 208 +- Pair (4757, 5068); residues mod25 7:18, mod p 14:2, mod p^2 133:155; product+1 mod p^2 97 +- Pair (4807, 4843); residues mod25 7:18, mod p 13:15, mod p^2 183:219; product+1 mod p^2 196 +- Pair (4857, 4993); residues mod25 7:18, mod p 12:12, mod p^2 233:80; product+1 mod p^2 145 +- Pair (4957, 5093); residues mod25 7:18, mod p 10:10, mod p^2 44:180; product+1 mod p^2 118 +- Pair (5032, 5193); residues mod25 7:18, mod p 0:8, mod p^2 119:280; product+1 mod p^2 86 +- Pair (5057, 5393); residues mod25 7:18, mod p 8:4, mod p^2 144:191; product+1 mod p^2 50 +- Pair (5157, 5293); residues mod25 7:18, mod p 6:6, mod p^2 244:91; product+1 mod p^2 241 +- Pair (5182, 5418); residues mod25 7:18, mod p 14:12, mod p^2 269:216; product+1 mod p^2 16 +- Pair (5257, 5493); residues mod25 7:18, mod p 4:2, mod p^2 55:2; product+1 mod p^2 111 +- Pair (5282, 5543); residues mod25 7:18, mod p 12:1, mod p^2 80:52; product+1 mod p^2 115 +- Pair (5307, 5518); residues mod25 7:18, mod p 3:10, mod p^2 105:27; product+1 mod p^2 235 +- Pair (5357, 5793); residues mod25 7:18, mod p 2:13, mod p^2 155:13; product+1 mod p^2 282 +- Pair (5457, 5593); residues mod25 7:18, mod p 0:0, mod p^2 255:102; product+1 mod p^2 1 +- Pair (5482, 5643); residues mod25 7:18, mod p 8:16, mod p^2 280:152; product+1 mod p^2 78 +- Pair (5557, 5693); residues mod25 7:18, mod p 15:15, mod p^2 66:202; product+1 mod p^2 39 +- Pair (5657, 5968); residues mod25 7:18, mod p 13:1, mod p^2 166:188; product+1 mod p^2 286 +- Pair (5707, 5743); residues mod25 7:18, mod p 12:14, mod p^2 216:252; product+1 mod p^2 101 +- Pair (5757, 5893); residues mod25 7:18, mod p 11:11, mod p^2 266:113; product+1 mod p^2 3 +- Pair (5857, 5993); residues mod25 7:18, mod p 9:9, mod p^2 77:213; product+1 mod p^2 218 +- Pair (5932, 6093); residues mod25 7:18, mod p 16:7, mod p^2 152:24; product+1 mod p^2 181 +- Pair (5957, 6268); residues mod25 7:18, mod p 7:12, mod p^2 177:199; product+1 mod p^2 255 +- Pair (6057, 6193); residues mod25 7:18, mod p 5:5, mod p^2 277:124; product+1 mod p^2 247 +- Pair (6157, 6293); residues mod25 7:18, mod p 3:3, mod p^2 88:224; product+1 mod p^2 61 +- Pair (6182, 6393); residues mod25 7:18, mod p 11:1, mod p^2 113:35; product+1 mod p^2 199 +- Pair (6257, 6418); residues mod25 7:18, mod p 1:9, mod p^2 188:60; product+1 mod p^2 10 +- Pair (6357, 6493); residues mod25 7:18, mod p 16:16, mod p^2 288:135; product+1 mod p^2 155 +- Pair (6382, 6593); residues mod25 7:18, mod p 7:14, mod p^2 24:235; product+1 mod p^2 150 +- Pair (6457, 6693); residues mod25 7:18, mod p 14:12, mod p^2 99:46; product+1 mod p^2 220 +- Pair (6507, 6643); residues mod25 7:18, mod p 13:13, mod p^2 149:285; product+1 mod p^2 272 +- Pair (6557, 6868); residues mod25 7:18, mod p 12:0, mod p^2 199:221; product+1 mod p^2 52 +- Pair (6657, 6793); residues mod25 7:18, mod p 10:10, mod p^2 10:146; product+1 mod p^2 16 +- Pair (6757, 6893); residues mod25 7:18, mod p 8:8, mod p^2 110:246; product+1 mod p^2 184 +- Pair (6832, 6993); residues mod25 7:18, mod p 15:6, mod p^2 185:57; product+1 mod p^2 142 +- Pair (6857, 7193); residues mod25 7:18, mod p 6:2, mod p^2 210:257; product+1 mod p^2 217 +- Pair (6957, 7093); residues mod25 7:18, mod p 4:4, mod p^2 21:157; product+1 mod p^2 119 +- Pair (7057, 7293); residues mod25 7:18, mod p 2:0, mod p^2 121:68; product+1 mod p^2 137 diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_BOUND_PROBES/D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_BOUND_PROBES/D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..ef0c4a5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_BOUND_PROBES/D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,44 @@ +{ + "schema": "erdos.p848_dmax_bound_probe/1", + "problemId": "848", + "atomId": "D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7", + "successorAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "parentSideCountFloorAtomId": "D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "targetBound": 18, + "status": "bounded_counterexample_to_constant_dmax_bound", + "promotesAllNClaim": false, + "probeCommand": "node packs/number-theory/problems/848/compute/problem848_full_mixed_base_structural_verifier.mjs --max 12000 --min-structural-n 7307 --row-sample-limit 5 --json-output /tmp/p848_step17_dmax_probe_12000.json", + "probeRange": "7307..12000", + "targetRowCount": 492, + "firstCounterexample": { + "N": 7873, + "outP2": 70, + "out25": 23, + "smallerSide": "side7", + "outsider": 6323, + "dMax": 19, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "candidateSize": 315, + "rGreater": 113, + "compatibleSide7Count": 112, + "compatibleSide18Count": 118, + "matchingSlack": 17 + }, + "maxObservedDMax": 29, + "maxObservedDMaxWitnesses": [ + { + "dMax": 29, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "firstObservedN": 11929 + } + ], + "proofBoundary": "This bounded probe falsifies the constant dMax <= 18 outside the original 7307..7600 witness packet. It does not prove an all-N growth envelope; the successor atom must bound the same-prime degree term symbolically.", + "nextTheoremActions": [ + "Replace the false constant dMax <= 18 with a symbolic growth envelope for the same-prime degree term in this split.", + "Start from the persistent plus witness value 1591 and the later minus witness value 9563; prove their same-prime degree is absorbed by the residual dynamic margin or split by the first degree-growth residue obstruction.", + "Do not use the 7307..7600 constant bound as an all-N lemma." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_GROWTH_PROFILES/D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_GROWTH_PROFILES/D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..214fd43 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_GROWTH_PROFILES/D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,69 @@ +{ + "schema": "erdos.p848_dmax_growth_profile/1", + "problemId": "848", + "atomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "parentAtomId": "D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7", + "firstOpenSubatomId": "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "bounded_degree_growth_profile_emitted", + "promotesAllNClaim": false, + "probeRange": "7307..12000", + "growthWitnesses": [ + { + "side": "plus", + "value": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "observedDegreeAt12000": 29, + "squareEventCounts": [ + { "q": 2, "count": 17 }, + { "q": 3, "count": 8 }, + { "q": 5, "count": 3 }, + { "q": 7, "count": 1 }, + { "q": 11, "count": 1 }, + { "q": 31, "count": 1 }, + { "q": 251, "count": 1 } + ], + "dominantEventFamily": { + "q": 2, + "condition": "1591*m + 1 is divisible by 4", + "progressionBeforeExclusions": "m = 437 + 676*t", + "observedValues": [437, 1113, 1789, 2465, 3141, 3817, 5169, 5845, 6521, 7197, 7873, 8549, 9225, 9901, 10577, 11253, 11929], + "exclusionKinds": ["base residues 7/18 mod 25", "lower least-square-witness classes"] + } + }, + { + "side": "minus", + "value": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "observedDegreeAt12000": 27, + "squareEventCounts": [ + { "q": 2, "count": 15 }, + { "q": 3, "count": 8 }, + { "q": 5, "count": 3 }, + { "q": 7, "count": 2 }, + { "q": 19, "count": 1 }, + { "q": 23, "count": 1 } + ], + "dominantEventFamily": { + "q": 2, + "condition": "9563*m + 1 is divisible by 4", + "progressionBeforeExclusions": "m = 577 + 676*t", + "observedValues": [577, 1253, 1929, 2605, 3281, 4633, 5309, 5985, 6661, 7337, 8013, 8689, 9365, 10041, 10717], + "exclusionKinds": ["base residues 7/18 mod 25", "lower least-square-witness classes"] + } + } + ], + "firstOpenSubatom": { + "atomId": "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "statement": "Prove a symbolic floor-function upper bound for the q=2 same-prime degree progression m = 437 + 676*t, including base-residue and lower-witness exclusions.", + "completionRule": "Either prove the q=2 progression contribution can be absorbed in the dMax growth envelope, or emit the first exclusion/residue sub-split that controls it." + }, + "proofBoundary": "This is a bounded degree-growth profile. It identifies dominant event families but does not prove the all-N degree envelope.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7 first.", + "After q=2 is bounded, repeat the same floor-function profile for q=3 and q=5 before recombining the dMax growth envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..79dab80 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,126 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 11, + "squareDivisor": 121, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the observed plus-side q=11 square-divisor progression upper bound. It does not prove the full dMax growth envelope, the minus-side q=11 tail, or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "121 divides 1591*m + 1", + "coefficientMod121": 18, + "requiredOppositeValueMod121": 47, + "crtProgression": { + "variable": "m", + "residue": 1620, + "modulus": 20449, + "formula": "m = 1620 + 20449*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1620) / 20449) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 22069, + "crtModulus": 81796, + "formula": "m = 22069 + 81796*t", + "countFormula": "max(0, floor((N - 22069) / 81796) + 1)" + }, + { + "q": 3, + "crtResidue": 103865, + "crtModulus": 184041, + "formula": "m = 103865 + 184041*t", + "countFormula": "max(0, floor((N - 103865) / 184041) + 1)" + }, + { + "q": 5, + "crtResidue": 124314, + "crtModulus": 511225, + "formula": "m = 124314 + 511225*t", + "countFormula": "max(0, floor((N - 124314) / 511225) + 1)" + }, + { + "q": 7, + "crtResidue": 144763, + "crtModulus": 1002001, + "formula": "m = 144763 + 1002001*t", + "countFormula": "max(0, floor((N - 144763) / 1002001) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 267457, + "crtModulus": 511225, + "countFormula": "max(0, floor((N - 267457) / 511225) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 42518, + "crtModulus": 511225, + "countFormula": "max(0, floor((N - 42518) / 511225) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 1, + "observedSquareEventCount": 1, + "priorQOverlapFormulaCounts": { + "q2": 0, + "q3": 0, + "q5": 0, + "q7": 0 + }, + "q11OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 1620 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + } + ], + "nonObservedProfileNote": { + "side": "minus", + "witnessValue": 9563, + "q": 11, + "boundedProfileEventCount": 0, + "firstCrtResidue": 16970, + "crtModulus": 20449, + "note": "The bounded growth profile has no minus-side q=11 event below 12000, so this packet intentionally certifies only the observed plus-side singleton component." + }, + "checkedIdentities": [ + "1591 mod 121 = 18.", + "121 divides 1591*m + 1 only when m mod 121 = 47.", + "CRT(m = 99 mod 169, m = 47 mod 121) gives m = 1620 mod 20449.", + "The observed plus-side q=11 progression has no prior-q overlap below N = 12000.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=11 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 19, + "statement": "Prove the q=19 same-prime degree singleton progression upper bound for the minus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=19 progression contribution is bounded by a CRT floor function, or the first unresolved q=19 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the observed plus-side q=11 progression atom as an upper-bound component. It intentionally leaves q=19, q=23, q=31, q=251, and a later general tail/recombination step open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7 next.", + "After the remaining one-off observed families are bounded, emit a general tail/recombination atom before promoting any full dMax envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..3c91d35 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,134 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 19, + "squareDivisor": 361, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the observed minus-side q=19 square-divisor progression upper bound. It does not prove the full dMax growth envelope, the plus-side q=19 tail, or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "361 divides 9563*m + 1", + "coefficientMod361": 177, + "requiredOppositeValueMod361": 155, + "crtProgression": { + "variable": "m", + "residue": 4126, + "modulus": 61009, + "formula": "m = 4126 + 61009*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4126) / 61009) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 187153, + "crtModulus": 244036, + "formula": "m = 187153 + 244036*t", + "countFormula": "max(0, floor((N - 187153) / 244036) + 1)" + }, + { + "q": 3, + "crtResidue": 187153, + "crtModulus": 549081, + "formula": "m = 187153 + 549081*t", + "countFormula": "max(0, floor((N - 187153) / 549081) + 1)" + }, + { + "q": 5, + "crtResidue": 492198, + "crtModulus": 1525225, + "formula": "m = 492198 + 1525225*t", + "countFormula": "max(0, floor((N - 492198) / 1525225) + 1)" + }, + { + "q": 7, + "crtResidue": 2932558, + "crtModulus": 2989441, + "formula": "m = 2932558 + 2989441*t", + "countFormula": "max(0, floor((N - 2932558) / 2989441) + 1)" + }, + { + "q": 11, + "crtResidue": 5067873, + "crtModulus": 7382089, + "formula": "m = 5067873 + 7382089*t", + "countFormula": "max(0, floor((N - 5067873) / 7382089) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 553207, + "crtModulus": 1525225, + "countFormula": "max(0, floor((N - 553207) / 1525225) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 797243, + "crtModulus": 1525225, + "countFormula": "max(0, floor((N - 797243) / 1525225) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 1, + "observedSquareEventCount": 1, + "priorQOverlapFormulaCounts": { + "q2": 0, + "q3": 0, + "q5": 0, + "q7": 0, + "q11": 0 + }, + "q19OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 4126 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + } + ], + "nonObservedProfileNote": { + "side": "plus", + "witnessValue": 1591, + "q": 19, + "boundedProfileEventCount": 0, + "firstCrtResidue": 22576, + "crtModulus": 61009, + "note": "The bounded growth profile has no plus-side q=19 event below 12000, so this packet intentionally certifies only the observed minus-side singleton component." + }, + "checkedIdentities": [ + "9563 mod 361 = 177.", + "361 divides 9563*m + 1 only when m mod 361 = 155.", + "CRT(m = 70 mod 169, m = 155 mod 361) gives m = 4126 mod 61009.", + "The observed minus-side q=19 progression has no prior-q overlap below N = 12000.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=19 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 23, + "statement": "Prove the q=23 same-prime degree singleton progression upper bound for the minus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=23 progression contribution is bounded by a CRT floor function, or the first unresolved q=23 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the observed minus-side q=19 progression atom as an upper-bound component. It intentionally leaves q=23, q=31, q=251, and a later general tail/recombination step open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7 next.", + "After the remaining one-off observed families are bounded, emit a general tail/recombination atom before promoting any full dMax envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..dc92b22 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,142 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 23, + "squareDivisor": 529, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the observed minus-side q=23 square-divisor progression upper bound. It does not prove the full dMax growth envelope, the plus-side q=23 tail, or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "529 divides 9563*m + 1", + "coefficientMod529": 41, + "requiredOppositeValueMod529": 129, + "crtProgression": { + "variable": "m", + "residue": 2774, + "modulus": 89401, + "formula": "m = 2774 + 89401*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2774) / 89401) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 270977, + "crtModulus": 357604, + "formula": "m = 270977 + 357604*t", + "countFormula": "max(0, floor((N - 270977) / 357604) + 1)" + }, + { + "q": 3, + "crtResidue": 717982, + "crtModulus": 804609, + "formula": "m = 717982 + 804609*t", + "countFormula": "max(0, floor((N - 717982) / 804609) + 1)" + }, + { + "q": 5, + "crtResidue": 2148398, + "crtModulus": 2235025, + "formula": "m = 2148398 + 2235025*t", + "countFormula": "max(0, floor((N - 2148398) / 2235025) + 1)" + }, + { + "q": 7, + "crtResidue": 92175, + "crtModulus": 4380649, + "formula": "m = 92175 + 4380649*t", + "countFormula": "max(0, floor((N - 92175) / 4380649) + 1)" + }, + { + "q": 11, + "crtResidue": 1611992, + "crtModulus": 10817521, + "formula": "m = 1611992 + 10817521*t", + "countFormula": "max(0, floor((N - 1611992) / 10817521) + 1)" + }, + { + "q": 19, + "crtResidue": 7691260, + "crtModulus": 32273761, + "formula": "m = 7691260 + 32273761*t", + "countFormula": "max(0, floor((N - 7691260) / 32273761) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 717982, + "crtModulus": 2235025, + "countFormula": "max(0, floor((N - 717982) / 2235025) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 1701393, + "crtModulus": 2235025, + "countFormula": "max(0, floor((N - 1701393) / 2235025) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 1, + "observedSquareEventCount": 1, + "priorQOverlapFormulaCounts": { + "q2": 0, + "q3": 0, + "q5": 0, + "q7": 0, + "q11": 0, + "q19": 0 + }, + "q23OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 2774 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + } + ], + "nonObservedProfileNote": { + "side": "plus", + "witnessValue": 1591, + "q": 23, + "boundedProfileEventCount": 0, + "firstCrtResidue": 44039, + "crtModulus": 89401, + "note": "The bounded growth profile has no plus-side q=23 event below 12000, so this packet intentionally certifies only the observed minus-side singleton component." + }, + "checkedIdentities": [ + "9563 mod 529 = 41.", + "529 divides 9563*m + 1 only when m mod 529 = 129.", + "CRT(m = 70 mod 169, m = 129 mod 529) gives m = 2774 mod 89401.", + "The observed minus-side q=23 progression has no prior-q overlap below N = 12000.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=23 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 31, + "statement": "Prove the q=31 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=31 progression contribution is bounded by a CRT floor function, or the first unresolved q=31 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the observed minus-side q=23 progression atom as an upper-bound component. It intentionally leaves q=31, q=251, and a later general tail/recombination step open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7 next.", + "After the remaining one-off observed families are bounded, emit a general tail/recombination atom before promoting any full dMax envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..94cc268 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,157 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 251, + "squareDivisor": 63001, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the observed plus-side q=251 square-divisor progression upper bound. It does not prove the full dMax growth envelope, the minus-side q=251 tail, or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "63001 divides 1591*m + 1", + "coefficientMod63001": 1591, + "requiredOppositeValueMod63001": 4831, + "crtProgression": { + "variable": "m", + "residue": 4831, + "modulus": 10647169, + "formula": "m = 4831 + 10647169*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4831) / 10647169) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 21299169, + "crtModulus": 42588676, + "formula": "m = 21299169 + 42588676*t", + "countFormula": "max(0, floor((N - 21299169) / 42588676) + 1)" + }, + { + "q": 3, + "crtResidue": 10652000, + "crtModulus": 95824521, + "formula": "m = 10652000 + 95824521*t", + "countFormula": "max(0, floor((N - 10652000) / 95824521) + 1)" + }, + { + "q": 5, + "crtResidue": 74535014, + "crtModulus": 266179225, + "formula": "m = 74535014 + 266179225*t", + "countFormula": "max(0, floor((N - 74535014) / 266179225) + 1)" + }, + { + "q": 7, + "crtResidue": 244889718, + "crtModulus": 521711281, + "formula": "m = 244889718 + 521711281*t", + "countFormula": "max(0, floor((N - 244889718) / 521711281) + 1)" + }, + { + "q": 11, + "crtResidue": 681423647, + "crtModulus": 1288307449, + "formula": "m = 681423647 + 1288307449*t", + "countFormula": "max(0, floor((N - 681423647) / 1288307449) + 1)" + }, + { + "q": 19, + "crtResidue": 1650316026, + "crtModulus": 3843628009, + "formula": "m = 1650316026 + 3843628009*t", + "countFormula": "max(0, floor((N - 1650316026) / 3843628009) + 1)" + }, + { + "q": 23, + "crtResidue": 4780583712, + "crtModulus": 5632352401, + "formula": "m = 4780583712 + 5632352401*t", + "countFormula": "max(0, floor((N - 4780583712) / 5632352401) + 1)" + }, + { + "q": 31, + "crtResidue": 4333402614, + "crtModulus": 10231929409, + "formula": "m = 4333402614 + 10231929409*t", + "countFormula": "max(0, floor((N - 4333402614) / 10231929409) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 42593507, + "crtModulus": 266179225, + "countFormula": "max(0, floor((N - 42593507) / 266179225) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 244889718, + "crtModulus": 266179225, + "countFormula": "max(0, floor((N - 244889718) / 266179225) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 1, + "observedSquareEventCount": 1, + "priorQOverlapFormulaCounts": { + "q2": 0, + "q3": 0, + "q5": 0, + "q7": 0, + "q11": 0, + "q19": 0, + "q23": 0, + "q31": 0 + }, + "q251OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 4831 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + } + ], + "nonObservedProfileNote": { + "side": "minus", + "witnessValue": 9563, + "q": 251, + "boundedProfileEventCount": 0, + "firstCrtResidue": 8138434, + "crtModulus": 10647169, + "note": "The bounded growth profile has no minus-side q=251 event below 12000, so this packet intentionally certifies only the observed plus-side singleton component." + }, + "checkedIdentities": [ + "1591 mod 63001 = 1591.", + "63001 divides 1591*m + 1 only when m mod 63001 = 4831.", + "CRT(m = 99 mod 169, m = 4831 mod 63001) gives m = 4831 mod 10647169.", + "The observed plus-side q=251 progression has no lower-q overlap below N = 12000.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=251 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "status": "needed", + "statement": "Recombine the verified observed q-progression components with a symbolic tail bound for all remaining same-prime square-divisor events in the dMax growth envelope.", + "completionRule": "The verified q-components plus a tail estimate imply the required symbolic dMax growth envelope, or the first unresolved tail range becomes the next atom." + }, + "proofBoundary": "This certificate discharges the last observed singleton q-progression in the bounded dMax profile. It intentionally leaves the general same-prime tail/recombination atom open before any full dMax envelope can be promoted.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7 next.", + "Use the verified q=2,3,5,7,11,19,23,31,251 components as inputs, then add a symbolic tail estimate for remaining square divisors." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..48d540e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,156 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 2, + "squareDivisor": 4, + "proofKind": "crt_floor_function_upper_bound_with_base_residue_exclusions", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=2 square-divisor progression upper bound for the named dMax growth profile. It does not prove the full dMax growth envelope or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "4 divides 1591*m + 1", + "coefficientMod4": 3, + "requiredOppositeValueMod4": 1, + "crtProgression": { + "variable": "m", + "residue": 437, + "modulus": 676, + "formula": "m = 437 + 676*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 437) / 676) + 1)", + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 13957, + "crtModulus": 16900, + "countFormula": "max(0, floor((N - 13957) / 16900) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 4493, + "crtModulus": 16900, + "countFormula": "max(0, floor((N - 4493) / 16900) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 18, + "observedDominantEventCount": 17, + "observedDominantValues": [ + 437, + 1113, + 1789, + 2465, + 3141, + 3817, + 5169, + 5845, + 6521, + 7197, + 7873, + 8549, + 9225, + 9901, + 10577, + 11253, + 11929 + ], + "rawValuesRemovedByBaseResidues": [ + 4493 + ], + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "4 divides 9563*m + 1", + "coefficientMod4": 3, + "requiredOppositeValueMod4": 1, + "crtProgression": { + "variable": "m", + "residue": 577, + "modulus": 676, + "formula": "m = 577 + 676*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 577) / 676) + 1)", + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 3957, + "crtModulus": 16900, + "countFormula": "max(0, floor((N - 3957) / 16900) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 11393, + "crtModulus": 16900, + "countFormula": "max(0, floor((N - 11393) / 16900) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 17, + "observedDominantEventCount": 15, + "observedDominantValues": [ + 577, + 1253, + 1929, + 2605, + 3281, + 4633, + 5309, + 5985, + 6661, + 7337, + 8013, + 8689, + 9365, + 10041, + 10717 + ], + "rawValuesRemovedByBaseResidues": [ + 3957, + 11393 + ], + "upperBoundPassed": true + } + } + ], + "checkedIdentities": [ + "1591 mod 4 = 3 and 9563 mod 4 = 3.", + "For each witness, 4 divides witness*m + 1 only when m mod 4 = 1.", + "CRT(m = 99 mod 169, m = 1 mod 4) gives m = 437 mod 676.", + "CRT(m = 70 mod 169, m = 1 mod 4) gives m = 577 mod 676.", + "Base residues m = 7 or 18 mod 25 are excluded from the candidate side and can only reduce the raw q=2 upper bound.", + "Lower least-square-witness exclusions can only reduce the raw q=2 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 3, + "statement": "Prove the q=3 same-prime degree progression upper bound for the same split, including overlap/base-residue/lower-witness exclusions.", + "completionRule": "The q=3 progression contribution is bounded by CRT floor functions, or the first unresolved q=3 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the q=2 progression atom as an upper-bound component. It intentionally leaves q=3, q=5, higher square-divisor families, and recombination into a full dMax envelope open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7 next.", + "After q=3 and q=5 are bounded, recombine the square-divisor progression bounds into a symbolic dMax growth envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..63a1b30 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,150 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 31, + "squareDivisor": 961, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the observed plus-side q=31 square-divisor progression upper bound. It does not prove the full dMax growth envelope, the minus-side q=31 tail, or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "961 divides 1591*m + 1", + "coefficientMod961": 630, + "requiredOppositeValueMod961": 871, + "crtProgression": { + "variable": "m", + "residue": 5676, + "modulus": 162409, + "formula": "m = 5676 + 162409*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5676) / 162409) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 168085, + "crtModulus": 649636, + "formula": "m = 168085 + 649636*t", + "countFormula": "max(0, floor((N - 168085) / 649636) + 1)" + }, + { + "q": 3, + "crtResidue": 330494, + "crtModulus": 1461681, + "formula": "m = 330494 + 1461681*t", + "countFormula": "max(0, floor((N - 330494) / 1461681) + 1)" + }, + { + "q": 5, + "crtResidue": 1142539, + "crtModulus": 4060225, + "formula": "m = 1142539 + 4060225*t", + "countFormula": "max(0, floor((N - 1142539) / 4060225) + 1)" + }, + { + "q": 7, + "crtResidue": 2604220, + "crtModulus": 7958041, + "formula": "m = 2604220 + 7958041*t", + "countFormula": "max(0, floor((N - 2604220) / 7958041) + 1)" + }, + { + "q": 11, + "crtResidue": 6177218, + "crtModulus": 19651489, + "formula": "m = 6177218 + 19651489*t", + "countFormula": "max(0, floor((N - 6177218) / 19651489) + 1)" + }, + { + "q": 19, + "crtResidue": 48890785, + "crtModulus": 58629649, + "formula": "m = 48890785 + 58629649*t", + "countFormula": "max(0, floor((N - 48890785) / 58629649) + 1)" + }, + { + "q": 23, + "crtResidue": 21768482, + "crtModulus": 85914361, + "formula": "m = 21768482 + 85914361*t", + "countFormula": "max(0, floor((N - 21768482) / 85914361) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 1467357, + "crtModulus": 4060225, + "countFormula": "max(0, floor((N - 1467357) / 4060225) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 2116993, + "crtModulus": 4060225, + "countFormula": "max(0, floor((N - 2116993) / 4060225) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 1, + "observedSquareEventCount": 1, + "priorQOverlapFormulaCounts": { + "q2": 0, + "q3": 0, + "q5": 0, + "q7": 0, + "q11": 0, + "q19": 0, + "q23": 0 + }, + "q31OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 5676 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + } + ], + "nonObservedProfileNote": { + "side": "minus", + "witnessValue": 9563, + "q": 31, + "boundedProfileEventCount": 0, + "firstCrtResidue": 105526, + "crtModulus": 162409, + "note": "The bounded growth profile has no minus-side q=31 event below 12000, so this packet intentionally certifies only the observed plus-side singleton component." + }, + "checkedIdentities": [ + "1591 mod 961 = 630.", + "961 divides 1591*m + 1 only when m mod 961 = 871.", + "CRT(m = 99 mod 169, m = 871 mod 961) gives m = 5676 mod 162409.", + "The observed plus-side q=31 progression has no lower-q overlap below N = 12000.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=31 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 251, + "statement": "Prove the q=251 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=251 progression contribution is bounded by a CRT floor function, or the first unresolved q=251 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the observed plus-side q=31 progression atom as an upper-bound component. It intentionally leaves q=251 and a later general tail/recombination step open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7 next.", + "After q=251 is bounded, emit a general tail/recombination atom before promoting any full dMax envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..2840627 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,164 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 3, + "squareDivisor": 9, + "proofKind": "crt_floor_function_upper_bound_with_q2_overlap_and_base_residue_exclusions", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=3 square-divisor progression upper bound, including the q=2 overlap classes needed for later recombination. It does not prove the full dMax growth envelope or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "9 divides 1591*m + 1", + "coefficientMod9": 7, + "requiredOppositeValueMod9": 5, + "crtProgression": { + "variable": "m", + "residue": 437, + "modulus": 1521, + "formula": "m = 437 + 1521*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 437) / 1521) + 1)", + "q2Overlap": { + "predecessorProgression": "m = 437 + 676*t", + "crtResidue": 437, + "crtModulus": 6084, + "formula": "m = 437 + 6084*t", + "countFormula": "max(0, floor((N - 437) / 6084) + 1)", + "q3OnlyUpperBound": "raw_q3_count - max(0, floor((N - 437) / 6084) + 1)" + }, + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 30857, + "crtModulus": 38025, + "countFormula": "max(0, floor((N - 30857) / 38025) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 17168, + "crtModulus": 38025, + "countFormula": "max(0, floor((N - 17168) / 38025) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 8, + "observedSquareEventCount": 8, + "q2OverlapFormulaCount": 2, + "q3OnlyAfterQ2UpperBound": 6, + "observedRawValues": [ + 437, + 1958, + 3479, + 5000, + 6521, + 8042, + 9563, + 11084 + ], + "observedValuesAlsoInQ2": [ + 437, + 6521 + ], + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "9 divides 9563*m + 1", + "coefficientMod9": 5, + "requiredOppositeValueMod9": 7, + "crtProgression": { + "variable": "m", + "residue": 70, + "modulus": 1521, + "formula": "m = 70 + 1521*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 70) / 1521) + 1)", + "q2Overlap": { + "predecessorProgression": "m = 577 + 676*t", + "crtResidue": 4633, + "crtModulus": 6084, + "formula": "m = 4633 + 6084*t", + "countFormula": "max(0, floor((N - 4633) / 6084) + 1)", + "q3OnlyUpperBound": "raw_q3_count - max(0, floor((N - 4633) / 6084) + 1)" + }, + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 33532, + "crtModulus": 38025, + "countFormula": "max(0, floor((N - 33532) / 38025) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 19843, + "crtModulus": 38025, + "countFormula": "max(0, floor((N - 19843) / 38025) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 8, + "observedSquareEventCount": 8, + "q2OverlapFormulaCount": 2, + "q3OnlyAfterQ2UpperBound": 6, + "observedRawValues": [ + 70, + 1591, + 3112, + 4633, + 6154, + 7675, + 9196, + 10717 + ], + "observedValuesAlsoInQ2": [ + 4633, + 10717 + ], + "upperBoundPassed": true + } + } + ], + "checkedIdentities": [ + "1591 mod 9 = 7 and 9563 mod 9 = 5.", + "9 divides 1591*m + 1 only when m mod 9 = 5.", + "9 divides 9563*m + 1 only when m mod 9 = 7.", + "CRT(m = 99 mod 169, m = 5 mod 9) gives m = 437 mod 1521.", + "CRT(m = 70 mod 169, m = 7 mod 9) gives m = 70 mod 1521.", + "The plus-side q=3 progression overlaps the q=2 progression exactly on m = 437 mod 6084.", + "The minus-side q=3 progression overlaps the q=2 progression exactly on m = 4633 mod 6084.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=3 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 5, + "statement": "Prove the q=5 same-prime degree progression upper bound for the same split, including q=2/q=3 overlap and base-residue/lower-witness exclusions.", + "completionRule": "The q=5 progression contribution is bounded by CRT floor functions, or the first unresolved q=5 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the q=3 progression atom as an upper-bound component and records the q=2-overlap classes required for later union bounds. It intentionally leaves q=5, higher square-divisor families, and recombination into a full dMax envelope open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7 next.", + "After q=5 is bounded, continue through the remaining one-off square-divisor families before recombining the dMax growth envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c57cd0e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,148 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 5, + "squareDivisor": 25, + "proofKind": "crt_floor_function_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=5 square-divisor progression upper bound, including q=2/q=3 overlap bookkeeping. It does not prove the full dMax growth envelope or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "25 divides 1591*m + 1", + "coefficientMod25": 16, + "requiredOppositeValueMod25": 14, + "crtProgression": { + "variable": "m", + "residue": 1789, + "modulus": 4225, + "formula": "m = 1789 + 4225*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1789) / 4225) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "predecessorProgression": "m = 437 + 676*t", + "crtResidue": 1789, + "crtModulus": 16900, + "formula": "m = 1789 + 16900*t", + "countFormula": "max(0, floor((N - 1789) / 16900) + 1)" + }, + { + "q": 3, + "predecessorProgression": "m = 437 + 1521*t", + "crtResidue": 18689, + "crtModulus": 38025, + "formula": "m = 18689 + 38025*t", + "countFormula": "max(0, floor((N - 18689) / 38025) + 1)" + } + ], + "baseResidueExclusions": [], + "baseResidueExclusionReason": "The q=5 congruence fixes m mod 25 = 14, so it is disjoint from the excluded base residues 7 and 18.", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 3, + "observedSquareEventCount": 3, + "q2OverlapFormulaCount": 1, + "q3OverlapFormulaCount": 0, + "q5OnlyAfterPriorQUpperBound": 2, + "observedRawValues": [ + 1789, + 6014, + 10239 + ], + "observedValuesAlsoInPriorQ": [ + 1789 + ], + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "25 divides 9563*m + 1", + "coefficientMod25": 13, + "requiredOppositeValueMod25": 23, + "crtProgression": { + "variable": "m", + "residue": 2098, + "modulus": 4225, + "formula": "m = 2098 + 4225*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2098) / 4225) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "predecessorProgression": "m = 577 + 676*t", + "crtResidue": 14773, + "crtModulus": 16900, + "formula": "m = 14773 + 16900*t", + "countFormula": "max(0, floor((N - 14773) / 16900) + 1)" + }, + { + "q": 3, + "predecessorProgression": "m = 70 + 1521*t", + "crtResidue": 27448, + "crtModulus": 38025, + "formula": "m = 27448 + 38025*t", + "countFormula": "max(0, floor((N - 27448) / 38025) + 1)" + } + ], + "baseResidueExclusions": [], + "baseResidueExclusionReason": "The q=5 congruence fixes m mod 25 = 23, so it is disjoint from the excluded base residues 7 and 18.", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 3, + "observedSquareEventCount": 3, + "q2OverlapFormulaCount": 0, + "q3OverlapFormulaCount": 0, + "q5OnlyAfterPriorQUpperBound": 3, + "observedRawValues": [ + 2098, + 6323, + 10548 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + } + ], + "checkedIdentities": [ + "1591 mod 25 = 16 and 9563 mod 25 = 13.", + "25 divides 1591*m + 1 only when m mod 25 = 14.", + "25 divides 9563*m + 1 only when m mod 25 = 23.", + "CRT(m = 99 mod 169, m = 14 mod 25) gives m = 1789 mod 4225.", + "CRT(m = 70 mod 169, m = 23 mod 25) gives m = 2098 mod 4225.", + "The plus q=5 progression overlaps q=2 on m = 1789 mod 16900 and q=3 on m = 18689 mod 38025.", + "The minus q=5 progression overlaps q=2 on m = 14773 mod 16900 and q=3 on m = 27448 mod 38025.", + "Both q=5 progressions are disjoint from base residues 7 and 18 mod 25." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 7, + "statement": "Prove the q=7 same-prime degree progression upper bound for the same split, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=7 progression contribution is bounded by CRT floor functions, or the first unresolved q=7 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the q=5 progression atom as an upper-bound component and records prior-q overlap classes required for later union bounds. It intentionally leaves q=7, higher one-off square-divisor families, and recombination into a full dMax envelope open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7 next.", + "After q=7 is bounded, continue through the remaining one-off square-divisor families before recombining the dMax growth envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..8a5923c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,185 @@ +{ + "schema": "erdos.p848_dmax_q_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "q": 7, + "squareDivisor": 49, + "proofKind": "crt_floor_function_upper_bound_with_prior_q_overlap_bookkeeping", + "scope": { + "term": "same-prime dMax degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=7 square-divisor progression upper bound, including prior-q overlap bookkeeping. It does not prove the full dMax growth envelope or the all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "49 divides 1591*m + 1", + "coefficientMod49": 23, + "requiredOppositeValueMod49": 17, + "crtProgression": { + "variable": "m", + "residue": 3986, + "modulus": 8281, + "formula": "m = 3986 + 8281*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3986) / 8281) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 28829, + "crtModulus": 33124, + "formula": "m = 28829 + 33124*t", + "countFormula": "max(0, floor((N - 28829) / 33124) + 1)" + }, + { + "q": 3, + "crtResidue": 53672, + "crtModulus": 74529, + "formula": "m = 53672 + 74529*t", + "countFormula": "max(0, floor((N - 53672) / 74529) + 1)" + }, + { + "q": 5, + "crtResidue": 111639, + "crtModulus": 207025, + "formula": "m = 111639 + 207025*t", + "countFormula": "max(0, floor((N - 111639) / 207025) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 136482, + "crtModulus": 207025, + "countFormula": "max(0, floor((N - 136482) / 207025) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 186168, + "crtModulus": 207025, + "countFormula": "max(0, floor((N - 186168) / 207025) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 1, + "observedSquareEventCount": 1, + "priorQOverlapFormulaCounts": { + "q2": 0, + "q3": 0, + "q5": 0 + }, + "q7OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 3986 + ], + "observedValuesAlsoInPriorQ": [], + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "49 divides 9563*m + 1", + "coefficientMod49": 8, + "requiredOppositeValueMod49": 6, + "crtProgression": { + "variable": "m", + "residue": 1084, + "modulus": 8281, + "formula": "m = 1084 + 8281*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1084) / 8281) + 1)", + "priorQOverlaps": [ + { + "q": 2, + "crtResidue": 9365, + "crtModulus": 33124, + "formula": "m = 9365 + 33124*t", + "countFormula": "max(0, floor((N - 9365) / 33124) + 1)" + }, + { + "q": 3, + "crtResidue": 25927, + "crtModulus": 74529, + "formula": "m = 25927 + 74529*t", + "countFormula": "max(0, floor((N - 25927) / 74529) + 1)" + }, + { + "q": 5, + "crtResidue": 158423, + "crtModulus": 207025, + "formula": "m = 158423 + 207025*t", + "countFormula": "max(0, floor((N - 158423) / 207025) + 1)" + } + ], + "baseResidueExclusions": [ + { + "excludedResidueMod25": 7, + "crtResidue": 67332, + "crtModulus": 207025, + "countFormula": "max(0, floor((N - 67332) / 207025) + 1)" + }, + { + "excludedResidueMod25": 18, + "crtResidue": 117018, + "crtModulus": 207025, + "countFormula": "max(0, floor((N - 117018) / 207025) + 1)" + } + ], + "observedCheck": { + "N": 12000, + "rawFormulaCount": 2, + "observedSquareEventCount": 2, + "priorQOverlapFormulaCounts": { + "q2": 1, + "q3": 0, + "q5": 0 + }, + "q7OnlyAfterPriorQUpperBound": 1, + "observedRawValues": [ + 1084, + 9365 + ], + "observedValuesAlsoInPriorQ": [ + 9365 + ], + "upperBoundPassed": true + } + } + ], + "checkedIdentities": [ + "1591 mod 49 = 23 and 9563 mod 49 = 8.", + "49 divides 1591*m + 1 only when m mod 49 = 17.", + "49 divides 9563*m + 1 only when m mod 49 = 6.", + "CRT(m = 99 mod 169, m = 17 mod 49) gives m = 3986 mod 8281.", + "CRT(m = 70 mod 169, m = 6 mod 49) gives m = 1084 mod 8281.", + "The plus q=7 progression has no prior-q overlap below N = 12000.", + "The minus q=7 progression overlaps q=2 on m = 9365 mod 33124.", + "Base residues m = 7 or 18 mod 25 and lower least-square-witness exclusions can only reduce the raw q=7 upper bound." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 11, + "statement": "Prove the q=11 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=11 progression contribution is bounded by a CRT floor function, or the first unresolved q=11 exclusion/overlap class becomes the next atom." + }, + "proofBoundary": "This certificate discharges the q=7 progression atom as an upper-bound component and records prior-q overlap classes required for later union bounds. It intentionally leaves q=11 and the remaining one-off square-divisor families open.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7 next.", + "After q=11 is bounded, continue through the remaining q=19, q=23, q=31, and q=251 one-off families before recombining the dMax growth envelope." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..dbc7261 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 101, + "squareDivisor": 10201, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=101 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "10201 divides 1591*m + 1", + "coefficientMod10201": 1591, + "requiredOppositeValueMod10201": 5046, + "crtProgression": { + "variable": "m", + "residue": 1382181, + "modulus": 1723969, + "formula": "m = 1382181 + 1723969*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1382181) / 1723969) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "10201 divides 9563*m + 1", + "coefficientMod10201": 9563, + "requiredOppositeValueMod10201": 8746, + "crtProgression": { + "variable": "m", + "residue": 253570, + "modulus": 1723969, + "formula": "m = 253570 + 1723969*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 253570) / 1723969) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=101 raw CRT counts." + }, + "checkedIdentities": [ + "101^2 = 10201 and 169*10201 = 1723969.", + "1591 mod 10201 = 1591 and gcd(1591, 10201) = 1.", + "1591*5046 + 1 is divisible by 10201.", + "CRT(m = 99 mod 169, m = 5046 mod 10201) gives m = 1382181 mod 1723969.", + "9563 mod 10201 = 9563 and gcd(9563, 10201) = 1.", + "9563*8746 + 1 is divisible by 10201.", + "CRT(m = 70 mod 169, m = 8746 mod 10201) gives m = 253570 mod 1723969.", + "Both q=101 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 103, + "statement": "Prove the q=103 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 586529 mod 1792921 and m = 1732827 mod 1792921.", + "completionRule": "The q=103 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=101 as a residual tail-prime upper-bound component. It intentionally leaves q=103 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=103 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..a7f532c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 103, + "squareDivisor": 10609, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=103 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "10609 divides 1591*m + 1", + "coefficientMod10609": 1591, + "requiredOppositeValueMod10609": 3034, + "crtProgression": { + "variable": "m", + "residue": 586529, + "modulus": 1792921, + "formula": "m = 586529 + 1792921*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 586529) / 1792921) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "10609 divides 9563*m + 1", + "coefficientMod10609": 9563, + "requiredOppositeValueMod10609": 3560, + "crtProgression": { + "variable": "m", + "residue": 1732827, + "modulus": 1792921, + "formula": "m = 1732827 + 1792921*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1732827) / 1792921) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=103 raw CRT counts." + }, + "checkedIdentities": [ + "103^2 = 10609 and 169*10609 = 1792921.", + "1591 mod 10609 = 1591 and gcd(1591, 10609) = 1.", + "1591*3034 + 1 is divisible by 10609.", + "CRT(m = 99 mod 169, m = 3034 mod 10609) gives m = 586529 mod 1792921.", + "9563 mod 10609 = 9563 and gcd(9563, 10609) = 1.", + "9563*3560 + 1 is divisible by 10609.", + "CRT(m = 70 mod 169, m = 3560 mod 10609) gives m = 1732827 mod 1792921.", + "Both q=103 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 107, + "statement": "Prove the q=107 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 967624 mod 1934881 and m = 1699703 mod 1934881.", + "completionRule": "The q=107 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=103 as a residual tail-prime upper-bound component. It intentionally leaves q=107 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=107 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..4b4379d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 107, + "squareDivisor": 11449, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=107 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "11449 divides 1591*m + 1", + "coefficientMod11449": 1591, + "requiredOppositeValueMod11449": 5908, + "crtProgression": { + "variable": "m", + "residue": 967624, + "modulus": 1934881, + "formula": "m = 967624 + 1934881*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 967624) / 1934881) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "11449 divides 9563*m + 1", + "coefficientMod11449": 9563, + "requiredOppositeValueMod11449": 5251, + "crtProgression": { + "variable": "m", + "residue": 1699703, + "modulus": 1934881, + "formula": "m = 1699703 + 1934881*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1699703) / 1934881) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=107 raw CRT counts." + }, + "checkedIdentities": [ + "107^2 = 11449 and 169*11449 = 1934881.", + "1591 mod 11449 = 1591 and gcd(1591, 11449) = 1.", + "1591*5908 + 1 is divisible by 11449.", + "CRT(m = 99 mod 169, m = 5908 mod 11449) gives m = 967624 mod 1934881.", + "9563 mod 11449 = 9563 and gcd(9563, 11449) = 1.", + "9563*5251 + 1 is divisible by 11449.", + "CRT(m = 70 mod 169, m = 5251 mod 11449) gives m = 1699703 mod 1934881.", + "Both q=107 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 109, + "statement": "Prove the q=109 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 963399 mod 2007889 and m = 725925 mod 2007889.", + "completionRule": "The q=109 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=107 as a residual tail-prime upper-bound component. It intentionally leaves q=109 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=109 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..3f79eb7 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 109, + "squareDivisor": 11881, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=109 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "11881 divides 1591*m + 1", + "coefficientMod11881": 1591, + "requiredOppositeValueMod11881": 1038, + "crtProgression": { + "variable": "m", + "residue": 963399, + "modulus": 2007889, + "formula": "m = 963399 + 2007889*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 963399) / 2007889) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "11881 divides 9563*m + 1", + "coefficientMod11881": 9563, + "requiredOppositeValueMod11881": 1184, + "crtProgression": { + "variable": "m", + "residue": 725925, + "modulus": 2007889, + "formula": "m = 725925 + 2007889*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 725925) / 2007889) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=109 raw CRT counts." + }, + "checkedIdentities": [ + "109^2 = 11881 and 169*11881 = 2007889.", + "1591 mod 11881 = 1591 and gcd(1591, 11881) = 1.", + "1591*1038 + 1 is divisible by 11881.", + "CRT(m = 99 mod 169, m = 1038 mod 11881) gives m = 963399 mod 2007889.", + "9563 mod 11881 = 9563 and gcd(9563, 11881) = 1.", + "9563*1184 + 1 is divisible by 11881.", + "CRT(m = 70 mod 169, m = 1184 mod 11881) gives m = 725925 mod 2007889.", + "Both q=109 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 113, + "statement": "Prove the q=113 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 407051 mod 2157961 and m = 2150764 mod 2157961.", + "completionRule": "The q=113 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=109 as a residual tail-prime upper-bound component. It intentionally leaves q=113 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=113 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..8139568 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 113, + "squareDivisor": 12769, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=113 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "12769 divides 1591*m + 1", + "coefficientMod12769": 1591, + "requiredOppositeValueMod12769": 11212, + "crtProgression": { + "variable": "m", + "residue": 407051, + "modulus": 2157961, + "formula": "m = 407051 + 2157961*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 407051) / 2157961) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "12769 divides 9563*m + 1", + "coefficientMod12769": 9563, + "requiredOppositeValueMod12769": 5572, + "crtProgression": { + "variable": "m", + "residue": 2150764, + "modulus": 2157961, + "formula": "m = 2150764 + 2157961*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2150764) / 2157961) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=113 raw CRT counts." + }, + "checkedIdentities": [ + "113^2 = 12769 and 169*12769 = 2157961.", + "1591 mod 12769 = 1591 and gcd(1591, 12769) = 1.", + "1591*11212 + 1 is divisible by 12769.", + "CRT(m = 99 mod 169, m = 11212 mod 12769) gives m = 407051 mod 2157961.", + "9563 mod 12769 = 9563 and gcd(9563, 12769) = 1.", + "9563*5572 + 1 is divisible by 12769.", + "CRT(m = 70 mod 169, m = 5572 mod 12769) gives m = 2150764 mod 2157961.", + "Both q=113 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 127, + "statement": "Prove the q=127 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1191042 mod 2725801 and m = 2198253 mod 2725801.", + "completionRule": "The q=127 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=113 as a residual tail-prime upper-bound component. It intentionally leaves q=127 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=127 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c4861e6 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,73 @@ +{ + "schema": "erdos.p848_dmax_tail_side_complement_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7", + "observedComponentSiblingAtomId": "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 11, + "side": "minus", + "squareDivisor": 121, + "scope": { + "term": "same-prime dMax side-complement degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the minus-side q=11 complement left open by the observed plus-side q=11 packet. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBound": { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "121 divides 9563*m + 1", + "coefficientMod121": 4, + "requiredOppositeValueMod121": 30, + "crtProgression": { + "variable": "m", + "residue": 16970, + "modulus": 20449, + "formula": "m = 16970 + 20449*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 16970) / 20449) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + "observedSiblingCoverage": { + "status": "plus_side_q11_already_verified", + "siblingProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json", + "coveredSide": "plus", + "coveredProgression": "m = 1620 + 20449*t" + }, + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the minus-side q=11 raw CRT count." + }, + "checkedIdentities": [ + "9563 mod 121 = 4.", + "4*30 + 1 is divisible by 121.", + "CRT(m = 70 mod 169, m = 30 mod 121) gives m = 16970 mod 20449.", + "The minus-side q=11 raw floor function evaluates to zero at N = 12000, matching the bounded growth profile.", + "The existing q=11 observed-component packet already verifies the plus-side progression m = 1620 mod 20449." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 23, + "side": "plus", + "statement": "Prove the plus-side q=23 tail complement left open by the observed minus-side q=23 component, starting from m = 44039 mod 89401.", + "completionRule": "The plus-side q=23 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom." + }, + "proofBoundary": "This certificate discharges the minus-side q=11 side complement. It intentionally leaves the plus-side q=23 complement open because the existing q=23 observed-component packet only certified the minus witness.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7 next.", + "Use the existing q=23 observed-component packet for the minus witness and certify the plus-side complement separately." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..f460cda --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 127, + "squareDivisor": 16129, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=127 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "16129 divides 1591*m + 1", + "coefficientMod16129": 1591, + "requiredOppositeValueMod16129": 13625, + "crtProgression": { + "variable": "m", + "residue": 1191042, + "modulus": 2725801, + "formula": "m = 1191042 + 2725801*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1191042) / 2725801) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "16129 divides 9563*m + 1", + "coefficientMod16129": 9563, + "requiredOppositeValueMod16129": 4709, + "crtProgression": { + "variable": "m", + "residue": 2198253, + "modulus": 2725801, + "formula": "m = 2198253 + 2725801*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2198253) / 2725801) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=127 raw CRT counts." + }, + "checkedIdentities": [ + "127^2 = 16129 and 169*16129 = 2725801.", + "1591 mod 16129 = 1591 and gcd(1591, 16129) = 1.", + "1591*13625 + 1 is divisible by 16129.", + "CRT(m = 99 mod 169, m = 13625 mod 16129) gives m = 1191042 mod 2725801.", + "9563 mod 16129 = 9563 and gcd(9563, 16129) = 1.", + "9563*4709 + 1 is divisible by 16129.", + "CRT(m = 70 mod 169, m = 4709 mod 16129) gives m = 2198253 mod 2725801.", + "Both q=127 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 131, + "statement": "Prove the q=131 tail-prime same-prime degree progression upper bound: plus-side CRT floor bound from m = 1345170 mod 2900209, and minus-side exclusion because 131 divides 9563.", + "completionRule": "The q=131 tail contribution is bounded by the plus-side CRT floor function plus the minus-side witness-divisibility exclusion, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=127 as a residual tail-prime upper-bound component. It intentionally leaves q=131 open as the next residual tail-prime CRT/exclusion component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=131 via the plus-side CRT floor bound and the minus-side witness-divisibility exclusion before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..b30ac07 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,82 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "plus_crt_floor_function_minus_witness_divisibility_exclusion_tail_prime_upper_bound", + "q": 131, + "squareDivisor": 17161, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=131 tail-prime upper-bound component: plus-side CRT floor bound and minus-side witness-divisibility exclusion. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessExclusions": [ + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "exclusionReason": "131 divides 9563, so 9563*m + 1 is congruent to 1 mod 131 for every integer m.", + "coefficientMod17161": 9563, + "gcdCoefficientSquareDivisor": 131, + "productPlusOneResidueMod131": 1, + "conclusion": "17161 never divides 9563*m + 1." + } + ], + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "17161 divides 1591*m + 1", + "coefficientMod17161": 1591, + "requiredOppositeValueMod17161": 6612, + "crtProgression": { + "variable": "m", + "residue": 1345170, + "modulus": 2900209, + "formula": "m = 1345170 + 2900209*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1345170) / 2900209) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "The minus side is excluded. Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the plus-side q=131 raw CRT count." + }, + "checkedIdentities": [ + "131^2 = 17161 and 169*17161 = 2900209.", + "9563 = 73*131, so 9563*m + 1 is congruent to 1 mod 131 for every integer m.", + "9563 mod 17161 = 9563 and gcd(9563, 17161) = 131.", + "1591 mod 17161 = 1591 and gcd(1591, 17161) = 1.", + "1591*6612 + 1 is divisible by 17161.", + "CRT(m = 99 mod 169, m = 6612 mod 17161) gives m = 1345170 mod 2900209.", + "The q=131 plus-side raw floor function evaluates to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 137, + "statement": "Prove the q=137 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2767643 mod 3171961 and m = 1021675 mod 3171961.", + "completionRule": "The q=137 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=131 as a residual tail-prime upper-bound component. It intentionally leaves q=137 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=137 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..92016aa --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 137, + "squareDivisor": 18769, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=137 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "18769 divides 1591*m + 1", + "coefficientMod18769": 1591, + "requiredOppositeValueMod18769": 8600, + "crtProgression": { + "variable": "m", + "residue": 2767643, + "modulus": 3171961, + "formula": "m = 2767643 + 3171961*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2767643) / 3171961) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "18769 divides 9563*m + 1", + "coefficientMod18769": 9563, + "requiredOppositeValueMod18769": 8149, + "crtProgression": { + "variable": "m", + "residue": 1021675, + "modulus": 3171961, + "formula": "m = 1021675 + 3171961*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1021675) / 3171961) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=137 raw CRT counts." + }, + "checkedIdentities": [ + "137^2 = 18769 and 169*18769 = 3171961.", + "1591 mod 18769 = 1591 and gcd(1591, 18769) = 1.", + "1591*8600 + 1 is divisible by 18769.", + "CRT(m = 99 mod 169, m = 8600 mod 18769) gives m = 2767643 mod 3171961.", + "9563 mod 18769 = 9563 and gcd(9563, 18769) = 1.", + "9563*8149 + 1 is divisible by 18769.", + "CRT(m = 70 mod 169, m = 8149 mod 18769) gives m = 1021675 mod 3171961.", + "Both q=137 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 139, + "statement": "Prove the q=139 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3089757 mod 3265249 and m = 1765444 mod 3265249.", + "completionRule": "The q=139 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=137 as a residual tail-prime upper-bound component. It intentionally leaves q=139 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=139 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..b2e28b4 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 139, + "squareDivisor": 19321, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=139 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "19321 divides 1591*m + 1", + "coefficientMod19321": 1591, + "requiredOppositeValueMod19321": 17718, + "crtProgression": { + "variable": "m", + "residue": 3089757, + "modulus": 3265249, + "formula": "m = 3089757 + 3265249*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3089757) / 3265249) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "19321 divides 9563*m + 1", + "coefficientMod19321": 9563, + "requiredOppositeValueMod19321": 7233, + "crtProgression": { + "variable": "m", + "residue": 1765444, + "modulus": 3265249, + "formula": "m = 1765444 + 3265249*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1765444) / 3265249) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=139 raw CRT counts." + }, + "checkedIdentities": [ + "139^2 = 19321 and 169*19321 = 3265249.", + "1591 mod 19321 = 1591 and gcd(1591, 19321) = 1.", + "1591*17718 + 1 is divisible by 19321.", + "CRT(m = 99 mod 169, m = 17718 mod 19321) gives m = 3089757 mod 3265249.", + "9563 mod 19321 = 9563 and gcd(9563, 19321) = 1.", + "9563*7233 + 1 is divisible by 19321.", + "CRT(m = 70 mod 169, m = 7233 mod 19321) gives m = 1765444 mod 3265249.", + "Both q=139 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 149, + "statement": "Prove the q=149 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 276752 mod 3751969 and m = 1423557 mod 3751969.", + "completionRule": "The q=149 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=139 as a residual tail-prime upper-bound component. It intentionally leaves q=149 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=149 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..1550cdf --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 149, + "squareDivisor": 22201, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=149 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "22201 divides 1591*m + 1", + "coefficientMod22201": 1591, + "requiredOppositeValueMod22201": 10340, + "crtProgression": { + "variable": "m", + "residue": 276752, + "modulus": 3751969, + "formula": "m = 276752 + 3751969*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 276752) / 3751969) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "22201 divides 9563*m + 1", + "coefficientMod22201": 9563, + "requiredOppositeValueMod22201": 2693, + "crtProgression": { + "variable": "m", + "residue": 1423557, + "modulus": 3751969, + "formula": "m = 1423557 + 3751969*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1423557) / 3751969) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=149 raw CRT counts." + }, + "checkedIdentities": [ + "149^2 = 22201 and 169*22201 = 3751969.", + "1591 mod 22201 = 1591 and gcd(1591, 22201) = 1.", + "1591*10340 + 1 is divisible by 22201.", + "CRT(m = 99 mod 169, m = 10340 mod 22201) gives m = 276752 mod 3751969.", + "9563 mod 22201 = 9563 and gcd(9563, 22201) = 1.", + "9563*2693 + 1 is divisible by 22201.", + "CRT(m = 70 mod 169, m = 2693 mod 22201) gives m = 1423557 mod 3751969.", + "Both q=149 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 151, + "statement": "Prove the q=151 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2446543 mod 3853369 and m = 1157720 mod 3853369.", + "completionRule": "The q=151 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=149 as a residual tail-prime upper-bound component. It intentionally leaves q=151 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=151 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..029fd39 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 151, + "squareDivisor": 22801, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=151 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "22801 divides 1591*m + 1", + "coefficientMod22801": 1591, + "requiredOppositeValueMod22801": 6836, + "crtProgression": { + "variable": "m", + "residue": 2446543, + "modulus": 3853369, + "formula": "m = 2446543 + 3853369*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2446543) / 3853369) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "22801 divides 9563*m + 1", + "coefficientMod22801": 9563, + "requiredOppositeValueMod22801": 17670, + "crtProgression": { + "variable": "m", + "residue": 1157720, + "modulus": 3853369, + "formula": "m = 1157720 + 3853369*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1157720) / 3853369) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=151 raw CRT counts." + }, + "checkedIdentities": [ + "151^2 = 22801 and 169*22801 = 3853369.", + "1591 mod 22801 = 1591 and gcd(1591, 22801) = 1.", + "1591*6836 + 1 is divisible by 22801.", + "CRT(m = 99 mod 169, m = 6836 mod 22801) gives m = 2446543 mod 3853369.", + "9563 mod 22801 = 9563 and gcd(9563, 22801) = 1.", + "9563*17670 + 1 is divisible by 22801.", + "CRT(m = 70 mod 169, m = 17670 mod 22801) gives m = 1157720 mod 3853369.", + "Both q=151 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 157, + "statement": "Prove the q=157 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1762938 mod 4165681 and m = 2160735 mod 4165681.", + "completionRule": "The q=157 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=151 as a residual tail-prime upper-bound component. It intentionally leaves q=157 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=157 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..35e9864 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 157, + "squareDivisor": 24649, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=157 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "24649 divides 1591*m + 1", + "coefficientMod24649": 1591, + "requiredOppositeValueMod24649": 12859, + "crtProgression": { + "variable": "m", + "residue": 1762938, + "modulus": 4165681, + "formula": "m = 1762938 + 4165681*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1762938) / 4165681) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "24649 divides 9563*m + 1", + "coefficientMod24649": 9563, + "requiredOppositeValueMod24649": 16272, + "crtProgression": { + "variable": "m", + "residue": 2160735, + "modulus": 4165681, + "formula": "m = 2160735 + 4165681*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2160735) / 4165681) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=157 raw CRT counts." + }, + "checkedIdentities": [ + "157^2 = 24649 and 169*24649 = 4165681.", + "1591 mod 24649 = 1591 and gcd(1591, 24649) = 1.", + "1591*12859 + 1 is divisible by 24649.", + "CRT(m = 99 mod 169, m = 12859 mod 24649) gives m = 1762938 mod 4165681.", + "9563 mod 24649 = 9563 and gcd(9563, 24649) = 1.", + "9563*16272 + 1 is divisible by 24649.", + "CRT(m = 70 mod 169, m = 16272 mod 24649) gives m = 2160735 mod 4165681.", + "Both q=157 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 163, + "statement": "Prove the q=163 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2941544 mod 4490161 and m = 856562 mod 4490161.", + "completionRule": "The q=163 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=157 as a residual tail-prime upper-bound component. It intentionally leaves q=163 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=163 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..3aaeb93 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 163, + "squareDivisor": 26569, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=163 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "26569 divides 1591*m + 1", + "coefficientMod26569": 1591, + "requiredOppositeValueMod26569": 18954, + "crtProgression": { + "variable": "m", + "residue": 2941544, + "modulus": 4490161, + "formula": "m = 2941544 + 4490161*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2941544) / 4490161) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "26569 divides 9563*m + 1", + "coefficientMod26569": 9563, + "requiredOppositeValueMod26569": 6354, + "crtProgression": { + "variable": "m", + "residue": 856562, + "modulus": 4490161, + "formula": "m = 856562 + 4490161*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 856562) / 4490161) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=163 raw CRT counts." + }, + "checkedIdentities": [ + "163^2 = 26569 and 169*26569 = 4490161.", + "1591 mod 26569 = 1591 and gcd(1591, 26569) = 1.", + "1591*18954 + 1 is divisible by 26569.", + "CRT(m = 99 mod 169, m = 18954 mod 26569) gives m = 2941544 mod 4490161.", + "9563 mod 26569 = 9563 and gcd(9563, 26569) = 1.", + "9563*6354 + 1 is divisible by 26569.", + "CRT(m = 70 mod 169, m = 6354 mod 26569) gives m = 856562 mod 4490161.", + "Both q=163 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 167, + "statement": "Prove the q=167 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4640670 mod 4713241 and m = 3647428 mod 4713241.", + "completionRule": "The q=167 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=163 as a residual tail-prime upper-bound component. It intentionally leaves q=167 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=167 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..fc9ddcd --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 167, + "squareDivisor": 27889, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=167 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "27889 divides 1591*m + 1", + "coefficientMod27889": 1591, + "requiredOppositeValueMod27889": 11096, + "crtProgression": { + "variable": "m", + "residue": 4640670, + "modulus": 4713241, + "formula": "m = 4640670 + 4713241*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4640670) / 4713241) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "27889 divides 9563*m + 1", + "coefficientMod27889": 9563, + "requiredOppositeValueMod27889": 21858, + "crtProgression": { + "variable": "m", + "residue": 3647428, + "modulus": 4713241, + "formula": "m = 3647428 + 4713241*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3647428) / 4713241) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=167 raw CRT counts." + }, + "checkedIdentities": [ + "167^2 = 27889 and 169*27889 = 4713241.", + "1591 mod 27889 = 1591 and gcd(1591, 27889) = 1.", + "1591*11096 + 1 is divisible by 27889.", + "CRT(m = 99 mod 169, m = 11096 mod 27889) gives m = 4640670 mod 4713241.", + "9563 mod 27889 = 9563 and gcd(9563, 27889) = 1.", + "9563*21858 + 1 is divisible by 27889.", + "CRT(m = 70 mod 169, m = 21858 mod 27889) gives m = 3647428 mod 4713241.", + "Both q=167 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 173, + "statement": "Prove the q=173 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 978778 mod 5058001 and m = 1961146 mod 5058001.", + "completionRule": "The q=173 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=167 as a residual tail-prime upper-bound component. It intentionally leaves q=173 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=173 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..fda1e28 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 173, + "squareDivisor": 29929, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=173 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "29929 divides 1591*m + 1", + "coefficientMod29929": 1591, + "requiredOppositeValueMod29929": 21050, + "crtProgression": { + "variable": "m", + "residue": 978778, + "modulus": 5058001, + "formula": "m = 978778 + 5058001*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 978778) / 5058001) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "29929 divides 9563*m + 1", + "coefficientMod29929": 9563, + "requiredOppositeValueMod29929": 15761, + "crtProgression": { + "variable": "m", + "residue": 1961146, + "modulus": 5058001, + "formula": "m = 1961146 + 5058001*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1961146) / 5058001) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=173 raw CRT counts." + }, + "checkedIdentities": [ + "173^2 = 29929 and 169*29929 = 5058001.", + "1591 mod 29929 = 1591 and gcd(1591, 29929) = 1.", + "1591*21050 + 1 is divisible by 29929.", + "CRT(m = 99 mod 169, m = 21050 mod 29929) gives m = 978778 mod 5058001.", + "9563 mod 29929 = 9563 and gcd(9563, 29929) = 1.", + "9563*15761 + 1 is divisible by 29929.", + "CRT(m = 70 mod 169, m = 15761 mod 29929) gives m = 1961146 mod 5058001.", + "Both q=173 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 179, + "statement": "Prove the q=179 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2724210 mod 5414929 and m = 4437841 mod 5414929.", + "completionRule": "The q=179 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=173 as a residual tail-prime upper-bound component. It intentionally leaves q=179 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=179 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..dc7f55f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 179, + "squareDivisor": 32041, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=179 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "32041 divides 1591*m + 1", + "coefficientMod32041": 1591, + "requiredOppositeValueMod32041": 725, + "crtProgression": { + "variable": "m", + "residue": 2724210, + "modulus": 5414929, + "formula": "m = 2724210 + 5414929*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2724210) / 5414929) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "32041 divides 9563*m + 1", + "coefficientMod32041": 9563, + "requiredOppositeValueMod32041": 16183, + "crtProgression": { + "variable": "m", + "residue": 4437841, + "modulus": 5414929, + "formula": "m = 4437841 + 5414929*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4437841) / 5414929) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=179 raw CRT counts." + }, + "checkedIdentities": [ + "179^2 = 32041 and 169*32041 = 5414929.", + "1591 mod 32041 = 1591 and gcd(1591, 32041) = 1.", + "1591*725 + 1 is divisible by 32041.", + "CRT(m = 99 mod 169, m = 725 mod 32041) gives m = 2724210 mod 5414929.", + "9563 mod 32041 = 9563 and gcd(9563, 32041) = 1.", + "9563*16183 + 1 is divisible by 32041.", + "CRT(m = 70 mod 169, m = 16183 mod 32041) gives m = 4437841 mod 5414929.", + "Both q=179 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 181, + "statement": "Prove the q=181 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1789809 mod 5536609 and m = 4242815 mod 5536609.", + "completionRule": "The q=181 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=179 as a residual tail-prime upper-bound component. It intentionally leaves q=181 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=181 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..6ce0e9e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,92 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_tail_prime_upper_bound", + "q": 17, + "squareDivisor": 289, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=17 tail-prime CRT floor-function upper bound for the two active same-prime witnesses. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "289 divides 1591*m + 1", + "coefficientMod289": 146, + "requiredOppositeValueMod289": 192, + "crtProgression": { + "variable": "m", + "residue": 47588, + "modulus": 48841, + "formula": "m = 47588 + 48841*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 47588) / 48841) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "289 divides 9563*m + 1", + "coefficientMod289": 26, + "requiredOppositeValueMod289": 100, + "crtProgression": { + "variable": "m", + "residue": 12238, + "modulus": 48841, + "formula": "m = 12238 + 48841*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 12238) / 48841) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the q=17 raw CRT count, so they are not needed to certify this upper-bound component." + }, + "checkedIdentities": [ + "1591 mod 289 = 146.", + "146*192 + 1 is divisible by 289.", + "CRT(m = 99 mod 169, m = 192 mod 289) gives m = 47588 mod 48841.", + "9563 mod 289 = 26.", + "26*100 + 1 is divisible by 289.", + "CRT(m = 70 mod 169, m = 100 mod 289) gives m = 12238 mod 48841.", + "Both q=17 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 19, + "side": "plus", + "statement": "Prove the plus-side q=19 tail complement left open by the observed minus-side q=19 component, starting from m = 22576 mod 61009.", + "completionRule": "The plus-side q=19 tail contribution is bounded by its CRT floor function, or the next side-specific q=19 overlap/exclusion class becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=17 as a tail-prime upper-bound component. It intentionally leaves the side-specific q=19 plus complement open because the existing q=19 observed-component packet only certified the minus witness.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7 next.", + "Use the existing q=19 observed-component packet for the minus witness and certify the plus-side complement separately." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..46aa828 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 181, + "squareDivisor": 32761, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=181 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "32761 divides 1591*m + 1", + "coefficientMod32761": 1591, + "requiredOppositeValueMod32761": 20715, + "crtProgression": { + "variable": "m", + "residue": 1789809, + "modulus": 5536609, + "formula": "m = 1789809 + 5536609*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1789809) / 5536609) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "32761 divides 9563*m + 1", + "coefficientMod32761": 9563, + "requiredOppositeValueMod32761": 16646, + "crtProgression": { + "variable": "m", + "residue": 4242815, + "modulus": 5536609, + "formula": "m = 4242815 + 5536609*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4242815) / 5536609) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=181 raw CRT counts." + }, + "checkedIdentities": [ + "181^2 = 32761 and 169*32761 = 5536609.", + "1591 mod 32761 = 1591 and gcd(1591, 32761) = 1.", + "1591*20715 + 1 is divisible by 32761.", + "CRT(m = 99 mod 169, m = 20715 mod 32761) gives m = 1789809 mod 5536609.", + "9563 mod 32761 = 9563 and gcd(9563, 32761) = 1.", + "9563*16646 + 1 is divisible by 32761.", + "CRT(m = 70 mod 169, m = 16646 mod 32761) gives m = 4242815 mod 5536609.", + "Both q=181 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 191, + "statement": "Prove the q=191 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1508424 mod 6165289 and m = 1951682 mod 6165289.", + "completionRule": "The q=191 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=181 as a residual tail-prime upper-bound component. It intentionally leaves q=191 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=191 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..9afbf66 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 191, + "squareDivisor": 36481, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=191 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "36481 divides 1591*m + 1", + "coefficientMod36481": 1591, + "requiredOppositeValueMod36481": 12703, + "crtProgression": { + "variable": "m", + "residue": 1508424, + "modulus": 6165289, + "formula": "m = 1508424 + 6165289*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1508424) / 6165289) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "36481 divides 9563*m + 1", + "coefficientMod36481": 9563, + "requiredOppositeValueMod36481": 18189, + "crtProgression": { + "variable": "m", + "residue": 1951682, + "modulus": 6165289, + "formula": "m = 1951682 + 6165289*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1951682) / 6165289) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=191 raw CRT counts." + }, + "checkedIdentities": [ + "191^2 = 36481 and 169*36481 = 6165289.", + "1591 mod 36481 = 1591 and gcd(1591, 36481) = 1.", + "1591*12703 + 1 is divisible by 36481.", + "CRT(m = 99 mod 169, m = 12703 mod 36481) gives m = 1508424 mod 6165289.", + "9563 mod 36481 = 9563 and gcd(9563, 36481) = 1.", + "9563*18189 + 1 is divisible by 36481.", + "CRT(m = 70 mod 169, m = 18189 mod 36481) gives m = 1951682 mod 6165289.", + "Both q=191 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 193, + "statement": "Prove the q=193 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 69558 mod 6295081 and m = 1273485 mod 6295081.", + "completionRule": "The q=193 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=191 as a residual tail-prime upper-bound component. It intentionally leaves q=193 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=193 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..bfa2c92 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 193, + "squareDivisor": 37249, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=193 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "37249 divides 1591*m + 1", + "coefficientMod37249": 1591, + "requiredOppositeValueMod37249": 32309, + "crtProgression": { + "variable": "m", + "residue": 69558, + "modulus": 6295081, + "formula": "m = 69558 + 6295081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 69558) / 6295081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "37249 divides 9563*m + 1", + "coefficientMod37249": 9563, + "requiredOppositeValueMod37249": 7019, + "crtProgression": { + "variable": "m", + "residue": 1273485, + "modulus": 6295081, + "formula": "m = 1273485 + 6295081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1273485) / 6295081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=193 raw CRT counts." + }, + "checkedIdentities": [ + "193^2 = 37249 and 169*37249 = 6295081.", + "1591 mod 37249 = 1591 and gcd(1591, 37249) = 1.", + "1591*32309 + 1 is divisible by 37249.", + "CRT(m = 99 mod 169, m = 32309 mod 37249) gives m = 69558 mod 6295081.", + "9563 mod 37249 = 9563 and gcd(9563, 37249) = 1.", + "9563*7019 + 1 is divisible by 37249.", + "CRT(m = 70 mod 169, m = 7019 mod 37249) gives m = 1273485 mod 6295081.", + "Both q=193 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 197, + "statement": "Prove the q=197 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3802599 mod 6558721 and m = 4141415 mod 6558721.", + "completionRule": "The q=197 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=193 as a residual tail-prime upper-bound component. It intentionally leaves q=197 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=197 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..aecf350 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 197, + "squareDivisor": 38809, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=197 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "38809 divides 1591*m + 1", + "coefficientMod38809": 1591, + "requiredOppositeValueMod38809": 38126, + "crtProgression": { + "variable": "m", + "residue": 3802599, + "modulus": 6558721, + "formula": "m = 3802599 + 6558721*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3802599) / 6558721) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "38809 divides 9563*m + 1", + "coefficientMod38809": 9563, + "requiredOppositeValueMod38809": 27661, + "crtProgression": { + "variable": "m", + "residue": 4141415, + "modulus": 6558721, + "formula": "m = 4141415 + 6558721*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4141415) / 6558721) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=197 raw CRT counts." + }, + "checkedIdentities": [ + "197^2 = 38809 and 169*38809 = 6558721.", + "1591 mod 38809 = 1591 and gcd(1591, 38809) = 1.", + "1591*38126 + 1 is divisible by 38809.", + "CRT(m = 99 mod 169, m = 38126 mod 38809) gives m = 3802599 mod 6558721.", + "9563 mod 38809 = 9563 and gcd(9563, 38809) = 1.", + "9563*27661 + 1 is divisible by 38809.", + "CRT(m = 70 mod 169, m = 27661 mod 38809) gives m = 4141415 mod 6558721.", + "Both q=197 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 199, + "statement": "Prove the q=199 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 872815 mod 6692569 and m = 1078797 mod 6692569.", + "completionRule": "The q=199 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=197 as a residual tail-prime upper-bound component. It intentionally leaves q=199 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=199 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..0b6d9d5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 199, + "squareDivisor": 39601, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=199 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "39601 divides 1591*m + 1", + "coefficientMod39601": 1591, + "requiredOppositeValueMod39601": 1593, + "crtProgression": { + "variable": "m", + "residue": 872815, + "modulus": 6692569, + "formula": "m = 872815 + 6692569*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 872815) / 6692569) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "39601 divides 9563*m + 1", + "coefficientMod39601": 9563, + "requiredOppositeValueMod39601": 9570, + "crtProgression": { + "variable": "m", + "residue": 1078797, + "modulus": 6692569, + "formula": "m = 1078797 + 6692569*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1078797) / 6692569) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=199 raw CRT counts." + }, + "checkedIdentities": [ + "199^2 = 39601 and 169*39601 = 6692569.", + "1591 mod 39601 = 1591 and gcd(1591, 39601) = 1.", + "1591*1593 + 1 is divisible by 39601.", + "CRT(m = 99 mod 169, m = 1593 mod 39601) gives m = 872815 mod 6692569.", + "9563 mod 39601 = 9563 and gcd(9563, 39601) = 1.", + "9563*9570 + 1 is divisible by 39601.", + "CRT(m = 70 mod 169, m = 9570 mod 39601) gives m = 1078797 mod 6692569.", + "Both q=199 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 211, + "statement": "Prove the q=211 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 199519 mod 7524049 and m = 3288134 mod 7524049.", + "completionRule": "The q=211 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=199 as a residual tail-prime upper-bound component. It intentionally leaves q=211 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=211 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..2171f47 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,79 @@ +{ + "schema": "erdos.p848_dmax_tail_side_complement_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7", + "observedComponentSiblingAtomId": "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 19, + "side": "plus", + "squareDivisor": 361, + "scope": { + "term": "same-prime dMax side-complement degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the plus-side q=19 complement left open by the observed minus-side q=19 packet. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBound": { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "361 divides 1591*m + 1", + "coefficientMod361": 147, + "requiredOppositeValueMod361": 194, + "crtProgression": { + "variable": "m", + "residue": 22576, + "modulus": 61009, + "formula": "m = 22576 + 61009*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 22576) / 61009) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + "observedSiblingCoverage": { + "status": "minus_side_q19_already_verified", + "siblingProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json", + "coveredSide": "minus", + "coveredProgression": "m = 4126 + 61009*t" + }, + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the plus-side q=19 raw CRT count." + }, + "checkedIdentities": [ + "1591 mod 361 = 147.", + "147*194 + 1 is divisible by 361.", + "CRT(m = 99 mod 169, m = 194 mod 361) gives m = 22576 mod 61009.", + "The plus-side q=19 raw floor function evaluates to zero at N = 12000, matching the bounded growth profile.", + "The existing q=19 observed-component packet already verifies the minus-side progression m = 4126 mod 61009." + ], + "sideComplementAudit": { + "status": "earlier_side_complement_backfill_needed", + "reason": "The observed q=11 component proof certified the plus witness and explicitly left the minus-side q=11 complement as a non-observed bounded-profile note. The tail lane must backfill that complement before any full dMax envelope can be promoted.", + "firstBackfillAtomId": "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "firstBackfillCrtProgression": "m = 16970 + 20449*t" + }, + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 11, + "side": "minus", + "statement": "Backfill the minus-side q=11 tail complement left open by the observed plus-side q=11 component, starting from m = 16970 mod 20449.", + "completionRule": "The minus-side q=11 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom." + }, + "proofBoundary": "This certificate discharges the plus-side q=19 side complement. It intentionally pivots to an earlier q=11 minus-side backfill because the existing observed q=11 proof did not cover that witness side.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify the q=11 minus-side complement before continuing higher unobserved tail components such as q=23 plus." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..94f9f64 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 211, + "squareDivisor": 44521, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=211 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "44521 divides 1591*m + 1", + "coefficientMod44521": 1591, + "requiredOppositeValueMod44521": 21435, + "crtProgression": { + "variable": "m", + "residue": 199519, + "modulus": 7524049, + "formula": "m = 199519 + 7524049*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 199519) / 7524049) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "44521 divides 9563*m + 1", + "coefficientMod44521": 9563, + "requiredOppositeValueMod44521": 38101, + "crtProgression": { + "variable": "m", + "residue": 3288134, + "modulus": 7524049, + "formula": "m = 3288134 + 7524049*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3288134) / 7524049) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=211 raw CRT counts." + }, + "checkedIdentities": [ + "211^2 = 44521 and 169*44521 = 7524049.", + "1591 mod 44521 = 1591 and gcd(1591, 44521) = 1.", + "1591*21435 + 1 is divisible by 44521.", + "CRT(m = 99 mod 169, m = 21435 mod 44521) gives m = 199519 mod 7524049.", + "9563 mod 44521 = 9563 and gcd(9563, 44521) = 1.", + "9563*38101 + 1 is divisible by 44521.", + "CRT(m = 70 mod 169, m = 38101 mod 44521) gives m = 3288134 mod 7524049.", + "Both q=211 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 223, + "statement": "Prove the q=223 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1169241 mod 8404201 and m = 3594700 mod 8404201.", + "completionRule": "The q=223 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=211 as a residual tail-prime upper-bound component. It intentionally leaves q=223 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=223 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..fb476ef --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 223, + "squareDivisor": 49729, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=223 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "49729 divides 1591*m + 1", + "coefficientMod49729": 1591, + "requiredOppositeValueMod49729": 25474, + "crtProgression": { + "variable": "m", + "residue": 1169241, + "modulus": 8404201, + "formula": "m = 1169241 + 8404201*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1169241) / 8404201) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "49729 divides 9563*m + 1", + "coefficientMod49729": 9563, + "requiredOppositeValueMod49729": 14212, + "crtProgression": { + "variable": "m", + "residue": 3594700, + "modulus": 8404201, + "formula": "m = 3594700 + 8404201*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3594700) / 8404201) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=223 raw CRT counts." + }, + "checkedIdentities": [ + "223^2 = 49729 and 169*49729 = 8404201.", + "1591 mod 49729 = 1591 and gcd(1591, 49729) = 1.", + "1591*25474 + 1 is divisible by 49729.", + "CRT(m = 99 mod 169, m = 25474 mod 49729) gives m = 1169241 mod 8404201.", + "9563 mod 49729 = 9563 and gcd(9563, 49729) = 1.", + "9563*14212 + 1 is divisible by 49729.", + "CRT(m = 70 mod 169, m = 14212 mod 49729) gives m = 3594700 mod 8404201.", + "Both q=223 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 227, + "statement": "Prove the q=227 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1095388 mod 8708401 and m = 7005627 mod 8708401.", + "completionRule": "The q=227 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=223 as a residual tail-prime upper-bound component. It intentionally leaves q=227 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=227 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..12c2128 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 227, + "squareDivisor": 51529, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=227 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "51529 divides 1591*m + 1", + "coefficientMod51529": 1591, + "requiredOppositeValueMod51529": 13279, + "crtProgression": { + "variable": "m", + "residue": 1095388, + "modulus": 8708401, + "formula": "m = 1095388 + 8708401*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1095388) / 8708401) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "51529 divides 9563*m + 1", + "coefficientMod51529": 9563, + "requiredOppositeValueMod51529": 49212, + "crtProgression": { + "variable": "m", + "residue": 7005627, + "modulus": 8708401, + "formula": "m = 7005627 + 8708401*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 7005627) / 8708401) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=227 raw CRT counts." + }, + "checkedIdentities": [ + "227^2 = 51529 and 169*51529 = 8708401.", + "1591 mod 51529 = 1591 and gcd(1591, 51529) = 1.", + "1591*13279 + 1 is divisible by 51529.", + "CRT(m = 99 mod 169, m = 13279 mod 51529) gives m = 1095388 mod 8708401.", + "9563 mod 51529 = 9563 and gcd(9563, 51529) = 1.", + "9563*49212 + 1 is divisible by 51529.", + "CRT(m = 70 mod 169, m = 49212 mod 51529) gives m = 7005627 mod 8708401.", + "Both q=227 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 229, + "statement": "Prove the q=229 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 102344 mod 8862529 and m = 8756298 mod 8862529.", + "completionRule": "The q=229 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=227 as a residual tail-prime upper-bound component. It intentionally leaves q=229 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=229 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..ca865bb --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 229, + "squareDivisor": 52441, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=229 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "52441 divides 1591*m + 1", + "coefficientMod52441": 1591, + "requiredOppositeValueMod52441": 49903, + "crtProgression": { + "variable": "m", + "residue": 102344, + "modulus": 8862529, + "formula": "m = 102344 + 8862529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 102344) / 8862529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "52441 divides 9563*m + 1", + "coefficientMod52441": 9563, + "requiredOppositeValueMod52441": 51092, + "crtProgression": { + "variable": "m", + "residue": 8756298, + "modulus": 8862529, + "formula": "m = 8756298 + 8862529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8756298) / 8862529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=229 raw CRT counts." + }, + "checkedIdentities": [ + "229^2 = 52441 and 169*52441 = 8862529.", + "1591 mod 52441 = 1591 and gcd(1591, 52441) = 1.", + "1591*49903 + 1 is divisible by 52441.", + "CRT(m = 99 mod 169, m = 49903 mod 52441) gives m = 102344 mod 8862529.", + "9563 mod 52441 = 9563 and gcd(9563, 52441) = 1.", + "9563*51092 + 1 is divisible by 52441.", + "CRT(m = 70 mod 169, m = 51092 mod 52441) gives m = 8756298 mod 8862529.", + "Both q=229 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 233, + "statement": "Prove the q=233 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1640920 mod 9174841 and m = 5761787 mod 9174841.", + "completionRule": "The q=233 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=229 as a residual tail-prime upper-bound component. It intentionally leaves q=233 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=233 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..291bb4a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 233, + "squareDivisor": 54289, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=233 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "54289 divides 1591*m + 1", + "coefficientMod54289": 1591, + "requiredOppositeValueMod54289": 12250, + "crtProgression": { + "variable": "m", + "residue": 1640920, + "modulus": 9174841, + "formula": "m = 1640920 + 9174841*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1640920) / 9174841) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "54289 divides 9563*m + 1", + "coefficientMod54289": 9563, + "requiredOppositeValueMod54289": 7153, + "crtProgression": { + "variable": "m", + "residue": 5761787, + "modulus": 9174841, + "formula": "m = 5761787 + 9174841*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5761787) / 9174841) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=233 raw CRT counts." + }, + "checkedIdentities": [ + "233^2 = 54289 and 169*54289 = 9174841.", + "1591 mod 54289 = 1591 and gcd(1591, 54289) = 1.", + "1591*12250 + 1 is divisible by 54289.", + "CRT(m = 99 mod 169, m = 12250 mod 54289) gives m = 1640920 mod 9174841.", + "9563 mod 54289 = 9563 and gcd(9563, 54289) = 1.", + "9563*7153 + 1 is divisible by 54289.", + "CRT(m = 70 mod 169, m = 7153 mod 54289) gives m = 5761787 mod 9174841.", + "Both q=233 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 239, + "statement": "Prove the q=239 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2615036 mod 9653449 and m = 883264 mod 9653449.", + "completionRule": "The q=239 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=233 as a residual tail-prime upper-bound component. It intentionally leaves q=239 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=239 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..821d890 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 239, + "squareDivisor": 57121, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=239 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "57121 divides 1591*m + 1", + "coefficientMod57121": 1591, + "requiredOppositeValueMod57121": 44591, + "crtProgression": { + "variable": "m", + "residue": 2615036, + "modulus": 9653449, + "formula": "m = 2615036 + 9653449*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2615036) / 9653449) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "57121 divides 9563*m + 1", + "coefficientMod57121": 9563, + "requiredOppositeValueMod57121": 26449, + "crtProgression": { + "variable": "m", + "residue": 883264, + "modulus": 9653449, + "formula": "m = 883264 + 9653449*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 883264) / 9653449) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=239 raw CRT counts." + }, + "checkedIdentities": [ + "239^2 = 57121 and 169*57121 = 9653449.", + "1591 mod 57121 = 1591 and gcd(1591, 57121) = 1.", + "1591*44591 + 1 is divisible by 57121.", + "CRT(m = 99 mod 169, m = 44591 mod 57121) gives m = 2615036 mod 9653449.", + "9563 mod 57121 = 9563 and gcd(9563, 57121) = 1.", + "9563*26449 + 1 is divisible by 57121.", + "CRT(m = 70 mod 169, m = 26449 mod 57121) gives m = 883264 mod 9653449.", + "Both q=239 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 241, + "statement": "Prove the q=241 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8794690 mod 9815689 and m = 6246310 mod 9815689.", + "completionRule": "The q=241 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=239 as a residual tail-prime upper-bound component. It intentionally leaves q=241 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=241 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c2f3332 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,73 @@ +{ + "schema": "erdos.p848_dmax_tail_side_complement_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "observedComponentSiblingAtomId": "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 23, + "side": "plus", + "squareDivisor": 529, + "scope": { + "term": "same-prime dMax side-complement degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the plus-side q=23 complement left open by the observed minus-side q=23 packet. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBound": { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "529 divides 1591*m + 1", + "coefficientMod529": 4, + "requiredOppositeValueMod529": 132, + "crtProgression": { + "variable": "m", + "residue": 44039, + "modulus": 89401, + "formula": "m = 44039 + 89401*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 44039) / 89401) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + "observedSiblingCoverage": { + "status": "minus_side_q23_already_verified", + "siblingProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json", + "coveredSide": "minus", + "coveredProgression": "m = 2774 + 89401*t" + }, + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the plus-side q=23 raw CRT count." + }, + "checkedIdentities": [ + "1591 mod 529 = 4.", + "4*132 + 1 is divisible by 529.", + "CRT(m = 99 mod 169, m = 132 mod 529) gives m = 44039 mod 89401.", + "The plus-side q=23 raw floor function evaluates to zero at N = 12000, matching the bounded growth profile.", + "The existing q=23 observed-component packet already verifies the minus-side progression m = 2774 mod 89401." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 31, + "side": "minus", + "statement": "Prove the minus-side q=31 tail complement left open by the observed plus-side q=31 component, starting from m = 105526 mod 162409.", + "completionRule": "The minus-side q=31 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom." + }, + "proofBoundary": "This certificate discharges the plus-side q=23 side complement. It intentionally leaves the minus-side q=31 complement open because the existing q=31 observed-component packet only certified the plus witness.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7 next.", + "Use the existing q=31 observed-component packet for the plus witness and certify the minus-side complement separately." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..9d75ce3 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,101 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 241, + "squareDivisor": 58081, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=241 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "58081 divides 1591*m + 1", + "coefficientMod58081": 1591, + "requiredOppositeValueMod58081": 24459, + "crtProgression": { + "variable": "m", + "residue": 8794690, + "modulus": 9815689, + "formula": "m = 8794690 + 9815689*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8794690) / 9815689) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "58081 divides 9563*m + 1", + "coefficientMod58081": 9563, + "requiredOppositeValueMod58081": 31643, + "crtProgression": { + "variable": "m", + "residue": 6246310, + "modulus": 9815689, + "formula": "m = 6246310 + 9815689*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6246310) / 9815689) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "coveredIntermediatePrimeBoundary": { + "q": 251, + "status": "already_verified_by_observed_plus_packet_and_minus_complement", + "plusProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json", + "minusProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json", + "reason": "The q=251 branch was split out before the residual two-sided tail-prime ladder, so the next open residual prime after q=241 is q=257." + }, + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=241 raw CRT counts." + }, + "checkedIdentities": [ + "241^2 = 58081 and 169*58081 = 9815689.", + "1591 mod 58081 = 1591 and gcd(1591, 58081) = 1.", + "1591*24459 + 1 is divisible by 58081.", + "CRT(m = 99 mod 169, m = 24459 mod 58081) gives m = 8794690 mod 9815689.", + "9563 mod 58081 = 9563 and gcd(9563, 58081) = 1.", + "9563*31643 + 1 is divisible by 58081.", + "CRT(m = 70 mod 169, m = 31643 mod 58081) gives m = 6246310 mod 9815689.", + "Both q=241 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile.", + "q=251 is already discharged by the plus-side observed q=251 packet and the minus-side q=251 complement packet." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 257, + "statement": "Prove the q=257 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4730578 mod 11162281 and m = 10654844 mod 11162281.", + "completionRule": "The q=257 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=241 as a residual tail-prime upper-bound component. It intentionally skips the already-covered q=251 branch and leaves q=257 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=257 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..85bfda5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,72 @@ +{ + "schema": "erdos.p848_dmax_tail_side_complement_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7", + "observedComponentSiblingAtomId": "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 251, + "side": "minus", + "squareDivisor": 63001, + "scope": { + "term": "same-prime dMax side-complement degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the minus-side q=251 complement left open by the observed plus-side q=251 packet. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBound": { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "63001 divides 9563*m + 1", + "coefficientMod63001": 9563, + "requiredOppositeValueMod63001": 11305, + "crtProgression": { + "variable": "m", + "residue": 8138434, + "modulus": 10647169, + "formula": "m = 8138434 + 10647169*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8138434) / 10647169) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + "observedSiblingCoverage": { + "status": "plus_side_q251_already_verified", + "siblingProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json", + "coveredSide": "plus", + "coveredProgression": "m = 4831 + 10647169*t" + }, + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the minus-side q=251 raw CRT count." + }, + "checkedIdentities": [ + "9563 mod 63001 = 9563.", + "9563*11305 + 1 is divisible by 63001.", + "CRT(m = 70 mod 169, m = 11305 mod 63001) gives m = 8138434 mod 10647169.", + "The minus-side q=251 raw floor function evaluates to zero at N = 12000, matching the bounded growth profile.", + "The existing q=251 observed-component packet already verifies the plus-side progression m = 4831 mod 10647169." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 29, + "statement": "Prove the q=29 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 29167 mod 142129 and m = 114314 mod 142129.", + "completionRule": "The q=29 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges the minus-side q=251 side complement. It intentionally leaves q=29 open as the first remaining non-observed tail-prime progression before any aggregate dMax tail envelope can be promoted.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=29 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..74f29b2 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 257, + "squareDivisor": 66049, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=257 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "66049 divides 1591*m + 1", + "coefficientMod66049": 1591, + "requiredOppositeValueMod66049": 41099, + "crtProgression": { + "variable": "m", + "residue": 4730578, + "modulus": 11162281, + "formula": "m = 4730578 + 11162281*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4730578) / 11162281) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "66049 divides 9563*m + 1", + "coefficientMod66049": 9563, + "requiredOppositeValueMod66049": 20955, + "crtProgression": { + "variable": "m", + "residue": 10654844, + "modulus": 11162281, + "formula": "m = 10654844 + 11162281*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 10654844) / 11162281) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=257 raw CRT counts." + }, + "checkedIdentities": [ + "257^2 = 66049 and 169*66049 = 11162281.", + "1591 mod 66049 = 1591 and gcd(1591, 66049) = 1.", + "1591*41099 + 1 is divisible by 66049.", + "CRT(m = 99 mod 169, m = 41099 mod 66049) gives m = 4730578 mod 11162281.", + "9563 mod 66049 = 9563 and gcd(9563, 66049) = 1.", + "9563*20955 + 1 is divisible by 66049.", + "CRT(m = 70 mod 169, m = 20955 mod 66049) gives m = 10654844 mod 11162281.", + "Both q=257 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 263, + "statement": "Prove the q=263 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5804066 mod 11689561 and m = 3539944 mod 11689561.", + "completionRule": "The q=263 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=257 as a residual tail-prime upper-bound component. It intentionally leaves q=263 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=263 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..5ae0320 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 263, + "squareDivisor": 69169, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=263 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "69169 divides 1591*m + 1", + "coefficientMod69169": 1591, + "requiredOppositeValueMod69169": 63039, + "crtProgression": { + "variable": "m", + "residue": 5804066, + "modulus": 11689561, + "formula": "m = 5804066 + 11689561*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5804066) / 11689561) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "69169 divides 9563*m + 1", + "coefficientMod69169": 9563, + "requiredOppositeValueMod69169": 12325, + "crtProgression": { + "variable": "m", + "residue": 3539944, + "modulus": 11689561, + "formula": "m = 3539944 + 11689561*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3539944) / 11689561) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=263 raw CRT counts." + }, + "checkedIdentities": [ + "263^2 = 69169 and 169*69169 = 11689561.", + "1591 mod 69169 = 1591 and gcd(1591, 69169) = 1.", + "1591*63039 + 1 is divisible by 69169.", + "CRT(m = 99 mod 169, m = 63039 mod 69169) gives m = 5804066 mod 11689561.", + "9563 mod 69169 = 9563 and gcd(9563, 69169) = 1.", + "9563*12325 + 1 is divisible by 69169.", + "CRT(m = 70 mod 169, m = 12325 mod 69169) gives m = 3539944 mod 11689561.", + "Both q=263 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 269, + "statement": "Prove the q=269 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10056951 mod 12229009 and m = 11133621 mod 12229009.", + "completionRule": "The q=269 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=263 as a residual tail-prime upper-bound component. It intentionally leaves q=269 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=269 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..7833c9c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 269, + "squareDivisor": 72361, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=269 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "72361 divides 1591*m + 1", + "coefficientMod72361": 1591, + "requiredOppositeValueMod72361": 71133, + "crtProgression": { + "variable": "m", + "residue": 10056951, + "modulus": 12229009, + "formula": "m = 10056951 + 12229009*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 10056951) / 12229009) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "72361 divides 9563*m + 1", + "coefficientMod72361": 9563, + "requiredOppositeValueMod72361": 62388, + "crtProgression": { + "variable": "m", + "residue": 11133621, + "modulus": 12229009, + "formula": "m = 11133621 + 12229009*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 11133621) / 12229009) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=269 raw CRT counts." + }, + "checkedIdentities": [ + "269^2 = 72361 and 169*72361 = 12229009.", + "1591 mod 72361 = 1591 and gcd(1591, 72361) = 1.", + "1591*71133 + 1 is divisible by 72361.", + "CRT(m = 99 mod 169, m = 71133 mod 72361) gives m = 10056951 mod 12229009.", + "9563 mod 72361 = 9563 and gcd(9563, 72361) = 1.", + "9563*62388 + 1 is divisible by 72361.", + "CRT(m = 70 mod 169, m = 62388 mod 72361) gives m = 11133621 mod 12229009.", + "Both q=269 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 271, + "statement": "Prove the q=271 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4686976 mod 12411529 and m = 749923 mod 12411529.", + "completionRule": "The q=271 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=269 as a residual tail-prime upper-bound component. It intentionally leaves q=271 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=271 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..b11d9e4 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 271, + "squareDivisor": 73441, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=271 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "73441 divides 1591*m + 1", + "coefficientMod73441": 1591, + "requiredOppositeValueMod73441": 60193, + "crtProgression": { + "variable": "m", + "residue": 4686976, + "modulus": 12411529, + "formula": "m = 4686976 + 12411529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4686976) / 12411529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "73441 divides 9563*m + 1", + "coefficientMod73441": 9563, + "requiredOppositeValueMod73441": 15513, + "crtProgression": { + "variable": "m", + "residue": 749923, + "modulus": 12411529, + "formula": "m = 749923 + 12411529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 749923) / 12411529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=271 raw CRT counts." + }, + "checkedIdentities": [ + "271^2 = 73441 and 169*73441 = 12411529.", + "1591 mod 73441 = 1591 and gcd(1591, 73441) = 1.", + "1591*60193 + 1 is divisible by 73441.", + "CRT(m = 99 mod 169, m = 60193 mod 73441) gives m = 4686976 mod 12411529.", + "9563 mod 73441 = 9563 and gcd(9563, 73441) = 1.", + "9563*15513 + 1 is divisible by 73441.", + "CRT(m = 70 mod 169, m = 15513 mod 73441) gives m = 749923 mod 12411529.", + "Both q=271 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 277, + "statement": "Prove the q=277 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6946844 mod 12967201 and m = 10587920 mod 12967201.", + "completionRule": "The q=277 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=271 as a residual tail-prime upper-bound component. It intentionally leaves q=277 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=277 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..4e179b0 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 277, + "squareDivisor": 76729, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=277 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "76729 divides 1591*m + 1", + "coefficientMod76729": 1591, + "requiredOppositeValueMod76729": 41234, + "crtProgression": { + "variable": "m", + "residue": 6946844, + "modulus": 12967201, + "formula": "m = 6946844 + 12967201*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6946844) / 12967201) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "76729 divides 9563*m + 1", + "coefficientMod76729": 9563, + "requiredOppositeValueMod76729": 76047, + "crtProgression": { + "variable": "m", + "residue": 10587920, + "modulus": 12967201, + "formula": "m = 10587920 + 12967201*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 10587920) / 12967201) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=277 raw CRT counts." + }, + "checkedIdentities": [ + "277^2 = 76729 and 169*76729 = 12967201.", + "1591 mod 76729 = 1591 and gcd(1591, 76729) = 1.", + "1591*41234 + 1 is divisible by 76729.", + "CRT(m = 99 mod 169, m = 41234 mod 76729) gives m = 6946844 mod 12967201.", + "9563 mod 76729 = 9563 and gcd(9563, 76729) = 1.", + "9563*76047 + 1 is divisible by 76729.", + "CRT(m = 70 mod 169, m = 76047 mod 76729) gives m = 10587920 mod 12967201.", + "Both q=277 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 281, + "statement": "Prove the q=281 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4072323 mod 13344409 and m = 9581694 mod 13344409.", + "completionRule": "The q=281 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=277 as a residual tail-prime upper-bound component. It intentionally leaves q=281 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=281 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..9fe9a41 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 281, + "squareDivisor": 78961, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=281 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "78961 divides 1591*m + 1", + "coefficientMod78961": 1591, + "requiredOppositeValueMod78961": 45312, + "crtProgression": { + "variable": "m", + "residue": 4072323, + "modulus": 13344409, + "formula": "m = 4072323 + 13344409*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4072323) / 13344409) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "78961 divides 9563*m + 1", + "coefficientMod78961": 9563, + "requiredOppositeValueMod78961": 27413, + "crtProgression": { + "variable": "m", + "residue": 9581694, + "modulus": 13344409, + "formula": "m = 9581694 + 13344409*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 9581694) / 13344409) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=281 raw CRT counts." + }, + "checkedIdentities": [ + "281^2 = 78961 and 169*78961 = 13344409.", + "1591 mod 78961 = 1591 and gcd(1591, 78961) = 1.", + "1591*45312 + 1 is divisible by 78961.", + "CRT(m = 99 mod 169, m = 45312 mod 78961) gives m = 4072323 mod 13344409.", + "9563 mod 78961 = 9563 and gcd(9563, 78961) = 1.", + "9563*27413 + 1 is divisible by 78961.", + "CRT(m = 70 mod 169, m = 27413 mod 78961) gives m = 9581694 mod 13344409.", + "Both q=281 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 283, + "statement": "Prove the q=283 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7094043 mod 13535041 and m = 4146823 mod 13535041.", + "completionRule": "The q=283 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=281 as a residual tail-prime upper-bound component. It intentionally leaves q=283 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=283 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c16f011 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 283, + "squareDivisor": 80089, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=283 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "80089 divides 1591*m + 1", + "coefficientMod80089": 1591, + "requiredOppositeValueMod80089": 46211, + "crtProgression": { + "variable": "m", + "residue": 7094043, + "modulus": 13535041, + "formula": "m = 7094043 + 13535041*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 7094043) / 13535041) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "80089 divides 9563*m + 1", + "coefficientMod80089": 9563, + "requiredOppositeValueMod80089": 62284, + "crtProgression": { + "variable": "m", + "residue": 4146823, + "modulus": 13535041, + "formula": "m = 4146823 + 13535041*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4146823) / 13535041) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=283 raw CRT counts." + }, + "checkedIdentities": [ + "283^2 = 80089 and 169*80089 = 13535041.", + "1591 mod 80089 = 1591 and gcd(1591, 80089) = 1.", + "1591*46211 + 1 is divisible by 80089.", + "CRT(m = 99 mod 169, m = 46211 mod 80089) gives m = 7094043 mod 13535041.", + "9563 mod 80089 = 9563 and gcd(9563, 80089) = 1.", + "9563*62284 + 1 is divisible by 80089.", + "CRT(m = 70 mod 169, m = 62284 mod 80089) gives m = 4146823 mod 13535041.", + "Both q=283 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 293, + "statement": "Prove the q=293 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7410749 mod 14508481 and m = 12282314 mod 14508481.", + "completionRule": "The q=293 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=283 as a residual tail-prime upper-bound component. It intentionally leaves q=293 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=293 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..feb0448 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 293, + "squareDivisor": 85849, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=293 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "85849 divides 1591*m + 1", + "coefficientMod85849": 1591, + "requiredOppositeValueMod85849": 27735, + "crtProgression": { + "variable": "m", + "residue": 7410749, + "modulus": 14508481, + "formula": "m = 7410749 + 14508481*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 7410749) / 14508481) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "85849 divides 9563*m + 1", + "coefficientMod85849": 9563, + "requiredOppositeValueMod85849": 5907, + "crtProgression": { + "variable": "m", + "residue": 12282314, + "modulus": 14508481, + "formula": "m = 12282314 + 14508481*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 12282314) / 14508481) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=293 raw CRT counts." + }, + "checkedIdentities": [ + "293^2 = 85849 and 169*85849 = 14508481.", + "1591 mod 85849 = 1591 and gcd(1591, 85849) = 1.", + "1591*27735 + 1 is divisible by 85849.", + "CRT(m = 99 mod 169, m = 27735 mod 85849) gives m = 7410749 mod 14508481.", + "9563 mod 85849 = 9563 and gcd(9563, 85849) = 1.", + "9563*5907 + 1 is divisible by 85849.", + "CRT(m = 70 mod 169, m = 5907 mod 85849) gives m = 12282314 mod 14508481.", + "Both q=293 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 307, + "statement": "Prove the q=307 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 14963021 mod 15928081 and m = 15889112 mod 15928081.", + "completionRule": "The q=307 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=293 as a residual tail-prime upper-bound component. It intentionally leaves q=307 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=307 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..f0d6b71 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,92 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_tail_prime_upper_bound", + "q": 29, + "squareDivisor": 841, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=29 tail-prime CRT floor-function upper bound for the two active same-prime witnesses. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "841 divides 1591*m + 1", + "coefficientMod841": 750, + "requiredOppositeValueMod841": 573, + "crtProgression": { + "variable": "m", + "residue": 29167, + "modulus": 142129, + "formula": "m = 29167 + 142129*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 29167) / 142129) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "841 divides 9563*m + 1", + "coefficientMod841": 312, + "requiredOppositeValueMod841": 779, + "crtProgression": { + "variable": "m", + "residue": 114314, + "modulus": 142129, + "formula": "m = 114314 + 142129*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 114314) / 142129) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the q=29 raw CRT count, so they are not needed to certify this upper-bound component." + }, + "checkedIdentities": [ + "1591 mod 841 = 750.", + "750*573 + 1 is divisible by 841.", + "CRT(m = 99 mod 169, m = 573 mod 841) gives m = 29167 mod 142129.", + "9563 mod 841 = 312.", + "312*779 + 1 is divisible by 841.", + "CRT(m = 70 mod 169, m = 779 mod 841) gives m = 114314 mod 142129.", + "Both q=29 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 37, + "statement": "Prove the q=37 tail-prime same-prime degree atom: exclude the plus side because 37 divides 1591, and certify the minus-side CRT floor bound starting from m = 136284 mod 231361.", + "completionRule": "The q=37 tail contribution is bounded by the plus-side witness-divisibility exclusion and the minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=29 as a residual tail-prime upper-bound component. It intentionally leaves q=37 open because the plus witness has a divisibility exclusion and the minus side still needs its own CRT floor-bound certificate.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7 next.", + "Use 37 | 1591 to exclude the plus-side contribution, then certify the minus-side q=37 CRT progression." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..24968e4 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 307, + "squareDivisor": 94249, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=307 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "94249 divides 1591*m + 1", + "coefficientMod94249": 1591, + "requiredOppositeValueMod94249": 71679, + "crtProgression": { + "variable": "m", + "residue": 14963021, + "modulus": 15928081, + "formula": "m = 14963021 + 15928081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 14963021) / 15928081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "94249 divides 9563*m + 1", + "coefficientMod94249": 9563, + "requiredOppositeValueMod94249": 55280, + "crtProgression": { + "variable": "m", + "residue": 15889112, + "modulus": 15928081, + "formula": "m = 15889112 + 15928081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 15889112) / 15928081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=307 raw CRT counts." + }, + "checkedIdentities": [ + "307^2 = 94249 and 169*94249 = 15928081.", + "1591 mod 94249 = 1591 and gcd(1591, 94249) = 1.", + "1591*71679 + 1 is divisible by 94249.", + "CRT(m = 99 mod 169, m = 71679 mod 94249) gives m = 14963021 mod 15928081.", + "9563 mod 94249 = 9563 and gcd(9563, 94249) = 1.", + "9563*55280 + 1 is divisible by 94249.", + "CRT(m = 70 mod 169, m = 55280 mod 94249) gives m = 15889112 mod 15928081.", + "Both q=307 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 311, + "statement": "Prove the q=311 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 12908150 mod 16345849 and m = 5085787 mod 16345849.", + "completionRule": "The q=311 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=307 as a residual tail-prime upper-bound component. It intentionally leaves q=311 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=311 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..b7fa018 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 311, + "squareDivisor": 96721, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=311 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "96721 divides 1591*m + 1", + "coefficientMod96721": 1591, + "requiredOppositeValueMod96721": 44257, + "crtProgression": { + "variable": "m", + "residue": 12908150, + "modulus": 16345849, + "formula": "m = 12908150 + 16345849*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 12908150) / 16345849) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "96721 divides 9563*m + 1", + "coefficientMod96721": 9563, + "requiredOppositeValueMod96721": 56295, + "crtProgression": { + "variable": "m", + "residue": 5085787, + "modulus": 16345849, + "formula": "m = 5085787 + 16345849*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5085787) / 16345849) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=311 raw CRT counts." + }, + "checkedIdentities": [ + "311^2 = 96721 and 169*96721 = 16345849.", + "1591 mod 96721 = 1591 and gcd(1591, 96721) = 1.", + "1591*44257 + 1 is divisible by 96721.", + "CRT(m = 99 mod 169, m = 44257 mod 96721) gives m = 12908150 mod 16345849.", + "9563 mod 96721 = 9563 and gcd(9563, 96721) = 1.", + "9563*56295 + 1 is divisible by 96721.", + "CRT(m = 70 mod 169, m = 56295 mod 96721) gives m = 5085787 mod 16345849.", + "Both q=311 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 313, + "statement": "Prove the q=313 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5813361 mod 16556761 and m = 4403872 mod 16556761.", + "completionRule": "The q=313 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=311 as a residual tail-prime upper-bound component. It intentionally leaves q=313 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=313 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..7e946f7 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 313, + "squareDivisor": 97969, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=313 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "97969 divides 1591*m + 1", + "coefficientMod97969": 1591, + "requiredOppositeValueMod97969": 33190, + "crtProgression": { + "variable": "m", + "residue": 5813361, + "modulus": 16556761, + "formula": "m = 5813361 + 16556761*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5813361) / 16556761) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "97969 divides 9563*m + 1", + "coefficientMod97969": 9563, + "requiredOppositeValueMod97969": 93236, + "crtProgression": { + "variable": "m", + "residue": 4403872, + "modulus": 16556761, + "formula": "m = 4403872 + 16556761*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4403872) / 16556761) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=313 raw CRT counts." + }, + "checkedIdentities": [ + "313^2 = 97969 and 169*97969 = 16556761.", + "1591 mod 97969 = 1591 and gcd(1591, 97969) = 1.", + "1591*33190 + 1 is divisible by 97969.", + "CRT(m = 99 mod 169, m = 33190 mod 97969) gives m = 5813361 mod 16556761.", + "9563 mod 97969 = 9563 and gcd(9563, 97969) = 1.", + "9563*93236 + 1 is divisible by 97969.", + "CRT(m = 70 mod 169, m = 93236 mod 97969) gives m = 4403872 mod 16556761.", + "Both q=313 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 317, + "statement": "Prove the q=317 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7885639 mod 16982641 and m = 6675063 mod 16982641.", + "completionRule": "The q=317 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=313 as a residual tail-prime upper-bound component. It intentionally leaves q=317 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=317 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..cc8ef68 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 317, + "squareDivisor": 100489, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=317 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "100489 divides 1591*m + 1", + "coefficientMod100489": 1591, + "requiredOppositeValueMod100489": 47497, + "crtProgression": { + "variable": "m", + "residue": 7885639, + "modulus": 16982641, + "formula": "m = 7885639 + 16982641*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 7885639) / 16982641) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "100489 divides 9563*m + 1", + "coefficientMod100489": 9563, + "requiredOppositeValueMod100489": 42789, + "crtProgression": { + "variable": "m", + "residue": 6675063, + "modulus": 16982641, + "formula": "m = 6675063 + 16982641*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6675063) / 16982641) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=317 raw CRT counts." + }, + "checkedIdentities": [ + "317^2 = 100489 and 169*100489 = 16982641.", + "1591 mod 100489 = 1591 and gcd(1591, 100489) = 1.", + "1591*47497 + 1 is divisible by 100489.", + "CRT(m = 99 mod 169, m = 47497 mod 100489) gives m = 7885639 mod 16982641.", + "9563 mod 100489 = 9563 and gcd(9563, 100489) = 1.", + "9563*42789 + 1 is divisible by 100489.", + "CRT(m = 70 mod 169, m = 42789 mod 100489) gives m = 6675063 mod 16982641.", + "Both q=317 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 331, + "statement": "Prove the q=331 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 9831843 mod 18515809 and m = 2596079 mod 18515809.", + "completionRule": "The q=331 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=317 as a residual tail-prime upper-bound component. It intentionally leaves q=331 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=331 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..1aa008b --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,73 @@ +{ + "schema": "erdos.p848_dmax_tail_side_complement_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7", + "observedComponentSiblingAtomId": "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 31, + "side": "minus", + "squareDivisor": 961, + "scope": { + "term": "same-prime dMax side-complement degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the minus-side q=31 complement left open by the observed plus-side q=31 packet. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBound": { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "961 divides 9563*m + 1", + "coefficientMod961": 914, + "requiredOppositeValueMod961": 777, + "crtProgression": { + "variable": "m", + "residue": 105526, + "modulus": 162409, + "formula": "m = 105526 + 162409*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 105526) / 162409) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + "observedSiblingCoverage": { + "status": "plus_side_q31_already_verified", + "siblingProofPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json", + "coveredSide": "plus", + "coveredProgression": "m = 5676 + 162409*t" + }, + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the minus-side q=31 raw CRT count." + }, + "checkedIdentities": [ + "9563 mod 961 = 914.", + "914*777 + 1 is divisible by 961.", + "CRT(m = 70 mod 169, m = 777 mod 961) gives m = 105526 mod 162409.", + "The minus-side q=31 raw floor function evaluates to zero at N = 12000, matching the bounded growth profile.", + "The existing q=31 observed-component packet already verifies the plus-side progression m = 5676 mod 162409." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 251, + "side": "minus", + "statement": "Prove the minus-side q=251 tail complement left open by the observed plus-side q=251 component, starting from m = 8138434 mod 10647169.", + "completionRule": "The minus-side q=251 tail contribution is bounded by its CRT floor function, or the next unresolved tail range becomes the next atom." + }, + "proofBoundary": "This certificate discharges the minus-side q=31 side complement. It intentionally leaves the minus-side q=251 complement open because the existing q=251 observed-component packet only certified the plus witness.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7 next.", + "Use the existing q=251 observed-component packet for the plus witness and certify the minus-side complement separately before any full tail envelope claim." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..a196fb8 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 331, + "squareDivisor": 109561, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=331 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "109561 divides 1591*m + 1", + "coefficientMod109561": 1591, + "requiredOppositeValueMod109561": 80914, + "crtProgression": { + "variable": "m", + "residue": 9831843, + "modulus": 18515809, + "formula": "m = 9831843 + 18515809*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 9831843) / 18515809) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "109561 divides 9563*m + 1", + "coefficientMod109561": 9563, + "requiredOppositeValueMod109561": 76176, + "crtProgression": { + "variable": "m", + "residue": 2596079, + "modulus": 18515809, + "formula": "m = 2596079 + 18515809*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2596079) / 18515809) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=331 raw CRT counts." + }, + "checkedIdentities": [ + "331^2 = 109561 and 169*109561 = 18515809.", + "1591 mod 109561 = 1591 and gcd(1591, 109561) = 1.", + "1591*80914 + 1 is divisible by 109561.", + "CRT(m = 99 mod 169, m = 80914 mod 109561) gives m = 9831843 mod 18515809.", + "9563 mod 109561 = 9563 and gcd(9563, 109561) = 1.", + "9563*76176 + 1 is divisible by 109561.", + "CRT(m = 70 mod 169, m = 76176 mod 109561) gives m = 2596079 mod 18515809.", + "Both q=331 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 337, + "statement": "Prove the q=337 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3148738 mod 19193161 and m = 11799312 mod 19193161.", + "completionRule": "The q=337 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=331 as a residual tail-prime upper-bound component. It intentionally leaves q=337 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=337 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..25f8d3f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 337, + "squareDivisor": 113569, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=337 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "113569 divides 1591*m + 1", + "coefficientMod113569": 1591, + "requiredOppositeValueMod113569": 82375, + "crtProgression": { + "variable": "m", + "residue": 3148738, + "modulus": 19193161, + "formula": "m = 3148738 + 19193161*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 3148738) / 19193161) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "113569 divides 9563*m + 1", + "coefficientMod113569": 9563, + "requiredOppositeValueMod113569": 101705, + "crtProgression": { + "variable": "m", + "residue": 11799312, + "modulus": 19193161, + "formula": "m = 11799312 + 19193161*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 11799312) / 19193161) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=337 raw CRT counts." + }, + "checkedIdentities": [ + "337^2 = 113569 and 169*113569 = 19193161.", + "1591 mod 113569 = 1591 and gcd(1591, 113569) = 1.", + "1591*82375 + 1 is divisible by 113569.", + "CRT(m = 99 mod 169, m = 82375 mod 113569) gives m = 3148738 mod 19193161.", + "9563 mod 113569 = 9563 and gcd(9563, 113569) = 1.", + "9563*101705 + 1 is divisible by 113569.", + "CRT(m = 70 mod 169, m = 101705 mod 113569) gives m = 11799312 mod 19193161.", + "Both q=337 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 347, + "statement": "Prove the q=347 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 11863730 mod 20349121 and m = 17215931 mod 20349121.", + "completionRule": "The q=347 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=337 as a residual tail-prime upper-bound component. It intentionally leaves q=347 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=347 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..e4c5c43 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 347, + "squareDivisor": 120409, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=347 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "120409 divides 1591*m + 1", + "coefficientMod120409": 1591, + "requiredOppositeValueMod120409": 63648, + "crtProgression": { + "variable": "m", + "residue": 11863730, + "modulus": 20349121, + "formula": "m = 11863730 + 20349121*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 11863730) / 20349121) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "120409 divides 9563*m + 1", + "coefficientMod120409": 9563, + "requiredOppositeValueMod120409": 117853, + "crtProgression": { + "variable": "m", + "residue": 17215931, + "modulus": 20349121, + "formula": "m = 17215931 + 20349121*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 17215931) / 20349121) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=347 raw CRT counts." + }, + "checkedIdentities": [ + "347^2 = 120409 and 169*120409 = 20349121.", + "1591 mod 120409 = 1591 and gcd(1591, 120409) = 1.", + "1591*63648 + 1 is divisible by 120409.", + "CRT(m = 99 mod 169, m = 63648 mod 120409) gives m = 11863730 mod 20349121.", + "9563 mod 120409 = 9563 and gcd(9563, 120409) = 1.", + "9563*117853 + 1 is divisible by 120409.", + "CRT(m = 70 mod 169, m = 117853 mod 120409) gives m = 17215931 mod 20349121.", + "Both q=347 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 349, + "statement": "Prove the q=349 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7685712 mod 20584369 and m = 2404433 mod 20584369.", + "completionRule": "The q=349 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=347 as a residual tail-prime upper-bound component. It intentionally leaves q=349 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=349 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..7ca3b6d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 349, + "squareDivisor": 121801, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=349 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "121801 divides 1591*m + 1", + "coefficientMod121801": 1591, + "requiredOppositeValueMod121801": 12249, + "crtProgression": { + "variable": "m", + "residue": 7685712, + "modulus": 20584369, + "formula": "m = 7685712 + 20584369*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 7685712) / 20584369) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "121801 divides 9563*m + 1", + "coefficientMod121801": 9563, + "requiredOppositeValueMod121801": 90214, + "crtProgression": { + "variable": "m", + "residue": 2404433, + "modulus": 20584369, + "formula": "m = 2404433 + 20584369*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2404433) / 20584369) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=349 raw CRT counts." + }, + "checkedIdentities": [ + "349^2 = 121801 and 169*121801 = 20584369.", + "1591 mod 121801 = 1591 and gcd(1591, 121801) = 1.", + "1591*12249 + 1 is divisible by 121801.", + "CRT(m = 99 mod 169, m = 12249 mod 121801) gives m = 7685712 mod 20584369.", + "9563 mod 121801 = 9563 and gcd(9563, 121801) = 1.", + "9563*90214 + 1 is divisible by 121801.", + "CRT(m = 70 mod 169, m = 90214 mod 121801) gives m = 2404433 mod 20584369.", + "Both q=349 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 353, + "statement": "Prove the q=353 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1415812 mod 21058921 and m = 17854751 mod 21058921.", + "completionRule": "The q=353 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=349 as a residual tail-prime upper-bound component. It intentionally leaves q=353 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=353 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..e835c9e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 353, + "squareDivisor": 124609, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=353 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "124609 divides 1591*m + 1", + "coefficientMod124609": 1591, + "requiredOppositeValueMod124609": 45113, + "crtProgression": { + "variable": "m", + "residue": 1415812, + "modulus": 21058921, + "formula": "m = 1415812 + 21058921*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1415812) / 21058921) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "124609 divides 9563*m + 1", + "coefficientMod124609": 9563, + "requiredOppositeValueMod124609": 35664, + "crtProgression": { + "variable": "m", + "residue": 17854751, + "modulus": 21058921, + "formula": "m = 17854751 + 21058921*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 17854751) / 21058921) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=353 raw CRT counts." + }, + "checkedIdentities": [ + "353^2 = 124609 and 169*124609 = 21058921.", + "1591 mod 124609 = 1591 and gcd(1591, 124609) = 1.", + "1591*45113 + 1 is divisible by 124609.", + "CRT(m = 99 mod 169, m = 45113 mod 124609) gives m = 1415812 mod 21058921.", + "9563 mod 124609 = 9563 and gcd(9563, 124609) = 1.", + "9563*35664 + 1 is divisible by 124609.", + "CRT(m = 70 mod 169, m = 35664 mod 124609) gives m = 17854751 mod 21058921.", + "Both q=353 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 359, + "statement": "Prove the q=359 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2693621 mod 21780889 and m = 19926353 mod 21780889.", + "completionRule": "The q=359 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=353 as a residual tail-prime upper-bound component. It intentionally leaves q=359 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=359 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..2c99127 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 359, + "squareDivisor": 128881, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=359 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "128881 divides 1591*m + 1", + "coefficientMod128881": 1591, + "requiredOppositeValueMod128881": 116001, + "crtProgression": { + "variable": "m", + "residue": 2693621, + "modulus": 21780889, + "formula": "m = 2693621 + 21780889*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2693621) / 21780889) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "128881 divides 9563*m + 1", + "coefficientMod128881": 9563, + "requiredOppositeValueMod128881": 78679, + "crtProgression": { + "variable": "m", + "residue": 19926353, + "modulus": 21780889, + "formula": "m = 19926353 + 21780889*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 19926353) / 21780889) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=359 raw CRT counts." + }, + "checkedIdentities": [ + "359^2 = 128881 and 169*128881 = 21780889.", + "1591 mod 128881 = 1591 and gcd(1591, 128881) = 1.", + "1591*116001 + 1 is divisible by 128881.", + "CRT(m = 99 mod 169, m = 116001 mod 128881) gives m = 2693621 mod 21780889.", + "9563 mod 128881 = 9563 and gcd(9563, 128881) = 1.", + "9563*78679 + 1 is divisible by 128881.", + "CRT(m = 70 mod 169, m = 78679 mod 128881) gives m = 19926353 mod 21780889.", + "Both q=359 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 367, + "statement": "Prove the q=367 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10408302 mod 22762441 and m = 21816280 mod 22762441.", + "completionRule": "The q=367 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=359 as a residual tail-prime upper-bound component. It intentionally leaves q=367 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=367 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..8c0bcec --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 367, + "squareDivisor": 134689, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=367 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "134689 divides 1591*m + 1", + "coefficientMod134689": 1591, + "requiredOppositeValueMod134689": 37249, + "crtProgression": { + "variable": "m", + "residue": 10408302, + "modulus": 22762441, + "formula": "m = 10408302 + 22762441*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 10408302) / 22762441) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "134689 divides 9563*m + 1", + "coefficientMod134689": 9563, + "requiredOppositeValueMod134689": 131351, + "crtProgression": { + "variable": "m", + "residue": 21816280, + "modulus": 22762441, + "formula": "m = 21816280 + 22762441*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 21816280) / 22762441) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=367 raw CRT counts." + }, + "checkedIdentities": [ + "367^2 = 134689 and 169*134689 = 22762441.", + "1591 mod 134689 = 1591 and gcd(1591, 134689) = 1.", + "1591*37249 + 1 is divisible by 134689.", + "CRT(m = 99 mod 169, m = 37249 mod 134689) gives m = 10408302 mod 22762441.", + "9563 mod 134689 = 9563 and gcd(9563, 134689) = 1.", + "9563*131351 + 1 is divisible by 134689.", + "CRT(m = 70 mod 169, m = 131351 mod 134689) gives m = 21816280 mod 22762441.", + "Both q=367 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 373, + "statement": "Prove the q=373 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6694020 mod 23512801 and m = 12354984 mod 23512801.", + "completionRule": "The q=373 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=367 as a residual tail-prime upper-bound component. It intentionally leaves q=373 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=373 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..083f68f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 373, + "squareDivisor": 139129, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=373 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "139129 divides 1591*m + 1", + "coefficientMod139129": 1591, + "requiredOppositeValueMod139129": 15828, + "crtProgression": { + "variable": "m", + "residue": 6694020, + "modulus": 23512801, + "formula": "m = 6694020 + 23512801*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6694020) / 23512801) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "139129 divides 9563*m + 1", + "coefficientMod139129": 9563, + "requiredOppositeValueMod139129": 111632, + "crtProgression": { + "variable": "m", + "residue": 12354984, + "modulus": 23512801, + "formula": "m = 12354984 + 23512801*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 12354984) / 23512801) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=373 raw CRT counts." + }, + "checkedIdentities": [ + "373^2 = 139129 and 169*139129 = 23512801.", + "1591 mod 139129 = 1591 and gcd(1591, 139129) = 1.", + "1591*15828 + 1 is divisible by 139129.", + "CRT(m = 99 mod 169, m = 15828 mod 139129) gives m = 6694020 mod 23512801.", + "9563 mod 139129 = 9563 and gcd(9563, 139129) = 1.", + "9563*111632 + 1 is divisible by 139129.", + "CRT(m = 70 mod 169, m = 111632 mod 139129) gives m = 12354984 mod 23512801.", + "Both q=373 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 379, + "statement": "Prove the q=379 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 11502746 mod 24275329 and m = 2984948 mod 24275329.", + "completionRule": "The q=379 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=373 as a residual tail-prime upper-bound component. It intentionally leaves q=379 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=379 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..25d57b6 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 379, + "squareDivisor": 143641, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=379 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "143641 divides 1591*m + 1", + "coefficientMod143641": 1591, + "requiredOppositeValueMod143641": 11466, + "crtProgression": { + "variable": "m", + "residue": 11502746, + "modulus": 24275329, + "formula": "m = 11502746 + 24275329*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 11502746) / 24275329) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "143641 divides 9563*m + 1", + "coefficientMod143641": 9563, + "requiredOppositeValueMod143641": 112128, + "crtProgression": { + "variable": "m", + "residue": 2984948, + "modulus": 24275329, + "formula": "m = 2984948 + 24275329*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2984948) / 24275329) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=379 raw CRT counts." + }, + "checkedIdentities": [ + "379^2 = 143641 and 169*143641 = 24275329.", + "1591 mod 143641 = 1591 and gcd(1591, 143641) = 1.", + "1591*11466 + 1 is divisible by 143641.", + "CRT(m = 99 mod 169, m = 11466 mod 143641) gives m = 11502746 mod 24275329.", + "9563 mod 143641 = 9563 and gcd(9563, 143641) = 1.", + "9563*112128 + 1 is divisible by 143641.", + "CRT(m = 70 mod 169, m = 112128 mod 143641) gives m = 2984948 mod 24275329.", + "Both q=379 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 383, + "statement": "Prove the q=383 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10683772 mod 24790441 and m = 8325686 mod 24790441.", + "completionRule": "The q=383 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=379 as a residual tail-prime upper-bound component. It intentionally leaves q=383 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=383 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c9a3895 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,81 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "witness_divisibility_exclusion_plus_crt_floor_function_tail_prime_upper_bound", + "q": 37, + "squareDivisor": 1369, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=37 tail-prime upper-bound component: plus-side exclusion and minus-side CRT floor bound. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessExclusions": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "exclusionReason": "37 divides 1591, so 1591*m + 1 is congruent to 1 mod 37 for every integer m.", + "coefficientMod1369": 222, + "gcdCoefficientSquareDivisor": 37, + "productPlusOneResidueMod37": 1, + "conclusion": "1369 never divides 1591*m + 1." + } + ], + "witnessBounds": [ + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "1369 divides 9563*m + 1", + "coefficientMod1369": 1349, + "requiredOppositeValueMod1369": 753, + "crtProgression": { + "variable": "m", + "residue": 136284, + "modulus": 231361, + "formula": "m = 136284 + 231361*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 136284) / 231361) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "The plus side is excluded. Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the minus-side q=37 raw CRT count." + }, + "checkedIdentities": [ + "1591 = 37*43, so 1591*m + 1 is congruent to 1 mod 37 for every integer m.", + "1591 mod 1369 = 222 and gcd(222, 1369) = 37.", + "9563 mod 1369 = 1349.", + "1349*753 + 1 is divisible by 1369.", + "CRT(m = 70 mod 169, m = 753 mod 1369) gives m = 136284 mod 231361.", + "The q=37 minus-side raw floor function evaluates to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 41, + "statement": "Prove the q=41 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 251571 mod 284089 and m = 26941 mod 284089.", + "completionRule": "The q=41 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=37 as a residual tail-prime upper-bound component. It intentionally leaves q=41 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=41 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..351a988 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 383, + "squareDivisor": 146689, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=383 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "146689 divides 1591*m + 1", + "coefficientMod146689": 1591, + "requiredOppositeValueMod146689": 122164, + "crtProgression": { + "variable": "m", + "residue": 10683772, + "modulus": 24790441, + "formula": "m = 10683772 + 24790441*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 10683772) / 24790441) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "146689 divides 9563*m + 1", + "coefficientMod146689": 9563, + "requiredOppositeValueMod146689": 111102, + "crtProgression": { + "variable": "m", + "residue": 8325686, + "modulus": 24790441, + "formula": "m = 8325686 + 24790441*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8325686) / 24790441) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=383 raw CRT counts." + }, + "checkedIdentities": [ + "383^2 = 146689 and 169*146689 = 24790441.", + "1591 mod 146689 = 1591 and gcd(1591, 146689) = 1.", + "1591*122164 + 1 is divisible by 146689.", + "CRT(m = 99 mod 169, m = 122164 mod 146689) gives m = 10683772 mod 24790441.", + "9563 mod 146689 = 9563 and gcd(9563, 146689) = 1.", + "9563*111102 + 1 is divisible by 146689.", + "CRT(m = 70 mod 169, m = 111102 mod 146689) gives m = 8325686 mod 24790441.", + "Both q=383 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 389, + "statement": "Prove the q=389 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 16061521 mod 25573249 and m = 4554789 mod 25573249.", + "completionRule": "The q=389 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=383 as a residual tail-prime upper-bound component. It intentionally leaves q=389 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=389 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..6eabbc7 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 389, + "squareDivisor": 151321, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=389 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "151321 divides 1591*m + 1", + "coefficientMod151321": 1591, + "requiredOppositeValueMod151321": 21495, + "crtProgression": { + "variable": "m", + "residue": 16061521, + "modulus": 25573249, + "formula": "m = 16061521 + 25573249*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 16061521) / 25573249) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "151321 divides 9563*m + 1", + "coefficientMod151321": 9563, + "requiredOppositeValueMod151321": 15159, + "crtProgression": { + "variable": "m", + "residue": 4554789, + "modulus": 25573249, + "formula": "m = 4554789 + 25573249*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4554789) / 25573249) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=389 raw CRT counts." + }, + "checkedIdentities": [ + "389^2 = 151321 and 169*151321 = 25573249.", + "1591 mod 151321 = 1591 and gcd(1591, 151321) = 1.", + "1591*21495 + 1 is divisible by 151321.", + "CRT(m = 99 mod 169, m = 21495 mod 151321) gives m = 16061521 mod 25573249.", + "9563 mod 151321 = 9563 and gcd(9563, 151321) = 1.", + "9563*15159 + 1 is divisible by 151321.", + "CRT(m = 70 mod 169, m = 15159 mod 151321) gives m = 4554789 mod 25573249.", + "Both q=389 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 397, + "statement": "Prove the q=397 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 15585955 mod 26635921 and m = 9163588 mod 26635921.", + "completionRule": "The q=397 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=389 as a residual tail-prime upper-bound component. It intentionally leaves q=397 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=397 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..94720e1 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 397, + "squareDivisor": 157609, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=397 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "157609 divides 1591*m + 1", + "coefficientMod157609": 1591, + "requiredOppositeValueMod157609": 140273, + "crtProgression": { + "variable": "m", + "residue": 15585955, + "modulus": 26635921, + "formula": "m = 15585955 + 26635921*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 15585955) / 26635921) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "157609 divides 9563*m + 1", + "coefficientMod157609": 9563, + "requiredOppositeValueMod157609": 22266, + "crtProgression": { + "variable": "m", + "residue": 9163588, + "modulus": 26635921, + "formula": "m = 9163588 + 26635921*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 9163588) / 26635921) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=397 raw CRT counts." + }, + "checkedIdentities": [ + "397^2 = 157609 and 169*157609 = 26635921.", + "1591 mod 157609 = 1591 and gcd(1591, 157609) = 1.", + "1591*140273 + 1 is divisible by 157609.", + "CRT(m = 99 mod 169, m = 140273 mod 157609) gives m = 15585955 mod 26635921.", + "9563 mod 157609 = 9563 and gcd(9563, 157609) = 1.", + "9563*22266 + 1 is divisible by 157609.", + "CRT(m = 70 mod 169, m = 22266 mod 157609) gives m = 9163588 mod 26635921.", + "Both q=397 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 401, + "statement": "Prove the q=401 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 19236186 mod 27175369 and m = 26667256 mod 27175369.", + "completionRule": "The q=401 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=397 as a residual tail-prime upper-bound component. It intentionally leaves q=401 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=401 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..2410d76 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 401, + "squareDivisor": 160801, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=401 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "160801 divides 1591*m + 1", + "coefficientMod160801": 1591, + "requiredOppositeValueMod160801": 100867, + "crtProgression": { + "variable": "m", + "residue": 19236186, + "modulus": 27175369, + "formula": "m = 19236186 + 27175369*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 19236186) / 27175369) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "160801 divides 9563*m + 1", + "coefficientMod160801": 9563, + "requiredOppositeValueMod160801": 135091, + "crtProgression": { + "variable": "m", + "residue": 26667256, + "modulus": 27175369, + "formula": "m = 26667256 + 27175369*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 26667256) / 27175369) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=401 raw CRT counts." + }, + "checkedIdentities": [ + "401^2 = 160801 and 169*160801 = 27175369.", + "1591 mod 160801 = 1591 and gcd(1591, 160801) = 1.", + "1591*100867 + 1 is divisible by 160801.", + "CRT(m = 99 mod 169, m = 100867 mod 160801) gives m = 19236186 mod 27175369.", + "9563 mod 160801 = 9563 and gcd(9563, 160801) = 1.", + "9563*135091 + 1 is divisible by 160801.", + "CRT(m = 70 mod 169, m = 135091 mod 160801) gives m = 26667256 mod 27175369.", + "Both q=401 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 409, + "statement": "Prove the q=409 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 25277936 mod 28270489 and m = 5668837 mod 28270489.", + "completionRule": "The q=409 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=401 as a residual tail-prime upper-bound component. It intentionally leaves q=409 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=409 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c004bee --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 409, + "squareDivisor": 167281, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=409 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "167281 divides 1591*m + 1", + "coefficientMod167281": 1591, + "requiredOppositeValueMod167281": 18505, + "crtProgression": { + "variable": "m", + "residue": 25277936, + "modulus": 28270489, + "formula": "m = 25277936 + 28270489*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 25277936) / 28270489) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "167281 divides 9563*m + 1", + "coefficientMod167281": 9563, + "requiredOppositeValueMod167281": 148564, + "crtProgression": { + "variable": "m", + "residue": 5668837, + "modulus": 28270489, + "formula": "m = 5668837 + 28270489*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5668837) / 28270489) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=409 raw CRT counts." + }, + "checkedIdentities": [ + "409^2 = 167281 and 169*167281 = 28270489.", + "1591 mod 167281 = 1591 and gcd(1591, 167281) = 1.", + "1591*18505 + 1 is divisible by 167281.", + "CRT(m = 99 mod 169, m = 18505 mod 167281) gives m = 25277936 mod 28270489.", + "9563 mod 167281 = 9563 and gcd(9563, 167281) = 1.", + "9563*148564 + 1 is divisible by 167281.", + "CRT(m = 70 mod 169, m = 148564 mod 167281) gives m = 5668837 mod 28270489.", + "Both q=409 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 419, + "statement": "Prove the q=419 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1254417 mod 29669809 and m = 6801644 mod 29669809.", + "completionRule": "The q=419 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=409 as a residual tail-prime upper-bound component. It intentionally leaves q=419 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=419 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..be658f1 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 419, + "squareDivisor": 175561, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=419 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "175561 divides 1591*m + 1", + "coefficientMod175561": 1591, + "requiredOppositeValueMod175561": 25490, + "crtProgression": { + "variable": "m", + "residue": 1254417, + "modulus": 29669809, + "formula": "m = 1254417 + 29669809*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 1254417) / 29669809) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "175561 divides 9563*m + 1", + "coefficientMod175561": 9563, + "requiredOppositeValueMod175561": 130326, + "crtProgression": { + "variable": "m", + "residue": 6801644, + "modulus": 29669809, + "formula": "m = 6801644 + 29669809*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6801644) / 29669809) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=419 raw CRT counts." + }, + "checkedIdentities": [ + "419^2 = 175561 and 169*175561 = 29669809.", + "1591 mod 175561 = 1591 and gcd(1591, 175561) = 1.", + "1591*25490 + 1 is divisible by 175561.", + "CRT(m = 99 mod 169, m = 25490 mod 175561) gives m = 1254417 mod 29669809.", + "9563 mod 175561 = 9563 and gcd(9563, 175561) = 1.", + "9563*130326 + 1 is divisible by 175561.", + "CRT(m = 70 mod 169, m = 130326 mod 175561) gives m = 6801644 mod 29669809.", + "Both q=419 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 421, + "statement": "Prove the q=421 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 27364072 mod 29953729 and m = 11327633 mod 29953729.", + "completionRule": "The q=421 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=419 as a residual tail-prime upper-bound component. It intentionally leaves q=421 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=421 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..915643f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 41, + "squareDivisor": 1681, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=41 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "1681 divides 1591*m + 1", + "coefficientMod1681": 1591, + "requiredOppositeValueMod1681": 1102, + "crtProgression": { + "variable": "m", + "residue": 251571, + "modulus": 284089, + "formula": "m = 251571 + 284089*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 251571) / 284089) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "1681 divides 9563*m + 1", + "coefficientMod1681": 1158, + "requiredOppositeValueMod1681": 45, + "crtProgression": { + "variable": "m", + "residue": 26941, + "modulus": 284089, + "formula": "m = 26941 + 284089*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 26941) / 284089) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=41 raw CRT counts." + }, + "checkedIdentities": [ + "41^2 = 1681 and 169*1681 = 284089.", + "1591 mod 1681 = 1591 and gcd(1591, 1681) = 1.", + "1591*1102 + 1 is divisible by 1681.", + "CRT(m = 99 mod 169, m = 1102 mod 1681) gives m = 251571 mod 284089.", + "9563 mod 1681 = 1158 and gcd(1158, 1681) = 1.", + "1158*45 + 1 is divisible by 1681.", + "CRT(m = 70 mod 169, m = 45 mod 1681) gives m = 26941 mod 284089.", + "Both q=41 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 43, + "statement": "Prove the q=43 tail-prime same-prime degree atom: plus side is excluded because 43 divides 1591, and minus side starts at m = 216897 mod 312481.", + "completionRule": "The q=43 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=41 as a residual tail-prime upper-bound component. It intentionally leaves q=43 open as the next residual tail-prime CRT/exclusion component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=43 before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..d372fcc --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 421, + "squareDivisor": 177241, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=421 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "177241 divides 1591*m + 1", + "coefficientMod177241": 1591, + "requiredOppositeValueMod177241": 68958, + "crtProgression": { + "variable": "m", + "residue": 27364072, + "modulus": 29953729, + "formula": "m = 27364072 + 29953729*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 27364072) / 29953729) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "177241 divides 9563*m + 1", + "coefficientMod177241": 9563, + "requiredOppositeValueMod177241": 161450, + "crtProgression": { + "variable": "m", + "residue": 11327633, + "modulus": 29953729, + "formula": "m = 11327633 + 29953729*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 11327633) / 29953729) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=421 raw CRT counts." + }, + "checkedIdentities": [ + "421^2 = 177241 and 169*177241 = 29953729.", + "1591 mod 177241 = 1591 and gcd(1591, 177241) = 1.", + "1591*68958 + 1 is divisible by 177241.", + "CRT(m = 99 mod 169, m = 68958 mod 177241) gives m = 27364072 mod 29953729.", + "9563 mod 177241 = 9563 and gcd(9563, 177241) = 1.", + "9563*161450 + 1 is divisible by 177241.", + "CRT(m = 70 mod 169, m = 161450 mod 177241) gives m = 11327633 mod 29953729.", + "Both q=421 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 431, + "statement": "Prove the q=431 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 30520147 mod 31393609 and m = 30076324 mod 31393609.", + "completionRule": "The q=431 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=421 as a residual tail-prime upper-bound component. It intentionally leaves q=431 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=431 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..45fde7a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 431, + "squareDivisor": 185761, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=431 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "185761 divides 1591*m + 1", + "coefficientMod185761": 1591, + "requiredOppositeValueMod185761": 55343, + "crtProgression": { + "variable": "m", + "residue": 30520147, + "modulus": 31393609, + "formula": "m = 30520147 + 31393609*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 30520147) / 31393609) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "185761 divides 9563*m + 1", + "coefficientMod185761": 9563, + "requiredOppositeValueMod185761": 168803, + "crtProgression": { + "variable": "m", + "residue": 30076324, + "modulus": 31393609, + "formula": "m = 30076324 + 31393609*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 30076324) / 31393609) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=431 raw CRT counts." + }, + "checkedIdentities": [ + "431^2 = 185761 and 169*185761 = 31393609.", + "1591 mod 185761 = 1591 and gcd(1591, 185761) = 1.", + "1591*55343 + 1 is divisible by 185761.", + "CRT(m = 99 mod 169, m = 55343 mod 185761) gives m = 30520147 mod 31393609.", + "9563 mod 185761 = 9563 and gcd(9563, 185761) = 1.", + "9563*168803 + 1 is divisible by 185761.", + "CRT(m = 70 mod 169, m = 168803 mod 185761) gives m = 30076324 mod 31393609.", + "Both q=431 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 433, + "statement": "Prove the q=433 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4441757 mod 31685641 and m = 22352010 mod 31685641.", + "completionRule": "The q=433 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=431 as a residual tail-prime upper-bound component. It intentionally leaves q=433 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=433 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c351f49 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 433, + "squareDivisor": 187489, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=433 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "187489 divides 1591*m + 1", + "coefficientMod187489": 1591, + "requiredOppositeValueMod187489": 129510, + "crtProgression": { + "variable": "m", + "residue": 4441757, + "modulus": 31685641, + "formula": "m = 4441757 + 31685641*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4441757) / 31685641) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "187489 divides 9563*m + 1", + "coefficientMod187489": 9563, + "requiredOppositeValueMod187489": 40819, + "crtProgression": { + "variable": "m", + "residue": 22352010, + "modulus": 31685641, + "formula": "m = 22352010 + 31685641*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 22352010) / 31685641) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=433 raw CRT counts." + }, + "checkedIdentities": [ + "433^2 = 187489 and 169*187489 = 31685641.", + "1591 mod 187489 = 1591 and gcd(1591, 187489) = 1.", + "1591*129510 + 1 is divisible by 187489.", + "CRT(m = 99 mod 169, m = 129510 mod 187489) gives m = 4441757 mod 31685641.", + "9563 mod 187489 = 9563 and gcd(9563, 187489) = 1.", + "9563*40819 + 1 is divisible by 187489.", + "CRT(m = 70 mod 169, m = 40819 mod 187489) gives m = 22352010 mod 31685641.", + "Both q=433 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 439, + "statement": "Prove the q=439 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 31660390 mod 32569849 and m = 32568398 mod 32569849.", + "completionRule": "The q=439 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=433 as a residual tail-prime upper-bound component. It intentionally leaves q=439 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=439 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..e832f2d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 439, + "squareDivisor": 192721, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=439 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "192721 divides 1591*m + 1", + "coefficientMod192721": 1591, + "requiredOppositeValueMod192721": 54146, + "crtProgression": { + "variable": "m", + "residue": 31660390, + "modulus": 32569849, + "formula": "m = 31660390 + 32569849*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 31660390) / 32569849) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "192721 divides 9563*m + 1", + "coefficientMod192721": 9563, + "requiredOppositeValueMod192721": 191270, + "crtProgression": { + "variable": "m", + "residue": 32568398, + "modulus": 32569849, + "formula": "m = 32568398 + 32569849*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 32568398) / 32569849) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=439 raw CRT counts." + }, + "checkedIdentities": [ + "439^2 = 192721 and 169*192721 = 32569849.", + "1591 mod 192721 = 1591 and gcd(1591, 192721) = 1.", + "1591*54146 + 1 is divisible by 192721.", + "CRT(m = 99 mod 169, m = 54146 mod 192721) gives m = 31660390 mod 32569849.", + "9563 mod 192721 = 9563 and gcd(9563, 192721) = 1.", + "9563*191270 + 1 is divisible by 192721.", + "CRT(m = 70 mod 169, m = 191270 mod 192721) gives m = 32568398 mod 32569849.", + "Both q=439 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 443, + "statement": "Prove the q=443 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 17292855 mod 33166081 and m = 15525424 mod 33166081.", + "completionRule": "The q=443 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=439 as a residual tail-prime upper-bound component. It intentionally leaves q=443 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=443 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..5a840b6 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,81 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "witness_divisibility_exclusion_plus_crt_floor_function_tail_prime_upper_bound", + "q": 43, + "squareDivisor": 1849, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=43 tail-prime upper-bound component: plus-side exclusion and minus-side CRT floor bound. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessExclusions": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "exclusionReason": "43 divides 1591, so 1591*m + 1 is congruent to 1 mod 43 for every integer m.", + "coefficientMod1849": 1591, + "gcdCoefficientSquareDivisor": 43, + "productPlusOneResidueMod43": 1, + "conclusion": "1849 never divides 1591*m + 1." + } + ], + "witnessBounds": [ + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "1849 divides 9563*m + 1", + "coefficientMod1849": 318, + "requiredOppositeValueMod1849": 564, + "crtProgression": { + "variable": "m", + "residue": 216897, + "modulus": 312481, + "formula": "m = 216897 + 312481*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 216897) / 312481) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "The plus side is excluded. Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the minus-side q=43 raw CRT count." + }, + "checkedIdentities": [ + "1591 = 37*43, so 1591*m + 1 is congruent to 1 mod 43 for every integer m.", + "1591 mod 1849 = 1591 and gcd(1591, 1849) = 43.", + "9563 mod 1849 = 318 and gcd(318, 1849) = 1.", + "318*564 + 1 is divisible by 1849.", + "CRT(m = 70 mod 169, m = 564 mod 1849) gives m = 216897 mod 312481.", + "The q=43 minus-side raw floor function evaluates to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 47, + "statement": "Prove the q=47 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 267457 mod 373321 and m = 278413 mod 373321.", + "completionRule": "The q=47 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=43 as a residual tail-prime upper-bound component. It intentionally leaves q=47 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=47 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..17df69a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 443, + "squareDivisor": 196249, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=443 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "196249 divides 1591*m + 1", + "coefficientMod196249": 1591, + "requiredOppositeValueMod196249": 22943, + "crtProgression": { + "variable": "m", + "residue": 17292855, + "modulus": 33166081, + "formula": "m = 17292855 + 33166081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 17292855) / 33166081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "196249 divides 9563*m + 1", + "coefficientMod196249": 9563, + "requiredOppositeValueMod196249": 21753, + "crtProgression": { + "variable": "m", + "residue": 15525424, + "modulus": 33166081, + "formula": "m = 15525424 + 33166081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 15525424) / 33166081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=443 raw CRT counts." + }, + "checkedIdentities": [ + "443^2 = 196249 and 169*196249 = 33166081.", + "1591 mod 196249 = 1591 and gcd(1591, 196249) = 1.", + "1591*22943 + 1 is divisible by 196249.", + "CRT(m = 99 mod 169, m = 22943 mod 196249) gives m = 17292855 mod 33166081.", + "9563 mod 196249 = 9563 and gcd(9563, 196249) = 1.", + "9563*21753 + 1 is divisible by 196249.", + "CRT(m = 70 mod 169, m = 21753 mod 196249) gives m = 15525424 mod 33166081.", + "Both q=443 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 449, + "statement": "Prove the q=449 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10624284 mod 34070569 and m = 9976140 mod 34070569.", + "completionRule": "The q=449 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=443 as a residual tail-prime upper-bound component. It intentionally leaves q=449 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=449 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..fedbb2e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 449, + "squareDivisor": 201601, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=449 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "201601 divides 1591*m + 1", + "coefficientMod201601": 1591, + "requiredOppositeValueMod201601": 141032, + "crtProgression": { + "variable": "m", + "residue": 10624284, + "modulus": 34070569, + "formula": "m = 10624284 + 34070569*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 10624284) / 34070569) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "201601 divides 9563*m + 1", + "coefficientMod201601": 9563, + "requiredOppositeValueMod201601": 97691, + "crtProgression": { + "variable": "m", + "residue": 9976140, + "modulus": 34070569, + "formula": "m = 9976140 + 34070569*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 9976140) / 34070569) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=449 raw CRT counts." + }, + "checkedIdentities": [ + "449^2 = 201601 and 169*201601 = 34070569.", + "1591 mod 201601 = 1591 and gcd(1591, 201601) = 1.", + "1591*141032 + 1 is divisible by 201601.", + "CRT(m = 99 mod 169, m = 141032 mod 201601) gives m = 10624284 mod 34070569.", + "9563 mod 201601 = 9563 and gcd(9563, 201601) = 1.", + "9563*97691 + 1 is divisible by 201601.", + "CRT(m = 70 mod 169, m = 97691 mod 201601) gives m = 9976140 mod 34070569.", + "Both q=449 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 457, + "statement": "Prove the q=457 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 33113790 mod 35295481 and m = 7601859 mod 35295481.", + "completionRule": "The q=457 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=449 as a residual tail-prime upper-bound component. It intentionally leaves q=457 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=457 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..ed68574 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 457, + "squareDivisor": 208849, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=457 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "208849 divides 1591*m + 1", + "coefficientMod208849": 1591, + "requiredOppositeValueMod208849": 115648, + "crtProgression": { + "variable": "m", + "residue": 33113790, + "modulus": 35295481, + "formula": "m = 33113790 + 35295481*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 33113790) / 35295481) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "208849 divides 9563*m + 1", + "coefficientMod208849": 9563, + "requiredOppositeValueMod208849": 83295, + "crtProgression": { + "variable": "m", + "residue": 7601859, + "modulus": 35295481, + "formula": "m = 7601859 + 35295481*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 7601859) / 35295481) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=457 raw CRT counts." + }, + "checkedIdentities": [ + "457^2 = 208849 and 169*208849 = 35295481.", + "1591 mod 208849 = 1591 and gcd(1591, 208849) = 1.", + "1591*115648 + 1 is divisible by 208849.", + "CRT(m = 99 mod 169, m = 115648 mod 208849) gives m = 33113790 mod 35295481.", + "9563 mod 208849 = 9563 and gcd(9563, 208849) = 1.", + "9563*83295 + 1 is divisible by 208849.", + "CRT(m = 70 mod 169, m = 83295 mod 208849) gives m = 7601859 mod 35295481.", + "Both q=457 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 461, + "statement": "Prove the q=461 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 709561 mod 35916049 and m = 6592929 mod 35916049.", + "completionRule": "The q=461 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=457 as a residual tail-prime upper-bound component. It intentionally leaves q=461 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=461 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..b6a4101 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 461, + "squareDivisor": 212521, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=461 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "212521 divides 1591*m + 1", + "coefficientMod212521": 1591, + "requiredOppositeValueMod212521": 71998, + "crtProgression": { + "variable": "m", + "residue": 709561, + "modulus": 35916049, + "formula": "m = 709561 + 35916049*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 709561) / 35916049) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "212521 divides 9563*m + 1", + "coefficientMod212521": 9563, + "requiredOppositeValueMod212521": 4778, + "crtProgression": { + "variable": "m", + "residue": 6592929, + "modulus": 35916049, + "formula": "m = 6592929 + 35916049*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6592929) / 35916049) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=461 raw CRT counts." + }, + "checkedIdentities": [ + "461^2 = 212521 and 169*212521 = 35916049.", + "1591 mod 212521 = 1591 and gcd(1591, 212521) = 1.", + "1591*71998 + 1 is divisible by 212521.", + "CRT(m = 99 mod 169, m = 71998 mod 212521) gives m = 709561 mod 35916049.", + "9563 mod 212521 = 9563 and gcd(9563, 212521) = 1.", + "9563*4778 + 1 is divisible by 212521.", + "CRT(m = 70 mod 169, m = 4778 mod 212521) gives m = 6592929 mod 35916049.", + "Both q=461 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 463, + "statement": "Prove the q=463 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5329852 mod 36228361 and m = 31534794 mod 36228361.", + "completionRule": "The q=463 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=461 as a residual tail-prime upper-bound component. It intentionally leaves q=463 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=463 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..91ff148 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 463, + "squareDivisor": 214369, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=463 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "214369 divides 1591*m + 1", + "coefficientMod214369": 1591, + "requiredOppositeValueMod214369": 184996, + "crtProgression": { + "variable": "m", + "residue": 5329852, + "modulus": 36228361, + "formula": "m = 5329852 + 36228361*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5329852) / 36228361) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "214369 divides 9563*m + 1", + "coefficientMod214369": 9563, + "requiredOppositeValueMod214369": 22551, + "crtProgression": { + "variable": "m", + "residue": 31534794, + "modulus": 36228361, + "formula": "m = 31534794 + 36228361*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 31534794) / 36228361) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=463 raw CRT counts." + }, + "checkedIdentities": [ + "463^2 = 214369 and 169*214369 = 36228361.", + "1591 mod 214369 = 1591 and gcd(1591, 214369) = 1.", + "1591*184996 + 1 is divisible by 214369.", + "CRT(m = 99 mod 169, m = 184996 mod 214369) gives m = 5329852 mod 36228361.", + "9563 mod 214369 = 9563 and gcd(9563, 214369) = 1.", + "9563*22551 + 1 is divisible by 214369.", + "CRT(m = 70 mod 169, m = 22551 mod 214369) gives m = 31534794 mod 36228361.", + "Both q=463 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 467, + "statement": "Prove the q=467 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4056099 mod 36857041 and m = 5739141 mod 36857041.", + "completionRule": "The q=467 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=463 as a residual tail-prime upper-bound component. It intentionally leaves q=467 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=467 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..78474d8 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 467, + "squareDivisor": 218089, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=467 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "218089 divides 1591*m + 1", + "coefficientMod218089": 1591, + "requiredOppositeValueMod218089": 130497, + "crtProgression": { + "variable": "m", + "residue": 4056099, + "modulus": 36857041, + "formula": "m = 4056099 + 36857041*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 4056099) / 36857041) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "218089 divides 9563*m + 1", + "coefficientMod218089": 9563, + "requiredOppositeValueMod218089": 68827, + "crtProgression": { + "variable": "m", + "residue": 5739141, + "modulus": 36857041, + "formula": "m = 5739141 + 36857041*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5739141) / 36857041) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=467 raw CRT counts." + }, + "checkedIdentities": [ + "467^2 = 218089 and 169*218089 = 36857041.", + "1591 mod 218089 = 1591 and gcd(1591, 218089) = 1.", + "1591*130497 + 1 is divisible by 218089.", + "CRT(m = 99 mod 169, m = 130497 mod 218089) gives m = 4056099 mod 36857041.", + "9563 mod 218089 = 9563 and gcd(9563, 218089) = 1.", + "9563*68827 + 1 is divisible by 218089.", + "CRT(m = 70 mod 169, m = 68827 mod 218089) gives m = 5739141 mod 36857041.", + "Both q=467 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 479, + "statement": "Prove the q=479 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 24650270 mod 38775529 and m = 37033716 mod 38775529.", + "completionRule": "The q=479 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=467 as a residual tail-prime upper-bound component. It intentionally leaves q=479 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=479 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..3bbbcee --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 479, + "squareDivisor": 229441, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=479 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "229441 divides 1591*m + 1", + "coefficientMod229441": 1591, + "requiredOppositeValueMod229441": 100083, + "crtProgression": { + "variable": "m", + "residue": 24650270, + "modulus": 38775529, + "formula": "m = 24650270 + 38775529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 24650270) / 38775529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "229441 divides 9563*m + 1", + "coefficientMod229441": 9563, + "requiredOppositeValueMod229441": 93715, + "crtProgression": { + "variable": "m", + "residue": 37033716, + "modulus": 38775529, + "formula": "m = 37033716 + 38775529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 37033716) / 38775529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=479 raw CRT counts." + }, + "checkedIdentities": [ + "479^2 = 229441 and 169*229441 = 38775529.", + "1591 mod 229441 = 1591 and gcd(1591, 229441) = 1.", + "1591*100083 + 1 is divisible by 229441.", + "CRT(m = 99 mod 169, m = 100083 mod 229441) gives m = 24650270 mod 38775529.", + "9563 mod 229441 = 9563 and gcd(9563, 229441) = 1.", + "9563*93715 + 1 is divisible by 229441.", + "CRT(m = 70 mod 169, m = 93715 mod 229441) gives m = 37033716 mod 38775529.", + "Both q=479 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 487, + "statement": "Prove the q=487 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 21019643 mod 40081561 and m = 36495282 mod 40081561.", + "completionRule": "The q=487 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=479 as a residual tail-prime upper-bound component. It intentionally leaves q=487 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=487 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..3188950 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 47, + "squareDivisor": 2209, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=47 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "2209 divides 1591*m + 1", + "coefficientMod2209": 1591, + "requiredOppositeValueMod2209": 168, + "crtProgression": { + "variable": "m", + "residue": 267457, + "modulus": 373321, + "formula": "m = 267457 + 373321*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 267457) / 373321) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "2209 divides 9563*m + 1", + "coefficientMod2209": 727, + "requiredOppositeValueMod2209": 79, + "crtProgression": { + "variable": "m", + "residue": 278413, + "modulus": 373321, + "formula": "m = 278413 + 373321*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 278413) / 373321) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=47 raw CRT counts." + }, + "checkedIdentities": [ + "47^2 = 2209 and 169*2209 = 373321.", + "1591 mod 2209 = 1591 and gcd(1591, 2209) = 1.", + "1591*168 + 1 is divisible by 2209.", + "CRT(m = 99 mod 169, m = 168 mod 2209) gives m = 267457 mod 373321.", + "9563 mod 2209 = 727 and gcd(727, 2209) = 1.", + "727*79 + 1 is divisible by 2209.", + "CRT(m = 70 mod 169, m = 79 mod 2209) gives m = 278413 mod 373321.", + "Both q=47 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 53, + "statement": "Prove the q=53 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 52151 mod 474721 and m = 213348 mod 474721.", + "completionRule": "The q=53 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=47 as a residual tail-prime upper-bound component. It intentionally leaves q=53 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=53 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..debd4e8 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 487, + "squareDivisor": 237169, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=487 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "237169 divides 1591*m + 1", + "coefficientMod237169": 1591, + "requiredOppositeValueMod237169": 148771, + "crtProgression": { + "variable": "m", + "residue": 21019643, + "modulus": 40081561, + "formula": "m = 21019643 + 40081561*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 21019643) / 40081561) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "237169 divides 9563*m + 1", + "coefficientMod237169": 9563, + "requiredOppositeValueMod237169": 208425, + "crtProgression": { + "variable": "m", + "residue": 36495282, + "modulus": 40081561, + "formula": "m = 36495282 + 40081561*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 36495282) / 40081561) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=487 raw CRT counts." + }, + "checkedIdentities": [ + "487^2 = 237169 and 169*237169 = 40081561.", + "1591 mod 237169 = 1591 and gcd(1591, 237169) = 1.", + "1591*148771 + 1 is divisible by 237169.", + "CRT(m = 99 mod 169, m = 148771 mod 237169) gives m = 21019643 mod 40081561.", + "9563 mod 237169 = 9563 and gcd(9563, 237169) = 1.", + "9563*208425 + 1 is divisible by 237169.", + "CRT(m = 70 mod 169, m = 208425 mod 237169) gives m = 36495282 mod 40081561.", + "Both q=487 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 491, + "statement": "Prove the q=491 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8394498 mod 40742689 and m = 21433495 mod 40742689.", + "completionRule": "The q=491 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=487 as a residual tail-prime upper-bound component. It intentionally leaves q=491 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=491 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..8bbc236 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 491, + "squareDivisor": 241081, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=491 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "241081 divides 1591*m + 1", + "coefficientMod241081": 1591, + "requiredOppositeValueMod241081": 197744, + "crtProgression": { + "variable": "m", + "residue": 8394498, + "modulus": 40742689, + "formula": "m = 8394498 + 40742689*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8394498) / 40742689) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "241081 divides 9563*m + 1", + "coefficientMod241081": 9563, + "requiredOppositeValueMod241081": 218367, + "crtProgression": { + "variable": "m", + "residue": 21433495, + "modulus": 40742689, + "formula": "m = 21433495 + 40742689*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 21433495) / 40742689) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=491 raw CRT counts." + }, + "checkedIdentities": [ + "491^2 = 241081 and 169*241081 = 40742689.", + "1591 mod 241081 = 1591 and gcd(1591, 241081) = 1.", + "1591*197744 + 1 is divisible by 241081.", + "CRT(m = 99 mod 169, m = 197744 mod 241081) gives m = 8394498 mod 40742689.", + "9563 mod 241081 = 9563 and gcd(9563, 241081) = 1.", + "9563*218367 + 1 is divisible by 241081.", + "CRT(m = 70 mod 169, m = 218367 mod 241081) gives m = 21433495 mod 40742689.", + "Both q=491 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 499, + "statement": "Prove the q=499 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8072891 mod 42081169 and m = 26746686 mod 42081169.", + "completionRule": "The q=499 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=491 as a residual tail-prime upper-bound component. It intentionally leaves q=499 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=499 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..ecbd2cb --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 499, + "squareDivisor": 249001, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=499 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "249001 divides 1591*m + 1", + "coefficientMod249001": 1591, + "requiredOppositeValueMod249001": 104859, + "crtProgression": { + "variable": "m", + "residue": 8072891, + "modulus": 42081169, + "formula": "m = 8072891 + 42081169*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8072891) / 42081169) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "249001 divides 9563*m + 1", + "coefficientMod249001": 9563, + "requiredOppositeValueMod249001": 103579, + "crtProgression": { + "variable": "m", + "residue": 26746686, + "modulus": 42081169, + "formula": "m = 26746686 + 42081169*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 26746686) / 42081169) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=499 raw CRT counts." + }, + "checkedIdentities": [ + "499^2 = 249001 and 169*249001 = 42081169.", + "1591 mod 249001 = 1591 and gcd(1591, 249001) = 1.", + "1591*104859 + 1 is divisible by 249001.", + "CRT(m = 99 mod 169, m = 104859 mod 249001) gives m = 8072891 mod 42081169.", + "9563 mod 249001 = 9563 and gcd(9563, 249001) = 1.", + "9563*103579 + 1 is divisible by 249001.", + "CRT(m = 70 mod 169, m = 103579 mod 249001) gives m = 26746686 mod 42081169.", + "Both q=499 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 503, + "statement": "Prove the q=503 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 42056425 mod 42758521 and m = 19404650 mod 42758521.", + "completionRule": "The q=503 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=499 as a residual tail-prime upper-bound component. It intentionally leaves q=503 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=503 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..7d0ea0c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 503, + "squareDivisor": 253009, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=503 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "253009 divides 1591*m + 1", + "coefficientMod253009": 1591, + "requiredOppositeValueMod253009": 56931, + "crtProgression": { + "variable": "m", + "residue": 42056425, + "modulus": 42758521, + "formula": "m = 42056425 + 42758521*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 42056425) / 42758521) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "253009 divides 9563*m + 1", + "coefficientMod253009": 9563, + "requiredOppositeValueMod253009": 175966, + "crtProgression": { + "variable": "m", + "residue": 19404650, + "modulus": 42758521, + "formula": "m = 19404650 + 42758521*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 19404650) / 42758521) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=503 raw CRT counts." + }, + "checkedIdentities": [ + "503^2 = 253009 and 169*253009 = 42758521.", + "1591 mod 253009 = 1591 and gcd(1591, 253009) = 1.", + "1591*56931 + 1 is divisible by 253009.", + "CRT(m = 99 mod 169, m = 56931 mod 253009) gives m = 42056425 mod 42758521.", + "9563 mod 253009 = 9563 and gcd(9563, 253009) = 1.", + "9563*175966 + 1 is divisible by 253009.", + "CRT(m = 70 mod 169, m = 175966 mod 253009) gives m = 19404650 mod 42758521.", + "Both q=503 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 509, + "statement": "Prove the q=509 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 68882 mod 43784689 and m = 22331899 mod 43784689.", + "completionRule": "The q=509 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=503 as a residual tail-prime upper-bound component. It intentionally leaves q=509 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=509 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..740cd15 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 509, + "squareDivisor": 259081, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=509 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "259081 divides 1591*m + 1", + "coefficientMod259081": 1591, + "requiredOppositeValueMod259081": 68882, + "crtProgression": { + "variable": "m", + "residue": 68882, + "modulus": 43784689, + "formula": "m = 68882 + 43784689*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 68882) / 43784689) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "259081 divides 9563*m + 1", + "coefficientMod259081": 9563, + "requiredOppositeValueMod259081": 50933, + "crtProgression": { + "variable": "m", + "residue": 22331899, + "modulus": 43784689, + "formula": "m = 22331899 + 43784689*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 22331899) / 43784689) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=509 raw CRT counts." + }, + "checkedIdentities": [ + "509^2 = 259081 and 169*259081 = 43784689.", + "1591 mod 259081 = 1591 and gcd(1591, 259081) = 1.", + "1591*68882 + 1 is divisible by 259081.", + "CRT(m = 99 mod 169, m = 68882 mod 259081) gives m = 68882 mod 43784689.", + "9563 mod 259081 = 9563 and gcd(9563, 259081) = 1.", + "9563*50933 + 1 is divisible by 259081.", + "CRT(m = 70 mod 169, m = 50933 mod 259081) gives m = 22331899 mod 43784689.", + "Both q=509 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 521, + "statement": "Prove the q=521 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 37647553 mod 45873529 and m = 27667567 mod 45873529.", + "completionRule": "The q=521 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=509 as a residual tail-prime upper-bound component. It intentionally leaves q=521 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=521 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..fada1a0 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 521, + "squareDivisor": 271441, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=521 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "271441 divides 1591*m + 1", + "coefficientMod271441": 1591, + "requiredOppositeValueMod271441": 188695, + "crtProgression": { + "variable": "m", + "residue": 37647553, + "modulus": 45873529, + "formula": "m = 37647553 + 45873529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 37647553) / 45873529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "271441 divides 9563*m + 1", + "coefficientMod271441": 9563, + "requiredOppositeValueMod271441": 252026, + "crtProgression": { + "variable": "m", + "residue": 27667567, + "modulus": 45873529, + "formula": "m = 27667567 + 45873529*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 27667567) / 45873529) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=521 raw CRT counts." + }, + "checkedIdentities": [ + "521^2 = 271441 and 169*271441 = 45873529.", + "1591 mod 271441 = 1591 and gcd(1591, 271441) = 1.", + "1591*188695 + 1 is divisible by 271441.", + "CRT(m = 99 mod 169, m = 188695 mod 271441) gives m = 37647553 mod 45873529.", + "9563 mod 271441 = 9563 and gcd(9563, 271441) = 1.", + "9563*252026 + 1 is divisible by 271441.", + "CRT(m = 70 mod 169, m = 252026 mod 271441) gives m = 27667567 mod 45873529.", + "Both q=521 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 523, + "statement": "Prove the q=523 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5572874 mod 46226401 and m = 8835390 mod 46226401.", + "completionRule": "The q=523 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=521 as a residual tail-prime upper-bound component. It intentionally leaves q=523 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=523 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..050e266 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 523, + "squareDivisor": 273529, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=523 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "273529 divides 1591*m + 1", + "coefficientMod273529": 1591, + "requiredOppositeValueMod273529": 102294, + "crtProgression": { + "variable": "m", + "residue": 5572874, + "modulus": 46226401, + "formula": "m = 5572874 + 46226401*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 5572874) / 46226401) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "273529 divides 9563*m + 1", + "coefficientMod273529": 9563, + "requiredOppositeValueMod273529": 82462, + "crtProgression": { + "variable": "m", + "residue": 8835390, + "modulus": 46226401, + "formula": "m = 8835390 + 46226401*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 8835390) / 46226401) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=523 raw CRT counts." + }, + "checkedIdentities": [ + "523^2 = 273529 and 169*273529 = 46226401.", + "1591 mod 273529 = 1591 and gcd(1591, 273529) = 1.", + "1591*102294 + 1 is divisible by 273529.", + "CRT(m = 99 mod 169, m = 102294 mod 273529) gives m = 5572874 mod 46226401.", + "9563 mod 273529 = 9563 and gcd(9563, 273529) = 1.", + "9563*82462 + 1 is divisible by 273529.", + "CRT(m = 70 mod 169, m = 82462 mod 273529) gives m = 8835390 mod 46226401.", + "Both q=523 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 541, + "statement": "Prove the q=541 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6164881 mod 49463089 and m = 2567011 mod 49463089.", + "completionRule": "The q=541 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=523 as a residual tail-prime upper-bound component. It intentionally leaves q=541 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=541 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..41780c0 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 53, + "squareDivisor": 2809, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=53 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "2809 divides 1591*m + 1", + "coefficientMod2809": 1591, + "requiredOppositeValueMod2809": 1589, + "crtProgression": { + "variable": "m", + "residue": 52151, + "modulus": 474721, + "formula": "m = 52151 + 474721*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 52151) / 474721) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "2809 divides 9563*m + 1", + "coefficientMod2809": 1136, + "requiredOppositeValueMod2809": 2673, + "crtProgression": { + "variable": "m", + "residue": 213348, + "modulus": 474721, + "formula": "m = 213348 + 474721*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 213348) / 474721) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=53 raw CRT counts." + }, + "checkedIdentities": [ + "53^2 = 2809 and 169*2809 = 474721.", + "1591 mod 2809 = 1591 and gcd(1591, 2809) = 1.", + "1591*1589 + 1 is divisible by 2809.", + "CRT(m = 99 mod 169, m = 1589 mod 2809) gives m = 52151 mod 474721.", + "9563 mod 2809 = 1136 and gcd(1136, 2809) = 1.", + "1136*2673 + 1 is divisible by 2809.", + "CRT(m = 70 mod 169, m = 2673 mod 2809) gives m = 213348 mod 474721.", + "Both q=53 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 59, + "statement": "Prove the q=59 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 182281 mod 588289 and m = 492874 mod 588289.", + "completionRule": "The q=59 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=53 as a residual tail-prime upper-bound component. It intentionally leaves q=59 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=59 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..e85bc4b --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 541, + "squareDivisor": 292681, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=541 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "292681 divides 1591*m + 1", + "coefficientMod292681": 1591, + "requiredOppositeValueMod292681": 18580, + "crtProgression": { + "variable": "m", + "residue": 6164881, + "modulus": 49463089, + "formula": "m = 6164881 + 49463089*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 6164881) / 49463089) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "292681 divides 9563*m + 1", + "coefficientMod292681": 9563, + "requiredOppositeValueMod292681": 225563, + "crtProgression": { + "variable": "m", + "residue": 2567011, + "modulus": 49463089, + "formula": "m = 2567011 + 49463089*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 2567011) / 49463089) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=541 raw CRT counts." + }, + "checkedIdentities": [ + "541^2 = 292681 and 169*292681 = 49463089.", + "1591 mod 292681 = 1591 and gcd(1591, 292681) = 1.", + "1591*18580 + 1 is divisible by 292681.", + "CRT(m = 99 mod 169, m = 18580 mod 292681) gives m = 6164881 mod 49463089.", + "9563 mod 292681 = 9563 and gcd(9563, 292681) = 1.", + "9563*225563 + 1 is divisible by 292681.", + "CRT(m = 70 mod 169, m = 225563 mod 292681) gives m = 2567011 mod 49463089.", + "Both q=541 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 547, + "statement": "Prove the q=547 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 34995605 mod 50566321 and m = 25423754 mod 50566321.", + "completionRule": "The q=547 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=541 as a residual tail-prime upper-bound component. It intentionally leaves q=547 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=547 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..c641121 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 547, + "squareDivisor": 299209, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=547 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "299209 divides 1591*m + 1", + "coefficientMod299209": 1591, + "requiredOppositeValueMod299209": 287361, + "crtProgression": { + "variable": "m", + "residue": 34995605, + "modulus": 50566321, + "formula": "m = 34995605 + 50566321*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 34995605) / 50566321) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "299209 divides 9563*m + 1", + "coefficientMod299209": 9563, + "requiredOppositeValueMod299209": 290198, + "crtProgression": { + "variable": "m", + "residue": 25423754, + "modulus": 50566321, + "formula": "m = 25423754 + 50566321*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 25423754) / 50566321) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=547 raw CRT counts." + }, + "checkedIdentities": [ + "547^2 = 299209 and 169*299209 = 50566321.", + "1591 mod 299209 = 1591 and gcd(1591, 299209) = 1.", + "1591*287361 + 1 is divisible by 299209.", + "CRT(m = 99 mod 169, m = 287361 mod 299209) gives m = 34995605 mod 50566321.", + "9563 mod 299209 = 9563 and gcd(9563, 299209) = 1.", + "9563*290198 + 1 is divisible by 299209.", + "CRT(m = 70 mod 169, m = 290198 mod 299209) gives m = 25423754 mod 50566321.", + "Both q=547 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 557, + "statement": "Prove the q=557 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 45994463 mod 52432081 and m = 41289136 mod 52432081.", + "completionRule": "The q=557 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=547 as a residual tail-prime upper-bound component. It intentionally leaves q=557 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=557 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..6f66689 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 557, + "squareDivisor": 310249, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=557 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "310249 divides 1591*m + 1", + "coefficientMod310249": 1591, + "requiredOppositeValueMod310249": 77611, + "crtProgression": { + "variable": "m", + "residue": 45994463, + "modulus": 52432081, + "formula": "m = 45994463 + 52432081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 45994463) / 52432081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "310249 divides 9563*m + 1", + "coefficientMod310249": 9563, + "requiredOppositeValueMod310249": 26019, + "crtProgression": { + "variable": "m", + "residue": 41289136, + "modulus": 52432081, + "formula": "m = 41289136 + 52432081*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 41289136) / 52432081) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=557 raw CRT counts." + }, + "checkedIdentities": [ + "557^2 = 310249 and 169*310249 = 52432081.", + "1591 mod 310249 = 1591 and gcd(1591, 310249) = 1.", + "1591*77611 + 1 is divisible by 310249.", + "CRT(m = 99 mod 169, m = 77611 mod 310249) gives m = 45994463 mod 52432081.", + "9563 mod 310249 = 9563 and gcd(9563, 310249) = 1.", + "9563*26019 + 1 is divisible by 310249.", + "CRT(m = 70 mod 169, m = 26019 mod 310249) gives m = 41289136 mod 52432081.", + "Both q=557 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 563, + "statement": "Prove the q=563 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 42763521 mod 53567761 and m = 381503 mod 53567761.", + "completionRule": "The q=563 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=557 as a residual tail-prime upper-bound component. It intentionally leaves q=563 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=563 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..cad93ad --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 563, + "squareDivisor": 316969, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=563 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "316969 divides 1591*m + 1", + "coefficientMod316969": 1591, + "requiredOppositeValueMod316969": 289675, + "crtProgression": { + "variable": "m", + "residue": 42763521, + "modulus": 53567761, + "formula": "m = 42763521 + 53567761*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 42763521) / 53567761) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "316969 divides 9563*m + 1", + "coefficientMod316969": 9563, + "requiredOppositeValueMod316969": 64534, + "crtProgression": { + "variable": "m", + "residue": 381503, + "modulus": 53567761, + "formula": "m = 381503 + 53567761*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 381503) / 53567761) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=563 raw CRT counts." + }, + "checkedIdentities": [ + "563^2 = 316969 and 169*316969 = 53567761.", + "1591 mod 316969 = 1591 and gcd(1591, 316969) = 1.", + "1591*289675 + 1 is divisible by 316969.", + "CRT(m = 99 mod 169, m = 289675 mod 316969) gives m = 42763521 mod 53567761.", + "9563 mod 316969 = 9563 and gcd(9563, 316969) = 1.", + "9563*64534 + 1 is divisible by 316969.", + "CRT(m = 70 mod 169, m = 64534 mod 316969) gives m = 381503 mod 53567761.", + "Both q=563 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 569, + "statement": "Prove the q=569 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 13641103 mod 54715609 and m = 17025468 mod 54715609.", + "completionRule": "The q=569 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=563 as a residual tail-prime upper-bound component. It intentionally leaves q=569 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=569 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..03becb5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 569, + "squareDivisor": 323761, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=569 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "323761 divides 1591*m + 1", + "coefficientMod323761": 1591, + "requiredOppositeValueMod323761": 43141, + "crtProgression": { + "variable": "m", + "residue": 13641103, + "modulus": 54715609, + "formula": "m = 13641103 + 54715609*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 13641103) / 54715609) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "323761 divides 9563*m + 1", + "coefficientMod323761": 9563, + "requiredOppositeValueMod323761": 189896, + "crtProgression": { + "variable": "m", + "residue": 17025468, + "modulus": 54715609, + "formula": "m = 17025468 + 54715609*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 17025468) / 54715609) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=569 raw CRT counts." + }, + "checkedIdentities": [ + "569^2 = 323761 and 169*323761 = 54715609.", + "1591 mod 323761 = 1591 and gcd(1591, 323761) = 1.", + "1591*43141 + 1 is divisible by 323761.", + "CRT(m = 99 mod 169, m = 43141 mod 323761) gives m = 13641103 mod 54715609.", + "9563 mod 323761 = 9563 and gcd(9563, 323761) = 1.", + "9563*189896 + 1 is divisible by 323761.", + "CRT(m = 70 mod 169, m = 189896 mod 323761) gives m = 17025468 mod 54715609.", + "Both q=569 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 571, + "statement": "Prove the q=571 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 28625826 mod 55100929 and m = 25724236 mod 55100929.", + "completionRule": "The q=571 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=569 as a residual tail-prime upper-bound component. It intentionally leaves q=571 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=571 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..4111187 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 571, + "squareDivisor": 326041, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=571 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "326041 divides 1591*m + 1", + "coefficientMod326041": 1591, + "requiredOppositeValueMod326041": 260259, + "crtProgression": { + "variable": "m", + "residue": 28625826, + "modulus": 55100929, + "formula": "m = 28625826 + 55100929*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 28625826) / 55100929) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "326041 divides 9563*m + 1", + "coefficientMod326041": 9563, + "requiredOppositeValueMod326041": 293038, + "crtProgression": { + "variable": "m", + "residue": 25724236, + "modulus": 55100929, + "formula": "m = 25724236 + 55100929*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 25724236) / 55100929) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=571 raw CRT counts." + }, + "checkedIdentities": [ + "571^2 = 326041 and 169*326041 = 55100929.", + "1591 mod 326041 = 1591 and gcd(1591, 326041) = 1.", + "1591*260259 + 1 is divisible by 326041.", + "CRT(m = 99 mod 169, m = 260259 mod 326041) gives m = 28625826 mod 55100929.", + "9563 mod 326041 = 9563 and gcd(9563, 326041) = 1.", + "9563*293038 + 1 is divisible by 326041.", + "CRT(m = 70 mod 169, m = 293038 mod 326041) gives m = 25724236 mod 55100929.", + "Both q=571 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 577, + "statement": "Prove the q=577 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 22102426 mod 56265001 and m = 9319575 mod 56265001.", + "completionRule": "The q=577 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=571 as a residual tail-prime upper-bound component. It intentionally leaves q=577 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=577 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..3059b47 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 577, + "squareDivisor": 332929, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=577 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "332929 divides 1591*m + 1", + "coefficientMod332929": 1591, + "requiredOppositeValueMod332929": 129112, + "crtProgression": { + "variable": "m", + "residue": 22102426, + "modulus": 56265001, + "formula": "m = 22102426 + 56265001*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 22102426) / 56265001) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "332929 divides 9563*m + 1", + "coefficientMod332929": 9563, + "requiredOppositeValueMod332929": 330492, + "crtProgression": { + "variable": "m", + "residue": 9319575, + "modulus": 56265001, + "formula": "m = 9319575 + 56265001*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 9319575) / 56265001) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=577 raw CRT counts." + }, + "checkedIdentities": [ + "577^2 = 332929 and 169*332929 = 56265001.", + "1591 mod 332929 = 1591 and gcd(1591, 332929) = 1.", + "1591*129112 + 1 is divisible by 332929.", + "CRT(m = 99 mod 169, m = 129112 mod 332929) gives m = 22102426 mod 56265001.", + "9563 mod 332929 = 9563 and gcd(9563, 332929) = 1.", + "9563*330492 + 1 is divisible by 332929.", + "CRT(m = 70 mod 169, m = 330492 mod 332929) gives m = 9319575 mod 56265001.", + "Both q=577 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 587, + "statement": "Prove the q=587 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 57070892 mod 58232161 and m = 23141071 mod 58232161.", + "completionRule": "The q=587 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=577 as a residual tail-prime upper-bound component. It intentionally leaves q=587 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=587 via two witness-side CRT floor bounds before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..ff70904 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,136 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound_with_bounded_range_profile", + "q": 587, + "squareDivisor": 344569, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=587 tail-prime upper-bound component via two witness-side CRT floor bounds. It also records a bounded q>=587 zero-floor profile, but does not prove the full dMax tail envelope or any all-N side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "344569 divides 1591*m + 1", + "coefficientMod344569": 1591, + "requiredOppositeValueMod344569": 217007, + "crtProgression": { + "variable": "m", + "residue": 57070892, + "modulus": 58232161, + "formula": "m = 57070892 + 58232161*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 57070892) / 58232161) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "344569 divides 9563*m + 1", + "coefficientMod344569": 9563, + "requiredOppositeValueMod344569": 54948, + "crtProgression": { + "variable": "m", + "residue": 23141071, + "modulus": 58232161, + "formula": "m = 23141071 + 58232161*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 23141071) / 58232161) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "remainingTailRangeProfile": { + "status": "bounded_zero_floor_profile_verified_parametric_lift_needed", + "profileRange": "7307..12000", + "startPrime": 587, + "nextPrimeAfterStart": 593, + "plusWitnessProductCutoff": 4369, + "minusWitnessProductCutoff": 10712, + "lastPlusPrimeChecked": 4363, + "lastMinusPrimeChecked": 10711, + "plusWitnessSidePrimeCount": 490, + "minusWitnessSidePrimeCount": 1200, + "scannedWitnessSideRowCount": 1690, + "nonzeroRawFloorCount": 0, + "smallestCrtResidues": [ + { + "q": 1607, + "side": "plus", + "residue": 1220617, + "modulus": 436433881 + }, + { + "q": 1163, + "side": "minus", + "residue": 1275344, + "modulus": 228584161 + }, + { + "q": 607, + "side": "plus", + "residue": 2207915, + "modulus": 62267881 + }, + { + "q": 643, + "side": "minus", + "residue": 3930165, + "modulus": 69872881 + } + ], + "productCutoffReason": "For each witness side, primes q with q^2 > witnessValue*N + 1 cannot divide witnessValue*m + 1 for any 1 <= m <= N. The listed rows exhaust q>=587 up to the relevant product cutoffs at N=12000.", + "claimBoundary": "This is a bounded finite profile over N<=12000. It is useful evidence for the next theorem move, but it is not an all-N tail estimate." + }, + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_q587_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the q=587 raw CRT counts. The q>=587 range profile is bounded evidence only and still needs a parametric lift." + }, + "checkedIdentities": [ + "587^2 = 344569 and 169*344569 = 58232161.", + "1591 mod 344569 = 1591 and gcd(1591, 344569) = 1.", + "1591*217007 + 1 is divisible by 344569.", + "CRT(m = 99 mod 169, m = 217007 mod 344569) gives m = 57070892 mod 58232161.", + "9563 mod 344569 = 9563 and gcd(9563, 344569) = 1.", + "9563*54948 + 1 is divisible by 344569.", + "CRT(m = 70 mod 169, m = 54948 mod 344569) gives m = 23141071 mod 58232161.", + "Both q=587 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile.", + "A deterministic bounded sweep checked 1690 witness-side CRT rows for q>=587 through the side-specific product cutoffs at N = 12000; every raw floor count was zero." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7", + "status": "needed", + "qRange": "q>=587", + "statement": "Lift the bounded q>=587 zero-floor profile into a parametric tail lemma or aggregate recombination step; do not emit q=593 as another singleton unless the lift fails and returns a named exceptional class.", + "completionRule": "Either prove a theorem-facing q>=587 tail bound for both witness sides, or emit the first concrete exceptional prime/range that prevents the aggregate lift." + }, + "proofBoundary": "This certificate discharges q=587 as a residual tail-prime upper-bound component and records that the bounded q>=587 profile has no nonzero raw CRT floor rows through the product cutoffs. It intentionally leaves the parametric q>=587 tail lift open instead of spawning another singleton prime.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7 next.", + "Convert the bounded q>=587 zero-floor profile into a theorem-facing aggregate tail lemma before returning to the side-count floor or dynamic margin." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..8fad0f7 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 59, + "squareDivisor": 3481, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=59 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "3481 divides 1591*m + 1", + "coefficientMod3481": 1591, + "requiredOppositeValueMod3481": 1269, + "crtProgression": { + "variable": "m", + "residue": 182281, + "modulus": 588289, + "formula": "m = 182281 + 588289*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 182281) / 588289) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "3481 divides 9563*m + 1", + "coefficientMod3481": 2601, + "requiredOppositeValueMod3481": 2053, + "crtProgression": { + "variable": "m", + "residue": 492874, + "modulus": 588289, + "formula": "m = 492874 + 588289*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 492874) / 588289) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=59 raw CRT counts." + }, + "checkedIdentities": [ + "59^2 = 3481 and 169*3481 = 588289.", + "1591 mod 3481 = 1591 and gcd(1591, 3481) = 1.", + "1591*1269 + 1 is divisible by 3481.", + "CRT(m = 99 mod 169, m = 1269 mod 3481) gives m = 182281 mod 588289.", + "9563 mod 3481 = 2601 and gcd(2601, 3481) = 1.", + "2601*2053 + 1 is divisible by 3481.", + "CRT(m = 70 mod 169, m = 2053 mod 3481) gives m = 492874 mod 588289.", + "Both q=59 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 61, + "statement": "Prove the q=61 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 396573 mod 628849 and m = 477495 mod 628849.", + "completionRule": "The q=61 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=59 as a residual tail-prime upper-bound component. It intentionally leaves q=61 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=61 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..391bbb9 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 61, + "squareDivisor": 3721, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=61 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "3721 divides 1591*m + 1", + "coefficientMod3721": 1591, + "requiredOppositeValueMod3721": 2147, + "crtProgression": { + "variable": "m", + "residue": 396573, + "modulus": 628849, + "formula": "m = 396573 + 628849*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 396573) / 628849) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "3721 divides 9563*m + 1", + "coefficientMod3721": 2121, + "requiredOppositeValueMod3721": 1207, + "crtProgression": { + "variable": "m", + "residue": 477495, + "modulus": 628849, + "formula": "m = 477495 + 628849*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 477495) / 628849) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=61 raw CRT counts." + }, + "checkedIdentities": [ + "61^2 = 3721 and 169*3721 = 628849.", + "1591 mod 3721 = 1591 and gcd(1591, 3721) = 1.", + "1591*2147 + 1 is divisible by 3721.", + "CRT(m = 99 mod 169, m = 2147 mod 3721) gives m = 396573 mod 628849.", + "9563 mod 3721 = 2121 and gcd(2121, 3721) = 1.", + "2121*1207 + 1 is divisible by 3721.", + "CRT(m = 70 mod 169, m = 1207 mod 3721) gives m = 477495 mod 628849.", + "Both q=61 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 67, + "statement": "Prove the q=67 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 344183 mod 758641 and m = 736572 mod 758641.", + "completionRule": "The q=67 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=61 as a residual tail-prime upper-bound component. It intentionally leaves q=67 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=67 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..64d26db --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 67, + "squareDivisor": 4489, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=67 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "4489 divides 1591*m + 1", + "coefficientMod4489": 1591, + "requiredOppositeValueMod4489": 3019, + "crtProgression": { + "variable": "m", + "residue": 344183, + "modulus": 758641, + "formula": "m = 344183 + 758641*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 344183) / 758641) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "4489 divides 9563*m + 1", + "coefficientMod4489": 585, + "requiredOppositeValueMod4489": 376, + "crtProgression": { + "variable": "m", + "residue": 736572, + "modulus": 758641, + "formula": "m = 736572 + 758641*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 736572) / 758641) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=67 raw CRT counts." + }, + "checkedIdentities": [ + "67^2 = 4489 and 169*4489 = 758641.", + "1591 mod 4489 = 1591 and gcd(1591, 4489) = 1.", + "1591*3019 + 1 is divisible by 4489.", + "CRT(m = 99 mod 169, m = 3019 mod 4489) gives m = 344183 mod 758641.", + "9563 mod 4489 = 585 and gcd(585, 4489) = 1.", + "585*376 + 1 is divisible by 4489.", + "CRT(m = 70 mod 169, m = 376 mod 4489) gives m = 736572 mod 758641.", + "Both q=67 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 71, + "statement": "Prove the q=71 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 69389 mod 851929 and m = 783385 mod 851929.", + "completionRule": "The q=71 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=67 as a residual tail-prime upper-bound component. It intentionally leaves q=71 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=71 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..222051d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 71, + "squareDivisor": 5041, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=71 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "5041 divides 1591*m + 1", + "coefficientMod5041": 1591, + "requiredOppositeValueMod5041": 3856, + "crtProgression": { + "variable": "m", + "residue": 69389, + "modulus": 851929, + "formula": "m = 69389 + 851929*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 69389) / 851929) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "5041 divides 9563*m + 1", + "coefficientMod5041": 4522, + "requiredOppositeValueMod5041": 2030, + "crtProgression": { + "variable": "m", + "residue": 783385, + "modulus": 851929, + "formula": "m = 783385 + 851929*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 783385) / 851929) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=71 raw CRT counts." + }, + "checkedIdentities": [ + "71^2 = 5041 and 169*5041 = 851929.", + "1591 mod 5041 = 1591 and gcd(1591, 5041) = 1.", + "1591*3856 + 1 is divisible by 5041.", + "CRT(m = 99 mod 169, m = 3856 mod 5041) gives m = 69389 mod 851929.", + "9563 mod 5041 = 4522 and gcd(4522, 5041) = 1.", + "4522*2030 + 1 is divisible by 5041.", + "CRT(m = 70 mod 169, m = 2030 mod 5041) gives m = 783385 mod 851929.", + "Both q=71 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 73, + "statement": "Prove the q=73 tail-prime same-prime degree contribution: the plus witness has m = 229770 mod 900601, while the minus side is excluded because 73 divides 9563.", + "completionRule": "The q=73 tail contribution is bounded by the plus-side CRT floor function and minus-side witness-divisibility exclusion, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=71 as a residual tail-prime upper-bound component. It intentionally leaves q=73 open as the next residual tail-prime component with a minus-side exclusion.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=73 using the plus-side CRT floor bound and the minus-side witness-divisibility exclusion before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..9bfa36b --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,82 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "plus_crt_floor_function_minus_witness_divisibility_exclusion_tail_prime_upper_bound", + "q": 73, + "squareDivisor": 5329, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=73 tail-prime upper-bound component: plus-side CRT floor bound and minus-side witness-divisibility exclusion. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessExclusions": [ + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "exclusionReason": "73 divides 9563, so 9563*m + 1 is congruent to 1 mod 73 for every integer m.", + "coefficientMod5329": 4234, + "gcdCoefficientSquareDivisor": 73, + "productPlusOneResidueMod73": 1, + "conclusion": "5329 never divides 9563*m + 1." + } + ], + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "5329 divides 1591*m + 1", + "coefficientMod5329": 1591, + "requiredOppositeValueMod5329": 623, + "crtProgression": { + "variable": "m", + "residue": 229770, + "modulus": 900601, + "formula": "m = 229770 + 900601*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 229770) / 900601) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bound_suffices_for_upper_bound", + "reason": "The minus side is excluded. Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce the plus-side q=73 raw CRT count." + }, + "checkedIdentities": [ + "73^2 = 5329 and 169*5329 = 900601.", + "9563 = 73*131, so 9563*m + 1 is congruent to 1 mod 73 for every integer m.", + "9563 mod 5329 = 4234 and gcd(4234, 5329) = 73.", + "1591 mod 5329 = 1591 and gcd(1591, 5329) = 1.", + "1591*623 + 1 is divisible by 5329.", + "CRT(m = 99 mod 169, m = 623 mod 5329) gives m = 229770 mod 900601.", + "The q=73 plus-side raw floor function evaluates to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 79, + "statement": "Prove the q=79 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 901038 mod 1054729 and m = 280272 mod 1054729.", + "completionRule": "The q=79 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=73 as a residual tail-prime upper-bound component. It intentionally leaves q=79 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=79 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..837a16f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 79, + "squareDivisor": 6241, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=79 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "6241 divides 1591*m + 1", + "coefficientMod6241": 1591, + "requiredOppositeValueMod6241": 2334, + "crtProgression": { + "variable": "m", + "residue": 901038, + "modulus": 1054729, + "formula": "m = 901038 + 1054729*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 901038) / 1054729) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "6241 divides 9563*m + 1", + "coefficientMod6241": 3322, + "requiredOppositeValueMod6241": 5668, + "crtProgression": { + "variable": "m", + "residue": 280272, + "modulus": 1054729, + "formula": "m = 280272 + 1054729*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 280272) / 1054729) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=79 raw CRT counts." + }, + "checkedIdentities": [ + "79^2 = 6241 and 169*6241 = 1054729.", + "1591 mod 6241 = 1591 and gcd(1591, 6241) = 1.", + "1591*2334 + 1 is divisible by 6241.", + "CRT(m = 99 mod 169, m = 2334 mod 6241) gives m = 901038 mod 1054729.", + "9563 mod 6241 = 3322 and gcd(3322, 6241) = 1.", + "3322*5668 + 1 is divisible by 6241.", + "CRT(m = 70 mod 169, m = 5668 mod 6241) gives m = 280272 mod 1054729.", + "Both q=79 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 83, + "statement": "Prove the q=83 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 443048 mod 1164241 and m = 16125 mod 1164241.", + "completionRule": "The q=83 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=79 as a residual tail-prime upper-bound component. It intentionally leaves q=83 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=83 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..7abc1e5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 83, + "squareDivisor": 6889, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=83 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "6889 divides 1591*m + 1", + "coefficientMod6889": 1591, + "requiredOppositeValueMod6889": 2152, + "crtProgression": { + "variable": "m", + "residue": 443048, + "modulus": 1164241, + "formula": "m = 443048 + 1164241*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 443048) / 1164241) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "6889 divides 9563*m + 1", + "coefficientMod6889": 2674, + "requiredOppositeValueMod6889": 2347, + "crtProgression": { + "variable": "m", + "residue": 16125, + "modulus": 1164241, + "formula": "m = 16125 + 1164241*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 16125) / 1164241) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=83 raw CRT counts." + }, + "checkedIdentities": [ + "83^2 = 6889 and 169*6889 = 1164241.", + "1591 mod 6889 = 1591 and gcd(1591, 6889) = 1.", + "1591*2152 + 1 is divisible by 6889.", + "CRT(m = 99 mod 169, m = 2152 mod 6889) gives m = 443048 mod 1164241.", + "9563 mod 6889 = 2674 and gcd(2674, 6889) = 1.", + "2674*2347 + 1 is divisible by 6889.", + "CRT(m = 70 mod 169, m = 2347 mod 6889) gives m = 16125 mod 1164241.", + "Both q=83 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 89, + "statement": "Prove the q=89 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 30519 mod 1338649 and m = 791497 mod 1338649.", + "completionRule": "The q=89 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=83 as a residual tail-prime upper-bound component. It intentionally leaves q=89 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=89 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..90cbc5a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 89, + "squareDivisor": 7921, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=89 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "7921 divides 1591*m + 1", + "coefficientMod7921": 1591, + "requiredOppositeValueMod7921": 6756, + "crtProgression": { + "variable": "m", + "residue": 30519, + "modulus": 1338649, + "formula": "m = 30519 + 1338649*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 30519) / 1338649) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "7921 divides 9563*m + 1", + "coefficientMod7921": 1642, + "requiredOppositeValueMod7921": 7318, + "crtProgression": { + "variable": "m", + "residue": 791497, + "modulus": 1338649, + "formula": "m = 791497 + 1338649*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 791497) / 1338649) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=89 raw CRT counts." + }, + "checkedIdentities": [ + "89^2 = 7921 and 169*7921 = 1338649.", + "1591 mod 7921 = 1591 and gcd(1591, 7921) = 1.", + "1591*6756 + 1 is divisible by 7921.", + "CRT(m = 99 mod 169, m = 6756 mod 7921) gives m = 30519 mod 1338649.", + "9563 mod 7921 = 1642 and gcd(1642, 7921) = 1.", + "1642*7318 + 1 is divisible by 7921.", + "CRT(m = 70 mod 169, m = 7318 mod 7921) gives m = 791497 mod 1338649.", + "Both q=89 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 97, + "statement": "Prove the q=97 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 783076 mod 1590121 and m = 279765 mod 1590121.", + "completionRule": "The q=97 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=89 as a residual tail-prime upper-bound component. It intentionally leaves q=97 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=97 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..dca9184 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,93 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_progression_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "symbolic_upper_bound_verified", + "promotesAllNClaim": false, + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 97, + "squareDivisor": 9409, + "scope": { + "term": "same-prime dMax tail-prime degree contribution", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This proves only the q=97 tail-prime upper-bound component via two witness-side CRT floor bounds. It does not prove the full dMax tail envelope or any side-count floor." + }, + "witnessBounds": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeSide": "minus", + "oppositeResidueMod169": 99, + "productCondition": "9409 divides 1591*m + 1", + "coefficientMod9409": 1591, + "requiredOppositeValueMod9409": 2129, + "crtProgression": { + "variable": "m", + "residue": 783076, + "modulus": 1590121, + "formula": "m = 783076 + 1590121*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 783076) / 1590121) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeSide": "plus", + "oppositeResidueMod169": 70, + "productCondition": "9409 divides 9563*m + 1", + "coefficientMod9409": 154, + "requiredOppositeValueMod9409": 6904, + "crtProgression": { + "variable": "m", + "residue": 279765, + "modulus": 1590121, + "formula": "m = 279765 + 1590121*t", + "tLowerBound": 0 + }, + "rawCountUpperBound": "max(0, floor((N - 279765) / 1590121) + 1)", + "observedCheck": { + "N": 12000, + "rawFormulaCount": 0, + "observedSquareEventCount": 0, + "upperBoundPassed": true + } + } + ], + "overlapBoundary": { + "status": "raw_floor_bounds_suffice_for_upper_bound", + "reason": "Prior-q overlaps, base-residue exclusions, and lower least-square-witness exclusions can only reduce these q=97 raw CRT counts." + }, + "checkedIdentities": [ + "97^2 = 9409 and 169*9409 = 1590121.", + "1591 mod 9409 = 1591 and gcd(1591, 9409) = 1.", + "1591*2129 + 1 is divisible by 9409.", + "CRT(m = 99 mod 169, m = 2129 mod 9409) gives m = 783076 mod 1590121.", + "9563 mod 9409 = 154 and gcd(154, 9409) = 1.", + "154*6904 + 1 is divisible by 9409.", + "CRT(m = 70 mod 169, m = 6904 mod 9409) gives m = 279765 mod 1590121.", + "Both q=97 raw floor functions evaluate to zero at N = 12000, matching the bounded growth profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 101, + "statement": "Prove the q=101 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1382181 mod 1723969 and m = 253570 mod 1723969.", + "completionRule": "The q=101 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom." + }, + "proofBoundary": "This certificate discharges q=97 as a residual tail-prime upper-bound component. It intentionally leaves q=101 open as the next residual tail-prime CRT component.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7 next.", + "Certify q=101 as a two-sided tail-prime CRT floor-bound component before attempting any aggregate tail estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..6d1328b --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,91 @@ +{ + "schema": "erdos.p848_dmax_tail_prime_range_zero_floor_lift/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7", + "parentTailAtomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "bounded_parametric_zero_floor_verified", + "promotesAllNClaim": false, + "proofKind": "bounded_tail_prime_range_zero_floor_lift", + "qRange": { + "statement": "q>=587", + "startPrime": 587, + "profileRange": "7307..12000", + "plusWitnessProductCutoff": 4369, + "minusWitnessProductCutoff": 10712, + "lastPlusPrimeChecked": 4363, + "lastMinusPrimeChecked": 10711 + }, + "boundedProfile": { + "N": 12000, + "profileRange": "7307..12000", + "plusSide": { + "witnessValue": 1591, + "oppositeResidueMod169": 99, + "primeCount": 490, + "firstPrime": 587, + "lastPrimeChecked": 4363 + }, + "minusSide": { + "witnessValue": 9563, + "oppositeResidueMod169": 70, + "primeCount": 1200, + "firstPrime": 587, + "lastPrimeChecked": 10711 + }, + "scannedWitnessSideRowCount": 1690, + "nonzeroRawFloorCount": 0, + "smallestCrtResidues": [ + { + "q": 1607, + "side": "plus", + "residue": 1220617, + "modulus": 436433881 + }, + { + "q": 1163, + "side": "minus", + "residue": 1275344, + "modulus": 228584161 + }, + { + "q": 607, + "side": "plus", + "residue": 2207915, + "modulus": 62267881 + }, + { + "q": 643, + "side": "minus", + "residue": 3930165, + "modulus": 69872881 + } + ] + }, + "verificationMethod": { + "kind": "deterministic_crt_sweep_with_product_cutoff", + "description": "For every prime q>=587 through the side-specific product cutoff, solve the CRT row m = oppositeResidue mod 169 and witnessValue*m + 1 = 0 mod q^2, then evaluate the raw floor count at N=12000. For q beyond a side cutoff, q^2 > witnessValue*N + 1 makes a square event impossible for any 1 <= m <= N in the bounded profile.", + "plusProductCutoffReason": "floor(sqrt(1591*12000 + 1)) = 4369, so the plus-side scan ends at prime 4363.", + "minusProductCutoffReason": "floor(sqrt(9563*12000 + 1)) = 10712, so the minus-side scan ends at prime 10711." + }, + "checkedIdentities": [ + "The plus-side product cutoff is floor(sqrt(1591*12000 + 1)) = 4369; the last plus-side prime checked is 4363.", + "The minus-side product cutoff is floor(sqrt(9563*12000 + 1)) = 10712; the last minus-side prime checked is 10711.", + "The deterministic sweep checks 490 plus-side primes and 1200 minus-side primes, for 1690 witness-side CRT rows.", + "Every checked q>=587 row has raw floor count 0 at N=12000.", + "The smallest stored CRT residues are all greater than 12000, so the raw floor formula contributes zero over the bounded profile." + ], + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18", + "status": "needed_after_dmax_tail_range_lift", + "statement": "Re-derive the residual dynamic margin after the q>=587 dMax tail range profile is closed: prove side18Count + vMax + rGreater + 39 <= candidateSize, or emit a sharper side-count/rGreater successor atom.", + "completionRule": "The residual dynamic margin is proved symbolically for this split, or the first exact moving-count/rGreater obstruction becomes the next atom." + }, + "proofBoundary": "This certificate closes the generated q>=587 bounded-profile zero-floor tail atom for N<=12000 and the stored profile range. It does not promote an all-N dMax tail or side-count-floor claim; it only prevents the singleton q-prime ladder from continuing without a theorem-facing aggregate handoff.", + "nextTheoremActions": [ + "Attack D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18 next.", + "Re-derive side18Count + vMax + rGreater + 39 <= candidateSize; if the inequality fails, emit a sharper side-count or rGreater atom instead of reopening the q-prime staircase." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..4ab6817 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,144 @@ +{ + "schema": "erdos.p848_dmax_tail_recombination_proof/1", + "problemId": "848", + "atomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "parentGrowthAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "predecessorAtomId": "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "tail_scaffold_q13_residue_exclusion_verified_q17_needed", + "promotesAllNClaim": false, + "proofKind": "component_recombination_scaffold_with_target_prime_square_exclusion", + "scope": { + "term": "same-prime dMax degree tail/recombination envelope", + "boundedProfileRange": "7307..12000", + "claimBoundary": "This scaffold recombines the verified observed q-components and proves only the q=13 target-prime square-divisor exclusion for this split residue. It does not prove the full same-prime dMax envelope or the side-count floor." + }, + "verifiedComponentQs": [ + 2, + 3, + 5, + 7, + 11, + 19, + 23, + 31, + 251 + ], + "verifiedObservedComponents": { + "plusWitnessQs": [ + 2, + 3, + 5, + 7, + 11, + 31, + 251 + ], + "minusWitnessQs": [ + 2, + 3, + 5, + 7, + 19, + 23 + ], + "componentProofDirectory": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS" + }, + "samePrimeWitnesses": [ + { + "side": "plus", + "witnessValue": 1591, + "witnessResidueMod169": 70, + "oppositeSide": "minus", + "oppositeResidueMod169": 99 + }, + { + "side": "minus", + "witnessValue": 9563, + "witnessResidueMod169": 99, + "oppositeSide": "plus", + "oppositeResidueMod169": 70 + } + ], + "q13ResidueExclusion": { + "status": "verified_by_split_residue", + "q": 13, + "squareDivisor": 169, + "reason": "The split modulus is 13^2. For both same-prime witnesses, the required opposite residue makes witness*m + 1 congruent to 2 mod 169, so q=13 cannot divide witness*m + 1.", + "checks": [ + { + "side": "plus", + "witnessValue": 1591, + "witnessResidueMod169": 70, + "oppositeResidueMod169": 99, + "productPlusOneResidueMod169": 2, + "requiredResidueForDivisibilityMod169": 70, + "splitResidueMatchesRequiredResidue": false, + "conclusion": "169 does not divide 1591*m + 1 for any m = 99 mod 169." + }, + { + "side": "minus", + "witnessValue": 9563, + "witnessResidueMod169": 99, + "oppositeResidueMod169": 70, + "productPlusOneResidueMod169": 2, + "requiredResidueForDivisibilityMod169": 99, + "splitResidueMatchesRequiredResidue": false, + "conclusion": "169 does not divide 9563*m + 1 for any m = 70 mod 169." + } + ] + }, + "firstUnresolvedTailPrime": { + "q": 17, + "squareDivisor": 289, + "whyNext": "q=13 is excluded by the target-prime split residue, while q=17 is the first remaining prime square divisor not covered by an observed component proof.", + "crtPreview": [ + { + "side": "plus", + "witnessValue": 1591, + "oppositeResidueMod169": 99, + "requiredOppositeValueMod289": 192, + "crtResidue": 47588, + "crtModulus": 48841, + "rawCountUpperBound": "max(0, floor((N - 47588) / 48841) + 1)", + "observedCountAt12000": 0 + }, + { + "side": "minus", + "witnessValue": 9563, + "oppositeResidueMod169": 70, + "requiredOppositeValueMod289": 100, + "crtResidue": 12238, + "crtModulus": 48841, + "rawCountUpperBound": "max(0, floor((N - 12238) / 48841) + 1)", + "observedCountAt12000": 0 + } + ] + }, + "checkedIdentities": [ + "1591 mod 169 = 70.", + "9563 mod 169 = 99.", + "70*99 + 1 = 6931 = 41*169 + 2.", + "99*70 + 1 = 6931 = 41*169 + 2.", + "Therefore q=13 contributes zero same-prime square-divisor events throughout this split residue class.", + "For q=17, CRT(m = 99 mod 169, 1591*m + 1 = 0 mod 289) gives m = 47588 mod 48841.", + "For q=17, CRT(m = 70 mod 169, 9563*m + 1 = 0 mod 289) gives m = 12238 mod 48841." + ], + "tailObligationAfterQ13": { + "status": "open", + "statement": "For every remaining prime q not already covered by the observed q-component proofs and not q=13, derive CRT floor-function upper bounds for both witness sides and recombine them without bounded-only overclaim.", + "firstOpenAtomId": "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7" + }, + "nextSubatom": { + "atomId": "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7", + "status": "needed", + "q": 17, + "statement": "Prove the q=17 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 47588 mod 48841 and m = 12238 mod 48841.", + "completionRule": "The q=17 tail contribution is bounded by CRT floor functions for both witnesses, or the first unresolved q=17 overlap/exclusion class becomes the next atom." + }, + "proofBoundary": "This packet turns the broad tail/recombination atom into a checked scaffold and discharges only the q=13 target-prime residue exclusion. The q=17 tail-prime atom remains open before any full dMax envelope can be promoted.", + "nextTheoremActions": [ + "Attack D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7 next.", + "Derive q=17 CRT floor bounds for both witnesses and then continue through the remaining tail primes or replace the tail with a sharper aggregate estimate." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou.json new file mode 100644 index 0000000..8eadaec --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou.json @@ -0,0 +1,360 @@ +{ + "schema": "p848.dynamicMarginProof.v1", + "generatedAt": "2026-04-12T20:20:20Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "status": "bounded_direct_delta_minus1089_branch_falsified_delta_minus39_successor_needed", + "promotesAllNClaim": false, + "proofKind": "bounded_enlarged_menu_future_event_obstruction", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "testedEnlargedMenu": { + "sourceProfileMaxN": 40000, + "sourceFiniteMenuFailureN": 73607, + "addedDirectDelta": -1089, + "directDeltaCount": 26, + "directDeltas": [ + -1089, + -864, + -789, + -764, + -739, + -689, + -664, + -639, + -589, + -564, + -539, + -489, + -464, + -439, + -414, + -389, + -364, + -339, + -289, + -264, + -239, + -189, + -164, + -139, + -89, + -64 + ], + "replacementPathLeftValues": [ + 10807, + 12407, + 14407 + ], + "menuBoundary": "This replay adds the direct delta -1089 branch to the previously mined finite direct-delta plus three short replacement-path menu." + }, + "boundedReplayAgainstEnlargedMenu": { + "replayStartN": 73607, + "replayMaxN": 164507, + "leftInsertionRowsCheckedUntilFailure": 1336, + "leftInsertionRowsCoveredBeforeFailure": 1335, + "coverDeltaStatsBeforeFailure": [ + { + "delta": -864, + "count": 759 + }, + { + "delta": -1089, + "count": 498 + }, + { + "delta": -739, + "count": 27 + }, + { + "delta": -789, + "count": 19 + }, + { + "delta": -764, + "count": 13 + }, + { + "delta": -589, + "count": 7 + }, + { + "delta": -539, + "count": 5 + }, + { + "delta": -664, + "count": 2 + }, + { + "delta": -689, + "count": 1 + }, + { + "delta": -639, + "count": 1 + }, + { + "delta": -564, + "count": 1 + }, + { + "delta": -489, + "count": 1 + }, + { + "delta": -389, + "count": 1 + } + ], + "firstFailure": { + "N": 164507, + "left": 164507, + "leftMod25": 7, + "leftMod100": 7, + "leftMod625": 132, + "leftCompatibility": { + "outsiderProductPlusOne": 1040177762, + "squareWitnesses": [ + { + "prime": 13, + "square": 169 + } + ] + }, + "activeSide18Count": 2420, + "missingCrossEdgeCount": 196, + "menuDeltaCount": 26, + "menuCandidateStats": [ + { + "delta": -1089, + "right": 163418, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -864, + "right": 163643, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -789, + "right": 163718, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -764, + "right": 163743, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -739, + "right": 163768, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -689, + "right": 163818, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -664, + "right": 163843, + "active": true, + "outsiderCompatible": true, + "crossSquarefree": false + }, + { + "delta": -639, + "right": 163868, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -589, + "right": 163918, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -564, + "right": 163943, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -539, + "right": 163968, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -489, + "right": 164018, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -464, + "right": 164043, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -439, + "right": 164068, + "active": true, + "outsiderCompatible": true, + "crossSquarefree": false + }, + { + "delta": -414, + "right": 164093, + "active": true, + "outsiderCompatible": true, + "crossSquarefree": false + }, + { + "delta": -389, + "right": 164118, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -364, + "right": 164143, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -339, + "right": 164168, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -289, + "right": 164218, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -264, + "right": 164243, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -239, + "right": 164268, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -189, + "right": 164318, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -164, + "right": 164343, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -139, + "right": 164368, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -89, + "right": 164418, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -64, + "right": 164443, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + } + ], + "interpretation": "The enlarged menu reaches a row where the only menu candidates that are outsider-compatible are blocked by cross square divisors, while the squarefree menu candidates are not active side18-compatible vertices." + } + }, + "successorDirectEdgeWitness": { + "left": 164507, + "right": 164468, + "delta": -39, + "leftResidueMod25": 7, + "rightResidueMod25": 18, + "leftResidueMod100": 7, + "rightResidueMod100": 68, + "rightActiveAtN": true, + "rightCompatibility": { + "outsiderProductPlusOne": 1039931165, + "squareWitnesses": [ + { + "prime": 7, + "square": 49 + } + ] + }, + "crossProductPlusOne": 27056137277, + "crossSquarefree": true, + "crossSquarefreeCheckedThrough": 164487, + "interpretation": "The first row outside the enlarged delta -1089 menu is still matched by a direct missing-cross edge, but it requires the new delta -39." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 direct delta -39 successor", + "statement": "Prove the new direct-delta -39 branch exposed at side7 vertex 164507, integrate it with the enlarged augmenting menu, or emit the first future row where this menu fails.", + "completionRule": "The delta -39 branch is proved symbolically and merged into the matching-injection menu, or the first future row requiring a different direct delta or longer augmenting path becomes the next deterministic atom.", + "targetEdge": { + "left": 164507, + "right": 164468, + "delta": -39 + }, + "proofBoundary": "This successor is driven by the first bounded row outside the previously enlarged delta -1089 menu; it is not an all-N proof of any direct-delta family." + }, + "proofBoundary": "This packet falsifies the enlarged direct-delta -1089 menu by an exact bounded future event row. It does not falsify side7 saturation or the matching-injection target; it only shows that the menu needs at least the new direct delta -39 branch.", + "nextTheoremActions": [ + "Do not promote the direct-delta -1089 branch as all-N; it is bounded-successful only until the first failure at N=164507.", + "Attack the direct-delta -39 successor branch next, or replace the growing delta staircase with a residue-parametric delta-selection theorem." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs.json new file mode 100644 index 0000000..0916ffd --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs.json @@ -0,0 +1,228 @@ +{ + "schema": "p848.dynamicMarginProof.v1", + "generatedAt": "2026-04-12T20:28:29Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "status": "bounded_direct_delta_minus39_branch_falsified_residue_parametric_delta_selection_lift_needed", + "promotesAllNClaim": false, + "proofKind": "bounded_delta_staircase_generalization_trigger", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "phaseGuardDecision": { + "status": "stop_extending_single_delta_staircase", + "reason": "The finite augmenting menu has now required multiple bounded direct-delta repairs (-1089, then -39), and the -39 replay exposes another direct repair (-1664). The next durable theorem object should be a residue-parametric delta-selection lift rather than another one-off delta sibling.", + "forbiddenOverclaim": "Do not treat any bounded direct-delta menu as an all-N matching-injection proof." + }, + "testedEnlargedMenu": { + "sourceProfileMaxN": 40000, + "sourceFiniteMenuFailureN": 73607, + "deltaMinus1089FailureN": 164507, + "addedDirectDeltas": [ + -1089, + -39 + ], + "directDeltaCount": 27, + "directDeltas": [ + -1089, + -864, + -789, + -764, + -739, + -689, + -664, + -639, + -589, + -564, + -539, + -489, + -464, + -439, + -414, + -389, + -364, + -339, + -289, + -264, + -239, + -189, + -164, + -139, + -89, + -64, + -39 + ], + "replacementPathLeftValues": [ + 10807, + 12407, + 14407 + ], + "menuBoundary": "This replay adds the direct delta -39 branch to the previously enlarged direct-delta menu, then stops at the first future event row outside that menu." + }, + "boundedReplayAgainstEnlargedMenu": { + "replayStartN": 164507, + "replayMaxN": 468707, + "leftInsertionRowsCheckedUntilFailure": 4464, + "leftInsertionRowsCoveredBeforeFailure": 4463, + "coverDeltaStatsBeforeFailure": [ + { + "delta": -864, + "count": 2547 + }, + { + "delta": -1089, + "count": 1661 + }, + { + "delta": -739, + "count": 92 + }, + { + "delta": -764, + "count": 58 + }, + { + "delta": -789, + "count": 39 + }, + { + "delta": -539, + "count": 18 + }, + { + "delta": -689, + "count": 16 + }, + { + "delta": -589, + "count": 10 + }, + { + "delta": -389, + "count": 6 + }, + { + "delta": -639, + "count": 4 + }, + { + "delta": -489, + "count": 4 + }, + { + "delta": -564, + "count": 3 + }, + { + "delta": -664, + "count": 1 + }, + { + "delta": -364, + "count": 1 + }, + { + "delta": -339, + "count": 1 + }, + { + "delta": -239, + "count": 1 + }, + { + "delta": -39, + "count": 1 + } + ], + "firstFailure": { + "N": 468707, + "left": 468707, + "leftMod25": 7, + "leftMod100": 7, + "leftMod625": 582, + "leftCompatibility": { + "outsiderProductPlusOne": 2963634362, + "squareWitnesses": [ + { + "prime": 13, + "square": 169 + } + ] + }, + "activeSide18Count": 6882, + "missingCrossEdgeCount": 538, + "menuDeltaCount": 27, + "interpretation": "The enlarged -39 menu reaches a row where all currently named deltas fail to give an active side18-compatible squarefree missing-cross edge." + } + }, + "staircaseEvidence": { + "boundedDirectDeltaRepairs": [ + { + "failureN": 73607, + "repairDelta": -1089, + "right": 72518 + }, + { + "failureN": 164507, + "repairDelta": -39, + "right": 164468 + }, + { + "failureN": 468707, + "repairDelta": -1664, + "right": 467043, + "recordedAsGeneralizationSeedOnly": true + } + ], + "interpretation": "The evidence now favors a rule selecting from residue/floor blocks of available deltas, not an unbounded sequence of one-off successor atoms." + }, + "successorDirectEdgeWitness": { + "left": 468707, + "right": 467043, + "delta": -1664, + "leftResidueMod25": 7, + "rightResidueMod25": 18, + "leftResidueMod100": 7, + "rightResidueMod100": 43, + "rightActiveAtN": true, + "rightCompatibility": { + "outsiderProductPlusOne": 2953112890, + "squareWitnesses": [ + { + "prime": 7, + "square": 49 + } + ] + }, + "crossProductPlusOne": 218906323402, + "crossSquarefree": true, + "crossSquarefreeCheckedThrough": 467874, + "interpretation": "The first row outside the enlarged delta -39 menu is still matched by a direct missing-cross edge. The delta -1664 witness is retained as a seed for the parametric delta-selection lift, not promoted as another singleton rung." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 residue-parametric delta-selection lift", + "statement": "Replace the direct-delta staircase with a residue-parametric rule that selects a valid direct missing-cross edge or bounded augmenting path for every future side7-compatible event row in the outsider-6323 family.", + "completionRule": "A residue/block delta-selection theorem proves saturation without adding one-off direct-delta siblings, or the first event row not covered by any finite residue-parametric rule becomes the next obstruction packet.", + "seedFailures": [ + 73607, + 164507, + 468707 + ], + "seedDeltas": [ + -1089, + -39, + -1664 + ], + "proofBoundary": "This successor is a theorem-facing generalization target. Its seeds are bounded evidence only and do not prove the all-N matching injection." + }, + "proofBoundary": "This packet falsifies the enlarged direct-delta -39 menu by an exact bounded future event row and intentionally stops the singleton-delta staircase. It does not falsify side7 saturation or prove any all-N matching injection.", + "nextTheoremActions": [ + "Do not spawn a direct delta -1664 singleton sibling as the canonical next step.", + "Prove or falsify the residue-parametric delta-selection lift using the seed failures 73607, 164507, and 468707." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_632.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_632.json new file mode 100644 index 0000000..b8d320d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_632.json @@ -0,0 +1,156 @@ +{ + "schema": "p848.dynamicMarginProof.v1", + "generatedAt": "2026-04-12T20:12:38Z", + "problemId": 848, + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_finite_menu_falsified_direct_delta_successor_needed", + "proofKind": "bounded_future_event_menu_obstruction", + "predecessorAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "targetPrime": 13, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "promotesAllNClaim": false, + "testedFiniteMenu": { + "sourceProfileMaxN": 40000, + "directDeltaCount": 25, + "directDeltas": [ + -864, + -789, + -764, + -739, + -689, + -664, + -639, + -589, + -564, + -539, + -489, + -464, + -439, + -414, + -389, + -364, + -339, + -289, + -264, + -239, + -189, + -164, + -139, + -89, + -64 + ], + "replacementPathLeftValues": [ + 10807, + 12407, + 14407 + ], + "menuBoundary": "This is the finite direct-delta plus three short replacement-path menu mined from the bounded online profile through 40000." + }, + "boundedReplayAgainstMenu": { + "replayMaxN": 73607, + "postProfileLeftInsertionRowsCheckedUntilFailure": 494, + "postProfileRowsCoveredBeforeFailure": 493, + "firstFailure": { + "N": 73607, + "left": 73607, + "leftMod25": 7, + "leftMod100": 7, + "leftMod625": 482, + "leftCompatibility": { + "outsiderProductPlusOne": 465417062, + "squareWitnesses": [ + { + "prime": 11, + "square": 121 + } + ] + }, + "activeSide18Count": 1081, + "missingCrossEdgeCount": 97, + "oldDirectDeltaCandidateCount": 25, + "oldDirectDeltaActiveSide18ResidueCandidateCount": 25, + "oldDirectDeltaRightCompatibleCandidateCount": 3, + "oldDirectDeltaCrossSquarefreeCandidateCount": 22, + "oldDirectDeltaMissingCrossEdgeCount": 0, + "interpretation": "Every old direct-delta candidate is active on side18 residue, but none is simultaneously outsider-compatible on side18 and squarefree across the left/right pair." + }, + "coverDeltaStatsBeforeFailure": [ + { + "key": "-864", + "count": 445 + }, + { + "key": "-789", + "count": 21 + }, + { + "key": "-764", + "count": 5 + }, + { + "key": "-739", + "count": 13 + }, + { + "key": "-689", + "count": 3 + }, + { + "key": "-639", + "count": 3 + }, + { + "key": "-489", + "count": 1 + }, + { + "key": "-464", + "count": 1 + }, + { + "key": "-389", + "count": 1 + } + ] + }, + "successorDirectEdgeWitness": { + "left": 73607, + "right": 72518, + "delta": -1089, + "leftResidueMod25": 7, + "rightResidueMod25": 18, + "leftResidueMod100": 7, + "rightResidueMod100": 18, + "rightActiveAtN": true, + "rightCompatibility": { + "outsiderProductPlusOne": 458531315, + "squareWitnesses": [ + { + "prime": 11, + "square": 121 + } + ] + }, + "crossProductPlusOne": 5337832427, + "crossSquarefree": true, + "crossSquarefreeCheckedThrough": 73060, + "interpretation": "The first row outside the mined menu is still matched by a direct missing-cross edge, but it requires the new delta -1089." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 direct delta -1089 successor", + "statement": "Prove the new direct-delta -1089 branch exposed at side7 vertex 73607, integrate it with the existing augmenting menu, or emit the first future row where this enlarged menu fails.", + "completionRule": "The delta -1089 residue/block branch is proved symbolically and merged into the matching-injection menu, or the first future row requiring a different direct delta or longer augmenting path becomes the next deterministic atom.", + "targetEdge": { + "left": 73607, + "right": 72518, + "delta": -1089 + }, + "proofBoundary": "This successor is driven by the first bounded row outside the previously mined finite menu; it is not an all-N proof of the enlarged menu." + }, + "proofBoundary": "This packet falsifies the mined finite augmenting-path menu by an exact bounded future event row. It does not falsify side7 saturation or the matching-injection target; it only shows that the menu needs at least the new direct delta -1089 branch." +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323.json new file mode 100644 index 0000000..2c9a7ff --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323.json @@ -0,0 +1,1187 @@ +{ + "schema": "erdos.p848_dynamic_margin_exact_mixed_matching_injection_profile/1", + "generatedAt": "2026-04-12T19:37:58.225Z", + "problemId": "848", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "outsiderMod169": 70, + "outsiderMod25": 23, + "status": "bounded_prefix_matching_injection_verified_parametric_lift_needed", + "promotesAllNClaim": false, + "proofKind": "bounded_prefix_matching_injection_profile", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "targetInjection": "Inject every side7-compatible base vertex for outsider 6323 into a distinct side18-compatible base vertex along squarefree missing-cross edges.", + "sourceVerifier": { + "jsonPath": "/tmp/p848_full_mixed_10000_step48.json", + "assessedRange": "7307..10000", + "sourceThreatRowCount": 277 + }, + "boundedPrefixProfile": { + "sourceRowCount": 277, + "sourceNRange": "7307..10000", + "maxProfileN": 10000, + "firstRow": { + "N": 7307, + "side7Count": 105, + "side18Count": 110, + "matchingSize": 105 + }, + "maxProfileRow": { + "N": 10000, + "side7Count": 145, + "side18Count": 148, + "matchingSize": 145, + "missingCrossEdgeCount": 15951 + }, + "stableCorePairCount": 105, + "extensionPairCount": 40, + "prefixPairCountAtMaxProfileN": 145, + "sourceRowsAllSaturatedByMaxProfilePrefixRestriction": true, + "sourceRowsAllReconstructedByHopcroftKarp": true, + "firstSourcePrefixFailure": null, + "firstSourceReconstructionFailure": null, + "pairDeltaDistributionAtMaxProfileN": [ + { + "key": "-64", + "count": 25 + }, + { + "key": "-264", + "count": 24 + }, + { + "key": "36", + "count": 17 + }, + { + "key": "-364", + "count": 12 + }, + { + "key": "-189", + "count": 10 + }, + { + "key": "-164", + "count": 8 + }, + { + "key": "-39", + "count": 7 + }, + { + "key": "-289", + "count": 6 + }, + { + "key": "-89", + "count": 6 + }, + { + "key": "-239", + "count": 5 + }, + { + "key": "-464", + "count": 5 + }, + { + "key": "-389", + "count": 4 + }, + { + "key": "-339", + "count": 3 + }, + { + "key": "-139", + "count": 2 + }, + { + "key": "-439", + "count": 2 + }, + { + "key": "-639", + "count": 2 + }, + { + "key": "-114", + "count": 1 + }, + { + "key": "-14", + "count": 1 + }, + { + "key": "-564", + "count": 1 + }, + { + "key": "-764", + "count": 1 + } + ], + "extensionPairDeltaDistribution": [ + { + "key": "-264", + "count": 11 + }, + { + "key": "-364", + "count": 6 + }, + { + "key": "-189", + "count": 5 + }, + { + "key": "-464", + "count": 4 + }, + { + "key": "-389", + "count": 3 + }, + { + "key": "-64", + "count": 3 + }, + { + "key": "-164", + "count": 2 + }, + { + "key": "-289", + "count": 2 + }, + { + "key": "-339", + "count": 1 + }, + { + "key": "-439", + "count": 1 + }, + { + "key": "-639", + "count": 1 + }, + { + "key": "-89", + "count": 1 + } + ], + "stableCorePairSample": [ + { + "leftValue": 7, + "rightValue": 43, + "delta": 36 + }, + { + "leftValue": 57, + "rightValue": 93, + "delta": 36 + }, + { + "leftValue": 157, + "rightValue": 193, + "delta": 36 + }, + { + "leftValue": 232, + "rightValue": 268, + "delta": 36 + }, + { + "leftValue": 257, + "rightValue": 293, + "delta": 36 + }, + { + "leftValue": 357, + "rightValue": 318, + "delta": -39 + }, + { + "leftValue": 457, + "rightValue": 393, + "delta": -64 + }, + { + "leftValue": 557, + "rightValue": 493, + "delta": -64 + }, + { + "leftValue": 657, + "rightValue": 593, + "delta": -64 + }, + { + "leftValue": 682, + "rightValue": 693, + "delta": 11 + }, + { + "leftValue": 757, + "rightValue": 718, + "delta": -39 + }, + { + "leftValue": 857, + "rightValue": 793, + "delta": -64 + }, + { + "leftValue": 907, + "rightValue": 943, + "delta": 36 + }, + { + "leftValue": 957, + "rightValue": 893, + "delta": -64 + }, + { + "leftValue": 1007, + "rightValue": 1168, + "delta": 161 + }, + { + "leftValue": 1057, + "rightValue": 993, + "delta": -64 + }, + { + "leftValue": 1132, + "rightValue": 1093, + "delta": -39 + }, + { + "leftValue": 1157, + "rightValue": 1193, + "delta": 36 + }, + { + "leftValue": 1257, + "rightValue": 1293, + "delta": 36 + }, + { + "leftValue": 1357, + "rightValue": 1393, + "delta": 36 + }, + { + "leftValue": 1457, + "rightValue": 1493, + "delta": 36 + }, + { + "leftValue": 1557, + "rightValue": 1593, + "delta": 36 + }, + { + "leftValue": 1582, + "rightValue": 1543, + "delta": -39 + }, + { + "leftValue": 1657, + "rightValue": 1618, + "delta": -39 + } + ], + "extensionPairSample": [ + { + "leftValue": 7357, + "rightValue": 7093, + "delta": -264 + }, + { + "leftValue": 7432, + "rightValue": 7168, + "delta": -264 + }, + { + "leftValue": 7457, + "rightValue": 7193, + "delta": -264 + }, + { + "leftValue": 7557, + "rightValue": 7468, + "delta": -89 + }, + { + "leftValue": 7657, + "rightValue": 7293, + "delta": -364 + }, + { + "leftValue": 7757, + "rightValue": 7393, + "delta": -364 + }, + { + "leftValue": 7857, + "rightValue": 7593, + "delta": -264 + }, + { + "leftValue": 7882, + "rightValue": 7243, + "delta": -639 + }, + { + "leftValue": 7957, + "rightValue": 7493, + "delta": -464 + }, + { + "leftValue": 8057, + "rightValue": 7668, + "delta": -389 + }, + { + "leftValue": 8107, + "rightValue": 7918, + "delta": -189 + }, + { + "leftValue": 8157, + "rightValue": 7693, + "delta": -464 + }, + { + "leftValue": 8182, + "rightValue": 7718, + "delta": -464 + }, + { + "leftValue": 8207, + "rightValue": 8143, + "delta": -64 + }, + { + "leftValue": 8257, + "rightValue": 7793, + "delta": -464 + }, + { + "leftValue": 8332, + "rightValue": 7893, + "delta": -439 + }, + { + "leftValue": 8357, + "rightValue": 7993, + "delta": -364 + }, + { + "leftValue": 8457, + "rightValue": 8093, + "delta": -364 + }, + { + "leftValue": 8557, + "rightValue": 8193, + "delta": -364 + }, + { + "leftValue": 8657, + "rightValue": 8293, + "delta": -364 + }, + { + "leftValue": 8682, + "rightValue": 8393, + "delta": -289 + }, + { + "leftValue": 8757, + "rightValue": 8368, + "delta": -389 + }, + { + "leftValue": 8782, + "rightValue": 8493, + "delta": -289 + }, + { + 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"allEventRowsSaturateSide7": true, + "maxSide7Count": 175, + "maxSide18Count": 178, + "minSide18MinusSide7": 0, + "firstEventSaturationFailure": null, + "frozenMax12000PrefixInjectionFailsAt": { + "N": 10807, + "missingCount": 1, + "missingSample": [ + 10807 + ] + }, + "interpretation": "Saturation persists on 7307..12000 side-compatible event rows, but a single frozen max-12000 pair set is not prefix-stable from N=10807. The next proof should be an online/parametric insertion lift, not another frozen finite matching table." + }, + "checkedIdentities": [ + "At every source verifier row N=7307..10000 for outsider 6323, restricting the maxN=10000 pair set to pairs with both endpoints <= N covers every side7-compatible vertex.", + "Every recorded pair is a side7-to-side18 missing-cross edge, i.e. left*right+1 is squarefree in the checked range.", + "The stable 105-pair core saturates the first obstruction row N=7307; the 40 extension pairs cover the side7-compatible vertices added by N=10000.", + "A separate event-row probe through N=12000 found no saturation obstruction, but it did find that frozen-prefix reuse is too rigid at N=10807." + ], + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 parametric prefix-extension matching injection", + "statement": "Turn the bounded prefix injection into an online residue/block insertion proof for all future outsider-6323 rows, or emit the first exact future event row where side7 cannot be saturated.", + "completionRule": "A parametric insertion/replacement rule saturates side7 for every future row in this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom.", + "proofBoundary": "The bounded profile and event probe do not promote an all-N matching injection claim; they only identify the stable core and the next required parametric insertion lift." + }, + "proofBoundary": "This certificate is bounded evidence. It verifies a reusable prefix matching through the source 7307..10000 profile and a no-obstruction event probe through 12000, but it does not prove the all-N side7-to-side18 matching injection.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Use the stable 105-pair core plus the 40 bounded extension pairs as seed data for a residue/block insertion rule; do not claim the matching-injection sublemma until that rule is symbolic." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json new file mode 100644 index 0000000..bc0f70b --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json @@ -0,0 +1,433 @@ +{ + "schema": "p848.dynamicMarginProof.v1", + "generatedAt": "2026-04-12T19:54:19Z", + "problemId": 848, + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_online_augmentation_profile_verified_finite_menu_needed", + "proofKind": "bounded_online_augmenting_path_profile", + "predecessorAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "targetPrime": 13, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetInjection": "Match every side7-compatible vertex to a side18-compatible missing-cross neighbor in the outsider-6323 exact mixed row family.", + "promotesAllNClaim": false, + "boundedEventScan": { + "minN": 7307, + "maxN": 40000, + "eventRowCount": 953, + "leftInsertionEventCount": 474, + "rightOnlyEventCount": 479, + "initialSide7Count": 105, + "initialSide18Count": 110, + "finalSide7Count": 579, + "finalSide18Count": 589, + "finalMatchingSize": 579, + "allEventRowsSaturateSide7": true, + "firstEventSaturationFailure": null, + "minSide18MinusSide7": 0, + "minMatchingSlackAboveSide7": 0, + "interpretation": "The online matching stays side7-saturating at every side-compatible event row through 40000, but this bounded scan only identifies a small augmenting-path menu for the next symbolic proof." + }, + "onlineAugmentingPathProfile": { + "initialMatchingN": 7307, + "initialMatchingSize": 105, + "leftInsertionCount": 474, + "directInsertionCount": 471, + "replacementPathCount": 3, + "pathNodeDistribution": [ + { + "nodes": 2, + "count": 471 + }, + { + "nodes": 4, + "count": 3 + } + ], + "leftResidueMod100Distribution": [ + { + "key": "7", + "count": 47 + }, + { + "key": "32", + "count": 49 + }, + { + "key": "57", + "count": 327 + }, + { + "key": "82", + "count": 51 + } + ], + "directDeltaDistribution": [ + { + "key": "-864", + "count": 5 + }, + { + "key": "-789", + "count": 1 + }, + { + "key": "-764", + "count": 10 + }, + { + "key": "-739", + "count": 7 + }, + { + "key": "-689", + "count": 2 + }, + { + "key": "-664", + "count": 13 + }, + { + "key": "-639", + "count": 30 + }, + { + "key": "-589", + "count": 9 + }, + { + "key": "-564", + "count": 58 + }, + { + "key": "-539", + "count": 31 + }, + { + "key": "-489", + "count": 15 + }, + { + "key": "-464", + "count": 69 + }, + { + "key": "-439", + "count": 8 + }, + { + "key": "-414", + "count": 2 + }, + { + "key": "-389", + "count": 12 + }, + { + "key": "-364", + "count": 40 + }, + { + "key": "-339", + "count": 11 + }, + { + "key": "-289", + "count": 13 + }, + { + "key": "-264", + "count": 49 + }, + { + "key": "-239", + "count": 10 + }, + { + "key": "-189", + "count": 34 + }, + { + "key": "-164", + "count": 12 + }, + { + "key": "-139", + "count": 3 + }, + { + "key": "-89", + "count": 7 + }, + { + "key": "-64", + "count": 20 + } + ], + "topDirectResidueDeltaPairs": [ + { + "key": "57->-464", + "count": 65 + }, + { + "key": "57->-564", + "count": 58 + }, + { + "key": "57->-264", + "count": 47 + }, + { + "key": "57->-364", + "count": 38 + }, + { + "key": "82->-639", + "count": 20 + }, + { + "key": "57->-64", + "count": 19 + }, + { + "key": "7->-189", + "count": 19 + }, + { + "key": "32->-539", + "count": 13 + }, + { + "key": "57->-164", + "count": 12 + }, + { + "key": "57->-539", + "count": 12 + }, + { + "key": "57->-664", + "count": 12 + }, + { + "key": "57->-764", + "count": 10 + }, + { + "key": "57->-389", + "count": 9 + }, + { + "key": "32->-339", + "count": 8 + }, + { + "key": "57->-489", + "count": 8 + }, + { + "key": "82->-289", + "count": 8 + }, + { + "key": "32->-439", + "count": 7 + }, + { + "key": "57->-589", + "count": 7 + }, + { + "key": "57->-189", + "count": 6 + }, + { + "key": "57->-289", + "count": 5 + } + ], + "replacementPaths": [ + { + "N": 10807, + "newLeft": 10807, + "newLeftMod100": 7, + "path": [ + { + "side": "L", + "value": 10807 + }, + { + "side": "R", + "value": 268 + }, + { + "side": "L", + "value": 232 + }, + { + "side": "R", + "value": 10693 + } + ], + "replacementTemplate": { + "newLeftTakes": 268, + "displacedLeft": 232, + "displacedLeftReroutesTo": 10693 + }, + "edgeDeltas": [ + -10539, + 36, + 10461 + ] + }, + { + "N": 12407, + "newLeft": 12407, + "newLeftMod100": 7, + "path": [ + { + "side": "L", + "value": 12407 + }, + { + "side": "R", + "value": 318 + }, + { + "side": "L", + "value": 357 + }, + { + "side": "R", + "value": 12193 + } + ], + "replacementTemplate": { + "newLeftTakes": 318, + "displacedLeft": 357, + "displacedLeftReroutesTo": 12193 + }, + "edgeDeltas": [ + -12089, + -39, + 11836 + ] + }, + { + "N": 14407, + "newLeft": 14407, + "newLeftMod100": 7, + "path": [ + { + "side": "L", + "value": 14407 + }, + { + "side": "R", + "value": 718 + }, + { + "side": "L", + "value": 757 + }, + { + "side": "R", + "value": 14293 + } + ], + "replacementTemplate": { + "newLeftTakes": 718, + "displacedLeft": 757, + "displacedLeftReroutesTo": 14293 + }, + "edgeDeltas": [ + -13689, + -39, + 13536 + ] + } + ], + "directInsertionSamples": { + "firstFive": [ + { + "N": 7357, + "left": 7357, + "right": 7093, + "delta": -264 + }, + { + "N": 7432, + "left": 7432, + "right": 7168, + "delta": -264 + }, + { + "N": 7457, + "left": 7457, + "right": 7193, + "delta": -264 + }, + { + "N": 7557, + "left": 7557, + "right": 7468, + "delta": -89 + }, + { + "N": 7657, + "left": 7657, + "right": 7293, + "delta": -364 + } + ], + "lastFive": [ + { + "N": 39657, + "left": 39657, + "right": 38993, + "delta": -664 + }, + { + "N": 39757, + "left": 39757, + "right": 39093, + "delta": -664 + }, + { + "N": 39832, + "left": 39832, + "right": 39193, + "delta": -639 + }, + { + "N": 39857, + "left": 39857, + "right": 39293, + "delta": -564 + }, + { + "N": 39957, + "left": 39957, + "right": 39393, + "delta": -564 + } + ] + } + }, + "finiteMenuCandidate": { + "directCase": "For each future new side7 vertex, prove one of the finite residue/delta direct edges is present as a missing-cross edge to a currently free side18 vertex.", + "replacementCase": "Only three bounded rows through 40000 require a one-replacement augmenting path: N=10807, N=12407, and N=14407. The next theorem object should prove these are the initial members of a finite exceptional menu or emit the first future event row requiring a longer path.", + "menuBoundary": "The listed direct deltas and replacement paths are a bounded menu mined through 40000; they are not yet a residue-complete all-N augmenting-path proof." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 finite augmenting-path menu", + "statement": "Prove the finite direct-insertion plus short replacement-path menu for every future side7-compatible event row in the outsider-6323 split family, or emit the first event row whose side7 vertex needs a new obstruction atom.", + "completionRule": "A residue/block augmenting-path menu saturates side7 for every future event row, or the first future event row outside the menu becomes the next deterministic atom.", + "proofBoundary": "This is the symbolic menu target exposed by the bounded online augmentation profile; it must not be treated as discharged until the residue cases are proved." + }, + "proofBoundary": "This certificate is bounded evidence through N=40000. It verifies online side7 saturation and isolates the finite augmenting-path menu to prove next, but it does not prove the all-N outsider-6323 matching injection." +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid.json new file mode 100644 index 0000000..64a922e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid.json @@ -0,0 +1,104 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T20:55:20Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "symbolic_residue_direct_selector_lift_proved_selected_cross_squarefree_needed", + "proofKind": "symbolic_mod4_four_slot_direct_selector", + "promotesAllNClaim": false, + "provesDirectSelectorAllN": true, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "scope": { + "sourceSide": "side7", + "targetSide": "side18", + "sourceResidueMod25": 7, + "targetResidueMod25": 18, + "activeForLeftAtLeast": 107, + "structuralLaneMinLeft": 7307, + "universalOverFutureSide7Rows": true, + "requiresSourceOutsiderCompatibility": false, + "excludesCrossSquarefree": true, + "excludesCollisionFreeMatchingUpdate": true + }, + "selectorRule": { + "name": "previous_93_mod100_side18_slot", + "statement": "For any future side7 row left, choose right as the largest integer below left with right == 93 (mod 100).", + "formula": { + "right": "left - (14 + 25 * j)", + "j": "(left - 3) mod 4", + "deltaSet": [ + -14, + -39, + -64, + -89 + ] + }, + "residueChecks": [ + { + "claim": "right is a side18 vertex", + "calculation": "right == 93 (mod 100), hence right == 18 (mod 25)." + }, + { + "claim": "right is active before the side7 event row", + "calculation": "For left >= 107, delta is one of -14,-39,-64,-89, so 1 <= right < left." + }, + { + "claim": "right is outsider-compatible with outsider 6323", + "calculation": "right == 93 (mod 100) gives right == 1 (mod 4). Since 6323 == 3 (mod 4), 6323 * right + 1 == 0 (mod 4)." + }, + { + "claim": "outsider compatibility is non-squarefree", + "calculation": "The square 2^2 divides 6323 * right + 1." + } + ], + "leftResidueCases": [ + { + "leftMod100": 7, + "delta": -14, + "rightMod100": 93 + }, + { + "leftMod100": 32, + "delta": -39, + "rightMod100": 93 + }, + { + "leftMod100": 57, + "delta": -64, + "rightMod100": 93 + }, + { + "leftMod100": 82, + "delta": -89, + "rightMod100": 93 + } + ] + }, + "boundedSanityCheck": { + "maxN": 2000000, + "checkedSide7CompatibleEventRows": 29222, + "coveredByFourSlotEndpointRule": 29222, + "missCount": 0, + "note": "This sanity check is regression evidence only. The selector proof above is the symbolic reason for endpoint existence." + }, + "proofBoundary": "This packet proves only that every future side7-compatible event row has an active side18-compatible endpoint selected by the four-slot mod-4 rule. It does not prove that left * right + 1 is squarefree, and it does not prove that selected endpoints are collision-free for the online matching.", + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 selected cross-squarefree lift", + "statement": "Prove that the four-slot selected endpoint gives a squarefree cross product left * right + 1 for every future side7-compatible event row, or route the first residue class/future row where the selected cross product is non-squarefree into a bounded replacement-path exception menu.", + "completionRule": "The selected endpoint is a missing-cross edge for every future side7-compatible row, or the first square-divisor obstruction becomes the next deterministic exception packet.", + "dependsOnSublemma": "residue_direct_selector_lift", + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is about cross-squarefreeness of the selected direct endpoints only; even after it is proved, collision-free online matching still remains." + }, + "nextAction": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not return to singleton direct-delta successors unless the selected cross-squarefree lift emits a concrete exception packet." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s.json new file mode 100644 index 0000000..09acaec --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s.json @@ -0,0 +1,210 @@ +{ + "schema": "p848.dynamicMarginProof.v1", + "generatedAt": "2026-04-12T20:46:18Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "status": "residue_parametric_delta_selection_reduced_to_direct_selector_and_collision_sublemmas", + "proofKind": "theorem_reduction_to_residue_direct_selector", + "promotesAllNClaim": false, + "predecessorAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs", + "phaseGuardDecision": { + "status": "decompose_generalization_target", + "reason": "The direct-delta staircase produced seed repairs at 73607, 164507, and 468707. The next durable theorem move is to split the residue-parametric lift into direct-selector, cross-squarefree, and collision/augmentation obligations rather than adding another singleton delta." + }, + "seedDirectRepairs": [ + { + "left": 73607, + "right": 72518, + "delta": -1089, + "leftMod25": 7, + "rightMod25": 18, + "rightSquareWitnessPrime": 11, + "rightSquareWitness": 121, + "crossSquarefree": true + }, + { + "left": 164507, + "right": 164468, + "delta": -39, + "leftMod25": 7, + "rightMod25": 18, + "rightSquareWitnessPrime": 7, + "rightSquareWitness": 49, + "crossSquarefree": true + }, + { + "left": 468707, + "right": 467043, + "delta": -1664, + "leftMod25": 7, + "rightMod25": 18, + "rightSquareWitnessPrime": 7, + "rightSquareWitness": 49, + "crossSquarefree": true, + "recordedAsGeneralizationSeedOnly": true + } + ], + "boundedLocalWindowProbe": { + "probeKind": "nearest_negative_delta_congruent_11_mod25", + "minLeft": 7307, + "maxN": 1000000, + "checkedSide7CompatibleEventRows": 14557, + "originalNamedDeltaMenuCoveredRows": 14552, + "originalNamedDeltaMenuMissCount": 5, + "windowMaxAbsDelta": 5000, + "windowCoveredRows": 14557, + "firstWindowMiss": null, + "maxAbsDeltaActuallyUsed": 2164, + "distinctNearestWindowDeltaCount": 27, + "suggestedNearestWindowDeltas": [ + -64, + -39, + -89, + -189, + -164, + -14, + -139, + -264, + -239, + -339, + -539, + -289, + -639, + -114, + -464, + -364, + -489, + -1089, + -389, + -1039, + -1064, + -1239, + -1664, + -2164, + -564, + -764, + -864 + ], + "firstOriginalMenuMisses": [ + { + "left": 468707, + "leftMod100": 7, + "leftMod625": 582, + "leftSquareWitnessPrime": 13, + "leftSquareWitness": 169 + }, + { + "left": 529007, + "leftMod100": 7, + "leftMod625": 257, + "leftSquareWitnessPrime": 43, + "leftSquareWitness": 1849 + }, + { + "left": 592007, + "leftMod100": 7, + "leftMod625": 132, + "leftSquareWitnessPrime": 19, + "leftSquareWitness": 361 + }, + { + "left": 925007, + "leftMod100": 7, + "leftMod625": 7, + "leftSquareWitnessPrime": 13, + "leftSquareWitness": 169 + }, + { + "left": 982607, + "leftMod100": 7, + "leftMod625": 107, + "leftSquareWitnessPrime": 877, + "leftSquareWitness": 769129 + } + ], + "topNearestWindowDeltaCounts": [ + { + "delta": -64, + "count": 8089 + }, + { + "delta": -39, + "count": 3112 + }, + { + "delta": -89, + "count": 1391 + }, + { + "delta": -189, + "count": 982 + }, + { + "delta": -164, + "count": 307 + }, + { + "delta": -14, + "count": 254 + }, + { + "delta": -139, + "count": 205 + } + ], + "interpretation": "A local nearest-delta selector is a plausible direct-selector target: through N=1000000 every checked side7-compatible event row has a side18-compatible squarefree direct endpoint within the finite negative-delta window. This is bounded evidence only; it does not prove the all-N selector, cross-squarefreeness formula, or collision-free matching update." + }, + "reduction": { + "sourceStatement": "Replace the direct-delta staircase with a residue-parametric rule that selects a valid direct missing-cross edge or bounded augmenting path for every future side7-compatible event row in the outsider-6323 family.", + "sublemmas": [ + { + "sublemmaId": "residue_direct_selector_lift", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "statement": "For every future side7-compatible event row left in the outsider-6323 family, select a negative delta congruent to 11 mod 25 such that right = left + delta is active, side18-compatible with outsider 6323, and left/right is a missing-cross candidate.", + "whyFirst": "The seed repairs all remain direct side7-to-side18 repairs; before proving collision-free matching updates, the theorem lane needs a residue rule that produces the right-side endpoint." + }, + { + "sublemmaId": "selected_cross_squarefree_lift", + "statement": "For each selected direct endpoint, prove left * right + 1 is squarefree, or route the residue block into a bounded replacement-path exception menu." + }, + { + "sublemmaId": "selector_collision_or_augmentation_lift", + "statement": "Prove the selected direct endpoints can be used injectively by the online matching, or give a bounded augmenting-path replacement rule for collisions." + } + ], + "dependencyOrder": [ + "residue_direct_selector_lift", + "selected_cross_squarefree_lift", + "selector_collision_or_augmentation_lift" + ], + "completionCriterion": "The residue-parametric delta-selection lift is discharged only when all three sublemmas are symbolic; this packet is only the reduction and handoff to the first sublemma." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 residue direct-selector lift", + "statement": "Prove the residue-parametric direct-selector sublemma: every future side7-compatible event row has a residue-selected side18-compatible direct endpoint, or emit the first event row with no selected direct endpoint.", + "completionRule": "A residue/mod-square selector produces a side18-compatible direct endpoint for every future side7 event row, or the first uncovered event row becomes the next obstruction packet.", + "seedFailures": [ + 73607, + 164507, + 468707 + ], + "seedDeltas": [ + -1089, + -39, + -1664 + ], + "proofBoundary": "This direct-selector sublemma still does not prove cross-squarefreeness or matching collision-freedom; those remain explicit downstream obligations." + }, + "proofBoundary": "This packet decomposes the residue-parametric delta-selection target into theorem sublemmas. It does not prove the all-N matching injection and does not promote bounded seed repairs as a proof.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not spawn singleton delta -1664 as a sibling rung unless the direct-selector sublemma itself is falsified and the task model explicitly asks for a bounded obstruction packet." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_.json new file mode 100644 index 0000000..395435f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_.json @@ -0,0 +1,296 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T21:18:40Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_exception_menu_reduced_to_finite_window_lift", + "proofKind": "bounded_selected_cross_exception_window_profile", + "promotesAllNClaim": false, + "provesExceptionMenuAllN": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "phaseGuardDecision": { + "status": "generalize_exception_menu", + "reason": "The first selected-cross obstruction at left=8107 is not a singleton delta branch. It is the first row in a family where the previous-93 endpoint is side18-compatible but left * right + 1 has a square divisor, so the durable theorem object is the finite local-window replacement selector." + }, + "seedException": { + "left": 8107, + "selectedRight": 8093, + "selectedDelta": -14, + "selectedCrossProductPlusOne": 65609952, + "selectedCrossSquareDivisor": { + "prime": 2, + "square": 4, + "quotient": 16402488 + }, + "firstRepair": { + "right": 7918, + "delta": -189, + "rightResidueMod25": 18, + "rightOutsiderCompatibility": { + "prime": 3, + "square": 9, + "quotient": 5562835 + }, + "crossSquarefree": true + } + }, + "finiteWindowMenu": { + "source": "residue_parametric_delta_selection_lift.boundedLocalWindowProbe.suggestedNearestWindowDeltas", + "selectionRule": "On a selected-cross exception row, scan this delta list in order and take the first right = left + delta with right > 0, right < left, right == 18 (mod 25), 6323 * right + 1 non-squarefree, and left * right + 1 squarefree.", + "windowMaxAbsDelta": 5000, + "deltaSet": [ + -64, + -39, + -89, + -189, + -164, + -14, + -139, + -264, + -239, + -339, + -539, + -289, + -639, + -114, + -464, + -364, + -489, + -1089, + -389, + -1039, + -1064, + -1239, + -1664, + -2164, + -564, + -764, + -864 + ] + }, + "boundedExceptionProfile": { + "minLeft": 7307, + "maxN": 1000000, + "checkedSide7CompatibleEventRows": 14557, + "selectedCrossExceptions": 2241, + "coveredByFiniteWindowMenu": 2241, + "firstUncoveredReplacementRow": null, + "distinctRepairDeltaCount": 23, + "unusedMenuDeltasInProfile": [ + -564, + -764, + -864, + -114 + ], + "topSelectedExceptionSquareDivisors": [ + { + "square": "2^2", + "count": 1540 + }, + { + "square": "7^2", + "count": 405 + }, + { + "square": "13^2", + "count": 131 + }, + { + "square": "19^2", + "count": 59 + }, + { + "square": "41^2", + "count": 15 + }, + { + "square": "47^2", + "count": 11 + }, + { + "square": "17^2", + "count": 11 + }, + { + "square": "53^2", + "count": 8 + }, + { + "square": "29^2", + "count": 6 + }, + { + "square": "59^2", + "count": 6 + } + ], + "repairDeltaCounts": [ + { + "delta": -189, + "count": 1079 + }, + { + "delta": -164, + "count": 371 + }, + { + "delta": -89, + "count": 202 + }, + { + "delta": -39, + "count": 199 + }, + { + "delta": -64, + "count": 121 + }, + { + "delta": -264, + "count": 74 + }, + { + "delta": -139, + "count": 53 + }, + { + "delta": -339, + "count": 46 + }, + { + "delta": -239, + "count": 42 + }, + { + "delta": -539, + "count": 16 + }, + { + "delta": -639, + "count": 10 + }, + { + "delta": -289, + "count": 6 + }, + { + "delta": -1089, + "count": 5 + }, + { + "delta": -14, + "count": 4 + }, + { + "delta": -464, + "count": 3 + }, + { + "delta": -489, + "count": 2 + }, + { + "delta": -1239, + "count": 2 + }, + { + "delta": -389, + "count": 1 + }, + { + "delta": -364, + "count": 1 + }, + { + "delta": -1664, + "count": 1 + }, + { + "delta": -2164, + "count": 1 + }, + { + "delta": -1039, + "count": 1 + }, + { + "delta": -1064, + "count": 1 + } + ], + "firstCheckedRepairs": [ + { + "left": 8107, + "selectedRight": 8093, + "selectedDelta": -14, + "selectedFailureSquare": 4, + "repairRight": 7918, + "repairDelta": -189, + "repairRightWitnessSquare": 9 + }, + { + "left": 8207, + "selectedRight": 8193, + "selectedDelta": -14, + "selectedFailureSquare": 4, + "repairRight": 8143, + "repairDelta": -64, + "repairRightWitnessSquare": 9 + }, + { + "left": 9007, + "selectedRight": 8993, + "selectedDelta": -14, + "selectedFailureSquare": 4, + "repairRight": 8818, + "repairDelta": -189, + "repairRightWitnessSquare": 9 + }, + { + "left": 9957, + "selectedRight": 9893, + "selectedDelta": -64, + "selectedFailureSquare": 49, + "repairRight": 9793, + "repairDelta": -164, + "repairRightWitnessSquare": 4 + }, + { + "left": 12832, + "selectedRight": 12793, + "selectedDelta": -39, + "selectedFailureSquare": 11881, + "repairRight": 12643, + "repairDelta": -189, + "repairRightWitnessSquare": 9 + } + ], + "verificationMethod": "A deterministic local script marked side7 source rows by square divisors of 6323 * left + 1, detected selected previous-93 cross exceptions by exact square-divisor trial division, then replayed the 27-delta finite window menu with exact right-side and cross-squarefree checks." + }, + "reduction": { + "sourceStatement": "Replace every selected previous-93 endpoint whose cross product is non-squarefree by a side18-compatible squarefree direct endpoint from the finite local-window menu.", + "result": "The bounded profile through N=1000000 has no uncovered selected-cross exception row, so the next theorem move is the symbolic finite-window lift rather than another singleton repair delta.", + "whyThisIsNotAProof": "The finite window menu is verified only over the bounded profile. An all-N proof still has to show that every future selected-cross exception row is covered by one menu delta with right-side compatibility and squarefree cross product." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 selected cross-squarefree exception finite-window lift", + "statement": "Prove the finite 27-delta exception-window selector: every future selected-cross square-divisor exception row has a replacement right = left + delta from the menu with right side18-compatible, 6323 * right + 1 non-squarefree, and left * right + 1 squarefree, or emit the first uncovered row.", + "completionRule": "A symbolic finite-window lift covers all selected-cross exceptions without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_menu", + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is still only the exception-menu lift. Even after it is proved, collision-free online matching remains a separate downstream obligation." + }, + "proofBoundary": "This packet replaces the left=8107 local repair by a finite-window theorem target. It is bounded evidence and a handoff, not an all-N proof of the exception menu or the full matching injection.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not spawn singleton repair deltas from this exception menu unless the finite-window lift itself emits an uncovered-row packet." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift.json new file mode 100644 index 0000000..700e253 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift.json @@ -0,0 +1,162 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T22:24:17Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_period_shifted_endpoint_menu_profile_ready_symbolic_menu_lift_needed", + "proofKind": "bounded_p7_cross_bad_period_shifted_endpoint_menu_profile", + "promotesAllNClaim": false, + "provesCrossSquarefreeAllN": false, + "provesCollisionFreeMatchingAllN": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "phaseGuardDecision": { + "status": "replace_fallback_staircase_with_period_shifted_endpoint_menu", + "reason": "The 31 bounded p=7 endpoint cross-bad rows do not collapse to a single next-prime rule. They are all covered by a period-shifted local endpoint menu using small right-compatibility primes, so the next theorem object should be the finite menu lift rather than singleton repair deltas." + }, + "boundedFallbackProfile": { + "checker": "/tmp/p848_right_escape_mine.cpp", + "checkerKind": "exact_modular_sieve_replay_plus_p7_cross_bad_period_shifted_endpoint_profile", + "maxN": 10000000, + "escapeWindow": 10000, + "finiteWindowMisses": 52, + "p7EndpointCrossSquarefree": 21, + "p7EndpointCrossBad": 31, + "periodShiftedEndpointCovered": 31, + "firstNoPeriodShiftedEndpoint": null, + "chosenDeltaCounts": [ + { "delta": -1764, "count": 3 }, + { "delta": -2039, "count": 3 }, + { "delta": -1139, "count": 2 }, + { "delta": -1639, "count": 2 }, + { "delta": -1589, "count": 2 }, + { "delta": -3339, "count": 2 }, + { "delta": -1539, "count": 2 }, + { "delta": -1739, "count": 2 }, + { "delta": -1289, "count": 2 }, + { "delta": -1839, "count": 1 }, + { "delta": -1439, "count": 1 }, + { "delta": -2089, "count": 1 }, + { "delta": -1939, "count": 1 }, + { "delta": -2739, "count": 1 }, + { "delta": -4139, "count": 1 }, + { "delta": -1464, "count": 1 }, + { "delta": -689, "count": 1 }, + { "delta": -3839, "count": 1 }, + { "delta": -2439, "count": 1 }, + { "delta": -939, "count": 1 } + ], + "chosenRightPrimeCounts": [ + { "prime": 7, "count": 14 }, + { "prime": 11, "count": 6 }, + { "prime": 13, "count": 3 }, + { "prime": 17, "count": 2 }, + { "prime": 19, "count": 2 }, + { "prime": 37, "count": 2 }, + { "prime": 23, "count": 1 }, + { "prime": 41, "count": 1 } + ], + "firstSlotEndpointPrimeCounts": [ + { "prime": 11, "count": 12 }, + { "prime": 17, "count": 6 }, + { "prime": 19, "count": 5 }, + { "prime": 13, "count": 4 }, + { "prime": 37, "count": 2 }, + { "prime": 23, "count": 1 } + ], + "firstSlotEndpointMissRows": [ + 6400607 + ], + "interpretation": "The first-slot p=11 endpoint is only a partial fallback. The bounded repair rule that covers all observed p=7 cross-bad rows is the nearest period-shifted endpoint with a small right-compatibility square prime and squarefree cross product." + }, + "periodShiftedEndpointMenu": { + "menuId": "outsider_6323_small_prime_period_shifted_endpoint_menu_v1", + "primeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "deltaFamily": "For prime q in the menu and integer shift s >= 0, let k_q(left) be the least residue solving 6323*(left - 14 - 25*k)+1 = 0 mod q^2, and set d_{q,s}(left) = -14 - 25*(k_q(left) + s*q^2).", + "windowRule": "Keep only candidates with -10000 <= d_{q,s}(left) <= -14.", + "selectorRule": "Among window candidates, choose the nearest right endpoint whose cross product left*(left+d)+1 is squarefree.", + "provedSymbolicallyHere": [ + "Every retained candidate is side18-compatible because d_{q,s}(left) is congruent to 11 mod 25.", + "Every retained candidate has q^2 dividing 6323*right+1 by the defining linear congruence." + ], + "notProvedHere": [ + "That the menu always contains a squarefree cross product for every future p=7 cross-bad row.", + "That the selected endpoints are collision-free as an online matching." + ] + }, + "boundedRows": [ + { "left": 1229207, "p7Delta": -214, "p7CrossPrime": 2, "chosenDelta": -1139, "chosenRightPrime": 11 }, + { "left": 1360607, "p7Delta": -539, "p7CrossPrime": 19, "chosenDelta": -1764, "chosenRightPrime": 7 }, + { "left": 1381307, "p7Delta": -414, "p7CrossPrime": 2, "chosenDelta": -1639, "chosenRightPrime": 7 }, + { "left": 1533407, "p7Delta": -614, "p7CrossPrime": 2, "chosenDelta": -1839, "chosenRightPrime": 7 }, + { "left": 1685507, "p7Delta": -814, "p7CrossPrime": 2, "chosenDelta": -2039, "chosenRightPrime": 7 }, + { "left": 1837607, "p7Delta": -1014, "p7CrossPrime": 2, "chosenDelta": -1639, "chosenRightPrime": 37 }, + { "left": 2699807, "p7Delta": -814, "p7CrossPrime": 2, "chosenDelta": -1589, "chosenRightPrime": 11 }, + { "left": 2852807, "p7Delta": -689, "p7CrossPrime": 17, "chosenDelta": -3339, "chosenRightPrime": 11 }, + { "left": 3390107, "p7Delta": -214, "p7CrossPrime": 2, "chosenDelta": -1439, "chosenRightPrime": 7 }, + { "left": 3841007, "p7Delta": -314, "p7CrossPrime": 2, "chosenDelta": -1539, "chosenRightPrime": 7 }, + { "left": 4490807, "p7Delta": -864, "p7CrossPrime": 19, "chosenDelta": -2089, "chosenRightPrime": 7 }, + { "left": 5183807, "p7Delta": -514, "p7CrossPrime": 2, "chosenDelta": -1739, "chosenRightPrime": 7 }, + { "left": 5335907, "p7Delta": -714, "p7CrossPrime": 2, "chosenDelta": -1289, "chosenRightPrime": 17 }, + { "left": 5512307, "p7Delta": -714, "p7CrossPrime": 2, "chosenDelta": -1939, "chosenRightPrime": 7 }, + { "left": 5988407, "p7Delta": -289, "p7CrossPrime": 17, "chosenDelta": -2739, "chosenRightPrime": 7 }, + { "left": 6312407, "p7Delta": -889, "p7CrossPrime": 3, "chosenDelta": -1539, "chosenRightPrime": 13 }, + { "left": 6400607, "p7Delta": -889, "p7CrossPrime": 3, "chosenDelta": -3339, "chosenRightPrime": 7 }, + { "left": 6712907, "p7Delta": -814, "p7CrossPrime": 2, "chosenDelta": -1589, "chosenRightPrime": 19 }, + { "left": 6940607, "p7Delta": -664, "p7CrossPrime": 3, "chosenDelta": -2039, "chosenRightPrime": 17 }, + { "left": 7090007, "p7Delta": -614, "p7CrossPrime": 2, "chosenDelta": -1739, "chosenRightPrime": 13 }, + { "left": 7161107, "p7Delta": -664, "p7CrossPrime": 3, "chosenDelta": -4139, "chosenRightPrime": 23 }, + { "left": 8682107, "p7Delta": -214, "p7CrossPrime": 2, "chosenDelta": -1139, "chosenRightPrime": 37 }, + { "left": 8834207, "p7Delta": -414, "p7CrossPrime": 2, "chosenDelta": -1289, "chosenRightPrime": 11 }, + { "left": 8849507, "p7Delta": -1014, "p7CrossPrime": 2, "chosenDelta": -1464, "chosenRightPrime": 11 }, + { "left": 8986307, "p7Delta": -614, "p7CrossPrime": 2, "chosenDelta": -689, "chosenRightPrime": 19 }, + { "left": 9138407, "p7Delta": -814, "p7CrossPrime": 2, "chosenDelta": -2039, "chosenRightPrime": 7 }, + { "left": 9290507, "p7Delta": -1014, "p7CrossPrime": 2, "chosenDelta": -3839, "chosenRightPrime": 11 }, + { "left": 9442607, "p7Delta": -1214, "p7CrossPrime": 2, "chosenDelta": -2439, "chosenRightPrime": 7 }, + { "left": 9594707, "p7Delta": -189, "p7CrossPrime": 19, "chosenDelta": -1764, "chosenRightPrime": 41 }, + { "left": 9607307, "p7Delta": -539, "p7CrossPrime": 31, "chosenDelta": -939, "chosenRightPrime": 13 }, + { "left": 9871907, "p7Delta": -539, "p7CrossPrime": 43, "chosenDelta": -1764, "chosenRightPrime": 7 } + ], + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 period-shifted endpoint menu lift", + "statement": "Prove that every p=7 endpoint cross-bad row in this split family has a squarefree cross product inside the small-prime period-shifted endpoint menu, or emit the first future row outside the menu.", + "completionRule": "A symbolic finite endpoint-menu lift covers all p=7 endpoint cross-bad rows without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is still cross-squarefree selection only. It must not claim collision-free online matching, and bounded menu coverage is not an all-N proof." + }, + "proofBoundary": "This packet records a bounded period-shifted endpoint-menu profile and a symbolic right-compatibility skeleton. It does not prove all-N cross-squarefreeness or collision-free matching.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not add singleton fallback-delta rungs unless the period-shifted endpoint menu emits a first miss outside its rule." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json new file mode 100644 index 0000000..3389191 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json @@ -0,0 +1,130 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T22:37:13Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_prime_set_exact_replay_ready_squarefree_sieve_lift_needed", + "proofKind": "bounded_period_shifted_endpoint_menu_replay_plus_squarefree_sieve_reduction", + "promotesAllNClaim": false, + "provesEndpointMenuAllN": false, + "provesCrossSquarefreeAllN": false, + "provesCollisionFreeMatchingAllN": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "phaseGuardDecision": { + "status": "stop_bounded_replay_staircase_reduce_to_sieve_hitting_lemma", + "reason": "The exact period-shifted endpoint menu survives a doubled bounded replay through N=20000000. Since this is still bounded evidence, the next deterministic move is the squarefree sieve/hitting lemma for the endpoint menu, not another larger replay." + }, + "boundedReplay": { + "checker": "/tmp/p848_right_escape_mine.cpp", + "checkerKind": "exact_modular_sieve_replay_with_allowed_prime_set", + "maxN": 20000000, + "escapeWindow": 10000, + "allowedRightPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "sourceCount": 293270, + "selectedExceptionCount": 45005, + "finiteWindowMisses": 104, + "p7EndpointCrossSquarefree": 42, + "p7EndpointCrossBad": 62, + "periodShiftedEndpointCovered": 104, + "p7CrossBadPeriodShiftedEndpointCovered": 62, + "firstNoPeriodShiftedEndpoint": null, + "escapePrimeCounts": [ + { "prime": 7, "count": 64 }, + { "prime": 13, "count": 10 }, + { "prime": 11, "count": 8 }, + { "prime": 17, "count": 8 }, + { "prime": 37, "count": 6 }, + { "prime": 19, "count": 3 }, + { "prime": 23, "count": 2 }, + { "prime": 31, "count": 2 }, + { "prime": 41, "count": 1 } + ], + "p7CrossBadPrimeCounts": [ + { "prime": 2, "count": 45 }, + { "prime": 3, "count": 7 }, + { "prime": 19, "count": 4 }, + { "prime": 17, "count": 2 }, + { "prime": 23, "count": 1 }, + { "prime": 31, "count": 1 }, + { "prime": 43, "count": 1 }, + { "prime": 97, "count": 1 } + ], + "endpointPrimeSquarefreeSupport": [ + { "prime": 17, "count": 39 }, + { "prime": 19, "count": 36 }, + { "prime": 23, "count": 24 }, + { "prime": 11, "count": 22 }, + { "prime": 13, "count": 21 }, + { "prime": 31, "count": 17 }, + { "prime": 37, "count": 14 }, + { "prime": 41, "count": 11 } + ], + "interpretation": "The exact named menu, excluding prime 29, covers every bounded finite-window miss through 20000000. This strengthens the menu target but remains bounded evidence." + }, + "sieveReduction": { + "reductionId": "outsider_6323_period_shifted_endpoint_menu_squarefree_sieve_reduction_v1", + "candidateFamily": "For each q in {7,11,13,17,19,23,31,37,41} and shift s with -10000 <= d_{q,s}(left) <= -14, the right endpoint is left + d_{q,s}(left), where d_{q,s}(left) = -14 - 25*(k_q(left) + s*q^2).", + "targetPredicate": "At least one candidate in the finite local menu has left*(left+d_{q,s}(left))+1 squarefree whenever the first p=7 endpoint candidate is cross-bad.", + "suggestedProofShape": [ + "Partition p=7 cross-bad rows by the square divisor of the p=7 cross product.", + "For each partition, prove that not all menu candidates can be simultaneously hit by square divisors using residue incompatibility or a density/gap lemma.", + "Use the bounded rows as falsifier examples only; do not promote the 20000000 replay to an all-N claim." + ], + "firstOpenRisk": "A future row may have every candidate in the finite menu blocked by a cross-square divisor; such a row should become the next deterministic obstruction packet." + }, + "sampleRows": [ + { "left": 1138307, "selectedDelta": -14, "escapeDelta": -989, "right": 1137318, "rightSquarePrime": 11 }, + { "left": 1229207, "selectedDelta": -14, "escapeDelta": -1139, "right": 1228068, "rightSquarePrime": 11 }, + { "left": 1360607, "selectedDelta": -14, "escapeDelta": -1764, "right": 1358843, "rightSquarePrime": 7 }, + { "left": 1381307, "selectedDelta": -14, "escapeDelta": -1639, "right": 1379668, "rightSquarePrime": 7 }, + { "left": 1533407, "selectedDelta": -14, "escapeDelta": -1839, "right": 1531568, "rightSquarePrime": 7 }, + { "left": 1685507, "selectedDelta": -14, "escapeDelta": -2039, "right": 1683468, "rightSquarePrime": 7 }, + { "left": 1837607, "selectedDelta": -14, "escapeDelta": -1639, "right": 1835968, "rightSquarePrime": 37 }, + { "left": 2598107, "selectedDelta": -14, "escapeDelta": -789, "right": 2597318, "rightSquarePrime": 7 }, + { "left": 2699807, "selectedDelta": -14, "escapeDelta": -1589, "right": 2698218, "rightSquarePrime": 11 }, + { "left": 2852807, "selectedDelta": -14, "escapeDelta": -3339, "right": 2849468, "rightSquarePrime": 11 } + ], + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 period-shifted endpoint-menu squarefree sieve lift", + "statement": "Prove the squarefree hitting lemma for the period-shifted endpoint menu: every p=7 endpoint cross-bad row has at least one menu endpoint with squarefree cross product, or emit the first row where every menu endpoint is cross-blocked.", + "completionRule": "A symbolic sieve/hitting lemma proves cross-squarefree endpoint existence for the menu, or the first fully cross-blocked row becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is cross-squarefree selection only. It must not claim collision-free online matching, and bounded menu coverage is not an all-N proof." + }, + "proofBoundary": "This packet extends the exact named period-shifted endpoint-menu replay and reduces the all-N work to a squarefree sieve/hitting lemma. It does not prove all-N menu coverage or matching collision-freedom.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "If the sieve lemma fails, emit the first fully cross-blocked row rather than adding singleton delta rungs." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift.json new file mode 100644 index 0000000..af2519b --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift.json @@ -0,0 +1,167 @@ +{ + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_q17_residual_falsified_cross_bad_fallback_needed", + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift", + "proofKind": "bounded_p7_shift_q17_residual_cross_bad_obstruction", + "generatedAt": "2026-04-12T23:06:00Z", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "statement": "The bounded p7-shift plus q17 residual fallback is false as a standalone cross-squarefree selector: the first residual-class row after N=20000000 where the q17 endpoint is cross-blocked is left=20016257.", + "endpointFormulae": { + "p7": { + "kFormula": "k_7(left) = (2*left - 27) mod 49", + "dFormula": "d_7(left) = -14 - 25*k_7(left)", + "compatibility": "49 divides 6323*(left + d_7(left)) + 1" + }, + "q17": { + "kFormula": "k_17(left) = (185*left + 47) mod 289", + "dFormula": "d_17(left) = -14 - 25*k_17(left)", + "compatibility": "289 divides 6323*(left + d_17(left)) + 1" + } + }, + "residualClass": { + "description": "left == 5882 mod 11025", + "modulus": 11025, + "residue": 5882, + "leftMod1225": 982, + "p7Delta": -664, + "p7K": 26 + }, + "boundedResidualScan": { + "priorProfileMaxN": 20000000, + "scanKind": "targeted_residual_class_exact_square_divisor_check", + "checkedRowsAfterPriorBoundBeforeFailure": 2, + "certifiedRows": [ + { + "left": 20005232, + "leftMod11025": 5882, + "q17K": 154, + "q17Delta": -3864, + "q17Right": 20001368, + "q17RightMod25": 18, + "q17CompatibilityMod289": 0, + "crossProductPlusOne": "400132007157377", + "squareDivisorPrime": null, + "squarefree": true, + "primeCountChecked": 1270807, + "maxPrimeChecked": 20003299 + }, + { + "left": 20016257, + "leftMod11025": 5882, + "q17K": 17, + "q17Delta": -439, + "q17Right": 20015818, + "q17RightMod25": 18, + "q17CompatibilityMod289": 0, + "crossProductPlusOne": "400641757153227", + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false, + "primeCountChecked": 1271557, + "maxPrimeChecked": 20016037 + } + ], + "firstQ17CrossBadRow": { + "left": 20016257, + "right": 20015818, + "delta": -439, + "k": 17, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "crossProductPlusOne": "400641757153227" + } + }, + "localFallbackSeed": { + "left": 20016257, + "seedWindow": 10000, + "candidateEndpoints": [ + { + "prime": 11, + "k": 117, + "delta": -2939, + "right": 20013318, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "smallSquareDivisorPrime": null, + "crossProductPlusOne": "400591716510727", + "primeCountChecked": 1271482, + "maxPrimeChecked": 20014787, + "boundedSquarefree": true + }, + { + "prime": 19, + "k": 83, + "delta": -2089, + "right": 20014168, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "smallSquareDivisorPrime": null, + "crossProductPlusOne": "400608730329177", + "primeCountChecked": 1271507, + "maxPrimeChecked": 20015212, + "boundedSquarefree": true + }, + { + "prime": 23, + "k": 183, + "delta": -4589, + "right": 20011668, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "smallSquareDivisorPrime": null, + "crossProductPlusOne": "400558689686677", + "primeCountChecked": 1271433, + "maxPrimeChecked": 20013962, + "boundedSquarefree": true + }, + { + "prime": 31, + "k": 345, + "delta": -8639, + "right": 20007618, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "smallSquareDivisorPrime": null, + "crossProductPlusOne": "400477623845827", + "primeCountChecked": 1271316, + "maxPrimeChecked": 20011937, + "boundedSquarefree": true + } + ] + }, + "claims": { + "provesAllN": false, + "provesCollisionFreeMatching": false, + "provesQ17ResidualFallback": false, + "falsifiesStandaloneQ17ResidualFallback": true, + "emitsNextFallbackSelector": true + }, + "proofBoundary": "This packet only falsifies the standalone q17 residual fallback at the first certified residual-class row after the 20M bounded handoff. The local fallback seed is not an all-N proof and does not claim collision-free online matching.", + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 q17 residual cross-bad fallback selector lift", + "statement": "Prove that every q17 residual cross-bad row has a squarefree side18-compatible fallback endpoint in the small-prime local menu, or emit the first row with no bounded fallback endpoint.", + "completionRule": "A symbolic fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully fallback-blocked row becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift", + "seedPrimeSet": [ + 11, + 19, + 23, + 31 + ], + "seedEscapeWindow": 10000, + "firstCrossBadSeed": { + "left": 20016257, + "q17Right": 20015818, + "q17Delta": -439, + "q17SquareDivisorPrime": 3 + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This fallback subatom is still cross-squarefree endpoint selection only. It must not claim all-N coverage from bounded seeds or collision-free matching." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift.json new file mode 100644 index 0000000..bc7058c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift.json @@ -0,0 +1,139 @@ +{ + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_seed_fallback_menu_falsified_p13_expanded_menu_needed", + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift", + "proofKind": "bounded_q17_residual_cross_bad_seed_menu_obstruction", + "generatedAt": "2026-04-12T23:20:55Z", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "statement": "The q17 residual cross-bad seed fallback menu {11,19,23,31} is false under the 10000 local window. The first exactly certified fully fallback-blocked row is left=25153907, and the p=13 endpoint gives the next general repair seed.", + "residualClass": { + "description": "left == 5882 mod 11025", + "modulus": 11025, + "residue": 5882 + }, + "seedMenu": { + "primeSet": [ + 11, + 19, + 23, + 31 + ], + "escapeWindow": 10000, + "endpointRule": "For prime p, choose k in [0,p^2) so that p^2 divides 6323*(left - 14 - 25*k) + 1 and set right=left-14-25*k." + }, + "exactBoundedReplay": { + "priorProfileMaxN": 20000000, + "checkedThrough": 25153907, + "residualRowsChecked": 468, + "primeLimit": 27755824, + "primeCount": 1727233, + "q17CrossBadRowsBeforeAndAtFailure": 121, + "q17CrossBadRowsCoveredBeforeFailure": 120, + "q11CoversBeforeFailure": 86, + "windowEnforced": true, + "verificationKind": "exact_prime_square_divisor_scan_for_q17_endpoint_and_seed_fallback_candidates" + }, + "firstFullyFallbackBlockedRow": { + "left": 25153907, + "leftMod11025": 5882, + "q17K": 44, + "q17Delta": -1114, + "q17Right": 25152793, + "q17RightMod25": 18, + "q17CompatibilityMod289": 0, + "q17CrossProductPlusOne": "632691015912252", + "q17SquareDivisorPrime": 2, + "q17SquareDivisor": 4, + "seedFallbackResults": [ + { + "prime": 11, + "k": 44, + "delta": -1114, + "right": 25152793, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 19, + "k": 180, + "delta": -4514, + "right": 25149393, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 23, + "k": 437, + "delta": -10939, + "right": 25142968, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + }, + { + "prime": 31, + "k": 197, + "delta": -4939, + "right": 25148968, + "availableWithinWindow": true, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false + } + ] + }, + "localP13RepairSeed": { + "prime": 13, + "k": 150, + "delta": -3764, + "right": 25150143, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "632624358058702", + "primeCountChecked": 1574955, + "maxPrimeChecked": 25152025, + "squareDivisorPrime": null, + "squarefree": true, + "withinSeedWindow": true + }, + "claims": { + "provesAllN": false, + "provesCollisionFreeMatching": false, + "provesSeedMenuFallback": false, + "falsifiesSeedMenuFallback": true, + "emitsP13ExpandedFallbackMenu": true + }, + "proofBoundary": "This packet exactly falsifies only the {11,19,23,31} seed fallback menu through the first fully fallback-blocked q17 residual row under the 10000 window. The p=13 repair seed is a next theorem target, not an all-N proof or collision-free matching claim.", + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 q17 residual p13-expanded fallback menu lift", + "statement": "Prove that every q17 residual cross-bad row has a squarefree side18-compatible endpoint in the expanded local menu {11,13,19,23,31}, or emit the first row outside that expanded menu.", + "completionRule": "A symbolic expanded fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully expanded-menu-blocked row becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift", + "seedPrimeSet": [ + 11, + 13, + 19, + 23, + 31 + ], + "seedEscapeWindow": 10000, + "firstRepairSeed": { + "left": 25153907, + "prime": 13, + "right": 25150143, + "delta": -3764 + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This expanded fallback subatom is still cross-squarefree endpoint selection only. It must not claim all-N coverage from the seed or collision-free matching." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json new file mode 100644 index 0000000..147ec28 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json @@ -0,0 +1,216 @@ +{ + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed", + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "proofKind": "bounded_q17_residual_p13_expanded_menu_obstruction", + "generatedAt": "2026-04-12T23:45:00Z", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "statement": "The q17 residual p13-expanded fallback menu {11,13,19,23,31} is false under the 10000 local window. The first exactly certified fully expanded-menu-blocked row is left=27932207, and the local repairs move to a window-relaxed selector rather than a singleton prime rung.", + "residualClass": { + "description": "left == 5882 mod 11025", + "modulus": 11025, + "residue": 5882 + }, + "expandedMenu": { + "primeSet": [ + 11, + 13, + 19, + 23, + 31 + ], + "escapeWindow": 10000, + "endpointRule": "For prime p, choose k in [0,p^2) so that p^2 divides 6323*(left - 14 - 25*k) + 1 and set right=left-14-25*k." + }, + "exactBoundedReplay": { + "priorProfileMaxN": 20000000, + "checkedThrough": 27932207, + "residualRowsChecked": 720, + "primeLimit": 27932224, + "primeCount": 1737493, + "q17CrossBadRowsBeforeAndAtFailure": 190, + "q17CrossBadRowsCoveredBeforeFailure": 189, + "firstCoverPrimeCountsBeforeFailure": { + "11": 131, + "13": 38, + "19": 17, + "23": 2, + "31": 1 + }, + "windowEnforced": true, + "verificationKind": "exact_prime_square_divisor_scan_for_q17_endpoint_and_p13_expanded_fallback_candidates" + }, + "firstFullyExpandedMenuBlockedRow": { + "left": 27932207, + "leftMod11025": 5882, + "q17K": 200, + "q17Delta": -5014, + "q17Right": 27927193, + "q17RightMod25": 18, + "q17CompatibilityMod289": 0, + "q17CrossProductPlusOne": "780068135804952", + "q17SquareDivisorPrime": 2, + "q17SquareDivisor": 4, + "expandedFallbackResults": [ + { + "prime": 11, + "k": 98, + "delta": -2464, + "right": 27929743, + "availableWithinWindow": true, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false + }, + { + "prime": 13, + "k": 80, + "delta": -2014, + "right": 27930193, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 19, + "k": 124, + "delta": -3114, + "right": 27929093, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 23, + "k": 479, + "delta": -11989, + "right": 27920218, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + }, + { + "prime": 31, + "k": 814, + "delta": -20364, + "right": 27911843, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + } + ] + }, + "windowRelaxedRepairSeeds": [ + { + "prime": 23, + "k": 479, + "delta": -11989, + "right": 27920218, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "779873308661127", + "squareDivisorPrime": null, + "squarefree": true, + "within10000Window": false, + "within25000Window": true + }, + { + "prime": 31, + "k": 814, + "delta": -20364, + "right": 27911843, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "779639376427502", + "squareDivisorPrime": null, + "squarefree": true, + "within10000Window": false, + "within25000Window": true + }, + { + "prime": 37, + "k": 671, + "delta": -16789, + "right": 27915418, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "779739234067527", + "squareDivisorPrime": null, + "squarefree": true, + "within10000Window": false, + "within25000Window": true + }, + { + "prime": 41, + "k": 654, + "delta": -16364, + "right": 27915843, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "779751105255502", + "squareDivisorPrime": null, + "squarefree": true, + "within10000Window": false, + "within25000Window": true + }, + { + "prime": 61, + "k": 679, + "delta": -16989, + "right": 27915218, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "779733647626127", + "squareDivisorPrime": null, + "squarefree": true, + "within10000Window": false, + "within25000Window": true + } + ], + "claims": { + "provesAllN": false, + "provesCollisionFreeMatching": false, + "provesP13ExpandedFallbackMenu": false, + "falsifiesP13ExpandedFallbackMenu": true, + "emitsWindowRelaxedFallbackMenu": true + }, + "proofBoundary": "This packet exactly falsifies only the {11,13,19,23,31} p13-expanded fallback menu through the first fully expanded-menu-blocked q17 residual row under the 10000 window. The window-relaxed repair seeds are next theorem targets, not all-N coverage or collision-free matching claims.", + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 q17 residual window-relaxed fallback menu lift", + "statement": "Prove that every q17 residual cross-bad row blocked by the 10000-window expanded menu has a squarefree side18-compatible endpoint in a controlled 25000-window menu, or emit the first fully window-relaxed blocked row.", + "completionRule": "A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton prime repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "seedPrimeSet": [ + 23, + 31, + 37, + 41, + 61 + ], + "seedEscapeWindow": 25000, + "firstRepairSeeds": [ + { + "left": 27932207, + "prime": 23, + "right": 27920218, + "delta": -11989 + }, + { + "left": 27932207, + "prime": 31, + "right": 27911843, + "delta": -20364 + } + ], + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This window-relaxed fallback subatom is still cross-squarefree endpoint selection only. It must not claim all-N coverage from the seed or collision-free matching." + } +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.json new file mode 100644 index 0000000..3ea3a68 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.json @@ -0,0 +1,2159 @@ +{ + "schema": "erdos.number_theory.p848_endpoint_menu_compiler/1", + "generatedAt": "2026-04-14T03:01:44.700Z", + "problemId": "848", + "target": { + "description": "q17 residual window-relaxed fallback endpoint-menu selector", + "predecessorProof": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "outsider": 6323, + "residualClass": { + "residue": 5882, + "modulus": 11025 + }, + "start": 34414907, + "end": 34414907, + "rowCount": 1, + "targetWindow": 25000, + "predecessorWindow": 10000, + "squareCheck": { + "checkedPrimeLimit": 34414903, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "No full-menu covered endpoint was selected in this profile; inspect candidate square-divisor statuses and window availability." + } + }, + "endpointRule": { + "statement": "For each menu prime p, choose k_p(left) modulo p^2 so p^2 divides outsider*(left - 14 - 25*k_p(left)) + 1, then set right_p(left)=left-14-25*k_p(left).", + "invariant": "Every compiled endpoint has right congruent to 18 mod 25 and is outsider-compatible by construction." + }, + "primaryMenu": { + "primeSet": [ + 23, + 31, + 37, + 41, + 61, + 67 + ], + "formulasByPrime": { + "23": { + "prime": 23, + "primeSquare": 529, + "kFormula": { + "leftCoefficient": 127, + "constant": 79, + "modulus": 529, + "text": "k_23(left) = (127*left + 79) mod 529" + }, + "deltaRange": { + "min": -13214, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": true + } + }, + "31": { + "prime": 31, + "primeSquare": 961, + "kFormula": { + "leftCoefficient": 346, + "constant": 669, + "modulus": 961, + "text": "k_31(left) = (346*left + 669) mod 961" + }, + "deltaRange": { + "min": -24014, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": true + } + }, + "37": { + "prime": 37, + "primeSquare": 1369, + "kFormula": { + "leftCoefficient": 1150, + "constant": 651, + "modulus": 1369, + "text": "k_37(left) = (1150*left + 651) mod 1369" + }, + "deltaRange": { + "min": -34214, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + } + }, + "41": { + "prime": 41, + "primeSquare": 1681, + "kFormula": { + "leftCoefficient": 269, + "constant": 1029, + "modulus": 1681, + "text": "k_41(left) = (269*left + 1029) mod 1681" + }, + "deltaRange": { + "min": -42014, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + } + }, + "61": { + "prime": 61, + "primeSquare": 3721, + "kFormula": { + "leftCoefficient": 2828, + "constant": 2221, + "modulus": 3721, + "text": "k_61(left) = (2828*left + 2221) mod 3721" + }, + "deltaRange": { + "min": -93014, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + } + }, + "67": { + "prime": 67, + "primeSquare": 4489, + "kFormula": { + "leftCoefficient": 2873, + "constant": 511, + "modulus": 4489, + "text": "k_67(left) = (2873*left + 511) mod 4489" + }, + "deltaRange": { + "min": -112214, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + } + } + }, + "universalWindowAvailability": false + }, + "fallbackMenu": { + "primeSet": [ + 71, + 73, + 79, + 83, + 89, + 97, + 101, + 103, + 107, + 109, + 113 + ], + "formulasByPrime": { + "71": { + "prime": 71, + "primeSquare": 5041, + "kFormula": { + "leftCoefficient": 2823, + "constant": 4760, + "modulus": 5041, + "text": "k_71(left) = (2823*left + 4760) mod 5041" + }, + "deltaRange": { + "min": -126014, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + } + }, + "73": { + "prime": 73, + "primeSquare": 5329, + "kFormula": { + "leftCoefficient": 1279, + "constant": 5218, + "modulus": 5329, + "text": "k_73(left) = (1279*left + 5218) mod 5329" + }, + 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"compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1179888174037727", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": null, + "squareDivisor": null, + "squarefree": true, + "squarefreeStatus": "exact_squarefree", + "profileUsable": true + }, + { + "prime": 79, + "k": 1606, + "delta": -40164, + "right": 34374743, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1183003583493902", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": null, + "squareDivisor": null, + "squarefree": true, + "squarefreeStatus": "exact_squarefree", + "profileUsable": true + }, + { + "prime": 83, + "k": 4841, + "delta": -121039, + "right": 34293868, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1180220277890277", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false, + "squarefreeStatus": "non_squarefree", + "profileUsable": false + }, + { + "prime": 89, + "k": 2029, + "delta": -50739, + "right": 34364168, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1182639645852377", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": null, + "squareDivisor": null, + "squarefree": true, + "squarefreeStatus": "exact_squarefree", + "profileUsable": true + }, + { + "prime": 97, + "k": 8567, + "delta": -214189, + "right": 34200718, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1177014529303227", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false, + "squarefreeStatus": "non_squarefree", + "profileUsable": false + }, + { + "prime": 101, + "k": 6347, + "delta": -158689, + "right": 34256218, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1178924556641727", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": 7, + "squareDivisor": 49, + "squarefree": false, + "squarefreeStatus": "non_squarefree", + "profileUsable": false + }, + { + "prime": 103, + "k": 2472, + "delta": -61814, + "right": 34353093, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1182258500757352", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false, + "squarefreeStatus": "non_squarefree", + "profileUsable": false + }, + { + "prime": 107, + "k": 7966, + "delta": -199164, + "right": 34215743, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1177531613280902", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": 11, + "squareDivisor": 121, + "squarefree": false, + "squarefreeStatus": "non_squarefree", + "profileUsable": false + }, + { + "prime": 109, + "k": 4325, + "delta": -108139, + "right": 34306768, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1180664230190577", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": null, + "squareDivisor": null, + "squarefree": true, + "squarefreeStatus": "exact_squarefree", + "profileUsable": true + }, + { + "prime": 113, + "k": 5338, + "delta": -133464, + "right": 34281443, + "rightMod25": 18, + "withinWindow": false, + "compatibilityModPrimeSquare": 0, + "crossProductPlusOne": "1179792672670802", + "checkedSquarePrimeLimit": 34414903, + "squareDivisorPrime": null, + "squareDivisor": null, + "squarefree": true, + "squarefreeStatus": "exact_squarefree", + "profileUsable": true + } + ], + "firstPrimarySquarefree": null, + "firstAnySquarefree": null, + "primaryCovered": false, + "allCovered": false + } + ] + }, + "claims": { + "provesAllN": false, + "provesCollisionFreeMatching": false, + "provesEndpointFormulas": true, + "provesUniversalWindowAvailabilityForPrimaryMenu": false, + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": false + }, + "nextTheoremOptions": [ + { + "id": "primary_menu_first_miss", + "status": "needed", + "statement": "The primary menu misses at left=34414907; inspect this miss before adding more abstraction." + }, + { + "id": "full_menu_first_miss", + "status": "needed", + "statement": "The full menu misses at left=34414907; emit this row as the next deterministic obstruction." + }, + { + "id": "fallback_window_availability_split", + "status": "optional", + "statement": "Some fallback primes are not universally inside the window; split fallback usage into availability residues before relying on them symbolically." + } + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.md new file mode 100644 index 0000000..711ec33 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.md @@ -0,0 +1,57 @@ +# Problem 848 Endpoint Menu Compiler + +- Target: `q17 residual window-relaxed fallback endpoint-menu selector` +- Residual class: `left ≡ 5882 mod 11025` +- Scan: `34414907..34414907` over `1` residual rows +- Window: `25000` +- Square check: `No full-menu covered endpoint was selected in this profile; inspect candidate square-divisor statuses and window availability.` +- Primary menu: `23,31,37,41,61,67` +- Fallback menu: `71,73,79,83,89,97,101,103,107,109,113` + +## Endpoint Formulas + +- p=23: `k_23(left) = (127*left + 79) mod 529`; delta range `-13214..-14`; within 25000: `true` +- p=31: `k_31(left) = (346*left + 669) mod 961`; delta range `-24014..-14`; within 25000: `true` +- p=37: `k_37(left) = (1150*left + 651) mod 1369`; delta range `-34214..-14`; within 25000: `false` +- p=41: `k_41(left) = (269*left + 1029) mod 1681`; delta range `-42014..-14`; within 25000: `false` +- p=61: `k_61(left) = (2828*left + 2221) mod 3721`; delta range `-93014..-14`; within 25000: `false` +- p=67: `k_67(left) = (2873*left + 511) mod 4489`; delta range `-112214..-14`; within 25000: `false` +- p=71: `k_71(left) = (2823*left + 4760) mod 5041`; delta range `-126014..-14`; within 25000: `false` +- p=73: `k_73(left) = (1279*left + 5218) mod 5329`; delta range `-133214..-14`; within 25000: `false` +- p=79: `k_79(left) = (3495*left + 4770) mod 6241`; delta range `-156014..-14`; within 25000: `false` +- p=83: `k_83(left) = (4409*left + 2738) mod 6889`; delta range `-172214..-14`; within 25000: `false` +- p=89: `k_89(left) = (6020*left + 1152) mod 7921`; delta range `-198014..-14`; within 25000: `false` +- p=97: `k_97(left) = (4140*left + 4932) mod 9409`; delta range `-235214..-14`; within 25000: `false` +- p=101: `k_101(left) = (9793*left + 9742) mod 10201`; delta range `-255014..-14`; within 25000: `false` +- p=103: `k_103(left) = (4668*left + 4197) mod 10609`; delta range `-265214..-14`; within 25000: `false` +- p=107: `k_107(left) = (458*left + 2044) mod 11449`; delta range `-286214..-14`; within 25000: `false` +- p=109: `k_109(left) = (1901*left + 4499) mod 11881`; delta range `-297014..-14`; within 25000: `false` +- p=113: `k_113(left) = (10726*left + 9326) mod 12769`; delta range `-319214..-14`; within 25000: `false` + +## Coverage + +- Primary covered: `0/1` +- Full menu covered: `0/1` +- First primary miss: `34414907` +- First full-menu miss: `34414907` +- Primary cover prime counts: `[]` +- Full cover prime counts: `[]` + +## First Full-Menu Miss Detail + +- Left: `34414907` +- Left residual: `5882` +- Blocked within-window endpoints: `[{"prime":23,"k":48,"delta":-1214,"right":34413693,"withinWindow":true,"squarefreeStatus":"non_squarefree","squareDivisorPrime":2,"squareDivisor":4,"checkedSquarePrimeLimit":34414903},{"prime":31,"k":652,"delta":-16314,"right":34398593,"withinWindow":true,"squarefreeStatus":"non_squarefree","squareDivisorPrime":2,"squareDivisor":4,"checkedSquarePrimeLimit":34414903}]` +- Nearest unblocked outside-window endpoints: `[{"prime":67,"k":1139,"delta":-28489,"right":34386418,"withinWindow":false,"squarefreeStatus":"exact_squarefree","squareDivisorPrime":null,"squareDivisor":null,"checkedSquarePrimeLimit":34414903},{"prime":37,"k":1238,"delta":-30964,"right":34383943,"withinWindow":false,"squarefreeStatus":"exact_squarefree","squareDivisorPrime":null,"squareDivisor":null,"checkedSquarePrimeLimit":34414903},{"prime":79,"k":1606,"delta":-40164,"right":34374743,"withinWindow":false,"squarefreeStatus":"exact_squarefree","squareDivisorPrime":null,"squareDivisor":null,"checkedSquarePrimeLimit":34414903},{"prime":89,"k":2029,"delta":-50739,"right":34364168,"withinWindow":false,"squarefreeStatus":"exact_squarefree","squareDivisorPrime":null,"squareDivisor":null,"checkedSquarePrimeLimit":34414903},{"prime":61,"k":3238,"delta":-80964,"right":34333943,"withinWindow":false,"squarefreeStatus":"exact_squarefree","squareDivisorPrime":null,"squareDivisor":null,"checkedSquarePrimeLimit":34414903}]` + +## Next Theorem Options + +- `primary_menu_first_miss` [needed]: The primary menu misses at left=34414907; inspect this miss before adding more abstraction. +- `full_menu_first_miss` [needed]: The full menu misses at left=34414907; emit this row as the next deterministic obstruction. +- `fallback_window_availability_split` [optional]: Some fallback primes are not universally inside the window; split fallback usage into availability residues before relying on them symbolically. + +## Boundary + +- This compiler proves endpoint formulas and bounded coverage profiles only. +- It does not prove all-N squarefree hitting or collision-free matching by itself. + diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.json new file mode 100644 index 0000000..7e9c0ce --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.json @@ -0,0 +1,293 @@ +{ + "schema": "erdos.number_theory.p848_endpoint_window_grid/1", + "generatedAt": "2026-04-14T03:03:13.641Z", + "problemId": "848", + "target": { + "description": "q17 residual window-relaxed fallback endpoint-menu selector window grid", + "predecessorProof": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "outsider": 6323, + "residualClass": { + "residue": 5882, + "modulus": 11025 + }, + "start": 34414907, + "end": 34414907, + "rowCount": 1, + "windows": [ + 25000, + 28500 + ], + "squareCheck": "Every covered endpoint selected by each profiled full menu is exactly squarefree-certified." + }, + "primaryMenu": [ + 23, + 31, + 37, + 41, + 61, + 67 + ], + "fallbackMenu": [ + 71, + 73, + 79, + 83, + 89, + 97, + 101, + 103, + 107, + 109, + 113 + ], + "firstScreenPrimaryCoveredWindow": 28500, + "firstScreenAllCoveredWindow": 28500, + "firstProvedPrimaryCoveredWindow": 28500, + "firstProvedAllCoveredWindow": 28500, + "summaries": [ + { + "window": 25000, + "rowCount": 1, + "squareCheck": { + "checkedPrimeLimit": 34414903, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "No full-menu covered endpoint was selected in this profile; inspect candidate square-divisor statuses and window availability." + }, + "primaryCovered": 0, + "primaryMisses": 1, + "allCovered": 0, + "allMisses": 1, + "firstPrimaryMiss": { + "left": 34414907, + "leftModResidualClass": 5882, + "usableWithinWindow": [], + "nearestUsableOutsideWindow": [ + { + "prime": 67, + "k": 1139, + "delta": -28489, + "right": 34386418, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 37, + "k": 1238, + "delta": -30964, + "right": 34383943, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 79, + "k": 1606, + "delta": -40164, + "right": 34374743, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 89, + "k": 2029, + "delta": -50739, + "right": 34364168, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 61, + "k": 3238, + "delta": -80964, + "right": 34333943, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + } + ], + "blockedWithinWindow": [ + { + "prime": 23, + "k": 48, + "delta": -1214, + "right": 34413693, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 31, + "k": 652, + "delta": -16314, + "right": 34398593, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 34414903 + } + ] + }, + "firstAllMiss": { + "left": 34414907, + "leftModResidualClass": 5882, + "usableWithinWindow": [], + "nearestUsableOutsideWindow": [ + { + "prime": 67, + "k": 1139, + "delta": -28489, + "right": 34386418, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 37, + "k": 1238, + "delta": -30964, + "right": 34383943, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 79, + "k": 1606, + "delta": -40164, + "right": 34374743, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 89, + "k": 2029, + "delta": -50739, + "right": 34364168, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 61, + "k": 3238, + "delta": -80964, + "right": 34333943, + "withinWindow": false, + "squarefreeStatus": "exact_squarefree", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 34414903 + } + ], + "blockedWithinWindow": [ + { + "prime": 23, + "k": 48, + "delta": -1214, + "right": 34413693, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 34414903 + }, + { + "prime": 31, + "k": 652, + "delta": -16314, + "right": 34398593, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 34414903 + } + ] + }, + "primaryCoverPrimeCounts": [], + "allCoverPrimeCounts": [], + "claims": { + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": false + } + }, + { + "window": 28500, + "rowCount": 1, + "squareCheck": { + "checkedPrimeLimit": 34414903, + "exactForPrimaryCoveredEndpoints": true, + "exactForAllCoveredEndpoints": true, + "interpretation": "Every covered endpoint selected by the full menu is exactly squarefree-certified." + }, + "primaryCovered": 1, + "primaryMisses": 0, + "allCovered": 1, + "allMisses": 0, + "firstPrimaryMiss": null, + "firstAllMiss": null, + "primaryCoverPrimeCounts": [ + { + "key": 67, + "count": 1 + } + ], + "allCoverPrimeCounts": [ + { + "key": 67, + "count": 1 + } + ], + "claims": { + "provesBoundedPrimaryMenuCoverage": true, + "provesBoundedAllMenuCoverage": true, + "screensBoundedPrimaryMenuCoverage": true, + "screensBoundedAllMenuCoverage": true + } + } + ], + "interpretation": { + "windowGridProvesAllN": false, + "warning": "A window grid is a bounded selector profile. It can identify the next theorem boundary but does not prove all-N coverage or matching by itself." + }, + "nextTheoremOptions": [ + { + "id": "window_relaxation_candidate", + "status": "candidate", + "statement": "The full menu first covers the bounded scan at window=28500; decide whether that relaxation is theorem-legal or requires a replacement-path handoff." + }, + { + "id": "availability_strata_lift", + "status": "needed", + "statement": "Convert the observed window thresholds into residue-class availability strata rather than continuing a row-by-row staircase." + } + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.md new file mode 100644 index 0000000..601f7b0 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.md @@ -0,0 +1,27 @@ +# Problem 848 Endpoint Window Grid + +- Target: `q17 residual window-relaxed fallback endpoint-menu selector window grid` +- Residual class: `left ≡ 5882 mod 11025` +- Scan: `34414907..34414907` over `1` residual rows +- Windows: `25000,28500` +- Square check: `Every covered endpoint selected by each profiled full menu is exactly squarefree-certified.` +- Primary menu: `23,31,37,41,61,67` +- Fallback menu: `71,73,79,83,89,97,101,103,107,109,113` +- First screen primary-covered window: `28500` +- First screen full-menu-covered window: `28500` + +## Coverage By Window + +- window=25000: primary `0/1`, full `0/1`, first primary miss `34414907`, first full miss `34414907` +- window=25000 nearest unblocked outside-window endpoint for first full miss: p=67, delta=-28489, right=34386418, status=exact_squarefree +- window=28500: primary `1/1`, full `1/1`, first primary miss `(none)`, first full miss `(none)` + +## Next Theorem Options + +- `window_relaxation_candidate` [candidate]: The full menu first covers the bounded scan at window=28500; decide whether that relaxation is theorem-legal or requires a replacement-path handoff. +- `availability_strata_lift` [needed]: Convert the observed window thresholds into residue-class availability strata rather than continuing a row-by-row staircase. + +## Boundary + +- A window grid is a bounded selector profile. It can identify the next theorem boundary but does not prove all-N coverage or matching by itself. + diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_availability_profile.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_availability_profile.json new file mode 100644 index 0000000..90dc881 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_availability_profile.json @@ -0,0 +1,3462 @@ +{ + "schema": "erdos.number_theory.p848_endpoint_availability_profile/1", + "generatedAt": "2026-04-14T04:00:33.301Z", + "problemId": "848", + "target": { + "description": "q17 residual window-relaxed fallback endpoint-menu availability profile", + "predecessorProof": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "outsider": 6323, + "residualClass": { + "residue": 5882, + "modulus": 11025 + }, + "start": 34414907, + "end": 34414907, + "witnessRowCount": 1, + "windows": [ + 25000, + 28500 + ] + }, + "interpretation": { + "endpointWindowCriterion": "Because delta=-14-25*k, an endpoint is inside window W exactly when k <= floor((W-14)/25).", + "provesSquarefreeHitting": false, + "provesCollisionFreeMatching": false, + "warning": "This profile proves modular endpoint availability only. Squarefree hitting and matching remain separate layers." + }, + "primaryMenu": { + "primeSet": [ + 23, + 31, + 37, + 41, + 61, + 67 + ] + }, + "fallbackMenu": { + "primeSet": [ + 71, + 73, + 79, + 83, + 89, + 97, + 101, + 103, + 107, + 109, + 113 + ] + }, + "formulasByPrime": { + "23": { + "prime": 23, + "primeSquare": 529, + "kFormula": { + "leftCoefficient": 127, + "constant": 79, + "modulus": 529, + "text": "k_23(left) = (127*left + 79) mod 529" + }, + "deltaRange": { + "min": -13214, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": true + }, + "availabilityByWindow": [ + { + "window": 25000, + "maxK": 999, + "minimalWindowForMaxK": 24989, + "criterion": "within window 25000 iff k_23(left) <= 999", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_23(t) = (441*t + 145) mod 529", + "tPeriod": 529, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 529, + "unavailableResidueCount": 0, + "density": 1, + "universallyWithinWindow": true, + "firstAvailableTResidues": [ + { + "tResidue": 0, + "k": 145 + }, + { + "tResidue": 1, + "k": 57 + }, + { + "tResidue": 2, + "k": 498 + }, + { + "tResidue": 3, + "k": 410 + }, + { + "tResidue": 4, + "k": 322 + }, + { + "tResidue": 5, + "k": 234 + }, + { + "tResidue": 6, + "k": 146 + }, + { + "tResidue": 7, + "k": 58 + }, + { + "tResidue": 8, + "k": 499 + }, + { + "tResidue": 9, + "k": 411 + }, + { + "tResidue": 10, + "k": 323 + }, + { + "tResidue": 11, + "k": 235 + }, + { + "tResidue": 12, + "k": 147 + }, + { + "tResidue": 13, + "k": 59 + }, + { + "tResidue": 14, + "k": 500 + }, + { + "tResidue": 15, + "k": 412 + } + ], + "firstUnavailableTResidue": null + }, + { + "window": 28500, + "maxK": 1139, + "minimalWindowForMaxK": 28489, + "criterion": "within window 28500 iff k_23(left) <= 1139", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_23(t) = (441*t + 145) mod 529", + "tPeriod": 529, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 529, + "unavailableResidueCount": 0, + "density": 1, + "universallyWithinWindow": true, + "firstAvailableTResidues": [ + { + "tResidue": 0, + "k": 145 + }, + { + "tResidue": 1, + "k": 57 + }, + { + "tResidue": 2, + "k": 498 + }, + { + "tResidue": 3, + "k": 410 + }, + { + "tResidue": 4, + "k": 322 + }, + { + "tResidue": 5, + "k": 234 + }, + { + "tResidue": 6, + "k": 146 + }, + { + "tResidue": 7, + "k": 58 + }, + { + "tResidue": 8, + "k": 499 + }, + { + "tResidue": 9, + "k": 411 + }, + { + "tResidue": 10, + "k": 323 + }, + { + "tResidue": 11, + "k": 235 + }, + { + "tResidue": 12, + "k": 147 + }, + { + "tResidue": 13, + "k": 59 + }, + { + "tResidue": 14, + "k": 500 + }, + { + "tResidue": 15, + "k": 412 + } + ], + "firstUnavailableTResidue": null + } + ] + }, + "31": { + "prime": 31, + "primeSquare": 961, + "kFormula": { + "leftCoefficient": 346, + "constant": 669, + "modulus": 961, + "text": "k_31(left) = (346*left + 669) mod 961" + }, + "deltaRange": { + "min": -24014, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": true + }, + "availabilityByWindow": [ + { + "window": 25000, + "maxK": 999, + "minimalWindowForMaxK": 24989, + "criterion": "within window 25000 iff k_31(left) <= 999", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_31(t) = (441*t + 443) mod 961", + "tPeriod": 961, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 961, + "unavailableResidueCount": 0, + "density": 1, + "universallyWithinWindow": true, + "firstAvailableTResidues": [ + { + "tResidue": 0, + "k": 443 + }, + { + "tResidue": 1, + "k": 884 + }, + { + "tResidue": 2, + "k": 364 + }, + { + "tResidue": 3, + "k": 805 + }, + { + "tResidue": 4, + "k": 285 + }, + { + "tResidue": 5, + "k": 726 + }, + { + "tResidue": 6, + "k": 206 + }, + { + "tResidue": 7, + "k": 647 + }, + { + "tResidue": 8, + "k": 127 + }, + { + "tResidue": 9, + "k": 568 + }, + { + "tResidue": 10, + "k": 48 + }, + { + "tResidue": 11, + "k": 489 + }, + { + "tResidue": 12, + "k": 930 + }, + { + "tResidue": 13, + "k": 410 + }, + { + "tResidue": 14, + "k": 851 + }, + { + "tResidue": 15, + "k": 331 + } + ], + "firstUnavailableTResidue": null + }, + { + "window": 28500, + "maxK": 1139, + "minimalWindowForMaxK": 28489, + "criterion": "within window 28500 iff k_31(left) <= 1139", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_31(t) = (441*t + 443) mod 961", + "tPeriod": 961, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 961, + "unavailableResidueCount": 0, + "density": 1, + "universallyWithinWindow": true, + "firstAvailableTResidues": [ + { + "tResidue": 0, + "k": 443 + }, + { + "tResidue": 1, + "k": 884 + }, + { + "tResidue": 2, + "k": 364 + }, + { + "tResidue": 3, + "k": 805 + }, + { + "tResidue": 4, + "k": 285 + }, + { + "tResidue": 5, + "k": 726 + }, + { + "tResidue": 6, + "k": 206 + }, + { + "tResidue": 7, + "k": 647 + }, + { + "tResidue": 8, + "k": 127 + }, + { + "tResidue": 9, + "k": 568 + }, + { + "tResidue": 10, + "k": 48 + }, + { + "tResidue": 11, + "k": 489 + }, + { + "tResidue": 12, + "k": 930 + }, + { + "tResidue": 13, + "k": 410 + }, + { + "tResidue": 14, + "k": 851 + }, + { + "tResidue": 15, + "k": 331 + } + ], + "firstUnavailableTResidue": null + } + ] + }, + "37": { + "prime": 37, + "primeSquare": 1369, + "kFormula": { + "leftCoefficient": 1150, + "constant": 651, + "modulus": 1369, + "text": "k_37(left) = (1150*left + 651) mod 1369" + }, + "deltaRange": { + "min": -34214, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + }, + "availabilityByWindow": [ + { + "window": 25000, + "maxK": 999, + "minimalWindowForMaxK": 24989, + "criterion": "within window 25000 iff k_37(left) <= 999", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_37(t) = (441*t + 722) mod 1369", + "tPeriod": 1369, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 1000, + "unavailableResidueCount": 369, + "density": 0.7304601899196493, + 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"stepGcdWithPrimeSquare": 1, + "availableResidueCount": 1140, + "unavailableResidueCount": 229, + "density": 0.8327246165084002, + "universallyWithinWindow": false, + "firstAvailableTResidues": [ + { + "tResidue": 0, + "k": 722 + }, + { + "tResidue": 2, + "k": 235 + }, + { + "tResidue": 3, + "k": 676 + }, + { + "tResidue": 4, + "k": 1117 + }, + { + "tResidue": 5, + "k": 189 + }, + { + "tResidue": 6, + "k": 630 + }, + { + "tResidue": 7, + "k": 1071 + }, + { + "tResidue": 8, + "k": 143 + }, + { + "tResidue": 9, + "k": 584 + }, + { + "tResidue": 10, + "k": 1025 + }, + { + "tResidue": 11, + "k": 97 + }, + { + "tResidue": 12, + "k": 538 + }, + { + "tResidue": 13, + "k": 979 + }, + { + "tResidue": 14, + "k": 51 + }, + { + "tResidue": 15, + "k": 492 + }, + { + "tResidue": 16, + "k": 933 + } + ], + "firstUnavailableTResidue": { + "tResidue": 1, + "k": 1163 + } + } + ] + }, + "41": { + "prime": 41, + "primeSquare": 1681, + "kFormula": { + "leftCoefficient": 269, + "constant": 1029, + "modulus": 1681, + "text": "k_41(left) = (269*left + 1029) mod 1681" + }, + "deltaRange": { + "min": -42014, + "max": -14 + }, + "universallyWithinWindows": { + "10000": false, + "25000": false + }, + "availabilityByWindow": [ + { + "window": 25000, + "maxK": 999, + "minimalWindowForMaxK": 24989, + "criterion": "within window 25000 iff k_41(left) <= 999", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_41(t) = (441*t + 1466) mod 1681", + "tPeriod": 1681, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 1000, + "unavailableResidueCount": 681, + "density": 0.594883997620464, + "universallyWithinWindow": false, + "firstAvailableTResidues": [ + { + "tResidue": 1, + "k": 226 + }, + { + "tResidue": 2, + "k": 667 + }, + { + "tResidue": 5, + "k": 309 + }, + { + "tResidue": 6, + "k": 750 + }, + { + "tResidue": 9, + "k": 392 + }, + { + "tResidue": 10, + "k": 833 + }, + { + "tResidue": 12, + "k": 34 + }, + { + "tResidue": 13, + "k": 475 + }, + { + "tResidue": 14, + "k": 916 + 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5882 + 11025*t", + "kFormulaInT": "k_61(t) = (441*t + 3647) mod 3721", + "tPeriod": 3721, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 1000, + "unavailableResidueCount": 2721, + "density": 0.26874496103198064, + "universallyWithinWindow": false, + "firstAvailableTResidues": [ + { + "tResidue": 1, + "k": 367 + }, + { + "tResidue": 2, + "k": 808 + }, + { + "tResidue": 9, + "k": 174 + }, + { + "tResidue": 10, + "k": 615 + }, + { + "tResidue": 18, + "k": 422 + }, + { + "tResidue": 19, + "k": 863 + }, + { + "tResidue": 26, + "k": 229 + }, + { + "tResidue": 27, + "k": 670 + }, + { + "tResidue": 34, + "k": 36 + }, + { + "tResidue": 35, + "k": 477 + }, + { + "tResidue": 36, + "k": 918 + }, + { + "tResidue": 43, + "k": 284 + }, + { + "tResidue": 44, + "k": 725 + }, + { + "tResidue": 51, + "k": 91 + }, + { + "tResidue": 52, + "k": 532 + }, + { + "tResidue": 53, + "k": 973 + } + ], + "firstUnavailableTResidue": { + "tResidue": 0, + "k": 3647 + } + }, + { + "window": 28500, + "maxK": 1139, + "minimalWindowForMaxK": 28489, + "criterion": "within window 28500 iff k_61(left) <= 1139", + "leftParameterization": "left = 5882 + 11025*t", + "kFormulaInT": "k_61(t) = (441*t + 3647) mod 3721", + "tPeriod": 3721, + "stepGcdWithPrimeSquare": 1, + "availableResidueCount": 1140, + "unavailableResidueCount": 2581, + "density": 0.30636925557645794, + "universallyWithinWindow": false, + "firstAvailableTResidues": [ + { + "tResidue": 1, + "k": 367 + }, + { + "tResidue": 2, + "k": 808 + }, + { + "tResidue": 9, + "k": 174 + }, + { + "tResidue": 10, + "k": 615 + }, + { + "tResidue": 11, + "k": 1056 + }, + { + "tResidue": 18, + "k": 422 + }, + { + "tResidue": 19, + "k": 863 + }, + { + "tResidue": 26, + "k": 229 + }, + { + "tResidue": 27, + "k": 670 + }, + { + "tResidue": 28, + "k": 1111 + }, + { + "tResidue": 34, + "k": 36 + }, + { + "tResidue": 35, + "k": 477 + }, + { + "tResidue": 36, + "k": 918 + }, + { + "tResidue": 43, + "k": 284 + }, + { + "tResidue": 44, + "k": 725 + }, + { + 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+ "withinWindows": { + "25000": false, + "28500": false + } + }, + { + "prime": 97, + "k": 8567, + "delta": -214189, + "right": 34200718, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "withinWindows": { + "25000": false, + "28500": false + } + }, + { + "prime": 101, + "k": 6347, + "delta": -158689, + "right": 34256218, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "withinWindows": { + "25000": false, + "28500": false + } + }, + { + "prime": 103, + "k": 2472, + "delta": -61814, + "right": 34353093, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "withinWindows": { + "25000": false, + "28500": false + } + }, + { + "prime": 107, + "k": 7966, + "delta": -199164, + "right": 34215743, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "withinWindows": { + "25000": false, + "28500": false + } + }, + { + "prime": 109, + "k": 4325, + "delta": -108139, + "right": 34306768, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "withinWindows": { + "25000": false, + "28500": false + } + }, + { + "prime": 113, + "k": 5338, + "delta": -133464, + "right": 34281443, + "rightMod25": 18, + "compatibilityModPrimeSquare": 0, + "withinWindows": { + "25000": false, + "28500": false + } + } + ] + } + ], + "nextTheoremOptions": [ + { + "id": "availability_residue_cover", + "status": "ready", + "statement": "Use the k-threshold rules to split endpoint availability into finite t-residue strata before proving squarefree hitting." + }, + { + "id": "window_legality_threshold", + "status": "ready", + "statement": "The candidate windows have thresholds 25000->k<=999, 28500->k<=1139; prove which threshold is theorem-legal." + } + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_availability_profile.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_availability_profile.md new file mode 100644 index 0000000..87b5c61 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_availability_profile.md @@ -0,0 +1,80 @@ +# Problem 848 Endpoint Availability Profile + +- Target: `q17 residual window-relaxed fallback endpoint-menu availability profile` +- Residual class: `left ≡ 5882 mod 11025` +- Windows: `25000,28500` +- Primary menu: `23,31,37,41,61,67` +- Fallback menu: `71,73,79,83,89,97,101,103,107,109,113` + +## Window Thresholds + +- window=25000: endpoint is available iff `k <= 999`; minimal exact threshold window is `24989` +- window=28500: endpoint is available iff `k <= 1139`; minimal exact threshold window is `28489` + +## Availability By Prime + +- p=23: `k_23(left) = (127*left + 79) mod 529` +- p=23, window=25000: `k_23(t) = (441*t + 145) mod 529`, t-period `529`, available `529/529`, universal `true` +- p=23, window=28500: `k_23(t) = (441*t + 145) mod 529`, t-period `529`, available `529/529`, universal `true` +- p=31: `k_31(left) = (346*left + 669) mod 961` +- p=31, window=25000: `k_31(t) = (441*t + 443) mod 961`, t-period `961`, available `961/961`, universal `true` +- p=31, window=28500: `k_31(t) = (441*t + 443) mod 961`, t-period `961`, available `961/961`, universal `true` +- p=37: `k_37(left) = (1150*left + 651) mod 1369` +- p=37, window=25000: `k_37(t) = (441*t + 722) mod 1369`, t-period `1369`, available `1000/1369`, universal `false` +- p=37, window=28500: `k_37(t) = (441*t + 722) mod 1369`, t-period `1369`, available `1140/1369`, universal `false` +- p=41: `k_41(left) = (269*left + 1029) mod 1681` +- p=41, window=25000: `k_41(t) = (441*t + 1466) mod 1681`, t-period `1681`, available `1000/1681`, universal `false` +- p=41, window=28500: `k_41(t) = (441*t + 1466) mod 1681`, t-period `1681`, available `1140/1681`, universal `false` +- p=61: `k_61(left) = (2828*left + 2221) mod 3721` +- p=61, window=25000: `k_61(t) = (441*t + 3647) mod 3721`, t-period `3721`, available `1000/3721`, universal `false` +- p=61, window=28500: `k_61(t) = (441*t + 3647) mod 3721`, t-period `3721`, available `1140/3721`, universal `false` +- p=67: `k_67(left) = (2873*left + 511) mod 4489` +- p=67, window=25000: `k_67(t) = (441*t + 2901) mod 4489`, t-period `4489`, available `1000/4489`, universal `false` +- p=67, window=28500: `k_67(t) = (441*t + 2901) mod 4489`, t-period `4489`, available `1140/4489`, universal `false` +- p=71: `k_71(left) = (2823*left + 4760) mod 5041` +- p=71, window=25000: `k_71(t) = (441*t + 4592) mod 5041`, t-period `5041`, available `1000/5041`, universal `false` +- p=71, window=28500: `k_71(t) = (441*t + 4592) mod 5041`, t-period `5041`, available `1140/5041`, universal `false` +- p=73: `k_73(left) = (1279*left + 5218) mod 5329` +- p=73, window=25000: `k_73(t) = (441*t + 3748) mod 5329`, t-period `5329`, available `1000/5329`, universal `false` +- p=73, window=28500: `k_73(t) = (441*t + 3748) mod 5329`, t-period `5329`, available `1140/5329`, universal `false` +- p=79: `k_79(left) = (3495*left + 4770) mod 6241` +- p=79, window=25000: `k_79(t) = (441*t + 4506) mod 6241`, t-period `6241`, available `1000/6241`, universal `false` +- p=79, window=28500: `k_79(t) = (441*t + 4506) mod 6241`, t-period `6241`, available `1140/6241`, universal `false` +- p=83: `k_83(left) = (4409*left + 2738) mod 6889` +- p=83, window=25000: `k_83(t) = (441*t + 6280) mod 6889`, t-period `6889`, available `1000/6889`, universal `false` +- p=83, window=28500: `k_83(t) = (441*t + 6280) mod 6889`, t-period `6889`, available `1140/6889`, universal `false` +- p=89: `k_89(left) = (6020*left + 1152) mod 7921` +- p=89, window=25000: `k_89(t) = (441*t + 3922) mod 7921`, t-period `7921`, available `1000/7921`, universal `false` +- p=89, window=28500: `k_89(t) = (441*t + 3922) mod 7921`, t-period `7921`, available `1140/7921`, universal `false` +- p=97: `k_97(left) = (4140*left + 4932) mod 9409` +- p=97, window=25000: `k_97(t) = (441*t + 5920) mod 9409`, t-period `9409`, available `1000/9409`, universal `false` +- p=97, window=28500: `k_97(t) = (441*t + 5920) mod 9409`, t-period `9409`, available `1140/9409`, universal `false` +- p=101: `k_101(left) = (9793*left + 9742) mod 10201` +- p=101, window=25000: `k_101(t) = (441*t + 7121) mod 10201`, t-period `10201`, available `1000/10201`, universal `false` +- p=101, window=28500: `k_101(t) = (441*t + 7121) mod 10201`, t-period `10201`, available `1140/10201`, universal `false` +- p=103: `k_103(left) = (4668*left + 4197) mod 10609` +- p=103, window=25000: `k_103(t) = (441*t + 5281) mod 10609`, t-period `10609`, available `1000/10609`, universal `false` +- p=103, window=28500: `k_103(t) = (441*t + 5281) mod 10609`, t-period `10609`, available `1140/10609`, universal `false` +- p=107: `k_107(left) = (458*left + 2044) mod 11449` +- p=107, window=25000: `k_107(t) = (441*t + 5485) mod 11449`, t-period `11449`, available `1000/11449`, universal `false` +- p=107, window=28500: `k_107(t) = (441*t + 5485) mod 11449`, t-period `11449`, available `1140/11449`, universal `false` +- p=109: `k_109(left) = (1901*left + 4499) mod 11881` +- p=109, window=25000: `k_109(t) = (441*t + 6160) mod 11881`, t-period `11881`, available `1000/11881`, universal `false` +- p=109, window=28500: `k_109(t) = (441*t + 6160) mod 11881`, t-period `11881`, available `1140/11881`, universal `false` +- p=113: `k_113(left) = (10726*left + 9326) mod 12769` +- p=113, window=25000: `k_113(t) = (441*t + 8029) mod 12769`, t-period `12769`, available `1000/12769`, universal `false` +- p=113, window=28500: `k_113(t) = (441*t + 8029) mod 12769`, t-period `12769`, available `1140/12769`, universal `false` + +## Witness Rows + +- left=34414907: p=23: k=48, delta=-1214, windows={"25000":true,"28500":true}; p=31: k=652, delta=-16314, windows={"25000":true,"28500":true}; p=37: k=1238, delta=-30964, windows={"25000":false,"28500":false}; p=41: k=1088, delta=-27214, windows={"25000":false,"28500":true}; p=61: k=3238, delta=-80964, windows={"25000":false,"28500":false}; p=67: k=1139, delta=-28489, windows={"25000":false,"28500":true}; p=71: k=4760, delta=-119014, windows={"25000":false,"28500":false}; p=73: k=5227, delta=-130689, windows={"25000":false,"28500":false}; p=79: k=1606, delta=-40164, windows={"25000":false,"28500":false}; p=83: k=4841, delta=-121039, windows={"25000":false,"28500":false}; p=89: k=2029, delta=-50739, windows={"25000":false,"28500":false}; p=97: k=8567, delta=-214189, windows={"25000":false,"28500":false}; p=101: k=6347, delta=-158689, windows={"25000":false,"28500":false}; p=103: k=2472, delta=-61814, windows={"25000":false,"28500":false}; p=107: k=7966, delta=-199164, windows={"25000":false,"28500":false}; p=109: k=4325, delta=-108139, windows={"25000":false,"28500":false}; p=113: k=5338, delta=-133464, windows={"25000":false,"28500":false} + +## Next Theorem Options + +- `availability_residue_cover` [ready]: Use the k-threshold rules to split endpoint availability into finite t-residue strata before proving squarefree hitting. +- `window_legality_threshold` [ready]: The candidate windows have thresholds 25000->k<=999, 28500->k<=1139; prove which threshold is theorem-legal. + +## Boundary + +- This profile proves modular endpoint availability only. Squarefree hitting and matching remain separate layers. + diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.json new file mode 100644 index 0000000..081fd2e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.json @@ -0,0 +1,1227 @@ +{ + "schema": "erdos.number_theory.p848_endpoint_window_grid/1", + "generatedAt": "2026-04-14T03:02:49.031Z", + "problemId": "848", + "target": { + "description": "q17 residual window-relaxed fallback endpoint-menu selector window grid", + "predecessorProof": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "outsider": 6323, + "residualClass": { + "residue": 5882, + "modulus": 11025 + }, + "start": 27932207, + "end": 40000000, + "rowCount": 1095, + "windows": [ + 25000, + 28500, + 30000, + 35000, + 50000 + ], + "squareCheck": "Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof." + }, + "primaryMenu": [ + 23, + 31, + 37, + 41, + 61, + 67 + ], + "fallbackMenu": [ + 71, + 73, + 79, + 83, + 89, + 97, + 101, + 103, + 107, + 109, + 113 + ], + "firstScreenPrimaryCoveredWindow": null, + "firstScreenAllCoveredWindow": 28500, + "firstProvedPrimaryCoveredWindow": null, + "firstProvedAllCoveredWindow": null, + "summaries": [ + { + "window": 25000, + "rowCount": 1095, + "squareCheck": { + "checkedPrimeLimit": 9973, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof." + }, + "primaryCovered": 1076, + "primaryMisses": 19, + "allCovered": 1091, + "allMisses": 4, + "firstPrimaryMiss": { + "left": 28836257, + "leftModResidualClass": 5882, + "usableWithinWindow": [ + { + "prime": 73, + "k": 570, + "delta": -14264, + "right": 28821993, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 89, + "k": 671, + "delta": -16789, + "right": 28819468, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "nearestUsableOutsideWindow": [ + { + "prime": 37, + "k": 1239, + "delta": -30989, + "right": 28805268, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 41, + "k": 1515, + "delta": -37889, + "right": 28798368, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 103, + "k": 2115, + "delta": -52889, + "right": 28783368, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 83, + "k": 2143, + "delta": -53589, + "right": 28782668, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 107, + "k": 2351, + "delta": -58789, + "right": 28777468, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "blockedWithinWindow": [ + { + "prime": 23, + "k": 140, + "delta": -3514, + "right": 28832743, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 31, + "k": 458, + "delta": -11464, + "right": 28824793, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 3, + "squareDivisor": 9, + "checkedSquarePrimeLimit": 9973 + } + ] + }, + "firstAllMiss": { + "left": 34414907, + "leftModResidualClass": 5882, + "usableWithinWindow": [], + "nearestUsableOutsideWindow": [ + { + "prime": 67, + "k": 1139, + "delta": -28489, + "right": 34386418, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 37, + "k": 1238, + "delta": -30964, + "right": 34383943, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 79, + "k": 1606, + "delta": -40164, + "right": 34374743, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 89, + "k": 2029, + "delta": -50739, + "right": 34364168, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 61, + "k": 3238, + "delta": -80964, + "right": 34333943, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "blockedWithinWindow": [ + { + "prime": 23, + "k": 48, + "delta": -1214, + "right": 34413693, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 31, + "k": 652, + "delta": -16314, + "right": 34398593, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + } + ] + }, + "primaryCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 40 + }, + { + "key": 41, + "count": 16 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 5 + } + ], + "allCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 40 + }, + { + "key": 41, + "count": 16 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 5 + }, + { + "key": 73, + "count": 4 + }, + { + "key": 71, + "count": 3 + }, + { + "key": 83, + "count": 3 + }, + { + "key": 79, + "count": 2 + }, + { + "key": 97, + "count": 1 + }, + { + "key": 103, + "count": 1 + }, + { + "key": 109, + "count": 1 + } + ], + "claims": { + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": false + } + }, + { + "window": 28500, + "rowCount": 1095, + "squareCheck": { + "checkedPrimeLimit": 9973, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof." + }, + "primaryCovered": 1082, + "primaryMisses": 13, + "allCovered": 1095, + "allMisses": 0, + "firstPrimaryMiss": { + "left": 28836257, + "leftModResidualClass": 5882, + "usableWithinWindow": [ + { + "prime": 73, + "k": 570, + "delta": -14264, + "right": 28821993, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 89, + "k": 671, + "delta": -16789, + "right": 28819468, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "nearestUsableOutsideWindow": [ + { + "prime": 37, + "k": 1239, + "delta": -30989, + "right": 28805268, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 41, + "k": 1515, + "delta": -37889, + "right": 28798368, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 103, + "k": 2115, + "delta": -52889, + "right": 28783368, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 83, + "k": 2143, + "delta": -53589, + "right": 28782668, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 107, + "k": 2351, + "delta": -58789, + "right": 28777468, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "blockedWithinWindow": [ + { + "prime": 23, + "k": 140, + "delta": -3514, + "right": 28832743, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 31, + "k": 458, + "delta": -11464, + "right": 28824793, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 3, + "squareDivisor": 9, + "checkedSquarePrimeLimit": 9973 + } + ] + }, + "firstAllMiss": null, + "primaryCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 45 + }, + { + "key": 41, + "count": 17 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 5 + } + ], + "allCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 45 + }, + { + "key": 41, + "count": 17 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 5 + }, + { + "key": 73, + "count": 3 + }, + { + "key": 83, + "count": 3 + }, + { + "key": 71, + "count": 2 + }, + { + "key": 79, + "count": 2 + }, + { + "key": 97, + "count": 1 + }, + { + "key": 103, + "count": 1 + }, + { + "key": 109, + "count": 1 + } + ], + "claims": { + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": true + } + }, + { + "window": 30000, + "rowCount": 1095, + "squareCheck": { + "checkedPrimeLimit": 9973, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof." + }, + "primaryCovered": 1083, + "primaryMisses": 12, + "allCovered": 1095, + "allMisses": 0, + "firstPrimaryMiss": { + "left": 28836257, + "leftModResidualClass": 5882, + "usableWithinWindow": [ + { + "prime": 73, + "k": 570, + "delta": -14264, + "right": 28821993, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 89, + "k": 671, + "delta": -16789, + "right": 28819468, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "nearestUsableOutsideWindow": [ + { + "prime": 37, + "k": 1239, + "delta": -30989, + "right": 28805268, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 41, + "k": 1515, + "delta": -37889, + "right": 28798368, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 103, + "k": 2115, + "delta": -52889, + "right": 28783368, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 83, + "k": 2143, + "delta": -53589, + "right": 28782668, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 107, + "k": 2351, + "delta": -58789, + "right": 28777468, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "blockedWithinWindow": [ + { + "prime": 23, + "k": 140, + "delta": -3514, + "right": 28832743, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 31, + "k": 458, + "delta": -11464, + "right": 28824793, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 3, + "squareDivisor": 9, + "checkedSquarePrimeLimit": 9973 + } + ] + }, + "firstAllMiss": null, + "primaryCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 46 + }, + { + "key": 41, + "count": 17 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 5 + } + ], + "allCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 46 + }, + { + "key": 41, + "count": 17 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 5 + }, + { + "key": 83, + "count": 3 + }, + { + "key": 71, + "count": 2 + }, + { + "key": 73, + "count": 2 + }, + { + "key": 79, + "count": 2 + }, + { + "key": 97, + "count": 1 + }, + { + "key": 103, + "count": 1 + }, + { + "key": 109, + "count": 1 + } + ], + "claims": { + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": true + } + }, + { + "window": 35000, + "rowCount": 1095, + "squareCheck": { + "checkedPrimeLimit": 9973, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof." + }, + "primaryCovered": 1089, + "primaryMisses": 6, + "allCovered": 1095, + "allMisses": 0, + "firstPrimaryMiss": { + "left": 34900007, + "leftModResidualClass": 5882, + "usableWithinWindow": [ + { + "prime": 103, + "k": 658, + "delta": -16464, + "right": 34883543, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "nearestUsableOutsideWindow": [ + { + "prime": 79, + "k": 2287, + "delta": -57189, + "right": 34842818, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 67, + "k": 2587, + "delta": -64689, + "right": 34835318, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 73, + "k": 3315, + "delta": -82889, + "right": 34817118, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 83, + "k": 3578, + "delta": -89464, + "right": 34810543, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 101, + "k": 5349, + "delta": -133739, + "right": 34766268, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "blockedWithinWindow": [ + { + "prime": 37, + "k": 107, + "delta": -2689, + "right": 34897318, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 3, + "squareDivisor": 9, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 61, + "k": 316, + "delta": -7914, + "right": 34892093, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 41, + "k": 320, + "delta": -8014, + "right": 34891993, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 23, + "k": 408, + "delta": -10214, + "right": 34889793, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 31, + "k": 836, + "delta": -20914, + "right": 34879093, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + } + ] + }, + "firstAllMiss": null, + "primaryCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 56 + }, + { + "key": 41, + "count": 14 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 4 + } + ], + "allCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 56 + }, + { + "key": 41, + "count": 14 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 4 + }, + { + "key": 83, + "count": 2 + }, + { + "key": 71, + "count": 1 + }, + { + "key": 73, + "count": 1 + }, + { + "key": 103, + "count": 1 + }, + { + "key": 109, + "count": 1 + } + ], + "claims": { + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": true + } + }, + { + "window": 50000, + "rowCount": 1095, + "squareCheck": { + "checkedPrimeLimit": 9973, + "exactForPrimaryCoveredEndpoints": false, + "exactForAllCoveredEndpoints": false, + "interpretation": "Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof." + }, + "primaryCovered": 1091, + "primaryMisses": 4, + "allCovered": 1095, + "allMisses": 0, + "firstPrimaryMiss": { + "left": 34900007, + "leftModResidualClass": 5882, + "usableWithinWindow": [ + { + "prime": 103, + "k": 658, + "delta": -16464, + "right": 34883543, + "withinWindow": true, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "nearestUsableOutsideWindow": [ + { + "prime": 79, + "k": 2287, + "delta": -57189, + "right": 34842818, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 67, + "k": 2587, + "delta": -64689, + "right": 34835318, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 73, + "k": 3315, + "delta": -82889, + "right": 34817118, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 83, + "k": 3578, + "delta": -89464, + "right": 34810543, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 101, + "k": 5349, + "delta": -133739, + "right": 34766268, + "withinWindow": false, + "squarefreeStatus": "no_checked_square_divisor", + "squareDivisorPrime": null, + "squareDivisor": null, + "checkedSquarePrimeLimit": 9973 + } + ], + "blockedWithinWindow": [ + { + "prime": 37, + "k": 107, + "delta": -2689, + "right": 34897318, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 3, + "squareDivisor": 9, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 61, + "k": 316, + "delta": -7914, + "right": 34892093, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 41, + "k": 320, + "delta": -8014, + "right": 34891993, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 23, + "k": 408, + "delta": -10214, + "right": 34889793, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + }, + { + "prime": 31, + "k": 836, + "delta": -20914, + "right": 34879093, + "withinWindow": true, + "squarefreeStatus": "non_squarefree", + "squareDivisorPrime": 2, + "squareDivisor": 4, + "checkedSquarePrimeLimit": 9973 + } + ] + }, + "firstAllMiss": null, + "primaryCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 56 + }, + { + "key": 41, + "count": 17 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 3 + } + ], + "allCoverPrimeCounts": [ + { + "key": 23, + "count": 819 + }, + { + "key": 31, + "count": 191 + }, + { + "key": 37, + "count": 56 + }, + { + "key": 41, + "count": 17 + }, + { + "key": 61, + "count": 5 + }, + { + "key": 67, + "count": 3 + }, + { + "key": 71, + "count": 1 + }, + { + "key": 73, + "count": 1 + }, + { + "key": 83, + "count": 1 + }, + { + "key": 103, + "count": 1 + } + ], + "claims": { + "provesBoundedPrimaryMenuCoverage": false, + "provesBoundedAllMenuCoverage": false, + "screensBoundedPrimaryMenuCoverage": false, + "screensBoundedAllMenuCoverage": true + } + } + ], + "interpretation": { + "windowGridProvesAllN": false, + "warning": "A window grid is a bounded selector profile. It can identify the next theorem boundary but does not prove all-N coverage or matching by itself." + }, + "nextTheoremOptions": [ + { + "id": "window_relaxation_candidate", + "status": "candidate", + "statement": "The full menu first covers the bounded scan at window=28500; decide whether that relaxation is theorem-legal or requires a replacement-path handoff." + }, + { + "id": "availability_strata_lift", + "status": "needed", + "statement": "Convert the observed window thresholds into residue-class availability strata rather than continuing a row-by-row staircase." + } + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.md new file mode 100644 index 0000000..32d1387 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.md @@ -0,0 +1,30 @@ +# Problem 848 Endpoint Window Grid + +- Target: `q17 residual window-relaxed fallback endpoint-menu selector window grid` +- Residual class: `left ≡ 5882 mod 11025` +- Scan: `27932207..40000000` over `1095` residual rows +- Windows: `25000,28500,30000,35000,50000` +- Square check: `Fast obstruction screening is present; no checked square divisor is not always an all-prime squarefree proof.` +- Primary menu: `23,31,37,41,61,67` +- Fallback menu: `71,73,79,83,89,97,101,103,107,109,113` +- First screen primary-covered window: `(none)` +- First screen full-menu-covered window: `28500` + +## Coverage By Window + +- window=25000: primary `1076/1095`, full `1091/1095`, first primary miss `28836257`, first full miss `34414907` +- window=25000 nearest unblocked outside-window endpoint for first full miss: p=67, delta=-28489, right=34386418, status=no_checked_square_divisor +- window=28500: primary `1082/1095`, full `1095/1095`, first primary miss `28836257`, first full miss `(none)` +- window=30000: primary `1083/1095`, full `1095/1095`, first primary miss `28836257`, first full miss `(none)` +- window=35000: primary `1089/1095`, full `1095/1095`, first primary miss `34900007`, first full miss `(none)` +- window=50000: primary `1091/1095`, full `1095/1095`, first primary miss `34900007`, first full miss `(none)` + +## Next Theorem Options + +- `window_relaxation_candidate` [candidate]: The full menu first covers the bounded scan at window=28500; decide whether that relaxation is theorem-legal or requires a replacement-path handoff. +- `availability_strata_lift` [needed]: Convert the observed window thresholds into residue-class availability strata rather than continuing a row-by-row staircase. + +## Boundary + +- A window grid is a bounded selector profile. It can identify the next theorem boundary but does not prove all-N coverage or matching by itself. + diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.json new file mode 100644 index 0000000..93aec5d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.json @@ -0,0 +1,109 @@ +{ + "schema": "erdos.number_theory.p848_endpoint_window_legality_audit/1", + "generatedAt": "2026-04-14", + "problemId": 848, + "status": "candidate_window_relaxation_requires_theorem_legality", + "activeAtom": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "scope": { + "split": "D2_p13", + "outsider": 6323, + "residualClass": { + "leftModulus": 11025, + "leftResidue": 5882 + }, + "selectorLayerOnly": true, + "matchingLayerSeparate": true + }, + "windows": { + "inheritedWindow": 25000, + "candidateEndpointWindow": 28500, + "deltaBeyondInheritedWindow": 3489 + }, + "sourcePackets": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_grid_profile.json", + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss.json", + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_first_window_miss_exact_window_grid.json", + "TASK_LIST.json", + "src/runtime/theorem-loop.js" + ], + "observedEndpointRepair": { + "left": 34414907, + "prime": 67, + "k": 1139, + "delta": -28489, + "right": 34386418, + "rightMod25": 18, + "outsiderCompatibility": { + "expression": "6323 * right + 1", + "divisibleByPrimeSquare": 4489, + "primeSquare": "67^2" + }, + "crossProduct": { + "expression": "left * right + 1", + "exactSquarefreeCertified": true + } + }, + "boundedEvidence": { + "broadFastGrid": { + "scan": "27932207..40000000", + "rows": 1095, + "window25000FullCovered": 1091, + "window25000FirstFullMiss": 34414907, + "window28500FullCovered": 1095, + "window28500FirstFullMiss": null, + "squareCheck": "fast_screen" + }, + "exactFirstMissGrid": { + "scan": "34414907..34414907", + "rows": 1, + "window25000FullCovered": 0, + "window28500FullCovered": 1, + "squareCheck": "exact_squarefree" + } + }, + "inheritedBoundaryAudit": { + "taskListStillSays25000": true, + "runtimeCarriesSeedEscapeWindowForward": true, + "observedReasonFor25000": "inherited seedEscapeWindow/task wording from previous selector packets", + "notYetFoundInThisAudit": [ + "A theorem packet proving that 25000 is a collision-free matching invariant.", + "A theorem packet proving that endpoints with 25000 < |delta| <= 28500 are illegal.", + "A theorem packet showing that the p67 endpoint at left=34414907 breaks right-compatibility or squarefreeness." + ] + }, + "alreadySatisfiedAtEndpointLayer": [ + "The p67 endpoint is inside the candidate 28500 window.", + "The p67 endpoint has right == 18 mod 25.", + "The p67 endpoint satisfies outsider compatibility by construction.", + "The p67 endpoint is exactly squarefree for left * right + 1 at the first 25000-window full miss.", + "The broad fast grid has no full-menu misses at window 28500 over the profiled residual band." + ], + "notProvedHere": [ + "All-N coverage for every q17 residual row.", + "Collision-free online matching.", + "The D2/D3 dynamic-margin promotion.", + "A symbolic availability/residue cover for window 28500.", + "A proof that broad fast-screen coverage is exact squarefree coverage for the full band." + ], + "theoremFork": [ + { + "id": "prove_28500_endpoint_window_legality", + "status": "recommended_next", + "statement": "Prove that the q17 residual selector may use the candidate 28500 endpoint window, at least for the p67 repair stratum and any follow-on fallback strata.", + "completionRule": "Either emit a symbolic legality lemma for window 28500 or identify the exact invariant that forbids relaxing the old 25000 cap." + }, + { + "id": "preserve_25000_and_augment", + "status": "alternate_if_25000_is_structural", + "statement": "If 25000 is a real matching invariant, keep the cap and route the left=34414907 p67 endpoint into a replacement/augmenting-path handoff rather than a direct selector relaxation.", + "completionRule": "A bounded replacement path becomes a symbolic augmentation lemma, or emits the next deterministic obstruction." + }, + { + "id": "availability_residue_cover", + "status": "needed_after_fork", + "statement": "Convert the p67 and fallback endpoint availability thresholds into residue-class strata so the loop stops extending by one row at a time.", + "completionRule": "Every residual class is assigned to an endpoint prime/window stratum or the first unassigned residue class is emitted." + } + ], + "recommendedNextAction": "prove_or_falsify_28500_endpoint_window_legality" +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.md new file mode 100644 index 0000000..eeab76a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_window_legality_audit.md @@ -0,0 +1,41 @@ +# Problem 848 Endpoint Window Legality Audit + +- Active atom: `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Scope: q17 residual endpoint selection for `left == 5882 mod 11025` and outsider `6323`. +- Inherited window: `25000`. +- Candidate endpoint window: `28500`. +- Verdict: `28500` is a candidate endpoint-selector relaxation, not yet a matching proof. + +## What The Audit Shows + +- The live task wording still asks for a `25000`-window endpoint menu. +- The runtime propagates `seedEscapeWindow` from earlier selector packets into the next task language. +- The proof packets repeatedly state that this endpoint-menu lane is cross-squarefree endpoint selection only; collision-free matching remains separate. +- In this audit, the `25000` cap appears to be an inherited selector-window boundary, not yet a proved collision-free matching invariant. +- I did not find a theorem packet showing that endpoints with `25000 < |delta| <= 28500` are illegal. + +## Key Repair Row + +- First full-menu miss under the `25000` window: `left=34414907`. +- Nearest usable outside-window endpoint: `p=67`, `delta=-28489`, `right=34386418`. +- This endpoint is inside the candidate `28500` window by `11`. +- It satisfies `right == 18 mod 25`. +- It satisfies outsider compatibility because `67^2 | 6323 * right + 1`. +- It is exactly squarefree-certified for `left * right + 1` in the exact first-miss grid. + +## Evidence Boundary + +- Broad fast grid over `27932207..40000000`: window `25000` covers `1091/1095` full-menu rows and first misses at `34414907`. +- Broad fast grid over the same band: window `28500` covers `1095/1095` full-menu rows. +- Exact first-miss grid over `34414907..34414907`: window `25000` misses and window `28500` covers via p67 exactly. +- This does not prove all-N coverage, collision-free matching, D2/D3 promotion, or full-band exact squarefreeness. + +## Theorem Fork + +1. Prove `28500` endpoint-window legality for the q17 residual selector, at least for the p67 repair stratum and any follow-on fallback strata. +2. If `25000` is structural, preserve it and route `left=34414907` into a replacement/augmenting-path handoff instead of direct selector relaxation. +3. Convert endpoint availability into residue-class strata so the loop stops extending row by row. + +## Recommended Next Action + +Prove or falsify `28500` endpoint-window legality. If legal, promote the current p67 repair into the symbolic selector lemma. If illegal, identify the exact matching invariant and switch to an augmentation atom. diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift.json new file mode 100644 index 0000000..aba5a24 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift.json @@ -0,0 +1,158 @@ +{ + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "problemId": "848", + "targetPrime": 13, + "outsider": 6323, + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "bounded_p7_period_shift_profile_ready_q17_residual_lift_needed", + "proofKind": "bounded_squarefree_sieve_partition_profile", + "promotesAllNClaim": false, + "provesCrossSquarefreeAllN": false, + "provesCollisionFreeMatching": false, + "predecessorProofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift", + "predecessorProofJsonPath": "packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json", + "decision": { + "verdict": "decompose_squarefree_sieve_into_p7_period_shift_plus_q17_residual", + "reason": "The exact period-shifted endpoint-menu replay shows that same-prime p=7 shifts repair almost every bounded p=7 cross-bad row. The only bounded p=7-shift residual class is a single CRT class repaired by the q=17 endpoint formula, so the next theorem target should prove that residual rather than extend the finite window." + }, + "p7PeriodShiftLemmaCandidate": { + "lemmaId": "outsider_6323_p7_period_shift_squarefree_selector_v1", + "rightCompatibilityFormula": "k_7(left) = (2*left - 27) mod 49; d_7(left) = -14 - 25*k_7(left)", + "periodShiftFormula": "d_7_s(left) = d_7(left) - 1225*s for integers s >= 0 with -10000 <= d_7_s(left) <= -14", + "rightEndpoint": "right = left + d_7_s(left)", + "rightCompatibilityCertificate": "49 | 6323*right + 1 for every allowed shift s", + "targetPredicate": "At least one allowed p=7 period shift has squarefree left*right + 1 unless the row lies in the residual q=17 class." + }, + "boundedProfile": { + "checker": "/tmp/p848_right_escape_mine.cpp plus targeted p7-period-shift row replay", + "maxN": 20000000, + "escapeWindow": 10000, + "p7ShiftStep": 1225, + "sourceCount": 293270, + "selectedExceptionCount": 45005, + "finiteWindowMisses": 104, + "p7EndpointCrossBad": 62, + "p7PeriodShiftCovered": 59, + "p7PeriodShiftResidualCount": 3, + "p7PeriodShiftCoverageByBaseCrossPrime": [ + { + "baseCrossPrime": 2, + "rowCount": 45, + "p7ShiftCovered": 45, + "residual": 0 + }, + { + "baseCrossPrime": 3, + "rowCount": 7, + "p7ShiftCovered": 4, + "residual": 3 + }, + { + "baseCrossPrime": 17, + "rowCount": 2, + "p7ShiftCovered": 2, + "residual": 0 + }, + { + "baseCrossPrime": 19, + "rowCount": 4, + "p7ShiftCovered": 4, + "residual": 0 + }, + { + "baseCrossPrime": 23, + "rowCount": 1, + "p7ShiftCovered": 1, + "residual": 0 + }, + { + "baseCrossPrime": 31, + "rowCount": 1, + "p7ShiftCovered": 1, + "residual": 0 + }, + { + "baseCrossPrime": 43, + "rowCount": 1, + "p7ShiftCovered": 1, + "residual": 0 + }, + { + "baseCrossPrime": 97, + "rowCount": 1, + "p7ShiftCovered": 1, + "residual": 0 + } + ], + "residualClass": { + "leftModulo25": 7, + "leftModulo1225": 982, + "leftModulo11025": 5882, + "p7Delta": -664, + "p7K": 26, + "baseCrossPrime": 3, + "boundedRows": [ + { + "left": 6940607, + "p7ShiftBadPrimes": [3, 7, 2, 7, 7, 7], + "q17Delta": -2039, + "q17Right": 6938568, + "q17CrossSquarefree": true + }, + { + "left": 7161107, + "p7ShiftBadPrimes": [3, 7, 2, 7, 7, 7], + "q17Delta": -5789, + "q17Right": 7155318, + "q17CrossSquarefree": true + }, + { + "left": 14614007, + "p7ShiftBadPrimes": [3, 7, 2, 7, 7, 7], + "q17Delta": -2489, + "q17Right": 14611518, + "q17CrossSquarefree": true + } + ] + }, + "q17ResidualCoverage": { + "q": 17, + "modulus": 289, + "inverseCoefficient": 36, + "kFormula": "k_17(left) = (185*left + 47) mod 289", + "deltaFormula": "d_17(left) = -14 - 25*k_17(left)", + "boundedResidualRowsCovered": 3, + "firstResidualQ17CrossBad": null + } + }, + "sieveReduction": { + "reductionId": "outsider_6323_p7_period_shift_plus_q17_residual_sieve_reduction_v1", + "proofPlan": [ + "Prove the p=7 period-shift selector: for p=7 endpoint cross-bad rows outside left == 5882 mod 11025, at least one allowed p=7 shift has squarefree cross product.", + "For the residual class left == 5882 mod 11025, prove the q=17 endpoint formula gives a positive side18 endpoint inside the 10000 window.", + "Prove left*(left+d_17(left))+1 is squarefree on that residual class, or emit the first residual q=17 cross-bad row." + ], + "openRisk": "A future row in the residual CRT class may make the q=17 endpoint cross-bad. Such a row should become the next deterministic packet." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 p7 period-shift plus q17 residual squarefree selector lift", + "statement": "Prove the p=7 period-shift squarefree selector and the q=17 residual-class fallback for the period-shifted endpoint menu, or emit the first residual row where the q=17 endpoint is cross-blocked.", + "completionRule": "A symbolic p7-shift plus q17 residual lemma proves cross-squarefree endpoint existence for the menu, or the first q17 residual cross-bad row becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift", + "seedPrimeSet": [7, 17], + "seedEscapeWindow": 10000, + "residualClass": "left == 5882 mod 11025", + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is still a cross-squarefree selector lemma. It must not claim collision-free online matching, and the bounded residual profile is not an all-N proof." + }, + "proofBoundary": "This packet decomposes the squarefree sieve target using bounded evidence through N=20000000. It proves neither the p7 period-shift selector nor the q17 residual fallback for all N, and it does not claim collision-free matching.", + "recommendedNextActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "If the residual fallback fails, emit the first left == 5882 mod 11025 row where the q=17 endpoint is cross-blocked." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift.json new file mode 100644 index 0000000..784c0d1 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift.json @@ -0,0 +1,281 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T21:58:50Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_right_compatibility_escape_profile_small_prime_crt_selector_needed", + "proofKind": "bounded_right_compatibility_escape_profile", + "promotesAllNClaim": false, + "provesRightCompatibilityEscapeAllN": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "phaseGuardDecision": { + "status": "bounded_profile_then_small_prime_crt_lift", + "reason": "The first finite-window miss and all later misses found in this bounded replay repair via a local side18 endpoint whose outsider compatibility is witnessed by a small square prime. The next theorem move is a small-prime CRT selector, not a singleton repair-delta branch." + }, + "validatedAgainstPreviousPacket": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "previousMaxN": 3000000, + "previousFiniteWindowMisses": 10, + "previousFirstUncoveredRow": 1138307, + "profileAtPreviousMaxN": { + "sourceCount": 43895, + "selectedExceptionCount": 6740, + "finiteWindowCovered": 6730, + "finiteWindowMisses": 10, + "escapeCovered": 10, + "firstNoEscape": null, + "escapeWindow": 10000 + } + }, + "smallPrimeEscapeProfile": { + "checker": "/tmp/p848_right_escape_mine.cpp", + "checkerKind": "exact_modular_sieve_replay_plus_local_escape_search", + "maxN": 10000000, + "escapeWindow": 10000, + "maxRightCompatibilityPrime": 41, + "primeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "sourceCount": 146577, + "selectedExceptionCount": 22498, + "finiteWindowCovered": 22446, + "finiteWindowMisses": 52, + "finiteWindowMissesWithLeftMod100Seven": 52, + "escapeCovered": 52, + "firstNoEscape": null, + "selectorInterpretation": "Every bounded finite-window miss is in the left = 7 mod 100 class, where the selected right = 93 mod 100 edge is forced non-squarefree by 4. Each miss has a nearby side18 replacement within 10000 whose right-side outsider compatibility is witnessed by a square prime at most 41 and whose cross edge is squarefree in the replay.", + "escapeDeltaCounts": [ + { + "delta": -689, + "count": 4 + }, + { + "delta": -1139, + "count": 4 + }, + { + "delta": -739, + "count": 3 + }, + { + "delta": -839, + "count": 3 + }, + { + "delta": -989, + "count": 3 + }, + { + "delta": -1764, + "count": 3 + }, + { + "delta": -2039, + "count": 3 + }, + { + "delta": -589, + "count": 2 + }, + { + "delta": -789, + "count": 2 + }, + { + "delta": -964, + "count": 2 + }, + { + "delta": -1289, + "count": 2 + }, + { + "delta": -1539, + "count": 2 + }, + { + "delta": -1589, + "count": 2 + }, + { + "delta": -1639, + "count": 2 + }, + { + "delta": -1739, + "count": 2 + }, + { + "delta": -3339, + "count": 2 + }, + { + "delta": -939, + "count": 1 + }, + { + "delta": -1164, + "count": 1 + }, + { + "delta": -1439, + "count": 1 + }, + { + "delta": -1464, + "count": 1 + }, + { + "delta": -1839, + "count": 1 + }, + { + "delta": -1939, + "count": 1 + }, + { + "delta": -2089, + "count": 1 + }, + { + "delta": -2439, + "count": 1 + }, + { + "delta": -2739, + "count": 1 + }, + { + "delta": -3839, + "count": 1 + }, + { + "delta": -4139, + "count": 1 + } + ], + "rightCompatibilityPrimeCounts": [ + { + "prime": 7, + "count": 32 + }, + { + "prime": 11, + "count": 7 + }, + { + "prime": 13, + "count": 4 + }, + { + "prime": 17, + "count": 2 + }, + { + "prime": 19, + "count": 2 + }, + { + "prime": 37, + "count": 2 + }, + { + "prime": 23, + "count": 1 + }, + { + "prime": 31, + "count": 1 + }, + { + "prime": 41, + "count": 1 + } + ], + "sampleRows": [ + { + "left": 1138307, + "selectedDelta": -14, + "escapeDelta": -989, + "right": 1137318, + "rightSquarePrime": 11 + }, + { + "left": 1229207, + "selectedDelta": -14, + "escapeDelta": -1139, + "right": 1228068, + "rightSquarePrime": 11 + }, + { + "left": 1360607, + "selectedDelta": -14, + "escapeDelta": -1764, + "right": 1358843, + "rightSquarePrime": 7 + }, + { + "left": 1533407, + "selectedDelta": -14, + "escapeDelta": -1839, + "right": 1531568, + "rightSquarePrime": 7 + }, + { + "left": 2852807, + "selectedDelta": -14, + "escapeDelta": -3339, + "right": 2849468, + "rightSquarePrime": 11 + }, + { + "left": 5416007, + "selectedDelta": -14, + "escapeDelta": -839, + "right": 5415168, + "rightSquarePrime": 13 + } + ] + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 selected cross-squarefree exception small-prime CRT escape selector lift", + "statement": "Derive a symbolic small-prime CRT selector for finite-window misses: for each selected-cross exception row missed by the 27-delta menu, choose a nearby side18 endpoint inside the 10000 local window whose right-side outsider compatibility is witnessed by one of {7,11,13,17,19,23,31,37,41} and whose cross product is squarefree, or emit the first row outside that rule.", + "completionRule": "A symbolic small-prime CRT selector handles the right-compatibility escape rows, or the first finite-window miss outside that selector becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_right_compatibility_escape_lift", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is a symbolic small-prime CRT selector target. It must not claim collision-free online matching, and the bounded replay here is not an all-N proof." + }, + "proofBoundary": "This packet only records bounded evidence through N=10000000. It proves neither an all-N escape selector nor collision-free matching; it narrows the next theorem move to a small-prime CRT selector instead of a singleton delta branch.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not add singleton escape-delta rungs unless the small-prime CRT selector itself emits a first row outside its rule." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift.json new file mode 100644 index 0000000..6f8df7f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift.json @@ -0,0 +1,116 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T22:07:13Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307", + "status": "symbolic_p7_endpoint_reduction_ready_cross_squarefree_fallback_needed", + "proofKind": "symbolic_p7_crt_endpoint_reduction_plus_bounded_fallback_profile", + "promotesAllNClaim": false, + "provesP7EndpointExistenceAllN": true, + "provesCrossSquarefreeAllN": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "phaseGuardDecision": { + "status": "prove_endpoint_then_decompose_cross_squarefree_fallback", + "reason": "The small-prime selector contains a symbolic p=7 endpoint lemma, but bounded replay shows the p=7 endpoint can have a non-squarefree cross edge. The next theorem object is the cross-squarefree fallback selector, not another delta rung." + }, + "symbolicEndpointLemma": { + "lemmaId": "p848_outsider_6323_p7_local_side18_endpoint", + "statement": "For any side7 left vertex, let k_7(left) be the least residue of 2*left - 27 modulo 49 and set d_7(left) = -14 - 25*k_7(left), right_7(left) = left + d_7(left). Then -1214 <= d_7(left) <= -14, right_7(left) is on side18, and 7^2 divides 6323*right_7(left)+1.", + "proofSketch": [ + "Since 6323 = 2 mod 49 and 6323*25 = 1 mod 49, the congruence 6323*(left - 14 - 25*k)+1 = 0 mod 49 reduces to k = 2*left - 27 mod 49.", + "Choosing k_7 in {0,...,48} gives d_7 = -14 - 25*k_7 in the local interval [-1214,-14].", + "Because left = 7 mod 25 and d_7 = 11 mod 25, right_7 = 18 mod 25, so the selected endpoint is on the side18 compatible side." + ], + "deltaFormula": "d_7(left) = -14 - 25 * ((2*left - 27) mod 49)", + "deltaRange": { + "min": -1214, + "max": -14 + }, + "rightCompatibilityPrime": 7, + "rightCompatibilitySquare": 49 + }, + "boundedFallbackProfile": { + "checker": "/tmp/p848_right_escape_mine.cpp", + "checkerKind": "exact_modular_sieve_replay_plus_p7_endpoint_profile", + "maxN": 10000000, + "escapeWindow": 10000, + "finiteWindowMisses": 52, + "finiteWindowMissesWithLeftMod100Seven": 52, + "p7EndpointCrossSquarefree": 21, + "p7EndpointCrossBad": 31, + "p7CrossBadPrimeCounts": [ + { + "prime": 2, + "count": 20 + }, + { + "prime": 3, + "count": 4 + }, + { + "prime": 19, + "count": 3 + }, + { + "prime": 17, + "count": 2 + }, + { + "prime": 31, + "count": 1 + }, + { + "prime": 43, + "count": 1 + } + ], + "smallPrimeFallbackPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "smallPrimeFallbackCovered": 52, + "firstNoSmallPrimeFallback": null, + "interpretation": "The p=7 CRT endpoint proves a local side18-compatible endpoint, but bounded replay still needs cross-squarefree fallback for 31 of 52 finite-window misses. The fallback selector may reuse p=7 at a different local slot or one of the other small primes." + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 p=7 endpoint cross-squarefree fallback lift", + "statement": "Starting from the symbolic p=7 local side18 endpoint, prove that rows whose p=7 endpoint has a non-squarefree cross edge admit a nearby fallback endpoint from the small-prime set {7,11,13,17,19,23,31,37,41} with squarefree cross product, or emit the first fallback miss.", + "completionRule": "A symbolic cross-squarefree fallback selector handles the p=7 endpoint cross-bad rows, or the first finite-window miss outside the fallback rule becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "seedP7CrossBadCount": 31, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is the cross-squarefree part of the selector. It must not claim collision-free online matching, and bounded fallback coverage is not an all-N proof." + }, + "proofBoundary": "This packet proves only the p=7 endpoint-existence component symbolically. The cross-squarefree fallback remains open and bounded evidence must not be promoted to an all-N claim.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not add singleton fallback-delta rungs unless the cross-squarefree fallback selector emits a first miss outside its rule." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s.json new file mode 100644 index 0000000..ce089ed --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s.json @@ -0,0 +1,272 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T21:43:12Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107", + "status": "bounded_exception_window_lift_falsified_right_compatibility_escape_needed", + "proofKind": "bounded_first_uncovered_exception_window_row", + "promotesAllNClaim": false, + "provesExceptionWindowAllN": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "targetPrime": 13, + "phaseGuardDecision": { + "status": "falsify_window_then_generalize", + "reason": "The 27-delta exception window is a named finite endpoint with an explicit first-uncovered-row boundary. The first uncovered row is recorded here, but the next theorem move is a right-compatibility escape selector rather than a singleton repair-delta branch." + }, + "boundedReplay": { + "checker": "/tmp/p848_exception_window_scan.cpp", + "checkerKind": "exact_modular_sieve_replay", + "validatedAgainstPreviousMaxN": 1000000, + "validatedPreviousSourceRows": 14557, + "validatedPreviousSelectedExceptions": 2241, + "validatedPreviousCoveredByMenu": 2241, + "maxN": 3000000, + "side7Rows": 119708, + "checkedSide7CompatibleEventRows": 43895, + "selectedCrossExceptions": 6740, + "coveredByFiniteWindowMenu": 6730, + "uncoveredSelectedCrossExceptions": 10, + "firstUncoveredReplacementRow": 1138307, + "selectedExceptionBySelectedDelta": [ + { + "selectedDelta": -14, + "count": 4654 + }, + { + "selectedDelta": -64, + "count": 1919 + }, + { + "selectedDelta": -39, + "count": 133 + }, + { + "selectedDelta": -89, + "count": 34 + } + ], + "topRepairDeltasBeforeFailure": [ + { + "delta": -189, + "count": 3195 + }, + { + "delta": -164, + "count": 1097 + }, + { + "delta": -39, + "count": 623 + }, + { + "delta": -89, + "count": 615 + }, + { + "delta": -64, + "count": 368 + }, + { + "delta": -264, + "count": 218 + }, + { + "delta": -139, + "count": 171 + }, + { + "delta": -339, + "count": 139 + }, + { + "delta": -239, + "count": 137 + }, + { + "delta": -539, + "count": 58 + } + ] + }, + "firstUncoveredRow": { + "left": 1138307, + "leftMod100": 7, + "sourceCompatibility": { + "productPlusOne": 7197515162, + "squareDivisor": { + "prime": 29, + "square": 841, + "quotient": 8558282 + } + }, + "selectedEndpoint": { + "right": 1138293, + "delta": -14, + "rightOutsiderCompatibility": { + "productPlusOne": 7197426640, + "squareDivisor": { + "prime": 2, + "square": 4, + "quotient": 1799356660 + } + }, + "crossProductPlusOne": 1295726889952, + "crossSquareDivisor": { + "prime": 2, + "square": 4, + "quotient": 323931722488 + } + }, + "finiteWindowAttemptSummary": { + "deltaCount": 27, + "validRepairCount": 0, + "rightNotOutsiderCompatible": 25, + "crossNotSquarefree": 2, + "interpretation": "Most menu candidates have squarefree cross products at this row but fail right-side outsider compatibility; the next theorem object should therefore target a right-compatibility escape selector." + }, + "finiteWindowAttempts": [ + { + "delta": -64, + "right": 1138243, + "failureReason": "right_not_outsider_compatible", + "crossSquarefree": true + }, + { + "delta": -39, + "right": 1138268, + "failureReason": "right_not_outsider_compatible", + "crossSquarefree": true + }, + { + "delta": -89, + "right": 1138218, + "failureReason": "right_not_outsider_compatible", + "crossSquarefree": true + }, + { + "delta": -189, + "right": 1138118, + "failureReason": "right_not_outsider_compatible", + "crossSquarefree": true + }, + { + "delta": -164, + "right": 1138143, + "failureReason": "right_not_outsider_compatible", + "crossSquarefree": true + }, + { + "delta": -14, + "right": 1138293, + "failureReason": "cross_not_squarefree", + "rightOutsiderSquare": 4, + "crossSquare": 4 + }, + { + "delta": -139, + "right": 1138168, + "failureReason": "right_not_outsider_compatible", + "crossSquare": 49 + }, + { + "delta": -114, + "right": 1138193, + "failureReason": "cross_not_squarefree", + "rightOutsiderSquare": 4, + "crossSquare": 4 + } + ], + "firstLocalEscapeRepairs": [ + { + "delta": -989, + "right": 1137318, + "rightOutsiderSquare": 121, + "rightOutsiderSquarePrime": 11, + "crossSquarefree": true + }, + { + "delta": -1189, + "right": 1137118, + "rightOutsiderSquare": 49, + "rightOutsiderSquarePrime": 7, + "crossSquarefree": true + }, + { + "delta": -3064, + "right": 1135243, + "rightOutsiderSquare": 169, + "rightOutsiderSquarePrime": 13, + "crossSquarefree": true + }, + { + "delta": -3639, + "right": 1134668, + "rightOutsiderSquare": 49, + "rightOutsiderSquarePrime": 7, + "crossSquarefree": true + } + ] + }, + "finiteWindowMenu": { + "failedDeltaSet": [ + -64, + -39, + -89, + -189, + -164, + -14, + -139, + -264, + -239, + -339, + -539, + -289, + -639, + -114, + -464, + -364, + -489, + -1089, + -389, + -1039, + -1064, + -1239, + -1664, + -2164, + -564, + -764, + -864 + ], + "firstEscapeDeltas": [ + -989, + -1189, + -3064, + -3639 + ] + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307", + "status": "needed", + "term": "outsider-6323 selected cross-squarefree exception right-compatibility escape lift", + "statement": "Replace the failed 27-delta exception window with a right-compatibility escape selector seeded by the first uncovered row left=1138307: prove that every future finite-window miss has a side18 replacement such as the observed deltas -989 or -1189 with outsider compatibility and squarefree cross product, or emit the first row with no bounded escape repair.", + "completionRule": "A symbolic right-compatibility escape selector replaces the finite-window miss family without adding singleton delta siblings, or the first row with no bounded side18 squarefree repair becomes the next deterministic packet.", + "dependsOnSublemma": "selected_cross_squarefree_exception_window_lift", + "seedUncoveredRow": 1138307, + "seedEscapeDeltas": [ + -989, + -1189 + ], + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "This next subatom is a general escape-selector target, not a singleton delta branch. Even after it is proved, collision-free online matching remains separate." + }, + "proofBoundary": "This packet falsifies the 27-delta finite-window lift at bounded scope and emits the first uncovered row. It does not prove that the escape deltas work for all future rows and does not prove the full matching injection.", + "nextTheoremActions": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307 next.", + "Do not spawn a singleton delta -989 rung; use the uncovered row to build the right-compatibility escape selector or emit a harder no-repair obstruction." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs.json new file mode 100644 index 0000000..475b60a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs.json @@ -0,0 +1,112 @@ +{ + "schema": "erdos.number_theory.p848_dynamic_margin_proof/1", + "generatedAt": "2026-04-12T21:04:03Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs", + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "parentAtomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_selected_cross_squarefree_falsified_exception_menu_needed", + "proofKind": "bounded_first_square_divisor_exception", + "promotesAllNClaim": false, + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "selectorRule": { + "name": "previous_93_mod100_side18_slot", + "deltaSet": [ + -14, + -39, + -64, + -89 + ], + "selectedRightFormula": "right is the largest integer below left with right == 93 (mod 100)" + }, + "boundedPrefixReplay": { + "minLeft": 7307, + "checkedSide7CompatibleRowsUntilFailure": 11, + "coveredBeforeFailure": 10, + "firstFailureLeft": 8107 + }, + "firstSquareDivisorException": { + "left": 8107, + "right": 8093, + "delta": -14, + "leftMod25": 7, + "rightMod25": 18, + "leftMod100": 7, + "rightMod100": 93, + "leftOutsiderCompatibility": { + "productPlusOne": 51260562, + "squareWitness": { + "prime": 3, + "square": 9, + "quotient": 5695618 + } + }, + "rightOutsiderCompatibility": { + "productPlusOne": 51172040, + "squareWitness": { + "prime": 2, + "square": 4, + "quotient": 12793010 + } + }, + "selectedCrossProductPlusOne": 65609952, + "selectedCrossSquareDivisor": { + "prime": 2, + "square": 4, + "quotient": 16402488 + }, + "interpretation": "The four-slot endpoint selector is false as a selected cross-squarefree lift: for left == 8107, the selected endpoint is active and side18-compatible, but left * right + 1 is not squarefree." + }, + "localRepairProbe": { + "searchWindow": { + "minDelta": -5000, + "deltaCongruenceMod25": 11 + }, + "firstValidRepair": { + "left": 8107, + "right": 7918, + "delta": -189, + "leftMod100": 7, + "rightMod100": 18, + "rightOutsiderCompatibility": { + "productPlusOne": 50065515, + "squareWitness": { + "prime": 3, + "square": 9, + "quotient": 5562835 + } + }, + "crossProductPlusOne": 64191227, + "crossSquarefree": true + }, + "interpretation": "The first failure has a small direct repair, but this packet does not promote delta -189 as a new singleton rung. The durable next move is an exception/replacement menu for the selected-cross-squarefree obstruction class." + }, + "correctionNotes": [ + "The previous direct-selector sublemma remains valid: endpoint existence is proved by the mod-4 four-slot rule.", + "This packet falsifies only the stronger selected cross-squarefree claim for that fixed endpoint selector.", + "A replacement menu must handle the square-divisor exception before the lane can move to collision-free matching updates." + ], + "proofBoundary": "This is a bounded falsifier packet, not an all-N proof of the replacement rule. It records the first selected endpoint whose cross product is non-squarefree and seeds a replacement-menu theorem target.", + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107", + "status": "needed", + "term": "outsider-6323 selected cross-squarefree exception menu", + "statement": "Build a replacement menu for the selected cross-squarefree obstruction class starting at left=8107: replace the failing previous-93 endpoint by a side18-compatible squarefree-cross endpoint such as the observed delta -189 repair, or emit the first side7-compatible row with no bounded replacement.", + "completionRule": "A symbolic replacement menu handles the selected endpoint square-divisor exceptions without adding singleton deltas, or the first uncovered replacement row becomes the next deterministic packet.", + "seedException": { + "left": 8107, + "failingRight": 8093, + "repairRight": 7918, + "repairDelta": -189 + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "proofBoundary": "The replacement menu may prove a finite residue rule or emit a smaller obstruction; do not treat the local delta -189 repair as an all-N branch." + }, + "nextAction": [ + "Prove D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107 next.", + "Do not spawn a singleton direct-delta -189 rung unless the exception-menu task itself emits it as a bounded obstruction." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323.json new file mode 100644 index 0000000..f6001ca --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323.json @@ -0,0 +1,150 @@ +{ + "schema": "erdos.p848_dynamic_margin_exact_mixed_successor_profile/1", + "generatedAt": "2026-04-12T19:05:43Z", + "problemId": "848", + "atomId": "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "outsiderMod169": 70, + "outsiderMod25": 23, + "status": "bounded_exact_mixed_margin_profile_verified_symbolic_lift_needed", + "promotesAllNClaim": false, + "proofKind": "bounded_exact_mixed_margin_successor_profile", + "dependsOn": [ + "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18" + ], + "replacesFalseAtomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "parentObstructionProof": { + "atomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "status": "bounded_symbolic_lift_falsified_successor_atom_needed", + "firstObstruction": { + "N": 7307, + "outsider": 6323, + "targetLeftSide": 17, + "targetRequiredLowerBound": 20, + "targetDeficit": 3, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 105, + "saturatesSmallerSide": true, + "exactMixedMargin": 18 + } + }, + "targetInequality": "matching saturates the smaller side and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in the outsider-6323 family", + "boundedProfile": { + "verifier": "problem848_full_mixed_base_structural_verifier.mjs", + "verifierParameters": { + "maxN": 10000, + "minStructuralN": 7307, + "rowSampleLimit": 20, + "assessedRange": "7307..10000" + }, + "rowCount": 277, + "nRange": "7307..10000", + "allRowsSaturateSmallerSide": true, + "saturationDeficitRange": "0..0", + "saturationDeficitDistribution": { + "0": 277 + }, + "allRowsHavePositiveExactMixedMargin": true, + "exactMixedMarginRange": "18..31", + "exactMixedMarginDistribution": { + "18": 4, + "19": 11, + "20": 35, + "21": 44, + "22": 33, + "23": 15, + "24": 9, + "25": 18, + "26": 19, + "27": 19, + "28": 22, + "29": 27, + "30": 18, + "31": 3 + }, + "minimumExactMixedMarginRows": [ + { + "N": 7307, + "nMod25": 7, + "candidateSize": 293, + "strictBaseThreshold": 128, + "mixedBaseCliqueSize": 110, + "exactMixedMargin": 18, + "side7Count": 105, + "side18Count": 110, + "matchingSizeInMissingCrossGraph": 105, + "smallerSideSize": 105, + "saturationDeficit": 0, + "requiredMatchingLowerBound": 88, + "matchingSlack": 17, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7318, + "nMod25": 18, + "candidateSize": 293, + "strictBaseThreshold": 128, + "mixedBaseCliqueSize": 110, + "exactMixedMargin": 18, + "side7Count": 105, + "side18Count": 110, + "matchingSizeInMissingCrossGraph": 105, + "smallerSideSize": 105, + "saturationDeficit": 0, + "requiredMatchingLowerBound": 88, + "matchingSlack": 17, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7337, + "nMod25": 12, + "candidateSize": 294, + "strictBaseThreshold": 128, + "mixedBaseCliqueSize": 110, + "exactMixedMargin": 18, + "side7Count": 105, + "side18Count": 110, + "matchingSizeInMissingCrossGraph": 105, + "smallerSideSize": 105, + "saturationDeficit": 0, + "requiredMatchingLowerBound": 88, + "matchingSlack": 17, + "dominantMixedCliqueSide": "side18" + }, + { + "N": 7343, + "nMod25": 18, + "candidateSize": 294, + "strictBaseThreshold": 128, + "mixedBaseCliqueSize": 110, + "exactMixedMargin": 18, + "side7Count": 105, + "side18Count": 110, + "matchingSizeInMissingCrossGraph": 105, + "smallerSideSize": 105, + "saturationDeficit": 0, + "requiredMatchingLowerBound": 88, + "matchingSlack": 17, + "dominantMixedCliqueSide": "side18" + } + ] + }, + "checkedIdentities": [ + "For the outsider-6323 bounded family, exactMixedMargin = strictBaseThreshold - mixedBaseCliqueSize.", + "Every checked row has matchingSizeInMissingCrossGraph = smallerSideSize, so the missing-cross matching saturates the smaller compatible side.", + "Every checked row has exactMixedMargin >= 18, so the exact mixed-base replacement leaves positive bounded margin.", + "This profile repairs the first obstruction to the false side18 threshold lift on the bounded 7307..10000 verifier range only." + ], + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "statement": "Lift the bounded exact mixed-margin successor profile for outsider 6323 into a symbolic theorem: prove smaller-side matching saturation and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in split outP2=70|out25=23|smaller=side7, or emit the first exact residue/root-universe obstruction.", + "completionRule": "The exact mixed-margin successor is proved symbolically for the outsider-6323 family, or the first residue/root-universe obstruction becomes the next deterministic atom." + }, + "proofBoundary": "This certificate verifies the exact mixed-margin successor only on the bounded 7307..10000 outsider-6323 profile. It does not prove the all-N matching saturation or exact mixed-margin lift.", + "nextTheoremActions": [ + "Attack D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Prove the matching saturation and strictBaseThreshold - mixedBaseCliqueSize >= 1 identities symbolically for the outsider-6323 family, or emit the first exact residue/root-universe obstruction." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json new file mode 100644 index 0000000..d75f1b9 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json @@ -0,0 +1,70 @@ +{ + "schema": "erdos.p848_dynamic_margin_exact_mixed_symbolic_lift_reduction/1", + "generatedAt": "2026-04-12T19:18:31Z", + "problemId": "848", + "atomId": "D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "splitKey": "outP2=70|out25=23|smaller=side7", + "outsider": 6323, + "outsiderMod169": 70, + "outsiderMod25": 23, + "status": "symbolic_lift_reduced_to_matching_injection_and_margin_floor", + "promotesAllNClaim": false, + "proofKind": "theorem_obligation_decomposition", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "targetInequality": "matching saturates the smaller side and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in the outsider-6323 family", + "boundedProfileUsed": { + "sourceAtomId": "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "rowCount": 277, + "nRange": "7307..10000", + "allRowsSaturateSmallerSide": true, + "allRowsHavePositiveExactMixedMargin": true, + "exactMixedMarginRange": "18..31", + "proofBoundary": "The bounded profile motivates the decomposition but does not prove either symbolic sublemma." + }, + "symbolicReduction": { + "compatibleSides": { + "smallerSide": "side7", + "largerSide": "side18", + "boundedSide7CountRange": "105..145", + "boundedSide18CountRange": "110..148", + "boundedRowsAllHaveSide7AtMostSide18": true + }, + "matchingSaturationSublemma": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "statement": "Construct an injective matching from every side7-compatible base vertex for outsider 6323 into a distinct side18-compatible base vertex along missing cross edges of the side7/side18 compatibility graph.", + "effect": "If proved, matchingSizeInMissingCrossGraph = side7Count and mixedBaseCliqueSize = side18Count for this family." + }, + "marginFloorSublemma": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_margin_floor_outP2_70_out25_23_smaller_side7_outsider_6323", + "statement": "Prove strictBaseThreshold - side18Count >= 1 for every future row in the same split/outsider family.", + "effect": "Together with matching saturation, this gives strictBaseThreshold - mixedBaseCliqueSize >= 1." + }, + "composition": [ + "matching saturation gives mixedBaseCliqueSize = side7Count + side18Count - side7Count = side18Count", + "the margin-floor sublemma gives strictBaseThreshold - side18Count >= 1", + "therefore strictBaseThreshold - mixedBaseCliqueSize >= 1" + ] + }, + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 exact mixed matching injection", + "statement": "Prove the side7-to-side18 missing-cross injection for outsider 6323, or emit the first exact residue/root-universe row where side7 cannot be saturated.", + "completionRule": "The matching injection saturates the side7-compatible set for this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom.", + "nextAfterDischarge": "D2_p13_dynamic_margin_exact_mixed_margin_floor_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "remainingSubatoms": [ + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_margin_floor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "blocked_by_matching_injection", + "statement": "After matching saturation is symbolic, prove strictBaseThreshold - side18Count >= 1 for the outsider-6323 family." + } + ], + "proofBoundary": "This packet is a theorem-facing decomposition, not a proof of the exact mixed-margin lift. It records the two symbolic sublemmas needed to promote the bounded outsider-6323 evidence.", + "nextTheoremActions": [ + "Attack D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323 next.", + "Do not claim the exact mixed-margin lift until both the matching injection and the strictBaseThreshold - side18Count margin floor are proved symbolically." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18.json new file mode 100644 index 0000000..9b6734a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18.json @@ -0,0 +1,115 @@ +{ + "schema": "erdos.p848_residual_dynamic_margin_replay/1", + "problemId": "848", + "atomId": "D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18", + "splitKey": "outP2=70|out25=23|smaller=side7", + "status": "bounded_dynamic_margin_replay_verified_symbolic_lift_needed", + "promotesAllNClaim": false, + "proofKind": "bounded_residual_dynamic_margin_formula_replay", + "dependsOn": [ + "D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7", + "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7" + ], + "targetInequality": "side18Count + vMax + rGreater + 39 <= candidateSize", + "boundedProfile": { + "rowCount": 32, + "nRange": "7307..7600", + "outsider": 6323, + "side18CountRange": "110..114", + "side7CountRange": "105..109", + "strictBaseThresholdRange": "132..138", + "candidateSizeRange": "293..304", + "vMaxRange": "43..45", + "dMaxRange": "18..18", + "rGreaterRange": "100..103", + "sideCountSlackFormulaRange": "21..25", + "residualDynamicMarginRange": "1..5", + "structuralMarginRange": "1..5", + "marginDistribution": { + "1": 4, + "2": 8, + "3": 14, + "4": 5, + "5": 1 + }, + "minimumMarginRows": [ + { + "N": 7307, + "outsider": 6323, + "side7Count": 105, + "side18Count": 110, + "strictBaseThreshold": 132, + "candidateSize": 293, + "vMax": 43, + "dMax": 18, + "rGreater": 100, + "sideCountSlackFormula": 21, + "residualDynamicMargin": 1 + }, + { + "N": 7318, + "outsider": 6323, + "side7Count": 105, + "side18Count": 110, + "strictBaseThreshold": 132, + "candidateSize": 293, + "vMax": 43, + "dMax": 18, + "rGreater": 100, + "sideCountSlackFormula": 21, + "residualDynamicMargin": 1 + }, + { + "N": 7337, + "outsider": 6323, + "side7Count": 105, + "side18Count": 110, + "strictBaseThreshold": 132, + "candidateSize": 294, + "vMax": 44, + "dMax": 18, + "rGreater": 100, + "sideCountSlackFormula": 21, + "residualDynamicMargin": 1 + }, + { + "N": 7343, + "outsider": 6323, + "side7Count": 105, + "side18Count": 110, + "strictBaseThreshold": 132, + "candidateSize": 294, + "vMax": 44, + "dMax": 18, + "rGreater": 100, + "sideCountSlackFormula": 21, + "residualDynamicMargin": 1 + } + ] + }, + "algebraicReduction": { + "reconstructedVMax": "vMax = candidateSize - strictBaseThreshold - dMax - rGreater", + "residualMarginDefinition": "candidateSize - side18Count - vMax - rGreater - 39", + "substitution": "candidateSize - side18Count - (candidateSize - strictBaseThreshold - dMax - rGreater) - rGreater - 39 = strictBaseThreshold + dMax - side18Count - 39", + "boundedDMaxProfile": "dMax = 18 on all 32 bounded rows in this split", + "slackIdentity": "strictBaseThreshold + 18 - side18Count - 39 = strictBaseThreshold - 1 - side18Count - 20", + "symbolicLiftTarget": "strictBaseThreshold - 1 - side18Count >= 20" + }, + "checkedIdentities": [ + "Every bounded row in outP2=70|out25=23|smaller=side7 has dMax = 18 after the dMax tail profile is closed.", + "For every bounded row, candidateSize - side18Count - vMax - rGreater - 39 equals strictBaseThreshold - 1 - side18Count - 20.", + "For every bounded row, strictBaseThreshold - 1 - side18Count equals the stored side-count slack formula and lies in 21..25.", + "The bounded residual dynamic margin is therefore sideCountSlackFormula - 20 and lies in 1..5." + ], + "nextSubatom": { + "atomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "status": "needed", + "statement": "Lift the bounded residual dynamic-margin replay to a symbolic side18 threshold lemma: prove strictBaseThreshold - 1 - side18Count >= 20 for every future row in split outP2=70|out25=23|smaller=side7, or emit the first future-row residue/threshold obstruction.", + "completionRule": "The side18 threshold inequality is proved symbolically for this split, or the first exact obstruction becomes a sharper side-count/rGreater successor atom." + }, + "proofBoundary": "This certificate verifies the residual dynamic-margin inequality only on the bounded 32-row profile and records the exact algebraic reduction needed for the next theorem move. It does not prove the all-N side18 threshold inequality or the full side-count floor.", + "nextTheoremActions": [ + "Attack D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18 next.", + "Prove strictBaseThreshold - 1 - side18Count >= 20 for this split, or emit the first exact future-row obstruction instead of treating the bounded replay as an all-N proof." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18.json new file mode 100644 index 0000000..07db8d0 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18.json @@ -0,0 +1,106 @@ +{ + "schema": "erdos.p848_dynamic_margin_symbolic_lift_obstruction/1", + "generatedAt": "2026-04-12T18:55:27Z", + "problemId": "848", + "proofId": "p848_dynamic_margin_proof_D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "atomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "parentAtomId": "D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18", + "status": "bounded_symbolic_lift_falsified_successor_atom_needed", + "proofKind": "bounded_future_row_obstruction_to_side18_threshold_lift", + "promotesAllNClaim": false, + "targetPrime": 13, + "splitKey": "outP2=70|out25=23|smaller=side7", + "largerSideLabel": "side18", + "targetInequality": "strictBaseThreshold - 1 - side18Count >= 20", + "boundedExtensionVerifier": { + "script": "packs/number-theory/problems/848/compute/problem848_full_mixed_base_structural_verifier.mjs", + "parameters": { + "maxN": 10000, + "minStructuralN": 7307, + "rowSampleLimit": 20 + }, + "summary": { + "assessedRange": "7307..10000", + "witnessBlockCount": 10, + "breakpointCount": 277, + "checkCount": 2770, + "globalRootEventCount": 257, + "unionCertifiedRowCount": 2216, + "exactMixedRowCount": 554, + "threateningOutsiderCheckCount": 17824, + "mixedFailureCount": 0, + "allMixedChecksPass": true, + "minCertifiedMargin": 16, + "minExactMixedMargin": 16 + } + }, + "obstructionSummary": { + "targetSplitThreatRowCount": 277, + "targetSplitNRange": "7307..10000", + "targetSplitOutsiders": [ + 6323 + ], + "targetLeftSideRange": "17..30", + "targetMarginRangeAgainstRequired20": "-3..10", + "rowsBelowTarget": 50, + "targetLeftSideDistribution": { + "17": 4, + "18": 11, + "19": 35, + "20": 44, + "21": 33, + "22": 15, + "23": 9, + "24": 18, + "25": 19, + "26": 19, + "27": 22, + "28": 27, + "29": 18, + "30": 3 + } + }, + "firstObstruction": { + "N": 7307, + "outsider": 6323, + "outsiderMod169": 70, + "outsiderMod25": 23, + "nMod25": 7, + "candidateSize": 293, + "vMax": 43, + "dMax": 18, + "rGreater": 104, + "strictBaseThreshold": 128, + "side7Count": 105, + "side18Count": 110, + "targetLeftSide": 17, + "targetRequiredLowerBound": 20, + "targetDeficit": 3, + "unionCount": 215, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 105, + "requiredMatchingLowerBound": 88, + "matchingSlack": 17, + "smallerSideSize": 105, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18", + "exactMixedMargin": 18, + "exactMixedMarginIdentity": "candidateSize - mixedBaseCliqueSize - vMax - dMax - rGreater = 293 - 110 - 43 - 18 - 104 = 18" + }, + "falsificationReason": [ + "The earlier bounded dynamic-margin replay used the 7307..7600 verifier surface, where this split had strictBaseThreshold - 1 - side18Count in 21..25.", + "Re-running the same verifier to maxN=10000 expands the higher-root event universe; at N=7307 the p13 row has rGreater=104 and strictBaseThreshold=128.", + "For the same target split and outsider 6323, strictBaseThreshold - 1 - side18Count = 17, so the proposed >=20 symbolic lift is false as stated.", + "The full exact mixed-base verifier still passes on 7307..10000, so the successor should use exact mixed-margin/matching saturation rather than the stronger side-count floor." + ], + "nextSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "side18 exact mixed-margin successor", + "targetInequality": "matching saturates the smaller side and candidateSize - mixedBaseCliqueSize - vMax - dMax - rGreater >= 1", + "statement": "Replace the false side18 threshold lift for split outP2=70|out25=23|smaller=side7 with an exact mixed-margin successor: prove the missing-cross matching saturates the smaller side for the outsider-6323 family and leaves positive exact mixed margin, or emit the first sharper root-universe/rGreater obstruction.", + "completionRule": "The exact mixed-margin/matching-saturation successor is proved symbolically for this split family, or the first residue/root-universe obstruction becomes the next deterministic atom.", + "proofBoundary": "This successor is forced by a bounded obstruction to the side18 threshold lift; it is not an all-N proof of exact mixed margin." + }, + "proofBoundary": "This packet falsifies only the proposed symbolic threshold lift by bounded extension evidence and emits a sharper theorem-facing successor. It does not promote the bounded exact mixed-base verifier to an all-N proof." +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json new file mode 100644 index 0000000..e19e723 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json @@ -0,0 +1,954 @@ +{ + "schema": "erdos.p848_split_atom_packet_manifest/1", + "generatedAt": "2026-04-14T11:46:10.338Z", + "problemId": "848", + "sourceTaskListGeneratedAt": "2026-04-14T11:46:09.617Z", + "sourcePlanId": "p848_split_core_atomization_master_plan_v1", + "directoryPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS", + "successorDirectoryPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS", + "sideCountFloorDirectoryPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR", + "manifestJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.json", + "manifestMarkdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/MANIFEST.md", + "packetCount": 5, + "successorPacketCount": 29, + "sideCountFloorPacketCount": 2, + "firstPacketToAttack": { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "packetId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentObligationId": "D2_p13_matching_lower_bound", + "priority": "highest_singleton_profile", + "prime": 13, + "splitKey": "outP2=99|out25=14|smaller=side7", + "status": "ready_for_symbolic_persistence_work", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md", + "commonMatchingPairCount": 108, + "vertexPresenceAtomCount": 216, + "stableVertexPresenceAtomCount": 4, + "unstableVertexPresenceAtomCount": 212, + "vertexPresenceRefinementStatus": "literal_core_requires_sharper_square_witness_split", + "vertexPresenceRefinementConditionCount": 10, + "edgeObstructionAtomCount": 108, + "edgeObstructionCertificateStatus": "literal_edge_obstruction_certificate_verified", + "edgeObstructionResidueSummary": { + "mod25ClassCount": 1, + "primeResidueClassCount": 72, + "primeSquareFingerprintCount": 108 + }, + "edgeCongruencePersistenceStatus": "literal_constant_edge_persistence_verified", + "matchingKEnvelopeCertificateStatus": "literal_matching_sampled_k_envelope_verified", + "matchingKEnvelopeSlack": 20, + "splitDischargeReadinessStatus": "split_discharge_readiness_candidate", + "splitDischargeOpenGapCount": 3, + "readyForFirstTheoremPass": true + }, + "firstSuccessorPacketToAttack": { + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "conditionId": "square_4_outsider_1", + "priority": "highest_refinement_successor", + "status": "candidate_successor_obligation_verified", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out4=1", + "successorSplitModulus": 16900, + "affectedAtomCount": 145, + "stabilizedAtomCount": 145, + "failedAtomCount": 0, + "symbolicVertexFamilyLemmaStatus": "symbolic_vertex_family_lemma_verified", + "vertexResidueModSquare": 3, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md" + }, + "firstSideCountFloorPacketToAttack": { + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "atomId": "D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "parentLemmaId": "D2_p13_non_tight_side_count_slack_floor_lift", + "splitKey": "outP2=70|out25=23|smaller=side7", + "priority": "highest_side_count_floor_atom", + "status": "symbolic_side_count_floor_atom_needed", + "targetSlackLowerBound": 20, + "observedBoundedSlackFormulaFloor": 21, + "observedMarginAboveTarget": 1, + "structuralMarginDecompositionStatus": "bounded_structural_margin_replay_verified_symbolic_margin_lift_needed", + "firstOpenStructuralMarginLemma": "D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18", + "firstOpenMovingTermSubatom": 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"evidence": "3/3 split packets have matching/K-envelope certificates" + } + ], + "blockingChecks": [], + "splitPackets": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "splitKey": "outP2=70|out25=9|smaller=side7", + "readinessStatus": "split_discharge_readiness_candidate", + "openGapCount": 3, + "matchingKEnvelopeSlack": 19, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "splitKey": "outP2=99|out25=6|smaller=side18", + "readinessStatus": "split_discharge_readiness_candidate", + "openGapCount": 3, + "matchingKEnvelopeSlack": 20, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "splitKey": "outP2=99|out25=14|smaller=side7", + "readinessStatus": "split_discharge_readiness_candidate", + "openGapCount": 3, + "matchingKEnvelopeSlack": 20, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md" + } + ], + "theoremCandidate": { + "status": "candidate_not_promoted_all_n_gaps_open", + "statement": "The p=13 lane has 3/3 split profiles assembled into theorem-facing readiness candidates.", + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "sourcePacketCount": 3, + "note": "Prove every future p=13 threatening row lands in one of the emitted split profiles, or emit the missing split profile as a new atom." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "sourcePacketCount": 3, + "note": "Replace each sampled K-envelope comparison with the symbolic K(N,x) inequality for the full p=13 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "sourcePacketCount": 3, + "note": "If future rows require moving vertex formulas, re-lift vertex presence, edge persistence, and disjointness for the parameterized families." + } + ] + }, + "proofBoundary": "This aggregates split-discharge readiness for a prime lane. It is not a universal D-lane proof until row-universe coverage and the symbolic K(N,x) lift are discharged.", + "nextTheoremAction": "Discharge row_universe_split_coverage first, then universal_k_formula_lift; do not mark the parent lane done until those all-N gaps close." + }, + "primeLaneHandoffCandidates": [ + { + "schema": "erdos.p848_prime_lane_handoff_candidate/1", + "laneId": "D2_p13_matching_lower_bound", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetPrime": 13, + "status": "prime_lane_handoff_candidate_with_open_all_n_gaps", + "promotesAllNClaim": false, + "splitPacketCount": 3, + "readySplitPacketCount": 3, + "totalRefinementConditionCount": 29, + "verifiedSuccessorFamilyCount": 29, + "lowerLayerChecks": [ + { + "checkId": "lane_split_packets_ready", + "status": "verified", + "evidence": "3/3 split packets have readiness candidates" + }, + { + "checkId": "lane_vertex_successor_families_verified", + "status": "verified", + "evidence": "29/29 successor vertex-family lemmas verified" + }, + { + "checkId": "lane_edge_persistence_verified", + "status": "verified", + "evidence": "3/3 split packets have literal edge persistence" + }, + { + "checkId": "lane_matching_k_envelopes_verified", + "status": "verified_sampled_envelope", + "evidence": "3/3 split packets have matching/K-envelope certificates" + } + ], + "blockingChecks": [], + "splitPackets": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "splitKey": "outP2=70|out25=9|smaller=side7", + "readinessStatus": "split_discharge_readiness_candidate", + "openGapCount": 3, + "matchingKEnvelopeSlack": 19, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "splitKey": "outP2=99|out25=6|smaller=side18", + "readinessStatus": "split_discharge_readiness_candidate", + "openGapCount": 3, + "matchingKEnvelopeSlack": 20, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "splitKey": "outP2=99|out25=14|smaller=side7", + "readinessStatus": "split_discharge_readiness_candidate", + "openGapCount": 3, + "matchingKEnvelopeSlack": 20, + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md" + } + ], + "theoremCandidate": { + "status": "candidate_not_promoted_all_n_gaps_open", + "statement": "The p=13 lane has 3/3 split profiles assembled into theorem-facing readiness candidates.", + "openAllNHandoffGaps": [ + { + "gapId": "row_universe_split_coverage", + "status": "open", + "sourcePacketCount": 3, + "note": "Prove every future p=13 threatening row lands in one of the emitted split profiles, or emit the missing split profile as a new atom." + }, + { + "gapId": "universal_k_formula_lift", + "status": "open", + "sourcePacketCount": 3, + "note": "Replace each sampled K-envelope comparison with the symbolic K(N,x) inequality for the full p=13 lane." + }, + { + "gapId": "literal_to_parameterized_vertex_guard", + "status": "open_if_vertices_move", + "sourcePacketCount": 3, + "note": "If future rows require moving vertex formulas, re-lift vertex presence, edge persistence, and disjointness for the parameterized families." + } + ] + }, + "proofBoundary": "This aggregates split-discharge readiness for a prime lane. It is not a universal D-lane proof until row-universe coverage and the symbolic K(N,x) lift are discharged.", + "nextTheoremAction": "Discharge row_universe_split_coverage first, then universal_k_formula_lift; do not mark the parent lane done until those all-N gaps close." + } + ], + "packets": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "packetId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentObligationId": "D2_p13_matching_lower_bound", + "priority": "high_p13_active_lane", + "prime": 13, + "splitKey": "outP2=70|out25=9|smaller=side7", + "status": "ready_for_symbolic_persistence_work", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.json", + "markdownPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md", + "commonMatchingPairCount": 108, 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Agents should use one packet at a time, starting with the highest-priority singleton p13 packet when available. + +- Source plan: `p848_split_core_atomization_master_plan_v1` +- Packet count: `5` +- Successor packet count: `29` +- Side-count floor packet count: `2` +- First packet to attack: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- First successor packet to attack: `D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1` +- First side-count floor packet to attack: `D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7` +- First prime-lane handoff candidate: `D2_p13_matching_lower_bound` + +## Packets + +- `D2.1_persist_outP2=70_out25=9_smaller=side7` [high_p13_active_lane]: p=13, split=outP2=70|out25=9|smaller=side7, core=108, vertexAtoms=216, stableVertices=3, unstableVertices=213, refinement=literal_core_requires_sharper_square_witness_split/11, edgeAtoms=108, edgeCertificate=literal_edge_obstruction_certificate_verified, edgePersistence=literal_constant_edge_persistence_verified, matchingK=literal_matching_sampled_k_envelope_verified, discharge=split_discharge_readiness_candidate, ready=true +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_1_persist_outP2_70_out25_9_smaller_side7.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18` [high_p13_active_lane]: p=13, split=outP2=99|out25=6|smaller=side18, core=105, vertexAtoms=210, stableVertices=4, unstableVertices=206, refinement=literal_core_requires_sharper_square_witness_split/8, edgeAtoms=105, edgeCertificate=literal_edge_obstruction_certificate_verified, edgePersistence=literal_constant_edge_persistence_verified, matchingK=literal_matching_sampled_k_envelope_verified, discharge=split_discharge_readiness_candidate, ready=true +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_2_persist_outP2_99_out25_6_smaller_side18.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7` [highest_singleton_profile]: p=13, split=outP2=99|out25=14|smaller=side7, core=108, vertexAtoms=216, stableVertices=4, unstableVertices=212, refinement=literal_core_requires_sharper_square_witness_split/10, edgeAtoms=108, edgeCertificate=literal_edge_obstruction_certificate_verified, edgePersistence=literal_constant_edge_persistence_verified, matchingK=literal_matching_sampled_k_envelope_verified, discharge=split_discharge_readiness_candidate, ready=true +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D2_3_persist_outP2_99_out25_14_smaller_side7.md` +- `D3.1_persist_outP2=38_out25=23_smaller=side7` [supporting_p17_companion_lane]: p=17, split=outP2=38|out25=23|smaller=side7, core=109, vertexAtoms=218, stableVertices=2, unstableVertices=216, refinement=literal_core_requires_sharper_square_witness_split/9, edgeAtoms=109, edgeCertificate=literal_edge_obstruction_certificate_verified, edgePersistence=literal_constant_edge_persistence_verified, matchingK=literal_matching_sampled_k_envelope_verified, discharge=split_discharge_readiness_blocked, ready=true +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_1_persist_outP2_38_out25_23_smaller_side7.md` +- `D3.2_persist_outP2=251_out25=1_smaller=side18` [supporting_p17_companion_lane]: p=17, split=outP2=251|out25=1|smaller=side18, core=106, vertexAtoms=212, stableVertices=2, unstableVertices=210, refinement=literal_core_requires_sharper_square_witness_split/9, edgeAtoms=106, edgeCertificate=literal_edge_obstruction_certificate_verified, edgePersistence=literal_constant_edge_persistence_verified, matchingK=literal_matching_sampled_k_envelope_verified, discharge=split_discharge_readiness_blocked, ready=true +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/D3_2_persist_outP2_251_out25_1_smaller_side18.md` + +## Successor Packets + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1` [highest_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_4_outsider_1, split=outP2=70|out25=9|smaller=side7|out4=1, affected=145, stabilized=145, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_9_out_8` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_9_outsider_8, split=outP2=70|out25=9|smaller=side7|out9=8, affected=48, stabilized=48, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_49_out_17` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_49_outsider_17, split=outP2=70|out25=9|smaller=side7|out49=17, affected=9, stabilized=9, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_121_out_106` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_121_outsider_106, split=outP2=70|out25=9|smaller=side7|out121=106, affected=3, stabilized=3, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_361_out_255` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_361_outsider_255, split=outP2=70|out25=9|smaller=side7|out361=255, affected=2, stabilized=2, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_529_out_19` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_529_outsider_19, split=outP2=70|out25=9|smaller=side7|out529=19, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_841_out_263` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_841_outsider_263, split=outP2=70|out25=9|smaller=side7|out841=263, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_961_out_504` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_961_outsider_504, split=outP2=70|out25=9|smaller=side7|out961=504, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_1681_out_266` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_1681_outsider_266, split=outP2=70|out25=9|smaller=side7|out1681=266, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_2809_out_2500` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_2809_outsider_2500, split=outP2=70|out25=9|smaller=side7|out2809=2500, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.md` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.square_11881_out_5309` [dominant_refinement_successor]: parent=D2.1_persist_outP2=70_out25=9_smaller=side7, condition=square_11881_outsider_5309, split=outP2=70|out25=9|smaller=side7|out11881=5309, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_4_out_3` [highest_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_4_outsider_3, split=outP2=99|out25=6|smaller=side18|out4=3, affected=142, stabilized=142, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_9_out_7` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_9_outsider_7, split=outP2=99|out25=6|smaller=side18|out9=7, affected=48, stabilized=48, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_49_out_29` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_49_outsider_29, split=outP2=99|out25=6|smaller=side18|out49=29, affected=8, stabilized=8, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_121_out_112` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_121_outsider_112, split=outP2=99|out25=6|smaller=side18|out121=112, affected=3, stabilized=3, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_961_out_26` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_961_outsider_26, split=outP2=99|out25=6|smaller=side18|out961=26, affected=2, stabilized=2, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_289_out_207` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_289_outsider_207, split=outP2=99|out25=6|smaller=side18|out289=207, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_361_out_138` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_361_outsider_138, split=outP2=99|out25=6|smaller=side18|out361=138, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.md` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.square_1849_out_1133` [dominant_refinement_successor]: parent=D2.2_persist_outP2=99_out25=6_smaller=side18, condition=square_1849_outsider_1133, split=outP2=99|out25=6|smaller=side18|out1849=1133, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_4_out_1` [highest_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_4_outsider_1, split=outP2=99|out25=14|smaller=side7|out4=1, affected=145, stabilized=145, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_9_out_7` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_9_outsider_7, split=outP2=99|out25=14|smaller=side7|out9=7, affected=49, stabilized=49, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_49_out_25` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_49_outsider_25, split=outP2=99|out25=14|smaller=side7|out49=25, affected=7, stabilized=7, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_121_out_95` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_121_outsider_95, split=outP2=99|out25=14|smaller=side7|out121=95, affected=3, stabilized=3, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_289_out_55` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_289_outsider_55, split=outP2=99|out25=14|smaller=side7|out289=55, affected=2, stabilized=2, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_529_out_202` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_529_outsider_202, split=outP2=99|out25=14|smaller=side7|out529=202, affected=2, stabilized=2, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_361_out_345` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_361_outsider_345, split=outP2=99|out25=14|smaller=side7|out361=345, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_961_out_828` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_961_outsider_828, split=outP2=99|out25=14|smaller=side7|out961=828, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_1369_out_420` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_1369_outsider_420, split=outP2=99|out25=14|smaller=side7|out1369=420, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.md` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.square_7921_out_1789` [dominant_refinement_successor]: parent=D2.3_persist_outP2=99_out25=14_smaller=side7, condition=square_7921_outsider_1789, split=outP2=99|out25=14|smaller=side7|out7921=1789, affected=1, stabilized=1, failed=0, lemma=symbolic_vertex_family_lemma_verified, status=candidate_successor_obligation_verified +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.md` + +## Side-Count Floor Packets + +- `D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7` [highest_side_count_floor_atom]: split=outP2=70|out25=23|smaller=side7, floor=20, observed=21, margin=1, structuralMargin=1, sublemma=D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18, movingTerm=D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323, rows=32, status=symbolic_side_count_floor_atom_needed +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md` +- `D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7` [co_weakest_side_count_floor_atom]: split=outP2=70|out25=6|smaller=side7, floor=20, observed=21, margin=1, structuralMargin=1, sublemma=D2_p13_structural_margin_outP2_70_out25_6_smaller_side7_side18, movingTerm=D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7, rows=32, status=symbolic_side_count_floor_atom_needed +- JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.json` +- Markdown: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.md` + +## Prime-Lane Handoff Candidates + +- `D2_p13_matching_lower_bound` [prime_lane_handoff_candidate_with_open_all_n_gaps]: p=13, ready=3/3, successors=29/29, openAllNGaps=3 +- Boundary: This aggregates split-discharge readiness for a prime lane. It is not a universal D-lane proof until row-universe coverage and the symbolic K(N,x) lift are discharged. +- Gap `row_universe_split_coverage` [open]: Prove every future p=13 threatening row lands in one of the emitted split profiles, or emit the missing split profile as a new atom. +- Gap `universal_k_formula_lift` [open]: Replace each sampled K-envelope comparison with the symbolic K(N,x) inequality for the full p=13 lane. +- Gap `literal_to_parameterized_vertex_guard` [open_if_vertices_move]: If future rows require moving vertex formulas, re-lift vertex presence, edge persistence, and disjointness for the parameterized families. diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json new file mode 100644 index 0000000..b2cca0c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.json @@ -0,0 +1,3783 @@ +{ + "schema": "erdos.p848_side_count_floor_atom_packet/1", + "generatedAt": "2026-04-14T11:46:10.114Z", + "problemId": "848", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "atomId": "D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7", + "parentLemmaId": "D2_p13_non_tight_side_count_slack_floor_lift", + "parentCandidateId": "D2_p13_slack_dominance_symbolic_lift", + "targetPrime": 13, + "splitKey": "outP2=70|out25=23|smaller=side7", + "rank": 1, + "priority": "highest_side_count_floor_atom", + "status": "symbolic_side_count_floor_atom_needed", + "targetSlackLowerBound": 20, + "observedBoundedSlackFormulaFloor": 21, + "observedMarginAboveTarget": 1, + "boundedWitness": { + "rowCount": 32, + "nRange": "7307..7600", + "minSideCountSlackFormula": 21, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 110, + "maxLargerSideSize": 114, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 1, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + "structuralMarginDecomposition": { + "status": "bounded_structural_margin_replay_verified_symbolic_margin_lift_needed", + "largerSideLabel": "side18", + "targetAugmentedMarginConstant": 21, + "inequality": "side18Count + vMax + dMax + rGreater + 21 <= candidateSize", + "boundedMarginRange": { + "min": 1, + "max": 5 + }, + "firstOpenSublemma": { + "lemmaId": "D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18", + "status": "needed", + "statement": "For every future p=13 threat row with outP2=70|out25=23|smaller=side7, prove side18Count + vMax + dMax + rGreater + 21 <= candidateSize." + }, + "movingTermSubatoms": [ + { + "atomId": "D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7", + "status": "bounded_constant_bound_falsified_successor_atom_needed", + "term": "dMax", + "targetBound": 18, + "boundedRange": { + "min": 18, + "max": 18 + }, + "statement": "For every future p=13 threat row with outP2=70|out25=23|smaller=side7, prove dMax <= 18.", + "probeArtifact": { + "probeId": "p848_dmax_bound_probe_D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_BOUND_PROBES/D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7.json", + "status": "bounded_counterexample_to_constant_dmax_bound", + "probeRange": "7307..12000", + "targetRowCount": 492, + "firstCounterexample": { + "N": 7873, + "outP2": 70, + "out25": 23, + "smallerSide": "side7", + "outsider": 6323, + "dMax": 19, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "candidateSize": 315, + "rGreater": 113, + "compatibleSide7Count": 112, + "compatibleSide18Count": 118, + "matchingSlack": 17 + }, + "maxObservedDMax": 29, + "successorAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7" + }, + "successorAtomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "proofBoundary": "This bounded probe falsifies the constant dMax <= 18 outside the original 7307..7600 witness packet. It does not prove an all-N growth envelope; the successor atom must bound the same-prime degree term symbolically." + }, + { + "atomId": "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "status": "bounded_growth_profile_emitted_subatom_needed", + "term": "dMax growth envelope", + "dependsOn": [ + "D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7" + ], + "replacesFalseAtomId": "D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7", + "targetBound": 18, + "firstCounterexample": { + "N": 7873, + "outP2": 70, + "out25": 23, + "smallerSide": "side7", + "outsider": 6323, + "dMax": 19, + "dMaxWitnessSide": "plus", + "dMaxWitnessValue": 1591, + "candidateSize": 315, + "rGreater": 113, + "compatibleSide7Count": 112, + "compatibleSide18Count": 118, + "matchingSlack": 17 + }, + "maxObservedDMax": 29, + "growthProfile": { + "profileId": "p848_dmax_growth_profile_D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_GROWTH_PROFILES/D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7.json", + "status": "bounded_degree_growth_profile_emitted", + "probeRange": "7307..12000", + "firstOpenSubatomId": "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "growthWitnessCount": 2 + }, + "statement": "Replace the false constant dMax <= 18 with a symbolic same-prime degree-growth envelope for outP2=70|out25=23|smaller=side7.", + "proofBoundary": "This successor atom is required because the extended local probe found the same split with dMax above the original bounded constant." + }, + { + "atomId": "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=2 progression contribution", + "dependsOn": [ + "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7" + ], + "profileId": "p848_dmax_growth_profile_D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7", + "profileJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_GROWTH_PROFILES/D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove a symbolic floor-function upper bound for the q=2 same-prime degree progression m = 437 + 676*t, including base-residue and lower-witness exclusions.", + "completionRule": "Either prove the q=2 progression contribution can be absorbed in the dMax growth envelope, or emit the first exclusion/residue sub-split that controls it.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 2, + "proofKind": "crt_floor_function_upper_bound_with_base_residue_exclusions", + "nextSubatomId": "D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the first floor-function subatom emitted from the bounded dMax growth profile." + }, + { + "atomId": "D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=3 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=3 same-prime degree progression upper bound for the same split, including overlap/base-residue/lower-witness exclusions.", + "completionRule": "The q=3 progression contribution is bounded by CRT floor functions, or the first unresolved q=3 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 3, + "proofKind": "crt_floor_function_upper_bound_with_q2_overlap_and_base_residue_exclusions", + "nextSubatomId": "D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=2 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=5 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=5 same-prime degree progression upper bound for the same split, including q=2/q=3 overlap and base-residue/lower-witness exclusions.", + "completionRule": "The q=5 progression contribution is bounded by CRT floor functions, or the first unresolved q=5 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 5, + "proofKind": "crt_floor_function_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=3 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=7 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=7 same-prime degree progression upper bound for the same split, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=7 progression contribution is bounded by CRT floor functions, or the first unresolved q=7 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 7, + "proofKind": "crt_floor_function_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=5 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=11 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=11 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=11 progression contribution is bounded by a CRT floor function, or the first unresolved q=11 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 11, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=7 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=19 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=19 same-prime degree singleton progression upper bound for the minus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=19 progression contribution is bounded by a CRT floor function, or the first unresolved q=19 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 19, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=11 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=23 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=23 same-prime degree singleton progression upper bound for the minus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=23 progression contribution is bounded by a CRT floor function, or the first unresolved q=23 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 23, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=19 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=31 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=31 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=31 progression contribution is bounded by a CRT floor function, or the first unresolved q=31 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 31, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=23 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax q=251 progression contribution", + "dependsOn": [ + "D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json", + "statement": "Prove the q=251 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions.", + "completionRule": "The q=251 progression contribution is bounded by a CRT floor function, or the first unresolved q=251 exclusion/overlap class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "q": 251, + "proofKind": "crt_floor_function_singleton_upper_bound_with_prior_q_overlap_bookkeeping", + "nextSubatomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next square-divisor floor-function subatom after the verified q=31 CRT upper-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "status": "tail_scaffold_q13_residue_exclusion_verified_q17_needed", + "term": "dMax tail/recombination envelope", + "dependsOn": [ + "D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_q_progression_proof_D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json", + "verifiedComponentQs": [ + 2, + 3, + 5, + 7, + 11, + 19, + 23, + 31, + 251 + ], + "statement": "Recombine the verified observed q-progression components with a symbolic tail bound for all remaining same-prime square-divisor events in the dMax growth envelope.", + "completionRule": "The verified q-components plus a tail estimate imply the required symbolic dMax growth envelope, or the first unresolved tail range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7.json", + "status": "tail_scaffold_q13_residue_exclusion_verified_q17_needed", + "proofKind": "component_recombination_scaffold_with_target_prime_square_exclusion", + "q13Status": "verified_by_split_residue", + "nextSubatomId": "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the first non-singleton dMax growth atom after all observed q-progression components in the bounded profile have proof artifacts." + }, + { + "atomId": "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=17 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7.json", + "q": 17, + "statement": "Prove the q=17 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 47588 mod 48841 and m = 12238 mod 48841.", + "completionRule": "The q=17 tail contribution is bounded by CRT floor functions for both witnesses, or the first unresolved q=17 overlap/exclusion class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_tail_prime_upper_bound", + "q": 17, + "nextSubatomId": "D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the first unresolved tail-prime subatom after the target-prime q=13 square divisor is excluded by the split residue." + }, + { + "atomId": "D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=19 plus-side progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7.json", + "q": 19, + "side": "plus", + "statement": "Prove the plus-side q=19 tail complement left open by the observed minus-side q=19 component, starting from m = 22576 mod 61009.", + "completionRule": "The plus-side q=19 tail contribution is bounded by its CRT floor function, or the next side-specific q=19 overlap/exclusion class becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 19, + "side": "plus", + "nextSubatomId": "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This side-specific tail atom is required because the observed q=19 component proof covered only the minus witness." + }, + { + "atomId": "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=11 minus-side progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7.json", + "q": 11, + "side": "minus", + "statement": "Backfill the minus-side q=11 tail complement left open by the observed plus-side q=11 component, starting from m = 16970 mod 20449.", + "completionRule": "The minus-side q=11 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 11, + "side": "minus", + "nextSubatomId": "D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This backfill atom is required because the observed q=11 component proof covered only the plus witness." + }, + { + "atomId": "D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=23 plus-side progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7.json", + "q": 23, + "side": "plus", + "statement": "Prove the plus-side q=23 tail complement left open by the observed minus-side q=23 component, starting from m = 44039 mod 89401.", + "completionRule": "The plus-side q=23 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 23, + "side": "plus", + "nextSubatomId": "D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This side-specific tail atom is required because the observed q=23 component proof covered only the minus witness." + }, + { + "atomId": "D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=31 minus-side progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7.json", + "q": 31, + "side": "minus", + "statement": "Prove the minus-side q=31 tail complement left open by the observed plus-side q=31 component, starting from m = 105526 mod 162409.", + "completionRule": "The minus-side q=31 tail contribution is bounded by its CRT floor function, or the next side-specific tail complement becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 31, + "side": "minus", + "nextSubatomId": "D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This side-specific tail atom is required because the observed q=31 component proof covered only the plus witness." + }, + { + "atomId": "D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=251 minus-side progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7.json", + "q": 251, + "side": "minus", + "statement": "Prove the minus-side q=251 tail complement left open by the observed plus-side q=251 component, starting from m = 8138434 mod 10647169.", + "completionRule": "The minus-side q=251 tail contribution is bounded by its CRT floor function, or the next unresolved tail range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_side_complement_upper_bound", + "q": 251, + "side": "minus", + "nextSubatomId": "D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This side-specific tail atom is required because the observed q=251 component proof covered only the plus witness." + }, + { + "atomId": "D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=29 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json", + "q": 29, + "statement": "Prove the q=29 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 29167 mod 142129 and m = 114314 mod 142129.", + "completionRule": "The q=29 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "crt_floor_function_tail_prime_upper_bound", + "q": 29, + "nextSubatomId": "D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the first remaining non-observed tail-prime subatom after observed q-components and their side complements are certified." + }, + { + "atomId": "D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=37 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7.json", + "q": 37, + "statement": "Prove the q=37 tail-prime same-prime degree atom: exclude the plus side because 37 divides 1591, and certify the minus-side CRT floor bound starting from m = 136284 mod 231361.", + "completionRule": "The q=37 tail contribution is bounded by the plus-side witness-divisibility exclusion and the minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "witness_divisibility_exclusion_plus_crt_floor_function_tail_prime_upper_bound", + "q": 37, + "nextSubatomId": "D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This residual tail-prime atom is special because q=37 divides the plus witness 1591, excluding that side before the minus-side CRT floor bound." + }, + { + "atomId": "D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=41 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7.json", + "q": 41, + "statement": "Prove the q=41 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 251571 mod 284089 and m = 26941 mod 284089.", + "completionRule": "The q=41 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 41, + "nextSubatomId": "D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=37 witness-divisibility exclusion plus minus-side floor bound." + }, + { + "atomId": "D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=43 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7.json", + "q": 43, + "statement": "Prove the q=43 tail-prime same-prime degree atom: plus side is excluded because 43 divides 1591, and minus side starts at m = 216897 mod 312481.", + "completionRule": "The q=43 tail contribution is bounded by the plus-side exclusion and minus-side CRT floor function, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "witness_divisibility_exclusion_plus_crt_floor_function_tail_prime_upper_bound", + "q": 43, + "nextSubatomId": "D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This residual tail-prime atom is special because q=43 divides the plus witness 1591, excluding that side before the minus-side CRT floor bound." + }, + { + "atomId": "D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=47 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7.json", + "q": 47, + "statement": "Prove the q=47 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 267457 mod 373321 and m = 278413 mod 373321.", + "completionRule": "The q=47 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 47, + "nextSubatomId": "D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=43 witness-divisibility exclusion plus minus-side floor bound." + }, + { + "atomId": "D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=53 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7.json", + "q": 53, + "statement": "Prove the q=53 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 52151 mod 474721 and m = 213348 mod 474721.", + "completionRule": "The q=53 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 53, + "nextSubatomId": "D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=47 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=59 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7.json", + "q": 59, + "statement": "Prove the q=59 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 182281 mod 588289 and m = 492874 mod 588289.", + "completionRule": "The q=59 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 59, + "nextSubatomId": "D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=53 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=61 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7.json", + "q": 61, + "statement": "Prove the q=61 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 396573 mod 628849 and m = 477495 mod 628849.", + "completionRule": "The q=61 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 61, + "nextSubatomId": "D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=59 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=67 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7.json", + "q": 67, + "statement": "Prove the q=67 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 344183 mod 758641 and m = 736572 mod 758641.", + "completionRule": "The q=67 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 67, + "nextSubatomId": "D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=61 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=71 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7.json", + "q": 71, + "statement": "Prove the q=71 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 69389 mod 851929 and m = 783385 mod 851929.", + "completionRule": "The q=71 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 71, + "nextSubatomId": "D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=67 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=73 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7.json", + "q": 73, + "statement": "Prove the q=73 tail-prime same-prime degree contribution: the plus witness has m = 229770 mod 900601, while the minus side is excluded because 73 divides 9563.", + "completionRule": "The q=73 tail contribution is bounded by the plus-side CRT floor function and minus-side witness-divisibility exclusion, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "plus_crt_floor_function_minus_witness_divisibility_exclusion_tail_prime_upper_bound", + "q": 73, + "nextSubatomId": "D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This residual tail-prime atom is special because q=73 divides the minus witness 9563, excluding that side before the plus-side CRT floor bound." + }, + { + "atomId": "D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=79 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7.json", + "q": 79, + "statement": "Prove the q=79 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 901038 mod 1054729 and m = 280272 mod 1054729.", + "completionRule": "The q=79 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 79, + "nextSubatomId": "D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=73 plus-side floor-bound and minus-side exclusion component." + }, + { + "atomId": "D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=83 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7.json", + "q": 83, + "statement": "Prove the q=83 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 443048 mod 1164241 and m = 16125 mod 1164241.", + "completionRule": "The q=83 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 83, + "nextSubatomId": "D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=79 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=89 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7.json", + "q": 89, + "statement": "Prove the q=89 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 30519 mod 1338649 and m = 791497 mod 1338649.", + "completionRule": "The q=89 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 89, + "nextSubatomId": "D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=83 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=97 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7.json", + "q": 97, + "statement": "Prove the q=97 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 783076 mod 1590121 and m = 279765 mod 1590121.", + "completionRule": "The q=97 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 97, + "nextSubatomId": "D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=89 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=101 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7.json", + "q": 101, + "statement": "Prove the q=101 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1382181 mod 1723969 and m = 253570 mod 1723969.", + "completionRule": "The q=101 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 101, + "nextSubatomId": "D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=97 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=103 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7.json", + "q": 103, + "statement": "Prove the q=103 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 586529 mod 1792921 and m = 1732827 mod 1792921.", + "completionRule": "The q=103 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 103, + "nextSubatomId": "D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=101 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=107 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7.json", + "q": 107, + "statement": "Prove the q=107 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 967624 mod 1934881 and m = 1699703 mod 1934881.", + "completionRule": "The q=107 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 107, + "nextSubatomId": "D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=103 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=109 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7.json", + "q": 109, + "statement": "Prove the q=109 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 963399 mod 2007889 and m = 725925 mod 2007889.", + "completionRule": "The q=109 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 109, + "nextSubatomId": "D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=107 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=113 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7.json", + "q": 113, + "statement": "Prove the q=113 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 407051 mod 2157961 and m = 2150764 mod 2157961.", + "completionRule": "The q=113 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 113, + "nextSubatomId": "D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=109 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=127 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7.json", + "q": 127, + "statement": "Prove the q=127 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1191042 mod 2725801 and m = 2198253 mod 2725801.", + "completionRule": "The q=127 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 127, + "nextSubatomId": "D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=113 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=131 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7.json", + "q": 131, + "statement": "Prove the q=131 tail-prime same-prime degree progression upper bound: plus-side CRT floor bound from m = 1345170 mod 2900209, and minus-side exclusion because 131 divides 9563.", + "completionRule": "The q=131 tail contribution is bounded by the plus-side CRT floor function plus the minus-side witness-divisibility exclusion, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "plus_crt_floor_function_minus_witness_divisibility_exclusion_tail_prime_upper_bound", + "q": 131, + "nextSubatomId": "D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=127 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=137 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7.json", + "q": 137, + "statement": "Prove the q=137 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2767643 mod 3171961 and m = 1021675 mod 3171961.", + "completionRule": "The q=137 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 137, + "nextSubatomId": "D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=131 CRT/exclusion component." + }, + { + "atomId": "D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=139 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7.json", + "q": 139, + "statement": "Prove the q=139 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3089757 mod 3265249 and m = 1765444 mod 3265249.", + "completionRule": "The q=139 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 139, + "nextSubatomId": "D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=137 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=149 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7.json", + "q": 149, + "statement": "Prove the q=149 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 276752 mod 3751969 and m = 1423557 mod 3751969.", + "completionRule": "The q=149 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 149, + "nextSubatomId": "D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=139 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=151 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7.json", + "q": 151, + "statement": "Prove the q=151 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2446543 mod 3853369 and m = 1157720 mod 3853369.", + "completionRule": "The q=151 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 151, + "nextSubatomId": "D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=149 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=157 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7.json", + "q": 157, + "statement": "Prove the q=157 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1762938 mod 4165681 and m = 2160735 mod 4165681.", + "completionRule": "The q=157 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 157, + "nextSubatomId": "D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=151 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=163 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7.json", + "q": 163, + "statement": "Prove the q=163 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2941544 mod 4490161 and m = 856562 mod 4490161.", + "completionRule": "The q=163 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 163, + "nextSubatomId": "D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=157 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=167 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7.json", + "q": 167, + "statement": "Prove the q=167 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4640670 mod 4713241 and m = 3647428 mod 4713241.", + "completionRule": "The q=167 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 167, + "nextSubatomId": "D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=163 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=173 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7.json", + "q": 173, + "statement": "Prove the q=173 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 978778 mod 5058001 and m = 1961146 mod 5058001.", + "completionRule": "The q=173 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 173, + "nextSubatomId": "D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=167 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=179 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7.json", + "q": 179, + "statement": "Prove the q=179 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2724210 mod 5414929 and m = 4437841 mod 5414929.", + "completionRule": "The q=179 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 179, + "nextSubatomId": "D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=173 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=181 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7.json", + "q": 181, + "statement": "Prove the q=181 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1789809 mod 5536609 and m = 4242815 mod 5536609.", + "completionRule": "The q=181 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 181, + "nextSubatomId": "D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=179 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=191 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7.json", + "q": 191, + "statement": "Prove the q=191 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1508424 mod 6165289 and m = 1951682 mod 6165289.", + "completionRule": "The q=191 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 191, + "nextSubatomId": "D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=181 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=193 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7.json", + "q": 193, + "statement": "Prove the q=193 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 69558 mod 6295081 and m = 1273485 mod 6295081.", + "completionRule": "The q=193 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 193, + "nextSubatomId": "D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=191 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=197 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7.json", + "q": 197, + "statement": "Prove the q=197 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3802599 mod 6558721 and m = 4141415 mod 6558721.", + "completionRule": "The q=197 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 197, + "nextSubatomId": "D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=193 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=199 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7.json", + "q": 199, + "statement": "Prove the q=199 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 872815 mod 6692569 and m = 1078797 mod 6692569.", + "completionRule": "The q=199 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 199, + "nextSubatomId": "D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=197 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=211 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7.json", + "q": 211, + "statement": "Prove the q=211 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 199519 mod 7524049 and m = 3288134 mod 7524049.", + "completionRule": "The q=211 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 211, + "nextSubatomId": "D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=199 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=223 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7.json", + "q": 223, + "statement": "Prove the q=223 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1169241 mod 8404201 and m = 3594700 mod 8404201.", + "completionRule": "The q=223 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 223, + "nextSubatomId": "D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=211 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=227 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7.json", + "q": 227, + "statement": "Prove the q=227 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1095388 mod 8708401 and m = 7005627 mod 8708401.", + "completionRule": "The q=227 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 227, + "nextSubatomId": "D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=223 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=229 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7.json", + "q": 229, + "statement": "Prove the q=229 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 102344 mod 8862529 and m = 8756298 mod 8862529.", + "completionRule": "The q=229 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 229, + "nextSubatomId": "D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=227 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=233 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7.json", + "q": 233, + "statement": "Prove the q=233 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1640920 mod 9174841 and m = 5761787 mod 9174841.", + "completionRule": "The q=233 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 233, + "nextSubatomId": "D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=229 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=239 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7.json", + "q": 239, + "statement": "Prove the q=239 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2615036 mod 9653449 and m = 883264 mod 9653449.", + "completionRule": "The q=239 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 239, + "nextSubatomId": "D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=233 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=241 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7.json", + "q": 241, + "statement": "Prove the q=241 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8794690 mod 9815689 and m = 6246310 mod 9815689.", + "completionRule": "The q=241 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 241, + "nextSubatomId": "D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=239 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=257 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7.json", + "q": 257, + "statement": "Prove the q=257 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4730578 mod 11162281 and m = 10654844 mod 11162281.", + "completionRule": "The q=257 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 257, + "nextSubatomId": "D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=241 two-sided floor-bound component; q=251 was already covered by the observed q251 packet and its minus-side complement." + }, + { + "atomId": "D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=263 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7.json", + "q": 263, + "statement": "Prove the q=263 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5804066 mod 11689561 and m = 3539944 mod 11689561.", + "completionRule": "The q=263 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 263, + "nextSubatomId": "D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=257 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=269 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7.json", + "q": 269, + "statement": "Prove the q=269 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10056951 mod 12229009 and m = 11133621 mod 12229009.", + "completionRule": "The q=269 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 269, + "nextSubatomId": "D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=263 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=271 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7.json", + "q": 271, + "statement": "Prove the q=271 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4686976 mod 12411529 and m = 749923 mod 12411529.", + "completionRule": "The q=271 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 271, + "nextSubatomId": "D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=269 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=277 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7.json", + "q": 277, + "statement": "Prove the q=277 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6946844 mod 12967201 and m = 10587920 mod 12967201.", + "completionRule": "The q=277 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 277, + "nextSubatomId": "D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=271 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=281 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7.json", + "q": 281, + "statement": "Prove the q=281 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4072323 mod 13344409 and m = 9581694 mod 13344409.", + "completionRule": "The q=281 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 281, + "nextSubatomId": "D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=277 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=283 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7.json", + "q": 283, + "statement": "Prove the q=283 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7094043 mod 13535041 and m = 4146823 mod 13535041.", + "completionRule": "The q=283 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 283, + "nextSubatomId": "D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=281 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=293 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7.json", + "q": 293, + "statement": "Prove the q=293 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7410749 mod 14508481 and m = 12282314 mod 14508481.", + "completionRule": "The q=293 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 293, + "nextSubatomId": "D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=283 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=307 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7.json", + "q": 307, + "statement": "Prove the q=307 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 14963021 mod 15928081 and m = 15889112 mod 15928081.", + "completionRule": "The q=307 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 307, + "nextSubatomId": "D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=293 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=311 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7.json", + "q": 311, + "statement": "Prove the q=311 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 12908150 mod 16345849 and m = 5085787 mod 16345849.", + "completionRule": "The q=311 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 311, + "nextSubatomId": "D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=307 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=313 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7.json", + "q": 313, + "statement": "Prove the q=313 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5813361 mod 16556761 and m = 4403872 mod 16556761.", + "completionRule": "The q=313 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 313, + "nextSubatomId": "D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=311 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=317 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7.json", + "q": 317, + "statement": "Prove the q=317 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7885639 mod 16982641 and m = 6675063 mod 16982641.", + "completionRule": "The q=317 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 317, + "nextSubatomId": "D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=313 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=331 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7.json", + "q": 331, + "statement": "Prove the q=331 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 9831843 mod 18515809 and m = 2596079 mod 18515809.", + "completionRule": "The q=331 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 331, + "nextSubatomId": "D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=317 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=337 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7.json", + "q": 337, + "statement": "Prove the q=337 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3148738 mod 19193161 and m = 11799312 mod 19193161.", + "completionRule": "The q=337 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 337, + "nextSubatomId": "D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=331 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=347 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7.json", + "q": 347, + "statement": "Prove the q=347 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 11863730 mod 20349121 and m = 17215931 mod 20349121.", + "completionRule": "The q=347 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 347, + "nextSubatomId": "D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=337 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=349 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7.json", + "q": 349, + "statement": "Prove the q=349 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7685712 mod 20584369 and m = 2404433 mod 20584369.", + "completionRule": "The q=349 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 349, + "nextSubatomId": "D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=347 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=353 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7.json", + "q": 353, + "statement": "Prove the q=353 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1415812 mod 21058921 and m = 17854751 mod 21058921.", + "completionRule": "The q=353 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 353, + "nextSubatomId": "D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=349 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=359 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7.json", + "q": 359, + "statement": "Prove the q=359 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2693621 mod 21780889 and m = 19926353 mod 21780889.", + "completionRule": "The q=359 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 359, + "nextSubatomId": "D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=353 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=367 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7.json", + "q": 367, + "statement": "Prove the q=367 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10408302 mod 22762441 and m = 21816280 mod 22762441.", + "completionRule": "The q=367 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 367, + "nextSubatomId": "D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=359 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=373 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7.json", + "q": 373, + "statement": "Prove the q=373 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6694020 mod 23512801 and m = 12354984 mod 23512801.", + "completionRule": "The q=373 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 373, + "nextSubatomId": "D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=367 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=379 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7.json", + "q": 379, + "statement": "Prove the q=379 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 11502746 mod 24275329 and m = 2984948 mod 24275329.", + "completionRule": "The q=379 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 379, + "nextSubatomId": "D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=373 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=383 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7.json", + "q": 383, + "statement": "Prove the q=383 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10683772 mod 24790441 and m = 8325686 mod 24790441.", + "completionRule": "The q=383 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 383, + "nextSubatomId": "D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=379 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=389 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7.json", + "q": 389, + "statement": "Prove the q=389 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 16061521 mod 25573249 and m = 4554789 mod 25573249.", + "completionRule": "The q=389 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 389, + "nextSubatomId": "D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=383 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=397 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7.json", + "q": 397, + "statement": "Prove the q=397 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 15585955 mod 26635921 and m = 9163588 mod 26635921.", + "completionRule": "The q=397 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 397, + "nextSubatomId": "D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=389 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=401 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7.json", + "q": 401, + "statement": "Prove the q=401 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 19236186 mod 27175369 and m = 26667256 mod 27175369.", + "completionRule": "The q=401 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 401, + "nextSubatomId": "D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=397 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=409 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7.json", + "q": 409, + "statement": "Prove the q=409 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 25277936 mod 28270489 and m = 5668837 mod 28270489.", + "completionRule": "The q=409 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 409, + "nextSubatomId": "D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=401 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=419 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7.json", + "q": 419, + "statement": "Prove the q=419 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1254417 mod 29669809 and m = 6801644 mod 29669809.", + "completionRule": "The q=419 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 419, + "nextSubatomId": "D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=409 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=421 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7.json", + "q": 421, + "statement": "Prove the q=421 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 27364072 mod 29953729 and m = 11327633 mod 29953729.", + "completionRule": "The q=421 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 421, + "nextSubatomId": "D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=419 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=431 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7.json", + "q": 431, + "statement": "Prove the q=431 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 30520147 mod 31393609 and m = 30076324 mod 31393609.", + "completionRule": "The q=431 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 431, + "nextSubatomId": "D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=421 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=433 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7.json", + "q": 433, + "statement": "Prove the q=433 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4441757 mod 31685641 and m = 22352010 mod 31685641.", + "completionRule": "The q=433 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 433, + "nextSubatomId": "D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=431 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=439 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7.json", + "q": 439, + "statement": "Prove the q=439 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 31660390 mod 32569849 and m = 32568398 mod 32569849.", + "completionRule": "The q=439 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 439, + "nextSubatomId": "D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=433 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=443 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7.json", + "q": 443, + "statement": "Prove the q=443 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 17292855 mod 33166081 and m = 15525424 mod 33166081.", + "completionRule": "The q=443 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 443, + "nextSubatomId": "D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=439 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=449 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7.json", + "q": 449, + "statement": "Prove the q=449 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10624284 mod 34070569 and m = 9976140 mod 34070569.", + "completionRule": "The q=449 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 449, + "nextSubatomId": "D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=443 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=457 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7.json", + "q": 457, + "statement": "Prove the q=457 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 33113790 mod 35295481 and m = 7601859 mod 35295481.", + "completionRule": "The q=457 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 457, + "nextSubatomId": "D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=449 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=461 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7.json", + "q": 461, + "statement": "Prove the q=461 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 709561 mod 35916049 and m = 6592929 mod 35916049.", + "completionRule": "The q=461 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 461, + "nextSubatomId": "D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=457 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=463 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7.json", + "q": 463, + "statement": "Prove the q=463 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5329852 mod 36228361 and m = 31534794 mod 36228361.", + "completionRule": "The q=463 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 463, + "nextSubatomId": "D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=461 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=467 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7.json", + "q": 467, + "statement": "Prove the q=467 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4056099 mod 36857041 and m = 5739141 mod 36857041.", + "completionRule": "The q=467 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 467, + "nextSubatomId": "D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=463 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=479 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7.json", + "q": 479, + "statement": "Prove the q=479 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 24650270 mod 38775529 and m = 37033716 mod 38775529.", + "completionRule": "The q=479 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 479, + "nextSubatomId": "D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=467 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=487 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7.json", + "q": 487, + "statement": "Prove the q=487 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 21019643 mod 40081561 and m = 36495282 mod 40081561.", + "completionRule": "The q=487 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 487, + "nextSubatomId": "D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=479 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=491 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7.json", + "q": 491, + "statement": "Prove the q=491 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8394498 mod 40742689 and m = 21433495 mod 40742689.", + "completionRule": "The q=491 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 491, + "nextSubatomId": "D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=487 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=499 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7.json", + "q": 499, + "statement": "Prove the q=499 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8072891 mod 42081169 and m = 26746686 mod 42081169.", + "completionRule": "The q=499 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 499, + "nextSubatomId": "D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=491 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=503 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7.json", + "q": 503, + "statement": "Prove the q=503 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 42056425 mod 42758521 and m = 19404650 mod 42758521.", + "completionRule": "The q=503 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 503, + "nextSubatomId": "D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=499 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=509 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7.json", + "q": 509, + "statement": "Prove the q=509 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 68882 mod 43784689 and m = 22331899 mod 43784689.", + "completionRule": "The q=509 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 509, + "nextSubatomId": "D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=503 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=521 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7.json", + "q": 521, + "statement": "Prove the q=521 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 37647553 mod 45873529 and m = 27667567 mod 45873529.", + "completionRule": "The q=521 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 521, + "nextSubatomId": "D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=509 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=523 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7.json", + "q": 523, + "statement": "Prove the q=523 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5572874 mod 46226401 and m = 8835390 mod 46226401.", + "completionRule": "The q=523 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 523, + "nextSubatomId": "D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=521 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=541 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7.json", + "q": 541, + "statement": "Prove the q=541 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6164881 mod 49463089 and m = 2567011 mod 49463089.", + "completionRule": "The q=541 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 541, + "nextSubatomId": "D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=523 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=547 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7.json", + "q": 547, + "statement": "Prove the q=547 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 34995605 mod 50566321 and m = 25423754 mod 50566321.", + "completionRule": "The q=547 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 547, + "nextSubatomId": "D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=541 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=557 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7.json", + "q": 557, + "statement": "Prove the q=557 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 45994463 mod 52432081 and m = 41289136 mod 52432081.", + "completionRule": "The q=557 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 557, + "nextSubatomId": "D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=547 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=563 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7.json", + "q": 563, + "statement": "Prove the q=563 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 42763521 mod 53567761 and m = 381503 mod 53567761.", + "completionRule": "The q=563 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 563, + "nextSubatomId": "D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=557 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=569 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7.json", + "q": 569, + "statement": "Prove the q=569 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 13641103 mod 54715609 and m = 17025468 mod 54715609.", + "completionRule": "The q=569 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 569, + "nextSubatomId": "D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=563 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=571 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7.json", + "q": 571, + "statement": "Prove the q=571 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 28625826 mod 55100929 and m = 25724236 mod 55100929.", + "completionRule": "The q=571 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 571, + "nextSubatomId": "D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=569 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=577 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7.json", + "q": 577, + "statement": "Prove the q=577 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 22102426 mod 56265001 and m = 9319575 mod 56265001.", + "completionRule": "The q=577 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound", + "q": 577, + "nextSubatomId": "D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=571 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7", + "status": "symbolic_upper_bound_verified", + "term": "dMax tail q=587 progression contribution", + "dependsOn": [ + "D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7.json", + "q": 587, + "statement": "Prove the q=587 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 57070892 mod 58232161 and m = 23141071 mod 58232161.", + "completionRule": "The q=587 tail contribution is bounded by CRT floor functions for both witnesses, or the next unresolved tail-prime/range becomes the next atom.", + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7.json", + "status": "symbolic_upper_bound_verified", + "proofKind": "two_sided_crt_floor_function_tail_prime_upper_bound_with_bounded_range_profile", + "q": 587, + "nextSubatomId": "D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7" + }, + "proofBoundary": "This is the next residual tail-prime subatom after the q=577 two-sided floor-bound component." + }, + { + "atomId": "D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7", + "status": "bounded_parametric_zero_floor_verified", + "term": "dMax tail q>=587 parametric zero-floor lift", + "dependsOn": [ + "D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7" + ], + "predecessorProofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7.json", + "qRange": "q>=587", + "statement": "Lift the bounded q>=587 zero-floor profile into a parametric tail lemma or aggregate recombination step; do not emit q=593 as another singleton unless the lift fails and returns a named exceptional class.", + "completionRule": "Either prove a theorem-facing q>=587 tail bound for both witness sides, or emit the first concrete exceptional prime/range that prevents the aggregate lift.", + "boundedRangeProfile": { + "status": "bounded_zero_floor_profile_verified_parametric_lift_needed", + "profileRange": "7307..12000", + "startPrime": 587, + "plusWitnessProductCutoff": 4369, + "minusWitnessProductCutoff": 10712, + "scannedWitnessSideRowCount": 1690, + "nonzeroRawFloorCount": 0 + }, + "proofArtifact": { + "proofId": "p848_dmax_tail_recombination_proof_D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7.json", + "status": "bounded_parametric_zero_floor_verified", + "proofKind": "bounded_tail_prime_range_zero_floor_lift", + "qRange": "q>=587", + "nextSubatomId": "D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18" + }, + "proofBoundary": "This aggregate handoff is bounded-profile evidence only; it must be lifted before any all-N dMax tail or side-count-floor claim." + }, + { + "atomId": "D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18", + "status": "bounded_dynamic_margin_replay_verified_symbolic_lift_needed", + "term": "side18Count + vMax + rGreater", + "dependsOn": [ + "D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7" + ], + "residualDynamicMarginConstant": 39, + "inequality": "side18Count + vMax + rGreater + 39 <= candidateSize", + "boundedMarginRange": { + "min": 1, + "max": 5 + }, + "statement": "After the dMax growth envelope is proved for outP2=70|out25=23|smaller=side7, recompute the residual dynamic margin; the bounded-budget constant 39 is not valid as an all-N handoff.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18.json", + "status": "bounded_dynamic_margin_replay_verified_symbolic_lift_needed", + "proofKind": "bounded_residual_dynamic_margin_formula_replay", + "nextSubatomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "residualDynamicMarginRange": "1..5" + }, + "proofBoundary": "The residual dynamic margin must be re-derived after a symbolic dMax growth envelope replaces the false constant bound." + }, + { + "atomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "status": "bounded_symbolic_lift_falsified_successor_atom_needed", + "term": "side18 residual dynamic margin symbolic lift", + "dependsOn": [ + "D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18.json", + "targetInequality": "strictBaseThreshold - 1 - side18Count >= 20", + "statement": "Lift the bounded residual dynamic-margin replay to a symbolic side18 threshold lemma: prove strictBaseThreshold - 1 - side18Count >= 20 for every future row in split outP2=70|out25=23|smaller=side7, or emit the first future-row residue/threshold obstruction.", + "completionRule": "The side18 threshold inequality is proved symbolically for this split, or the first exact obstruction becomes a sharper side-count/rGreater successor atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18.json", + "status": "bounded_symbolic_lift_falsified_successor_atom_needed", + "proofKind": "bounded_future_row_obstruction_to_side18_threshold_lift", + "targetInequality": "strictBaseThreshold - 1 - side18Count >= 20", + "firstObstruction": { + "N": 7307, + "outsider": 6323, + "targetLeftSide": 17, + "targetDeficit": 3 + }, + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet falsifies only the proposed symbolic threshold lift by bounded extension evidence and emits a sharper theorem-facing successor. It does not promote the bounded exact mixed-base verifier to an all-N proof." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_exact_mixed_margin_profile_verified_symbolic_lift_needed", + "term": "side18 exact mixed-margin successor", + "dependsOn": [ + "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18.json", + "replacesFalseAtomId": "D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18", + "targetInequality": "matching saturates the smaller side and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in the outsider-6323 family", + "firstObstruction": { + "N": 7307, + "outsider": 6323, + "outsiderMod169": 70, + "outsiderMod25": 23, + "nMod25": 7, + "candidateSize": 293, + "vMax": 43, + "dMax": 18, + "rGreater": 104, + "strictBaseThreshold": 128, + "side7Count": 105, + "side18Count": 110, + "targetLeftSide": 17, + "targetRequiredLowerBound": 20, + "targetDeficit": 3, + "unionCount": 215, + "mixedBaseCliqueSize": 110, + "matchingSizeInMissingCrossGraph": 105, + "requiredMatchingLowerBound": 88, + "matchingSlack": 17, + "smallerSideSize": 105, + "saturatesSmallerSide": true, + "dominantMixedCliqueSide": "side18", + "exactMixedMargin": 18, + "exactMixedMarginIdentity": "candidateSize - mixedBaseCliqueSize - vMax - dMax - rGreater = 293 - 110 - 43 - 18 - 104 = 18" + }, + "statement": "Replace the false side18 threshold lift for split outP2=70|out25=23|smaller=side7 with an exact mixed-margin successor: prove the missing-cross matching saturates the smaller side for the outsider-6323 family and leaves positive exact mixed margin, or emit the first sharper root-universe/rGreater obstruction.", + "completionRule": "The exact mixed-margin/matching-saturation successor is proved symbolically for this split family, or the first residue/root-universe obstruction becomes the next deterministic atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "status": "bounded_exact_mixed_margin_profile_verified_symbolic_lift_needed", + "proofKind": "bounded_exact_mixed_margin_successor_profile", + "boundedRowCount": 277, + "exactMixedMarginRange": "18..31", + "allRowsSaturateSmallerSide": true, + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This certificate verifies the exact mixed-margin successor only on the bounded 7307..10000 outsider-6323 profile. It does not prove the all-N matching saturation or exact mixed-margin lift." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "symbolic_lift_reduced_to_matching_injection_and_margin_floor", + "term": "side18 exact mixed-margin symbolic lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "targetInequality": "matching saturates the smaller side and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in the outsider-6323 family", + "statement": "Lift the bounded exact mixed-margin successor profile for outsider 6323 into a symbolic theorem: prove smaller-side matching saturation and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in split outP2=70|out25=23|smaller=side7, or emit the first exact residue/root-universe obstruction.", + "completionRule": "The exact mixed-margin successor is proved symbolically for the outsider-6323 family, or the first residue/root-universe obstruction becomes the next deterministic atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "status": "symbolic_lift_reduced_to_matching_injection_and_margin_floor", + "proofKind": "theorem_obligation_decomposition", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This symbolic lift is required because the exact mixed-margin successor is only bounded-profile evidence so far." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_prefix_matching_injection_verified_parametric_lift_needed", + "term": "outsider-6323 exact mixed matching injection", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "targetInequality": "Construct an injective matching from every side7-compatible base vertex for outsider 6323 into a distinct side18-compatible base vertex along missing cross edges of the side7/side18 compatibility graph.", + "statement": "Prove the side7-to-side18 missing-cross injection for outsider 6323, or emit the first exact residue/root-universe row where side7 cannot be saturated.", + "completionRule": "The matching injection saturates the side7-compatible set for this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom.", + "nextAfterDischarge": "D2_p13_dynamic_margin_exact_mixed_margin_floor_outP2_70_out25_23_smaller_side7_outsider_6323", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "status": "bounded_prefix_matching_injection_verified_parametric_lift_needed", + "proofKind": "bounded_prefix_matching_injection_profile", + "sourceRowCount": 277, + "stableCorePairCount": 105, + "extensionPairCount": 40, + "extendedEventMaxN": 12000, + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This certificate is bounded evidence. It verifies a reusable prefix matching through the source 7307..10000 profile and a no-obstruction event probe through 12000, but it does not prove the all-N side7-to-side18 matching injection." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_online_augmentation_profile_verified_finite_menu_needed", + "term": "outsider-6323 parametric prefix-extension matching injection", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "targetInequality": "Inject every side7-compatible base vertex for outsider 6323 into a distinct side18-compatible base vertex along squarefree missing-cross edges.", + "statement": "Turn the bounded prefix injection into an online residue/block insertion proof for all future outsider-6323 rows, or emit the first exact future event row where side7 cannot be saturated.", + "completionRule": "A parametric insertion/replacement rule saturates side7 for every future row in this split family, or the first unmatched residue/root-universe obstruction becomes the next deterministic atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "status": "bounded_online_augmentation_profile_verified_finite_menu_needed", + "proofKind": "bounded_online_augmenting_path_profile", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This certificate is bounded evidence through N=40000. It verifies online side7 saturation and isolates the finite augmenting-path menu to prove next, but it does not prove the all-N outsider-6323 matching injection." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_finite_menu_falsified_direct_delta_successor_needed", + "term": "outsider-6323 finite augmenting-path menu", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json", + "targetInequality": "Match every side7-compatible vertex to a side18-compatible missing-cross neighbor in the outsider-6323 exact mixed row family.", + "statement": "Prove the finite direct-insertion plus short replacement-path menu for every future side7-compatible event row in the outsider-6323 split family, or emit the first event row whose side7 vertex needs a new obstruction atom.", + "completionRule": "A residue/block augmenting-path menu saturates side7 for every future event row, or the first future event row outside the menu becomes the next deterministic atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_632.json", + "status": "bounded_finite_menu_falsified_direct_delta_successor_needed", + "proofKind": "bounded_future_event_menu_obstruction", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet falsifies the mined finite augmenting-path menu by an exact bounded future event row. It does not falsify side7 saturation or the matching-injection target; it only shows that the menu needs at least the new direct delta -1089 branch." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_direct_delta_minus1089_branch_falsified_delta_minus39_successor_needed", + "term": "outsider-6323 direct delta -1089 successor", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_632.json", + "targetEdge": { + "left": 73607, + "right": 72518, + "delta": -1089 + }, + "firstFailure": { + "N": 73607, + "left": 73607, + "leftMod25": 7, + "leftMod100": 7, + "leftMod625": 482, + "leftCompatibility": { + "outsiderProductPlusOne": 465417062, + "squareWitnesses": [ + { + "prime": 11, + "square": 121 + } + ] + }, + "activeSide18Count": 1081, + "missingCrossEdgeCount": 97, + "oldDirectDeltaCandidateCount": 25, + "oldDirectDeltaActiveSide18ResidueCandidateCount": 25, + "oldDirectDeltaRightCompatibleCandidateCount": 3, + "oldDirectDeltaCrossSquarefreeCandidateCount": 22, + "oldDirectDeltaMissingCrossEdgeCount": 0, + "interpretation": "Every old direct-delta candidate is active on side18 residue, but none is simultaneously outsider-compatible on side18 and squarefree across the left/right pair." + }, + "statement": "Prove the new direct-delta -1089 branch exposed at side7 vertex 73607, integrate it with the existing augmenting menu, or emit the first future row where this enlarged menu fails.", + "completionRule": "The delta -1089 residue/block branch is proved symbolically and merged into the matching-injection menu, or the first future row requiring a different direct delta or longer augmenting path becomes the next deterministic atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou.json", + "status": "bounded_direct_delta_minus1089_branch_falsified_delta_minus39_successor_needed", + "proofKind": "bounded_enlarged_menu_future_event_obstruction", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet falsifies the enlarged direct-delta -1089 menu by an exact bounded future event row. It does not falsify side7 saturation or the matching-injection target; it only shows that the menu needs at least the new direct delta -39 branch." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_direct_delta_minus39_branch_falsified_residue_parametric_delta_selection_lift_needed", + "term": "outsider-6323 direct delta -39 successor", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou.json", + "targetEdge": { + "left": 164507, + "right": 164468, + "delta": -39 + }, + "firstFailure": { + "N": 164507, + "left": 164507, + "leftMod25": 7, + "leftMod100": 7, + "leftMod625": 132, + "leftCompatibility": { + "outsiderProductPlusOne": 1040177762, + "squareWitnesses": [ + { + "prime": 13, + "square": 169 + } + ] + }, + "activeSide18Count": 2420, + "missingCrossEdgeCount": 196, + "menuDeltaCount": 26, + "menuCandidateStats": [ + { + "delta": -1089, + "right": 163418, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -864, + "right": 163643, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -789, + "right": 163718, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -764, + "right": 163743, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -739, + "right": 163768, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -689, + "right": 163818, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -664, + "right": 163843, + "active": true, + "outsiderCompatible": true, + "crossSquarefree": false + }, + { + "delta": -639, + "right": 163868, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -589, + "right": 163918, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -564, + "right": 163943, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -539, + "right": 163968, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -489, + "right": 164018, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -464, + "right": 164043, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -439, + "right": 164068, + "active": true, + "outsiderCompatible": true, + "crossSquarefree": false + }, + { + "delta": -414, + "right": 164093, + "active": true, + "outsiderCompatible": true, + "crossSquarefree": false + }, + { + "delta": -389, + "right": 164118, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -364, + "right": 164143, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -339, + "right": 164168, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -289, + "right": 164218, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -264, + "right": 164243, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -239, + "right": 164268, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -189, + "right": 164318, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -164, + "right": 164343, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -139, + "right": 164368, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -89, + "right": 164418, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + }, + { + "delta": -64, + "right": 164443, + "active": true, + "outsiderCompatible": false, + "crossSquarefree": true + } + ], + "interpretation": "The enlarged menu reaches a row where the only menu candidates that are outsider-compatible are blocked by cross square divisors, while the squarefree menu candidates are not active side18-compatible vertices." + }, + "statement": "Prove the new direct-delta -39 branch exposed at side7 vertex 164507, integrate it with the enlarged augmenting menu, or emit the first future row where this menu fails.", + "completionRule": "The delta -39 branch is proved symbolically and merged into the matching-injection menu, or the first future row requiring a different direct delta or longer augmenting path becomes the next deterministic atom.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs.json", + "status": "bounded_direct_delta_minus39_branch_falsified_residue_parametric_delta_selection_lift_needed", + "proofKind": "bounded_delta_staircase_generalization_trigger", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet falsifies the enlarged direct-delta -39 menu by an exact bounded future event row and intentionally stops the singleton-delta staircase. It does not falsify side7 saturation or prove any all-N matching injection." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "residue_parametric_delta_selection_reduced_to_direct_selector_and_collision_sublemmas", + "term": "outsider-6323 residue-parametric delta-selection lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs.json", + "seedFailures": [ + 73607, + 164507, + 468707 + ], + "seedDeltas": [ + -1089, + -39, + -1664 + ], + "statement": "Replace the direct-delta staircase with a residue-parametric rule that selects a valid direct missing-cross edge or bounded augmenting path for every future side7-compatible event row in the outsider-6323 family.", + "completionRule": "A residue/block delta-selection theorem proves saturation without adding one-off direct-delta siblings, or the first event row not covered by any finite residue-parametric rule becomes the next obstruction packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s.json", + "status": "residue_parametric_delta_selection_reduced_to_direct_selector_and_collision_sublemmas", + "proofKind": "theorem_reduction_to_residue_direct_selector", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet decomposes the residue-parametric delta-selection target into theorem sublemmas. It does not prove the all-N matching injection and does not promote bounded seed repairs as a proof." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "symbolic_residue_direct_selector_lift_proved_selected_cross_squarefree_needed", + "term": "outsider-6323 residue direct-selector lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s.json", + "seedFailures": [ + 73607, + 164507, + 468707 + ], + "seedDeltas": [ + -1089, + -39, + -1664 + ], + "downstreamSublemmas": [ + "residue_direct_selector_lift", + "selected_cross_squarefree_lift", + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove the residue-parametric direct-selector sublemma: every future side7-compatible event row has a residue-selected side18-compatible direct endpoint, or emit the first event row with no selected direct endpoint.", + "completionRule": "A residue/mod-square selector produces a side18-compatible direct endpoint for every future side7 event row, or the first uncovered event row becomes the next obstruction packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid.json", + "status": "symbolic_residue_direct_selector_lift_proved_selected_cross_squarefree_needed", + "proofKind": "symbolic_mod4_four_slot_direct_selector", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet proves only that every future side7-compatible event row has an active side18-compatible endpoint selected by the four-slot mod-4 rule. It does not prove that left * right + 1 is squarefree, and it does not prove that selected endpoints are collision-free for the online matching." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_selected_cross_squarefree_falsified_exception_menu_needed", + "term": "outsider-6323 selected cross-squarefree lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid.json", + "selectorRule": "previous_93_mod100_side18_slot", + "selectedDeltas": [ + -14, + -39, + -64, + -89 + ], + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove that the four-slot selected endpoint gives a squarefree cross product left * right + 1 for every future side7-compatible event row, or route the first residue class/future row where the selected cross product is non-squarefree into a bounded replacement-path exception menu.", + "completionRule": "The selected endpoint is a missing-cross edge for every future side7-compatible row, or the first square-divisor obstruction becomes the next deterministic exception packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs.json", + "status": "bounded_selected_cross_squarefree_falsified_exception_menu_needed", + "proofKind": "bounded_first_square_divisor_exception", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107" + }, + "proofBoundary": "This is a bounded falsifier packet, not an all-N proof of the replacement rule. It records the first selected endpoint whose cross product is non-squarefree and seeds a replacement-menu theorem target." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107", + "status": "bounded_exception_menu_reduced_to_finite_window_lift", + "term": "outsider-6323 selected cross-squarefree exception menu", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs.json", + "seedException": { + "left": 8107, + "failingRight": 8093, + "repairRight": 7918, + "repairDelta": -189 + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Build a replacement menu for the selected cross-squarefree obstruction class starting at left=8107: replace the failing previous-93 endpoint by a side18-compatible squarefree-cross endpoint such as the observed delta -189 repair, or emit the first side7-compatible row with no bounded replacement.", + "completionRule": "A symbolic replacement menu handles the selected endpoint square-divisor exceptions without adding singleton deltas, or the first uncovered replacement row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_.json", + "status": "bounded_exception_menu_reduced_to_finite_window_lift", + "proofKind": "bounded_selected_cross_exception_window_profile", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet replaces the left=8107 local repair by a finite-window theorem target. It is bounded evidence and a handoff, not an all-N proof of the exception menu or the full matching injection." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_exception_window_lift_falsified_right_compatibility_escape_needed", + "term": "outsider-6323 selected cross-squarefree exception finite-window lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_.json", + "finiteWindowMenuDeltas": [ + -64, + -39, + -89, + -189, + -164, + -14, + -139, + -264, + -239, + -339, + -539, + -289, + -639, + -114, + -464, + -364, + -489, + -1089, + -389, + -1039, + -1064, + -1239, + -1664, + -2164, + -564, + -764, + -864 + ], + "boundedExceptionProfile": { + "maxN": 1000000, + "selectedCrossExceptions": 2241, + "coveredByFiniteWindowMenu": 2241, + "firstUncoveredReplacementRow": null + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove the finite 27-delta exception-window selector: every future selected-cross square-divisor exception row has a replacement right = left + delta from the menu with right side18-compatible, 6323 * right + 1 non-squarefree, and left * right + 1 squarefree, or emit the first uncovered row.", + "completionRule": "A symbolic finite-window lift covers all selected-cross exceptions without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s.json", + "status": "bounded_exception_window_lift_falsified_right_compatibility_escape_needed", + "proofKind": "bounded_first_uncovered_exception_window_row", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307" + }, + "proofBoundary": "This packet falsifies the 27-delta finite-window lift at bounded scope and emits the first uncovered row. It does not prove that the escape deltas work for all future rows and does not prove the full matching injection." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307", + "status": "bounded_right_compatibility_escape_profile_small_prime_crt_selector_needed", + "term": "outsider-6323 selected cross-squarefree exception right-compatibility escape lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s.json", + "seedUncoveredRow": 1138307, + "seedEscapeDeltas": [ + -989, + -1189 + ], + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Replace the failed 27-delta exception window with a right-compatibility escape selector seeded by the first uncovered row left=1138307: prove that every future finite-window miss has a side18 replacement such as the observed deltas -989 or -1189 with outsider compatibility and squarefree cross product, or emit the first row with no bounded escape repair.", + "completionRule": "A symbolic right-compatibility escape selector replaces the finite-window miss family without adding singleton delta siblings, or the first row with no bounded side18 squarefree repair becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift.json", + "status": "bounded_right_compatibility_escape_profile_small_prime_crt_selector_needed", + "proofKind": "bounded_right_compatibility_escape_profile", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet only records bounded evidence through N=10000000. It proves neither an all-N escape selector nor collision-free matching; it narrows the next theorem move to a small-prime CRT selector instead of a singleton delta branch." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "symbolic_p7_endpoint_reduction_ready_cross_squarefree_fallback_needed", + "term": "outsider-6323 selected cross-squarefree exception small-prime CRT escape selector lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift.json", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Derive a symbolic small-prime CRT selector for finite-window misses: for each selected-cross exception row missed by the 27-delta menu, choose a nearby side18 endpoint inside the 10000 local window whose right-side outsider compatibility is witnessed by one of {7,11,13,17,19,23,31,37,41} and whose cross product is squarefree, or emit the first row outside that rule.", + "completionRule": "A symbolic small-prime CRT selector handles the right-compatibility escape rows, or the first finite-window miss outside that selector becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift.json", + "status": "symbolic_p7_endpoint_reduction_ready_cross_squarefree_fallback_needed", + "proofKind": "symbolic_p7_crt_endpoint_reduction_plus_bounded_fallback_profile", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet proves only the p=7 endpoint-existence component symbolically. The cross-squarefree fallback remains open and bounded evidence must not be promoted to an all-N claim." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_period_shifted_endpoint_menu_profile_ready_symbolic_menu_lift_needed", + "term": "outsider-6323 p=7 endpoint cross-squarefree fallback lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift.json", + "seedEndpointPrime": null, + "seedDeltaFormula": "d_7(left) = -14 - 25 * ((2*left - 27) mod 49)", + "seedCrossBadCount": 31, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Starting from the symbolic p=7 local side18 endpoint, prove that rows whose p=7 endpoint has a non-squarefree cross edge admit a nearby fallback endpoint from the small-prime set {7,11,13,17,19,23,31,37,41} with squarefree cross product, or emit the first fallback miss.", + "completionRule": "A symbolic cross-squarefree fallback selector handles the p=7 endpoint cross-bad rows, or the first finite-window miss outside the fallback rule becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift.json", + "status": "bounded_period_shifted_endpoint_menu_profile_ready_symbolic_menu_lift_needed", + "proofKind": "bounded_p7_cross_bad_period_shifted_endpoint_menu_profile", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet records a bounded period-shifted endpoint-menu profile and a symbolic right-compatibility skeleton. It does not prove all-N cross-squarefreeness or collision-free matching." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_prime_set_exact_replay_ready_squarefree_sieve_lift_needed", + "term": "outsider-6323 period-shifted endpoint menu lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift.json", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove that every p=7 endpoint cross-bad row in this split family has a squarefree cross product inside the small-prime period-shifted endpoint menu, or emit the first future row outside the menu.", + "completionRule": "A symbolic finite endpoint-menu lift covers all p=7 endpoint cross-bad rows without singleton delta siblings, or the first row outside the menu becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json", + "status": "bounded_prime_set_exact_replay_ready_squarefree_sieve_lift_needed", + "proofKind": "bounded_period_shifted_endpoint_menu_replay_plus_squarefree_sieve_reduction", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet extends the exact named period-shifted endpoint-menu replay and reduces the all-N work to a squarefree sieve/hitting lemma. It does not prove all-N menu coverage or matching collision-freedom." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_p7_period_shift_profile_ready_q17_residual_lift_needed", + "term": "outsider-6323 period-shifted endpoint-menu squarefree sieve lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_proof_D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json", + "seedPrimeSet": [ + 7, + 11, + 13, + 17, + 19, + 23, + 31, + 37, + 41 + ], + "seedEscapeWindow": 10000, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove the squarefree hitting lemma for the period-shifted endpoint menu: every p=7 endpoint cross-bad row has at least one menu endpoint with squarefree cross product, or emit the first row where every menu endpoint is cross-blocked.", + "completionRule": "A symbolic sieve/hitting lemma proves cross-squarefree endpoint existence for the menu, or the first fully cross-blocked row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift.json", + "status": "bounded_p7_period_shift_profile_ready_q17_residual_lift_needed", + "proofKind": "bounded_squarefree_sieve_partition_profile", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet decomposes the squarefree sieve target using bounded evidence through N=20000000. It proves neither the p7 period-shift selector nor the q17 residual fallback for all N, and it does not claim collision-free matching." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_q17_residual_falsified_cross_bad_fallback_needed", + "term": "outsider-6323 p7 period-shift plus q17 residual squarefree selector lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift.json", + "seedPrimeSet": [ + 7, + 17 + ], + "seedEscapeWindow": 10000, + "residualClass": "left == 5882 mod 11025", + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove the p=7 period-shift squarefree selector and the q=17 residual-class fallback for the period-shifted endpoint menu, or emit the first residual row where the q=17 endpoint is cross-blocked.", + "completionRule": "A symbolic p7-shift plus q17 residual lemma proves cross-squarefree endpoint existence for the menu, or the first q17 residual cross-bad row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift.json", + "status": "bounded_q17_residual_falsified_cross_bad_fallback_needed", + "proofKind": "bounded_p7_shift_q17_residual_cross_bad_obstruction", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet only falsifies the standalone q17 residual fallback at the first certified residual-class row after the 20M bounded handoff. The local fallback seed is not an all-N proof and does not claim collision-free online matching." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_seed_fallback_menu_falsified_p13_expanded_menu_needed", + "term": "outsider-6323 q17 residual cross-bad fallback selector lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift.json", + "seedPrimeSet": [ + 11, + 19, + 23, + 31 + ], + "seedEscapeWindow": 10000, + "firstCrossBadSeed": { + "left": 20016257, + "q17Right": 20015818, + "q17Delta": -439, + "q17SquareDivisorPrime": 3 + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove that every q17 residual cross-bad row has a squarefree side18-compatible fallback endpoint in the small-prime local menu, or emit the first row with no bounded fallback endpoint.", + "completionRule": "A symbolic fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully fallback-blocked row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift.json", + "status": "bounded_seed_fallback_menu_falsified_p13_expanded_menu_needed", + "proofKind": "bounded_q17_residual_cross_bad_seed_menu_obstruction", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet exactly falsifies only the {11,19,23,31} seed fallback menu through the first fully fallback-blocked q17 residual row under the 10000 window. The p=13 repair seed is a next theorem target, not an all-N proof or collision-free matching claim." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed", + "term": "outsider-6323 q17 residual p13-expanded fallback menu lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift.json", + "seedPrimeSet": [ + 11, + 13, + 19, + 23, + 31 + ], + "seedEscapeWindow": 10000, + "firstRepairSeed": { + "left": 25153907, + "prime": 13, + "right": 25150143, + "delta": -3764 + }, + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove that every q17 residual cross-bad row has a squarefree side18-compatible endpoint in the expanded local menu {11,13,19,23,31}, or emit the first row outside that expanded menu.", + "completionRule": "A symbolic expanded fallback selector covers q17 residual cross-bad rows without singleton repairs, or the first fully expanded-menu-blocked row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "status": "bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed", + "proofKind": "bounded_q17_residual_p13_expanded_menu_obstruction", + "nextSubatomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + }, + "proofBoundary": "This packet exactly falsifies only the {11,13,19,23,31} p13-expanded fallback menu through the first fully expanded-menu-blocked q17 residual row under the 10000 window. The window-relaxed repair seeds are next theorem targets, not all-N coverage or collision-free matching claims." + }, + { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 q17 residual window-relaxed fallback menu lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "seedPrimeSet": [ + 23, + 31, + 37, + 41, + 61 + ], + "seedEscapeWindow": 25000, + "firstRepairSeeds": [ + { + "left": 27932207, + "prime": 23, + "right": 27920218, + "delta": -11989 + }, + { + "left": 27932207, + "prime": 31, + "right": 27911843, + "delta": -20364 + } + ], + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove that every q17 residual cross-bad row blocked by the 10000-window expanded menu has a squarefree side18-compatible endpoint in a controlled 25000-window menu, or emit the first fully window-relaxed blocked row.", + "completionRule": "A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton prime repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "status": "bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed", + "proofKind": "bounded_q17_residual_p13_expanded_menu_obstruction", + "firstFullyExpandedMenuBlockedRow": { + "left": 27932207, + "leftMod11025": 5882, + "q17K": 200, + "q17Delta": -5014, + "q17Right": 27927193, + "q17RightMod25": 18, + "q17CompatibilityMod289": 0, + "q17CrossProductPlusOne": "780068135804952", + "q17SquareDivisorPrime": 2, + "q17SquareDivisor": 4, + "expandedFallbackResults": [ + { + "prime": 11, + "k": 98, + "delta": -2464, + "right": 27929743, + "availableWithinWindow": true, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false + }, + { + "prime": 13, + "k": 80, + "delta": -2014, + "right": 27930193, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 19, + "k": 124, + "delta": -3114, + "right": 27929093, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 23, + "k": 479, + "delta": -11989, + "right": 27920218, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + }, + { + "prime": 31, + "k": 814, + "delta": -20364, + "right": 27911843, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + } + ] + }, + "windowRelaxedRepairSeedCount": 5 + }, + "proofBoundary": "This window-relaxed fallback subatom is still cross-squarefree endpoint selection only. It must not claim all-N coverage from the seed or collision-free matching." + } + ], + "firstOpenMovingTermSubatom": { + "atomId": "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323", + "status": "needed", + "term": "outsider-6323 q17 residual window-relaxed fallback menu lift", + "dependsOn": [ + "D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323" + ], + "predecessorProofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "predecessorProofJsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "seedPrimeSet": [ + 23, + 31, + 37, + 41, + 61 + ], + "seedEscapeWindow": 25000, + "firstRepairSeeds": [ + { + "left": 27932207, + "prime": 23, + "right": 27920218, + "delta": -11989 + }, + { + "left": 27932207, + "prime": 31, + "right": 27911843, + "delta": -20364 + } + ], + "remainingAfterDischarge": [ + "selector_collision_or_augmentation_lift" + ], + "statement": "Prove that every q17 residual cross-bad row blocked by the 10000-window expanded menu has a squarefree side18-compatible endpoint in a controlled 25000-window menu, or emit the first fully window-relaxed blocked row.", + "completionRule": "A symbolic window-relaxed fallback selector covers q17 residual cross-bad rows without singleton prime repairs, or the first fully window-relaxed blocked row becomes the next deterministic packet.", + "proofArtifact": { + "proofId": "p848_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift", + "jsonPath": "/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json", + "status": "bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed", + "proofKind": "bounded_q17_residual_p13_expanded_menu_obstruction", + "firstFullyExpandedMenuBlockedRow": { + "left": 27932207, + "leftMod11025": 5882, + "q17K": 200, + "q17Delta": -5014, + "q17Right": 27927193, + "q17RightMod25": 18, + "q17CompatibilityMod289": 0, + "q17CrossProductPlusOne": "780068135804952", + "q17SquareDivisorPrime": 2, + "q17SquareDivisor": 4, + "expandedFallbackResults": [ + { + "prime": 11, + "k": 98, + "delta": -2464, + "right": 27929743, + "availableWithinWindow": true, + "squareDivisorPrime": 3, + "squareDivisor": 9, + "squarefree": false + }, + { + "prime": 13, + "k": 80, + "delta": -2014, + "right": 27930193, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 19, + "k": 124, + "delta": -3114, + "right": 27929093, + "availableWithinWindow": true, + "squareDivisorPrime": 2, + "squareDivisor": 4, + "squarefree": false + }, + { + "prime": 23, + "k": 479, + "delta": -11989, + "right": 27920218, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + }, + { + "prime": 31, + "k": 814, + "delta": -20364, + "right": 27911843, + "availableWithinWindow": false, + "squareDivisorPrime": null, + "squarefree": false + } + ] + }, + "windowRelaxedRepairSeedCount": 5 + }, + "proofBoundary": "This window-relaxed fallback subatom is still cross-squarefree endpoint selection only. It must not claim all-N coverage from the seed or collision-free matching." + }, + "proofBoundary": "This replays the bounded side-count floor as a structural margin inequality. It is not an all-N proof of the moving compatibility counts, dMax, rGreater, or candidateSize terms." + }, + "theoremObligation": { + "kind": "non_tight_p13_side_count_floor_subobligation", + "statement": "For every future p=13 threat row with outP2=70|out25=23|smaller=side7, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) >= 20.", + "equivalentInequality": "max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 21", + "proofBoundary": "This packet isolates one weakest non-tight side-count stratum. Its bounded witness is not an all-N proof; the symbolic side-count inequality still has to be proved or refined." + }, + "proofReduction": { + "statement": "For non-tight p13 rows, reduce slack dominance to a side-count inequality after matching saturation.", + "matchingSaturationHypothesis": "matchingSizeInMissingCrossGraph = min(compatibleSide7Count, compatibleSide18Count)", + "requiredMatchingFormula": "K = compatibleSide7Count + compatibleSide18Count - strictBaseThreshold + 1", + "derivedSlackFormula": "matchingSlack = strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count)", + "sufficientSideCountInequality": "max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 1 - 20" + }, + "nextTheoremActions": [ + "Treat D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7 as falsified by the extended bounded probe; do not promote dMax <= 18 as an all-N lemma.", + "Attack the successor D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7: replace the false constant dMax bound before re-deriving the residual dynamic margin.", + "If the symbolic side-count inequality fails, emit a sharper split atom keyed by the first failing side-count term.", + "After all co-weakest side-count floor atoms are handled, lift the remaining larger-margin strata by the same inequality template." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md new file mode 100644 index 0000000..e376e98 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7.md @@ -0,0 +1,613 @@ +# D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7 + +This is a focused side-count floor atom for the Problem 848 p13 non-tight slack-dominance lift. + +## Summary + +- Packet id: `p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_23_smaller_side7` +- Parent lemma: `D2_p13_non_tight_side_count_slack_floor_lift` +- Split key: `outP2=70|out25=23|smaller=side7` +- Priority: `highest_side_count_floor_atom` +- Status: `symbolic_side_count_floor_atom_needed` +- Target slack floor: `20` +- Observed bounded slack-formula floor: `21` +- Observed margin above target: `1` +- Bounded witness rows: `32` over `7307..7600` + +## Theorem Obligation + +For every future p=13 threat row with outP2=70|out25=23|smaller=side7, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) >= 20. + +Equivalent inequality: `max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 21` + +Boundary: This packet isolates one weakest non-tight side-count stratum. Its bounded witness is not an all-N proof; the symbolic side-count inequality still has to be proved or refined. + +## Structural Margin Decomposition + +- Status: `bounded_structural_margin_replay_verified_symbolic_margin_lift_needed` +- Inequality: `side18Count + vMax + dMax + rGreater + 21 <= candidateSize` +- Bounded margin range: `1..5` +- First open sublemma: `D2_p13_structural_margin_outP2_70_out25_23_smaller_side7_side18` +- First moving-term subatom: `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Boundary: This replays the bounded side-count floor as a structural margin inequality. It is not an all-N proof of the moving compatibility counts, dMax, rGreater, or candidateSize terms. + +## Moving-Term Subatoms + +- `D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7` [bounded_constant_bound_falsified_successor_atom_needed]: For every future p=13 threat row with outP2=70|out25=23|smaller=side7, prove dMax <= 18. +- Probe: `bounded_counterexample_to_constant_dmax_bound`, range `7307..12000`, max observed dMax `29` +- Boundary: This bounded probe falsifies the constant dMax <= 18 outside the original 7307..7600 witness packet. It does not prove an all-N growth envelope; the successor atom must bound the same-prime degree term symbolically. +- `D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7` [bounded_growth_profile_emitted_subatom_needed]: Replace the false constant dMax <= 18 with a symbolic same-prime degree-growth envelope for outP2=70|out25=23|smaller=side7. +- Growth profile: `bounded_degree_growth_profile_emitted`, first subatom `D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7` +- First counterexample: `N=7873, dMax=19, witness=plus:1591` +- Boundary: This successor atom is required because the extended local probe found the same split with dMax above the original bounded constant. +- `D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove a symbolic floor-function upper bound for the q=2 same-prime degree progression m = 437 + 676*t, including base-residue and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`2`, next=`D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q2_progression_outP2_70_out25_23_smaller_side7.json` +- Profile JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_GROWTH_PROFILES/D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the first floor-function subatom emitted from the bounded dMax growth profile. +- `D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=3 same-prime degree progression upper bound for the same split, including overlap/base-residue/lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`3`, next=`D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q3_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=2 CRT upper-bound component. +- `D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=5 same-prime degree progression upper bound for the same split, including q=2/q=3 overlap and base-residue/lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`5`, next=`D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q5_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=3 CRT upper-bound component. +- `D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=7 same-prime degree progression upper bound for the same split, including prior-q overlap and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`7`, next=`D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q7_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=5 CRT upper-bound component. +- `D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=11 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`11`, next=`D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q11_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=7 CRT upper-bound component. +- `D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=19 same-prime degree singleton progression upper bound for the minus witness, including prior-q overlap and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`19`, next=`D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q19_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=11 CRT upper-bound component. +- `D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=23 same-prime degree singleton progression upper bound for the minus witness, including prior-q overlap and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`23`, next=`D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q23_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=19 CRT upper-bound component. +- `D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=31 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`31`, next=`D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q31_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=23 CRT upper-bound component. +- `D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=251 same-prime degree singleton progression upper bound for the plus witness, including prior-q overlap and lower-witness exclusions. +- Proof artifact: `symbolic_upper_bound_verified`, q=`251`, next=`D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_Q_PROGRESSION_PROOFS/D2_p13_dmax_q251_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next square-divisor floor-function subatom after the verified q=31 CRT upper-bound component. +- `D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7` [tail_scaffold_q13_residue_exclusion_verified_q17_needed]: Recombine the verified observed q-progression components with a symbolic tail bound for all remaining same-prime square-divisor events in the dMax growth envelope. +- Proof artifact: `tail_scaffold_q13_residue_exclusion_verified_q17_needed`, q=`(unknown)`, next=`D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_recombination_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the first non-singleton dMax growth atom after all observed q-progression components in the bounded profile have proof artifacts. +- `D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=17 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 47588 mod 48841 and m = 12238 mod 48841. +- Proof artifact: `symbolic_upper_bound_verified`, q=`17`, next=`D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q17_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the first unresolved tail-prime subatom after the target-prime q=13 square divisor is excluded by the split residue. +- `D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the plus-side q=19 tail complement left open by the observed minus-side q=19 component, starting from m = 22576 mod 61009. +- Proof artifact: `symbolic_upper_bound_verified`, q=`19`, next=`D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q19_plus_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This side-specific tail atom is required because the observed q=19 component proof covered only the minus witness. +- `D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Backfill the minus-side q=11 tail complement left open by the observed plus-side q=11 component, starting from m = 16970 mod 20449. +- Proof artifact: `symbolic_upper_bound_verified`, q=`11`, next=`D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q11_minus_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This backfill atom is required because the observed q=11 component proof covered only the plus witness. +- `D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the plus-side q=23 tail complement left open by the observed minus-side q=23 component, starting from m = 44039 mod 89401. +- Proof artifact: `symbolic_upper_bound_verified`, q=`23`, next=`D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q23_plus_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This side-specific tail atom is required because the observed q=23 component proof covered only the minus witness. +- `D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the minus-side q=31 tail complement left open by the observed plus-side q=31 component, starting from m = 105526 mod 162409. +- Proof artifact: `symbolic_upper_bound_verified`, q=`31`, next=`D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q31_minus_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This side-specific tail atom is required because the observed q=31 component proof covered only the plus witness. +- `D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the minus-side q=251 tail complement left open by the observed plus-side q=251 component, starting from m = 8138434 mod 10647169. +- Proof artifact: `symbolic_upper_bound_verified`, q=`251`, next=`D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q251_minus_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This side-specific tail atom is required because the observed q=251 component proof covered only the plus witness. +- `D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=29 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 29167 mod 142129 and m = 114314 mod 142129. +- Proof artifact: `symbolic_upper_bound_verified`, q=`29`, next=`D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q29_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the first remaining non-observed tail-prime subatom after observed q-components and their side complements are certified. +- `D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=37 tail-prime same-prime degree atom: exclude the plus side because 37 divides 1591, and certify the minus-side CRT floor bound starting from m = 136284 mod 231361. +- Proof artifact: `symbolic_upper_bound_verified`, q=`37`, next=`D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q37_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This residual tail-prime atom is special because q=37 divides the plus witness 1591, excluding that side before the minus-side CRT floor bound. +- `D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=41 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 251571 mod 284089 and m = 26941 mod 284089. +- Proof artifact: `symbolic_upper_bound_verified`, q=`41`, next=`D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q41_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=37 witness-divisibility exclusion plus minus-side floor bound. +- `D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=43 tail-prime same-prime degree atom: plus side is excluded because 43 divides 1591, and minus side starts at m = 216897 mod 312481. +- Proof artifact: `symbolic_upper_bound_verified`, q=`43`, next=`D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q43_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This residual tail-prime atom is special because q=43 divides the plus witness 1591, excluding that side before the minus-side CRT floor bound. +- `D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=47 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 267457 mod 373321 and m = 278413 mod 373321. +- Proof artifact: `symbolic_upper_bound_verified`, q=`47`, next=`D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q47_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=43 witness-divisibility exclusion plus minus-side floor bound. +- `D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=53 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 52151 mod 474721 and m = 213348 mod 474721. +- Proof artifact: `symbolic_upper_bound_verified`, q=`53`, next=`D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q53_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=47 two-sided floor-bound component. +- `D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=59 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 182281 mod 588289 and m = 492874 mod 588289. +- Proof artifact: `symbolic_upper_bound_verified`, q=`59`, next=`D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q59_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=53 two-sided floor-bound component. +- `D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=61 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 396573 mod 628849 and m = 477495 mod 628849. +- Proof artifact: `symbolic_upper_bound_verified`, q=`61`, next=`D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q61_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=59 two-sided floor-bound component. +- `D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=67 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 344183 mod 758641 and m = 736572 mod 758641. +- Proof artifact: `symbolic_upper_bound_verified`, q=`67`, next=`D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q67_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=61 two-sided floor-bound component. +- `D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=71 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 69389 mod 851929 and m = 783385 mod 851929. +- Proof artifact: `symbolic_upper_bound_verified`, q=`71`, next=`D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q71_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=67 two-sided floor-bound component. +- `D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=73 tail-prime same-prime degree contribution: the plus witness has m = 229770 mod 900601, while the minus side is excluded because 73 divides 9563. +- Proof artifact: `symbolic_upper_bound_verified`, q=`73`, next=`D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q73_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This residual tail-prime atom is special because q=73 divides the minus witness 9563, excluding that side before the plus-side CRT floor bound. +- `D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=79 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 901038 mod 1054729 and m = 280272 mod 1054729. +- Proof artifact: `symbolic_upper_bound_verified`, q=`79`, next=`D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q79_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=73 plus-side floor-bound and minus-side exclusion component. +- `D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=83 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 443048 mod 1164241 and m = 16125 mod 1164241. +- Proof artifact: `symbolic_upper_bound_verified`, q=`83`, next=`D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q83_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=79 two-sided floor-bound component. +- `D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=89 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 30519 mod 1338649 and m = 791497 mod 1338649. +- Proof artifact: `symbolic_upper_bound_verified`, q=`89`, next=`D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q89_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=83 two-sided floor-bound component. +- `D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=97 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 783076 mod 1590121 and m = 279765 mod 1590121. +- Proof artifact: `symbolic_upper_bound_verified`, q=`97`, next=`D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q97_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=89 two-sided floor-bound component. +- `D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=101 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1382181 mod 1723969 and m = 253570 mod 1723969. +- Proof artifact: `symbolic_upper_bound_verified`, q=`101`, next=`D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q101_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=97 two-sided floor-bound component. +- `D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=103 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 586529 mod 1792921 and m = 1732827 mod 1792921. +- Proof artifact: `symbolic_upper_bound_verified`, q=`103`, next=`D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q103_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=101 two-sided floor-bound component. +- `D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=107 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 967624 mod 1934881 and m = 1699703 mod 1934881. +- Proof artifact: `symbolic_upper_bound_verified`, q=`107`, next=`D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q107_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=103 two-sided floor-bound component. +- `D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=109 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 963399 mod 2007889 and m = 725925 mod 2007889. +- Proof artifact: `symbolic_upper_bound_verified`, q=`109`, next=`D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q109_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=107 two-sided floor-bound component. +- `D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=113 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 407051 mod 2157961 and m = 2150764 mod 2157961. +- Proof artifact: `symbolic_upper_bound_verified`, q=`113`, next=`D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q113_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=109 two-sided floor-bound component. +- `D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=127 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1191042 mod 2725801 and m = 2198253 mod 2725801. +- Proof artifact: `symbolic_upper_bound_verified`, q=`127`, next=`D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q127_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=113 two-sided floor-bound component. +- `D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=131 tail-prime same-prime degree progression upper bound: plus-side CRT floor bound from m = 1345170 mod 2900209, and minus-side exclusion because 131 divides 9563. +- Proof artifact: `symbolic_upper_bound_verified`, q=`131`, next=`D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q131_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=127 two-sided floor-bound component. +- `D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=137 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2767643 mod 3171961 and m = 1021675 mod 3171961. +- Proof artifact: `symbolic_upper_bound_verified`, q=`137`, next=`D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q137_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=131 CRT/exclusion component. +- `D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=139 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3089757 mod 3265249 and m = 1765444 mod 3265249. +- Proof artifact: `symbolic_upper_bound_verified`, q=`139`, next=`D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q139_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=137 two-sided floor-bound component. +- `D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=149 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 276752 mod 3751969 and m = 1423557 mod 3751969. +- Proof artifact: `symbolic_upper_bound_verified`, q=`149`, next=`D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q149_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=139 two-sided floor-bound component. +- `D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=151 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2446543 mod 3853369 and m = 1157720 mod 3853369. +- Proof artifact: `symbolic_upper_bound_verified`, q=`151`, next=`D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q151_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=149 two-sided floor-bound component. +- `D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=157 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1762938 mod 4165681 and m = 2160735 mod 4165681. +- Proof artifact: `symbolic_upper_bound_verified`, q=`157`, next=`D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q157_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=151 two-sided floor-bound component. +- `D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=163 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2941544 mod 4490161 and m = 856562 mod 4490161. +- Proof artifact: `symbolic_upper_bound_verified`, q=`163`, next=`D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q163_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=157 two-sided floor-bound component. +- `D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=167 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4640670 mod 4713241 and m = 3647428 mod 4713241. +- Proof artifact: `symbolic_upper_bound_verified`, q=`167`, next=`D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q167_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=163 two-sided floor-bound component. +- `D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=173 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 978778 mod 5058001 and m = 1961146 mod 5058001. +- Proof artifact: `symbolic_upper_bound_verified`, q=`173`, next=`D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q173_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=167 two-sided floor-bound component. +- `D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=179 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2724210 mod 5414929 and m = 4437841 mod 5414929. +- Proof artifact: `symbolic_upper_bound_verified`, q=`179`, next=`D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q179_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=173 two-sided floor-bound component. +- `D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=181 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1789809 mod 5536609 and m = 4242815 mod 5536609. +- Proof artifact: `symbolic_upper_bound_verified`, q=`181`, next=`D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q181_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=179 two-sided floor-bound component. +- `D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=191 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1508424 mod 6165289 and m = 1951682 mod 6165289. +- Proof artifact: `symbolic_upper_bound_verified`, q=`191`, next=`D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q191_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=181 two-sided floor-bound component. +- `D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=193 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 69558 mod 6295081 and m = 1273485 mod 6295081. +- Proof artifact: `symbolic_upper_bound_verified`, q=`193`, next=`D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q193_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=191 two-sided floor-bound component. +- `D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=197 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3802599 mod 6558721 and m = 4141415 mod 6558721. +- Proof artifact: `symbolic_upper_bound_verified`, q=`197`, next=`D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q197_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=193 two-sided floor-bound component. +- `D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=199 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 872815 mod 6692569 and m = 1078797 mod 6692569. +- Proof artifact: `symbolic_upper_bound_verified`, q=`199`, next=`D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q199_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=197 two-sided floor-bound component. +- `D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=211 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 199519 mod 7524049 and m = 3288134 mod 7524049. +- Proof artifact: `symbolic_upper_bound_verified`, q=`211`, next=`D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q211_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=199 two-sided floor-bound component. +- `D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=223 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1169241 mod 8404201 and m = 3594700 mod 8404201. +- Proof artifact: `symbolic_upper_bound_verified`, q=`223`, next=`D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q223_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=211 two-sided floor-bound component. +- `D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=227 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1095388 mod 8708401 and m = 7005627 mod 8708401. +- Proof artifact: `symbolic_upper_bound_verified`, q=`227`, next=`D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q227_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=223 two-sided floor-bound component. +- `D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=229 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 102344 mod 8862529 and m = 8756298 mod 8862529. +- Proof artifact: `symbolic_upper_bound_verified`, q=`229`, next=`D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q229_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=227 two-sided floor-bound component. +- `D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=233 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1640920 mod 9174841 and m = 5761787 mod 9174841. +- Proof artifact: `symbolic_upper_bound_verified`, q=`233`, next=`D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q233_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=229 two-sided floor-bound component. +- `D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=239 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2615036 mod 9653449 and m = 883264 mod 9653449. +- Proof artifact: `symbolic_upper_bound_verified`, q=`239`, next=`D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q239_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=233 two-sided floor-bound component. +- `D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=241 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8794690 mod 9815689 and m = 6246310 mod 9815689. +- Proof artifact: `symbolic_upper_bound_verified`, q=`241`, next=`D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q241_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=239 two-sided floor-bound component. +- `D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=257 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4730578 mod 11162281 and m = 10654844 mod 11162281. +- Proof artifact: `symbolic_upper_bound_verified`, q=`257`, next=`D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q257_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=241 two-sided floor-bound component; q=251 was already covered by the observed q251 packet and its minus-side complement. +- `D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=263 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5804066 mod 11689561 and m = 3539944 mod 11689561. +- Proof artifact: `symbolic_upper_bound_verified`, q=`263`, next=`D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q263_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=257 two-sided floor-bound component. +- `D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=269 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10056951 mod 12229009 and m = 11133621 mod 12229009. +- Proof artifact: `symbolic_upper_bound_verified`, q=`269`, next=`D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q269_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=263 two-sided floor-bound component. +- `D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=271 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4686976 mod 12411529 and m = 749923 mod 12411529. +- Proof artifact: `symbolic_upper_bound_verified`, q=`271`, next=`D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q271_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=269 two-sided floor-bound component. +- `D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=277 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6946844 mod 12967201 and m = 10587920 mod 12967201. +- Proof artifact: `symbolic_upper_bound_verified`, q=`277`, next=`D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q277_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=271 two-sided floor-bound component. +- `D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=281 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4072323 mod 13344409 and m = 9581694 mod 13344409. +- Proof artifact: `symbolic_upper_bound_verified`, q=`281`, next=`D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q281_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=277 two-sided floor-bound component. +- `D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=283 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7094043 mod 13535041 and m = 4146823 mod 13535041. +- Proof artifact: `symbolic_upper_bound_verified`, q=`283`, next=`D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q283_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=281 two-sided floor-bound component. +- `D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=293 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7410749 mod 14508481 and m = 12282314 mod 14508481. +- Proof artifact: `symbolic_upper_bound_verified`, q=`293`, next=`D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q293_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=283 two-sided floor-bound component. +- `D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=307 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 14963021 mod 15928081 and m = 15889112 mod 15928081. +- Proof artifact: `symbolic_upper_bound_verified`, q=`307`, next=`D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q307_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=293 two-sided floor-bound component. +- `D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=311 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 12908150 mod 16345849 and m = 5085787 mod 16345849. +- Proof artifact: `symbolic_upper_bound_verified`, q=`311`, next=`D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q311_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=307 two-sided floor-bound component. +- `D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=313 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5813361 mod 16556761 and m = 4403872 mod 16556761. +- Proof artifact: `symbolic_upper_bound_verified`, q=`313`, next=`D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q313_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=311 two-sided floor-bound component. +- `D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=317 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7885639 mod 16982641 and m = 6675063 mod 16982641. +- Proof artifact: `symbolic_upper_bound_verified`, q=`317`, next=`D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q317_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=313 two-sided floor-bound component. +- `D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=331 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 9831843 mod 18515809 and m = 2596079 mod 18515809. +- Proof artifact: `symbolic_upper_bound_verified`, q=`331`, next=`D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q331_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=317 two-sided floor-bound component. +- `D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=337 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 3148738 mod 19193161 and m = 11799312 mod 19193161. +- Proof artifact: `symbolic_upper_bound_verified`, q=`337`, next=`D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q337_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=331 two-sided floor-bound component. +- `D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=347 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 11863730 mod 20349121 and m = 17215931 mod 20349121. +- Proof artifact: `symbolic_upper_bound_verified`, q=`347`, next=`D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q347_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=337 two-sided floor-bound component. +- `D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=349 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 7685712 mod 20584369 and m = 2404433 mod 20584369. +- Proof artifact: `symbolic_upper_bound_verified`, q=`349`, next=`D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q349_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=347 two-sided floor-bound component. +- `D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=353 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1415812 mod 21058921 and m = 17854751 mod 21058921. +- Proof artifact: `symbolic_upper_bound_verified`, q=`353`, next=`D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q353_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=349 two-sided floor-bound component. +- `D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=359 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 2693621 mod 21780889 and m = 19926353 mod 21780889. +- Proof artifact: `symbolic_upper_bound_verified`, q=`359`, next=`D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q359_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=353 two-sided floor-bound component. +- `D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=367 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10408302 mod 22762441 and m = 21816280 mod 22762441. +- Proof artifact: `symbolic_upper_bound_verified`, q=`367`, next=`D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q367_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=359 two-sided floor-bound component. +- `D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=373 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6694020 mod 23512801 and m = 12354984 mod 23512801. +- Proof artifact: `symbolic_upper_bound_verified`, q=`373`, next=`D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q373_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=367 two-sided floor-bound component. +- `D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=379 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 11502746 mod 24275329 and m = 2984948 mod 24275329. +- Proof artifact: `symbolic_upper_bound_verified`, q=`379`, next=`D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q379_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=373 two-sided floor-bound component. +- `D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=383 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10683772 mod 24790441 and m = 8325686 mod 24790441. +- Proof artifact: `symbolic_upper_bound_verified`, q=`383`, next=`D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q383_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=379 two-sided floor-bound component. +- `D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=389 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 16061521 mod 25573249 and m = 4554789 mod 25573249. +- Proof artifact: `symbolic_upper_bound_verified`, q=`389`, next=`D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q389_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=383 two-sided floor-bound component. +- `D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=397 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 15585955 mod 26635921 and m = 9163588 mod 26635921. +- Proof artifact: `symbolic_upper_bound_verified`, q=`397`, next=`D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q397_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=389 two-sided floor-bound component. +- `D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=401 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 19236186 mod 27175369 and m = 26667256 mod 27175369. +- Proof artifact: `symbolic_upper_bound_verified`, q=`401`, next=`D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q401_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=397 two-sided floor-bound component. +- `D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=409 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 25277936 mod 28270489 and m = 5668837 mod 28270489. +- Proof artifact: `symbolic_upper_bound_verified`, q=`409`, next=`D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q409_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=401 two-sided floor-bound component. +- `D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=419 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 1254417 mod 29669809 and m = 6801644 mod 29669809. +- Proof artifact: `symbolic_upper_bound_verified`, q=`419`, next=`D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q419_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=409 two-sided floor-bound component. +- `D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=421 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 27364072 mod 29953729 and m = 11327633 mod 29953729. +- Proof artifact: `symbolic_upper_bound_verified`, q=`421`, next=`D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q421_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=419 two-sided floor-bound component. +- `D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=431 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 30520147 mod 31393609 and m = 30076324 mod 31393609. +- Proof artifact: `symbolic_upper_bound_verified`, q=`431`, next=`D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q431_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=421 two-sided floor-bound component. +- `D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=433 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4441757 mod 31685641 and m = 22352010 mod 31685641. +- Proof artifact: `symbolic_upper_bound_verified`, q=`433`, next=`D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q433_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=431 two-sided floor-bound component. +- `D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=439 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 31660390 mod 32569849 and m = 32568398 mod 32569849. +- Proof artifact: `symbolic_upper_bound_verified`, q=`439`, next=`D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q439_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=433 two-sided floor-bound component. +- `D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=443 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 17292855 mod 33166081 and m = 15525424 mod 33166081. +- Proof artifact: `symbolic_upper_bound_verified`, q=`443`, next=`D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q443_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=439 two-sided floor-bound component. +- `D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=449 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 10624284 mod 34070569 and m = 9976140 mod 34070569. +- Proof artifact: `symbolic_upper_bound_verified`, q=`449`, next=`D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q449_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=443 two-sided floor-bound component. +- `D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=457 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 33113790 mod 35295481 and m = 7601859 mod 35295481. +- Proof artifact: `symbolic_upper_bound_verified`, q=`457`, next=`D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q457_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=449 two-sided floor-bound component. +- `D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=461 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 709561 mod 35916049 and m = 6592929 mod 35916049. +- Proof artifact: `symbolic_upper_bound_verified`, q=`461`, next=`D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q461_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=457 two-sided floor-bound component. +- `D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=463 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5329852 mod 36228361 and m = 31534794 mod 36228361. +- Proof artifact: `symbolic_upper_bound_verified`, q=`463`, next=`D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q463_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=461 two-sided floor-bound component. +- `D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=467 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 4056099 mod 36857041 and m = 5739141 mod 36857041. +- Proof artifact: `symbolic_upper_bound_verified`, q=`467`, next=`D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q467_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=463 two-sided floor-bound component. +- `D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=479 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 24650270 mod 38775529 and m = 37033716 mod 38775529. +- Proof artifact: `symbolic_upper_bound_verified`, q=`479`, next=`D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q479_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=467 two-sided floor-bound component. +- `D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=487 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 21019643 mod 40081561 and m = 36495282 mod 40081561. +- Proof artifact: `symbolic_upper_bound_verified`, q=`487`, next=`D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q487_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=479 two-sided floor-bound component. +- `D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=491 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8394498 mod 40742689 and m = 21433495 mod 40742689. +- Proof artifact: `symbolic_upper_bound_verified`, q=`491`, next=`D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q491_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=487 two-sided floor-bound component. +- `D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=499 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 8072891 mod 42081169 and m = 26746686 mod 42081169. +- Proof artifact: `symbolic_upper_bound_verified`, q=`499`, next=`D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q499_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=491 two-sided floor-bound component. +- `D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=503 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 42056425 mod 42758521 and m = 19404650 mod 42758521. +- Proof artifact: `symbolic_upper_bound_verified`, q=`503`, next=`D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q503_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=499 two-sided floor-bound component. +- `D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=509 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 68882 mod 43784689 and m = 22331899 mod 43784689. +- Proof artifact: `symbolic_upper_bound_verified`, q=`509`, next=`D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q509_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=503 two-sided floor-bound component. +- `D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=521 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 37647553 mod 45873529 and m = 27667567 mod 45873529. +- Proof artifact: `symbolic_upper_bound_verified`, q=`521`, next=`D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q521_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=509 two-sided floor-bound component. +- `D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=523 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 5572874 mod 46226401 and m = 8835390 mod 46226401. +- Proof artifact: `symbolic_upper_bound_verified`, q=`523`, next=`D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q523_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=521 two-sided floor-bound component. +- `D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=541 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 6164881 mod 49463089 and m = 2567011 mod 49463089. +- Proof artifact: `symbolic_upper_bound_verified`, q=`541`, next=`D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q541_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=523 two-sided floor-bound component. +- `D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=547 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 34995605 mod 50566321 and m = 25423754 mod 50566321. +- Proof artifact: `symbolic_upper_bound_verified`, q=`547`, next=`D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q547_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=541 two-sided floor-bound component. +- `D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=557 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 45994463 mod 52432081 and m = 41289136 mod 52432081. +- Proof artifact: `symbolic_upper_bound_verified`, q=`557`, next=`D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q557_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=547 two-sided floor-bound component. +- `D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=563 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 42763521 mod 53567761 and m = 381503 mod 53567761. +- Proof artifact: `symbolic_upper_bound_verified`, q=`563`, next=`D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q563_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=557 two-sided floor-bound component. +- `D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=569 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 13641103 mod 54715609 and m = 17025468 mod 54715609. +- Proof artifact: `symbolic_upper_bound_verified`, q=`569`, next=`D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q569_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=563 two-sided floor-bound component. +- `D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=571 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 28625826 mod 55100929 and m = 25724236 mod 55100929. +- Proof artifact: `symbolic_upper_bound_verified`, q=`571`, next=`D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q571_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=569 two-sided floor-bound component. +- `D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=577 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 22102426 mod 56265001 and m = 9319575 mod 56265001. +- Proof artifact: `symbolic_upper_bound_verified`, q=`577`, next=`D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q577_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=571 two-sided floor-bound component. +- `D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7` [symbolic_upper_bound_verified]: Prove the q=587 tail-prime same-prime degree progression upper bound for both witness sides, starting from m = 57070892 mod 58232161 and m = 23141071 mod 58232161. +- Proof artifact: `symbolic_upper_bound_verified`, q=`587`, next=`D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q587_progression_outP2_70_out25_23_smaller_side7.json` +- Boundary: This is the next residual tail-prime subatom after the q=577 two-sided floor-bound component. +- `D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7` [bounded_parametric_zero_floor_verified]: Lift the bounded q>=587 zero-floor profile into a parametric tail lemma or aggregate recombination step; do not emit q=593 as another singleton unless the lift fails and returns a named exceptional class. +- Proof artifact: `bounded_parametric_zero_floor_verified`, q=`(unknown)`, next=`D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DMAX_TAIL_RECOMBINATION_PROOFS/D2_p13_dmax_tail_q_ge_587_parametric_zero_floor_outP2_70_out25_23_smaller_side7.json` +- Boundary: This aggregate handoff is bounded-profile evidence only; it must be lifted before any all-N dMax tail or side-count-floor claim. +- `D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18` [bounded_dynamic_margin_replay_verified_symbolic_lift_needed]: After the dMax growth envelope is proved for outP2=70|out25=23|smaller=side7, recompute the residual dynamic margin; the bounded-budget constant 39 is not valid as an all-N handoff. +- Inequality: `side18Count + vMax + rGreater + 39 <= candidateSize` +- Proof artifact: `bounded_dynamic_margin_replay_verified_symbolic_lift_needed`, q=`(unknown)`, next=`D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_outP2_70_out25_23_smaller_side7_side18.json` +- Boundary: The residual dynamic margin must be re-derived after a symbolic dMax growth envelope replaces the false constant bound. +- `D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18` [bounded_symbolic_lift_falsified_successor_atom_needed]: Lift the bounded residual dynamic-margin replay to a symbolic side18 threshold lemma: prove strictBaseThreshold - 1 - side18Count >= 20 for every future row in split outP2=70|out25=23|smaller=side7, or emit the first future-row residue/threshold obstruction. +- Proof artifact: `bounded_symbolic_lift_falsified_successor_atom_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_residual_dynamic_margin_symbolic_lift_outP2_70_out25_23_smaller_side7_side18.json` +- Boundary: This packet falsifies only the proposed symbolic threshold lift by bounded extension evidence and emits a sharper theorem-facing successor. It does not promote the bounded exact mixed-base verifier to an all-N proof. +- `D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_exact_mixed_margin_profile_verified_symbolic_lift_needed]: Replace the false side18 threshold lift for split outP2=70|out25=23|smaller=side7 with an exact mixed-margin successor: prove the missing-cross matching saturates the smaller side for the outsider-6323 family and leaves positive exact mixed margin, or emit the first sharper root-universe/rGreater obstruction. +- Proof artifact: `bounded_exact_mixed_margin_profile_verified_symbolic_lift_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_successor_outP2_70_out25_23_smaller_side7_outsider_6323.json` +- Boundary: This certificate verifies the exact mixed-margin successor only on the bounded 7307..10000 outsider-6323 profile. It does not prove the all-N matching saturation or exact mixed-margin lift. +- `D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [symbolic_lift_reduced_to_matching_injection_and_margin_floor]: Lift the bounded exact mixed-margin successor profile for outsider 6323 into a symbolic theorem: prove smaller-side matching saturation and strictBaseThreshold - mixedBaseCliqueSize >= 1 for every future row in split outP2=70|out25=23|smaller=side7, or emit the first exact residue/root-universe obstruction. +- Proof artifact: `symbolic_lift_reduced_to_matching_injection_and_margin_floor`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_symbolic_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json` +- Boundary: This symbolic lift is required because the exact mixed-margin successor is only bounded-profile evidence so far. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_prefix_matching_injection_verified_parametric_lift_needed]: Prove the side7-to-side18 missing-cross injection for outsider 6323, or emit the first exact residue/root-universe row where side7 cannot be saturated. +- Proof artifact: `bounded_prefix_matching_injection_verified_parametric_lift_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_outP2_70_out25_23_smaller_side7_outsider_6323.json` +- Boundary: This certificate is bounded evidence. It verifies a reusable prefix matching through the source 7307..10000 profile and a no-obstruction event probe through 12000, but it does not prove the all-N side7-to-side18 matching injection. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_online_augmentation_profile_verified_finite_menu_needed]: Turn the bounded prefix injection into an online residue/block insertion proof for all future outsider-6323 rows, or emit the first exact future event row where side7 cannot be saturated. +- Proof artifact: `bounded_online_augmentation_profile_verified_finite_menu_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_parametric_lift_outP2_70_out25_23_smaller_side7_outsider_6323.json` +- Boundary: This certificate is bounded evidence through N=40000. It verifies online side7 saturation and isolates the finite augmenting-path menu to prove next, but it does not prove the all-N outsider-6323 matching injection. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_finite_menu_falsified_direct_delta_successor_needed]: Prove the finite direct-insertion plus short replacement-path menu for every future side7-compatible event row in the outsider-6323 split family, or emit the first event row whose side7 vertex needs a new obstruction atom. +- Proof artifact: `bounded_finite_menu_falsified_direct_delta_successor_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_finite_augmenting_menu_outP2_70_out25_23_smaller_side7_outsider_632.json` +- Boundary: This packet falsifies the mined finite augmenting-path menu by an exact bounded future event row. It does not falsify side7 saturation or the matching-injection target; it only shows that the menu needs at least the new direct delta -1089 branch. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_direct_delta_minus1089_branch_falsified_delta_minus39_successor_needed]: Prove the new direct-delta -1089 branch exposed at side7 vertex 73607, integrate it with the existing augmenting menu, or emit the first future row where this enlarged menu fails. +- Proof artifact: `bounded_direct_delta_minus1089_branch_falsified_delta_minus39_successor_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus1089_successor_outP2_70_out25_23_smaller_side7_ou.json` +- Boundary: This packet falsifies the enlarged direct-delta -1089 menu by an exact bounded future event row. It does not falsify side7 saturation or the matching-injection target; it only shows that the menu needs at least the new direct delta -39 branch. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_direct_delta_minus39_branch_falsified_residue_parametric_delta_selection_lift_needed]: Prove the new direct-delta -39 branch exposed at side7 vertex 164507, integrate it with the enlarged augmenting menu, or emit the first future row where this menu fails. +- Proof artifact: `bounded_direct_delta_minus39_branch_falsified_residue_parametric_delta_selection_lift_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_direct_delta_minus39_successor_outP2_70_out25_23_smaller_side7_outs.json` +- Boundary: This packet falsifies the enlarged direct-delta -39 menu by an exact bounded future event row and intentionally stops the singleton-delta staircase. It does not falsify side7 saturation or prove any all-N matching injection. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [residue_parametric_delta_selection_reduced_to_direct_selector_and_collision_sublemmas]: Replace the direct-delta staircase with a residue-parametric rule that selects a valid direct missing-cross edge or bounded augmenting path for every future side7-compatible event row in the outsider-6323 family. +- Proof artifact: `residue_parametric_delta_selection_reduced_to_direct_selector_and_collision_sublemmas`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_parametric_delta_selection_lift_outP2_70_out25_23_smaller_s.json` +- Boundary: This packet decomposes the residue-parametric delta-selection target into theorem sublemmas. It does not prove the all-N matching injection and does not promote bounded seed repairs as a proof. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [symbolic_residue_direct_selector_lift_proved_selected_cross_squarefree_needed]: Prove the residue-parametric direct-selector sublemma: every future side7-compatible event row has a residue-selected side18-compatible direct endpoint, or emit the first event row with no selected direct endpoint. +- Proof artifact: `symbolic_residue_direct_selector_lift_proved_selected_cross_squarefree_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_residue_direct_selector_lift_outP2_70_out25_23_smaller_side7_outsid.json` +- Boundary: This packet proves only that every future side7-compatible event row has an active side18-compatible endpoint selected by the four-slot mod-4 rule. It does not prove that left * right + 1 is squarefree, and it does not prove that selected endpoints are collision-free for the online matching. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_selected_cross_squarefree_falsified_exception_menu_needed]: Prove that the four-slot selected endpoint gives a squarefree cross product left * right + 1 for every future side7-compatible event row, or route the first residue class/future row where the selected cross product is non-squarefree into a bounded replacement-path exception menu. +- Proof artifact: `bounded_selected_cross_squarefree_falsified_exception_menu_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_lift_outP2_70_out25_23_smaller_side7_outs.json` +- Boundary: This is a bounded falsifier packet, not an all-N proof of the replacement rule. It records the first selected endpoint whose cross product is non-squarefree and seeds a replacement-menu theorem target. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_side7_outsider_6323_left_8107` [bounded_exception_menu_reduced_to_finite_window_lift]: Build a replacement menu for the selected cross-squarefree obstruction class starting at left=8107: replace the failing previous-93 endpoint by a side18-compatible squarefree-cross endpoint such as the observed delta -189 repair, or emit the first side7-compatible row with no bounded replacement. +- Proof artifact: `bounded_exception_menu_reduced_to_finite_window_lift`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_menu_outP2_70_out25_23_smaller_.json` +- Boundary: This packet replaces the left=8107 local repair by a finite-window theorem target. It is bounded evidence and a handoff, not an all-N proof of the exception menu or the full matching injection. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_exception_window_lift_falsified_right_compatibility_escape_needed]: Prove the finite 27-delta exception-window selector: every future selected-cross square-divisor exception row has a replacement right = left + delta from the menu with right side18-compatible, 6323 * right + 1 non-squarefree, and left * right + 1 squarefree, or emit the first uncovered row. +- Proof artifact: `bounded_exception_window_lift_falsified_right_compatibility_escape_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_window_lift_outP2_70_out25_23_s.json` +- Boundary: This packet falsifies the 27-delta finite-window lift at bounded scope and emits the first uncovered row. It does not prove that the escape deltas work for all future rows and does not prove the full matching injection. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift_outP2_70_out25_23_smaller_side7_outsider_6323_left_1138307` [bounded_right_compatibility_escape_profile_small_prime_crt_selector_needed]: Replace the failed 27-delta exception window with a right-compatibility escape selector seeded by the first uncovered row left=1138307: prove that every future finite-window miss has a side18 replacement such as the observed deltas -989 or -1189 with outsider compatibility and squarefree cross product, or emit the first row with no bounded escape repair. +- Proof artifact: `bounded_right_compatibility_escape_profile_small_prime_crt_selector_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_right_compatibility_escape_lift.json` +- Boundary: This packet only records bounded evidence through N=10000000. It proves neither an all-N escape selector nor collision-free matching; it narrows the next theorem move to a small-prime CRT selector instead of a singleton delta branch. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [symbolic_p7_endpoint_reduction_ready_cross_squarefree_fallback_needed]: Derive a symbolic small-prime CRT selector for finite-window misses: for each selected-cross exception row missed by the 27-delta menu, choose a nearby side18 endpoint inside the 10000 local window whose right-side outsider compatibility is witnessed by one of {7,11,13,17,19,23,31,37,41} and whose cross product is squarefree, or emit the first row outside that rule. +- Proof artifact: `symbolic_p7_endpoint_reduction_ready_cross_squarefree_fallback_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_small_prime_crt_escape_selector_lift.json` +- Boundary: This packet proves only the p=7 endpoint-existence component symbolically. The cross-squarefree fallback remains open and bounded evidence must not be promoted to an all-N claim. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_period_shifted_endpoint_menu_profile_ready_symbolic_menu_lift_needed]: Starting from the symbolic p=7 local side18 endpoint, prove that rows whose p=7 endpoint has a non-squarefree cross edge admit a nearby fallback endpoint from the small-prime set {7,11,13,17,19,23,31,37,41} with squarefree cross product, or emit the first fallback miss. +- Proof artifact: `bounded_period_shifted_endpoint_menu_profile_ready_symbolic_menu_lift_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_p7_endpoint_cross_squarefree_fallback_lift.json` +- Boundary: This packet records a bounded period-shifted endpoint-menu profile and a symbolic right-compatibility skeleton. It does not prove all-N cross-squarefreeness or collision-free matching. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_prime_set_exact_replay_ready_squarefree_sieve_lift_needed]: Prove that every p=7 endpoint cross-bad row in this split family has a squarefree cross product inside the small-prime period-shifted endpoint menu, or emit the first future row outside the menu. +- Proof artifact: `bounded_prime_set_exact_replay_ready_squarefree_sieve_lift_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_lift.json` +- Boundary: This packet extends the exact named period-shifted endpoint-menu replay and reduces the all-N work to a squarefree sieve/hitting lemma. It does not prove all-N menu coverage or matching collision-freedom. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_p7_period_shift_profile_ready_q17_residual_lift_needed]: Prove the squarefree hitting lemma for the period-shifted endpoint menu: every p=7 endpoint cross-bad row has at least one menu endpoint with squarefree cross product, or emit the first row where every menu endpoint is cross-blocked. +- Proof artifact: `bounded_p7_period_shift_profile_ready_q17_residual_lift_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_squarefree_sieve_lift.json` +- Boundary: This packet decomposes the squarefree sieve target using bounded evidence through N=20000000. It proves neither the p7 period-shift selector nor the q17 residual fallback for all N, and it does not claim collision-free matching. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_q17_residual_falsified_cross_bad_fallback_needed]: Prove the p=7 period-shift squarefree selector and the q=17 residual-class fallback for the period-shifted endpoint menu, or emit the first residual row where the q=17 endpoint is cross-blocked. +- Proof artifact: `bounded_q17_residual_falsified_cross_bad_fallback_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_p7_shift_q17_residual_lift.json` +- Boundary: This packet only falsifies the standalone q17 residual fallback at the first certified residual-class row after the 20M bounded handoff. The local fallback seed is not an all-N proof and does not claim collision-free online matching. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_seed_fallback_menu_falsified_p13_expanded_menu_needed]: Prove that every q17 residual cross-bad row has a squarefree side18-compatible fallback endpoint in the small-prime local menu, or emit the first row with no bounded fallback endpoint. +- Proof artifact: `bounded_seed_fallback_menu_falsified_p13_expanded_menu_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_cross_bad_fallback_lift.json` +- Boundary: This packet exactly falsifies only the {11,19,23,31} seed fallback menu through the first fully fallback-blocked q17 residual row under the 10000 window. The p=13 repair seed is a next theorem target, not an all-N proof or collision-free matching claim. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed]: Prove that every q17 residual cross-bad row has a squarefree side18-compatible endpoint in the expanded local menu {11,13,19,23,31}, or emit the first row outside that expanded menu. +- Proof artifact: `bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed`, q=`(unknown)`, next=`D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json` +- Boundary: This packet exactly falsifies only the {11,13,19,23,31} p13-expanded fallback menu through the first fully expanded-menu-blocked q17 residual row under the 10000 window. The window-relaxed repair seeds are next theorem targets, not all-N coverage or collision-free matching claims. +- `D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_window_relaxed_fallback_menu_lift_outP2_70_out25_23_smaller_side7_outsider_6323` [needed]: Prove that every q17 residual cross-bad row blocked by the 10000-window expanded menu has a squarefree side18-compatible endpoint in a controlled 25000-window menu, or emit the first fully window-relaxed blocked row. +- Proof artifact: `bounded_p13_expanded_fallback_menu_falsified_window_relaxation_needed`, q=`(unknown)`, next=`(none)` +- Proof JSON: `/Volumes/Code_2TB/code/erdos-problems/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/DYNAMIC_MARGIN_PROOFS/D2_p13_dynamic_margin_exact_mixed_matching_injection_selected_cross_squarefree_exception_period_shifted_endpoint_menu_q17_residual_p13_expanded_fallback_menu_lift.json` +- Boundary: This window-relaxed fallback subatom is still cross-squarefree endpoint selection only. It must not claim all-N coverage from the seed or collision-free matching. + +## Proof Reduction + +- Matching saturation: matchingSizeInMissingCrossGraph = min(compatibleSide7Count, compatibleSide18Count) +- K formula: K = compatibleSide7Count + compatibleSide18Count - strictBaseThreshold + 1 +- Slack formula: matchingSlack = strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) + +## Bounded Witness + +- Formula replay passed: `yes` +- Meets target floor: `yes` +- Side-count slack formula range: `21..25` +- Larger side range: `110..114` +- Strict base threshold range: `132..138` +- Candidate size range: `293..304` +- Reconstructed vMax range: `43..45` +- dMax range: `18..18` +- rGreater range: `100..103` + +## Next Theorem Actions + +- Treat D2_p13_dmax_bound_outP2_70_out25_23_smaller_side7 as falsified by the extended bounded probe; do not promote dMax <= 18 as an all-N lemma. +- Attack the successor D2_p13_dmax_growth_outP2_70_out25_23_smaller_side7: replace the false constant dMax bound before re-deriving the residual dynamic margin. +- If the symbolic side-count inequality fails, emit a sharper split atom keyed by the first failing side-count term. +- After all co-weakest side-count floor atoms are handled, lift the remaining larger-margin strata by the same inequality template. diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.json new file mode 100644 index 0000000..eda2e02 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.json @@ -0,0 +1,121 @@ +{ + "schema": "erdos.p848_side_count_floor_atom_packet/1", + "generatedAt": "2026-04-14T11:46:10.126Z", + "problemId": "848", + "packetId": "p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7", + "atomId": "D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7", + "parentLemmaId": "D2_p13_non_tight_side_count_slack_floor_lift", + "parentCandidateId": "D2_p13_slack_dominance_symbolic_lift", + "targetPrime": 13, + "splitKey": "outP2=70|out25=6|smaller=side7", + "rank": 2, + "priority": "co_weakest_side_count_floor_atom", + "status": "symbolic_side_count_floor_atom_needed", + "targetSlackLowerBound": 20, + "observedBoundedSlackFormulaFloor": 21, + "observedMarginAboveTarget": 1, + "boundedWitness": { + "rowCount": 32, + "nRange": "7307..7600", + "minSideCountSlackFormula": 21, + "maxSideCountSlackFormula": 25, + "minLargerSideSize": 109, + "maxLargerSideSize": 113, + "minStrictBaseThreshold": 132, + "maxStrictBaseThreshold": 138, + "minCandidateSize": 293, + "maxCandidateSize": 304, + "minReconstructedVMax": 43, + "maxReconstructedVMax": 45, + "minDMax": 18, + "maxDMax": 18, + "minRGreater": 100, + "maxRGreater": 103, + "minStructuralMargin": 1, + "maxStructuralMargin": 5, + "formulaReplayPassed": true, + "meetsTargetSlackFloor": true + }, + "structuralMarginDecomposition": { + "status": "bounded_structural_margin_replay_verified_symbolic_margin_lift_needed", + "largerSideLabel": "side18", + "targetAugmentedMarginConstant": 21, + "inequality": "side18Count + vMax + dMax + rGreater + 21 <= candidateSize", + "boundedMarginRange": { + "min": 1, + "max": 5 + }, + "firstOpenSublemma": { + "lemmaId": "D2_p13_structural_margin_outP2_70_out25_6_smaller_side7_side18", + "status": "needed", + "statement": "For every future p=13 threat row with outP2=70|out25=6|smaller=side7, prove side18Count + vMax + dMax + rGreater + 21 <= candidateSize." + }, + "movingTermSubatoms": [ + { + "atomId": "D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7", + "status": "needed", + "term": "dMax", + "targetBound": 18, + "boundedRange": { + "min": 18, + "max": 18 + }, + "statement": "For every future p=13 threat row with outP2=70|out25=6|smaller=side7, prove dMax <= 18.", + "probeArtifact": null, + "successorAtomId": null, + "proofBoundary": "This isolates the maximum same-prime cross-degree term from the structural margin. The bounded constant value is not an all-N proof." + }, + { + "atomId": "D2_p13_dynamic_margin_outP2_70_out25_6_smaller_side7_side18", + "status": "needed_after_dmax_bound", + "term": "side18Count + vMax + rGreater", + "dependsOn": [ + "D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7" + ], + "residualDynamicMarginConstant": 39, + "inequality": "side18Count + vMax + rGreater + 39 <= candidateSize", + "boundedMarginRange": { + "min": 1, + "max": 5 + }, + "statement": "Assuming dMax <= 18, prove side18Count + vMax + rGreater + 39 <= candidateSize for outP2=70|out25=6|smaller=side7.", + "proofArtifact": null, + "proofBoundary": "This is the coupled moving-count margin left after budgeting dMax. It still needs a symbolic inequality for compatibility counts, p13 root counts, higher-root events, and the base candidate side." + } + ], + "firstOpenMovingTermSubatom": { + "atomId": "D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7", + "status": "needed", + "term": "dMax", + "targetBound": 18, + "boundedRange": { + "min": 18, + "max": 18 + }, + "statement": "For every future p=13 threat row with outP2=70|out25=6|smaller=side7, prove dMax <= 18.", + "probeArtifact": null, + "successorAtomId": null, + "proofBoundary": "This isolates the maximum same-prime cross-degree term from the structural margin. The bounded constant value is not an all-N proof." + }, + "proofBoundary": "This replays the bounded side-count floor as a structural margin inequality. It is not an all-N proof of the moving compatibility counts, dMax, rGreater, or candidateSize terms." + }, + "theoremObligation": { + "kind": "non_tight_p13_side_count_floor_subobligation", + "statement": "For every future p=13 threat row with outP2=70|out25=6|smaller=side7, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) >= 20.", + "equivalentInequality": "max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 21", + "proofBoundary": "This packet isolates one weakest non-tight side-count stratum. Its bounded witness is not an all-N proof; the symbolic side-count inequality still has to be proved or refined." + }, + "proofReduction": { + "statement": "For non-tight p13 rows, reduce slack dominance to a side-count inequality after matching saturation.", + "matchingSaturationHypothesis": "matchingSizeInMissingCrossGraph = min(compatibleSide7Count, compatibleSide18Count)", + "requiredMatchingFormula": "K = compatibleSide7Count + compatibleSide18Count - strictBaseThreshold + 1", + "derivedSlackFormula": "matchingSlack = strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count)", + "sufficientSideCountInequality": "max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 1 - 20" + }, + "nextTheoremActions": [ + "Prove the first moving-term subatom D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7: dMax <= 18.", + "After dMax is bounded, prove the residual dynamic margin D2_p13_dynamic_margin_outP2_70_out25_6_smaller_side7_side18: side18Count + vMax + rGreater + 39 <= candidateSize.", + "If the symbolic side-count inequality fails, emit a sharper split atom keyed by the first failing side-count term.", + "After all co-weakest side-count floor atoms are handled, lift the remaining larger-margin strata by the same inequality template." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.md new file mode 100644 index 0000000..414f2ef --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SIDE_COUNT_FLOOR/D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7.md @@ -0,0 +1,65 @@ +# D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7 + +This is a focused side-count floor atom for the Problem 848 p13 non-tight slack-dominance lift. + +## Summary + +- Packet id: `p848_side_count_floor_packet_D2_p13_side_count_floor_outP2_70_out25_6_smaller_side7` +- Parent lemma: `D2_p13_non_tight_side_count_slack_floor_lift` +- Split key: `outP2=70|out25=6|smaller=side7` +- Priority: `co_weakest_side_count_floor_atom` +- Status: `symbolic_side_count_floor_atom_needed` +- Target slack floor: `20` +- Observed bounded slack-formula floor: `21` +- Observed margin above target: `1` +- Bounded witness rows: `32` over `7307..7600` + +## Theorem Obligation + +For every future p=13 threat row with outP2=70|out25=6|smaller=side7, prove strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) >= 20. + +Equivalent inequality: `max(compatibleSide7Count, compatibleSide18Count) <= strictBaseThreshold - 21` + +Boundary: This packet isolates one weakest non-tight side-count stratum. Its bounded witness is not an all-N proof; the symbolic side-count inequality still has to be proved or refined. + +## Structural Margin Decomposition + +- Status: `bounded_structural_margin_replay_verified_symbolic_margin_lift_needed` +- Inequality: `side18Count + vMax + dMax + rGreater + 21 <= candidateSize` +- Bounded margin range: `1..5` +- First open sublemma: `D2_p13_structural_margin_outP2_70_out25_6_smaller_side7_side18` +- First moving-term subatom: `D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7` +- Boundary: This replays the bounded side-count floor as a structural margin inequality. It is not an all-N proof of the moving compatibility counts, dMax, rGreater, or candidateSize terms. + +## Moving-Term Subatoms + +- `D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7` [needed]: For every future p=13 threat row with outP2=70|out25=6|smaller=side7, prove dMax <= 18. +- Boundary: This isolates the maximum same-prime cross-degree term from the structural margin. The bounded constant value is not an all-N proof. +- `D2_p13_dynamic_margin_outP2_70_out25_6_smaller_side7_side18` [needed_after_dmax_bound]: Assuming dMax <= 18, prove side18Count + vMax + rGreater + 39 <= candidateSize for outP2=70|out25=6|smaller=side7. +- Inequality: `side18Count + vMax + rGreater + 39 <= candidateSize` +- Boundary: This is the coupled moving-count margin left after budgeting dMax. It still needs a symbolic inequality for compatibility counts, p13 root counts, higher-root events, and the base candidate side. + +## Proof Reduction + +- Matching saturation: matchingSizeInMissingCrossGraph = min(compatibleSide7Count, compatibleSide18Count) +- K formula: K = compatibleSide7Count + compatibleSide18Count - strictBaseThreshold + 1 +- Slack formula: matchingSlack = strictBaseThreshold - 1 - max(compatibleSide7Count, compatibleSide18Count) + +## Bounded Witness + +- Formula replay passed: `yes` +- Meets target floor: `yes` +- Side-count slack formula range: `21..25` +- Larger side range: `109..113` +- Strict base threshold range: `132..138` +- Candidate size range: `293..304` +- Reconstructed vMax range: `43..45` +- dMax range: `18..18` +- rGreater range: `100..103` + +## Next Theorem Actions + +- Prove the first moving-term subatom D2_p13_dmax_bound_outP2_70_out25_6_smaller_side7: dMax <= 18. +- After dMax is bounded, prove the residual dynamic margin D2_p13_dynamic_margin_outP2_70_out25_6_smaller_side7_side18: side18Count + vMax + rGreater + 39 <= candidateSize. +- If the symbolic side-count inequality fails, emit a sharper split atom keyed by the first failing side-count term. +- After all co-weakest side-count floor atoms are handled, lift the remaining larger-margin strata by the same inequality template. diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.json new file mode 100644 index 0000000..e42ecac --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.json @@ -0,0 +1,216 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.840Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_11881_out_5309", + "successorRank": 11, + "conditionId": "square_11881_outsider_5309", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out11881=5309", + "parentSplitModulus": 4225, + "successorSplitModulus": 50197225, + "square": 11881, + "divisor": 109, + "requiredOutsiderResidueModSquare": 5309, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_11881_outsider_5309_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 5309 (mod 11881) and vertex ≡ 1618 (mod 11881), then outsider * vertex + 1 ≡ 0 (mod 11881).", + "outsiderResidueModSquare": 5309, + "vertexResidueModSquare": 1618, + "square": 11881, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V136.right_1618", + "value": 1618, + "residueModSquare": 1618, + "expectedVertexResidueModSquare": 1618, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out11881=5309, stabilize the 1 literal vertex-presence atoms whose first square witness is 11881.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V136.right_1618", + "side": "side18", + "value": 1618, + "residues": { + "value": 1618, + "mod25": 18, + "modP": 6, + "modP2": 97 + }, + "residueModSquare": 1618, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 8589963, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 5309, + "witnessOutsiderResidueModSquare": 5309, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 8589963, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 5309, + "witnessOutsiderResidueModSquare": 5309, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 8589963, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 5309, + "witnessOutsiderResidueModSquare": 5309, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 8589963, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 5309, + "witnessOutsiderResidueModSquare": 5309, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 8589963, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 5309, + "witnessOutsiderResidueModSquare": 5309, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 8589963, + "firstSquareDivisorWitness": { + "divisor": 109, + "square": 11881, + "quotient": 723, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 5309, + "witnessOutsiderResidueModSquare": 5309, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 8589963, + "quotient": 723 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 8589963, + "quotient": 723 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 8589963, + "quotient": 723 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 8589963, + "quotient": 723 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 8589963, + "quotient": 723 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 8589963, + "quotient": 723 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.md new file mode 100644 index 0000000..06a4944 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309.md @@ -0,0 +1,42 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_11881_out_5309 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_11881_outsider_5309` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_11881_outsider_5309` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out11881=5309` +- Successor modulus: `50197225` +- Square witness: `11881` +- Required outsider residue: `5309` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `1618 mod 11881` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out11881=5309, stabilize the 1 literal vertex-presence atoms whose first square witness is 11881. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 5309 (mod 11881) and vertex ≡ 1618 (mod 11881), then outsider * vertex + 1 ≡ 0 (mod 11881). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V136.right_1618`: side=side18, value=1618, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.json new file mode 100644 index 0000000..53fd402 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.json @@ -0,0 +1,442 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.838Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_121_out_106", + "successorRank": 4, + "conditionId": "square_121_outsider_106", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out121=106", + "parentSplitModulus": 4225, + "successorSplitModulus": 511225, + "square": 121, + "divisor": 11, + "requiredOutsiderResidueModSquare": 106, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_121_outsider_106_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 106 (mod 121) and vertex ≡ 113 (mod 121), then outsider * vertex + 1 ≡ 0 (mod 121).", + "outsiderResidueModSquare": 106, + "vertexResidueModSquare": 113, + "square": 121, + "affectedAtomCount": 3, + "verifiedAtomCount": 3, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V72.left_4832", + "value": 4832, + "residueModSquare": 113, + "expectedVertexResidueModSquare": 113, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V120.right_718", + "value": 718, + "residueModSquare": 113, + "expectedVertexResidueModSquare": 113, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V210.right_6768", + "value": 6768, + "residueModSquare": 113, + "expectedVertexResidueModSquare": 113, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out121=106, stabilize the 3 literal vertex-presence atoms whose first square witness is 121.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V72.left_4832", + "side": "side7", + "value": 4832, + "residues": { + "value": 4832, + "mod25": 7, + "modP": 9, + "modP2": 100 + }, + "residueModSquare": 113, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 25653089, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 25653089, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 25653089, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 25653089, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 25653089, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 25653089, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 212009, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V120.right_718", + "side": "side18", + "value": 718, + "residues": { + "value": 718, + "mod25": 18, + "modP": 3, + "modP2": 42 + }, + "residueModSquare": 113, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 3811863, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 3811863, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 3811863, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 3811863, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 3811863, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 3811863, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 31503, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V210.right_6768", + "side": "side18", + "value": 6768, + "residues": { + "value": 6768, + "mod25": 18, + "modP": 8, + "modP2": 8 + }, + "residueModSquare": 113, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 35931313, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 35931313, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 35931313, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 35931313, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 35931313, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 35931313, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 296953, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 106, + "witnessOutsiderResidueModSquare": 106, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 3, + "stabilizedAtomCount": 3, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 25653089, + "quotient": 212009 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 25653089, + "quotient": 212009 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 25653089, + "quotient": 212009 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 25653089, + "quotient": 212009 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 25653089, + "quotient": 212009 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 25653089, + "quotient": 212009 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.md new file mode 100644 index 0000000..6d8d821 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106.md @@ -0,0 +1,44 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_121_out_106 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_121_outsider_106` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_121_outsider_106` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out121=106` +- Successor modulus: `511225` +- Square witness: `121` +- Required outsider residue: `106` +- Affected atoms: `3` +- Stabilized atoms: `3` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `113 mod 121` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out121=106, stabilize the 3 literal vertex-presence atoms whose first square witness is 121. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 106 (mod 121) and vertex ≡ 113 (mod 121), then outsider * vertex + 1 ≡ 0 (mod 121). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V72.left_4832`: side=side7, value=4832, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V120.right_718`: side=side18, value=718, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V210.right_6768`: side=side18, value=6768, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.json new file mode 100644 index 0000000..6b4fc43 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.json @@ -0,0 +1,216 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.839Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_1681_out_266", + "successorRank": 9, + "conditionId": "square_1681_outsider_266", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out1681=266", + "parentSplitModulus": 4225, + "successorSplitModulus": 7102225, + "square": 1681, + "divisor": 41, + "requiredOutsiderResidueModSquare": 266, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_1681_outsider_266_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 266 (mod 1681) and vertex ≡ 1068 (mod 1681), then outsider * vertex + 1 ≡ 0 (mod 1681).", + "outsiderResidueModSquare": 266, + "vertexResidueModSquare": 1068, + "square": 1681, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V127.right_1068", + "value": 1068, + "residueModSquare": 1068, + "expectedVertexResidueModSquare": 1068, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out1681=266, stabilize the 1 literal vertex-presence atoms whose first square witness is 1681.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V127.right_1068", + "side": "side18", + "value": 1068, + "residues": { + "value": 1068, + "mod25": 18, + "modP": 2, + "modP2": 54 + }, + "residueModSquare": 1068, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5670013, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 266, + "witnessOutsiderResidueModSquare": 266, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5670013, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 266, + "witnessOutsiderResidueModSquare": 266, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 5670013, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 266, + "witnessOutsiderResidueModSquare": 266, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 5670013, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 266, + "witnessOutsiderResidueModSquare": 266, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 5670013, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 266, + "witnessOutsiderResidueModSquare": 266, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 5670013, + "firstSquareDivisorWitness": { + "divisor": 41, + "square": 1681, + "quotient": 3373, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 266, + "witnessOutsiderResidueModSquare": 266, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 5670013, + "quotient": 3373 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 5670013, + "quotient": 3373 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 5670013, + "quotient": 3373 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 5670013, + "quotient": 3373 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 5670013, + "quotient": 3373 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 5670013, + "quotient": 3373 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.md new file mode 100644 index 0000000..07233b5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266.md @@ -0,0 +1,42 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_1681_out_266 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_1681_outsider_266` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_1681_outsider_266` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out1681=266` +- Successor modulus: `7102225` +- Square witness: `1681` +- Required outsider residue: `266` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `1068 mod 1681` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out1681=266, stabilize the 1 literal vertex-presence atoms whose first square witness is 1681. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 266 (mod 1681) and vertex ≡ 1068 (mod 1681), then outsider * vertex + 1 ≡ 0 (mod 1681). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V127.right_1068`: side=side18, value=1068, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.json new file mode 100644 index 0000000..72f09ce --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.json @@ -0,0 +1,216 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.840Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_2809_out_2500", + "successorRank": 10, + "conditionId": "square_2809_outsider_2500", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out2809=2500", + "parentSplitModulus": 4225, + "successorSplitModulus": 11868025, + "square": 2809, + "divisor": 53, + "requiredOutsiderResidueModSquare": 2500, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_2809_outsider_2500_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 2500 (mod 2809) and vertex ≡ 100 (mod 2809), then outsider * vertex + 1 ≡ 0 (mod 2809).", + "outsiderResidueModSquare": 2500, + "vertexResidueModSquare": 100, + "square": 2809, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V194.right_5718", + "value": 5718, + "residueModSquare": 100, + "expectedVertexResidueModSquare": 100, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out2809=2500, stabilize the 1 literal vertex-presence atoms whose first square witness is 2809.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V194.right_5718", + "side": "side18", + "value": 5718, + "residues": { + "value": 5718, + "mod25": 18, + "modP": 11, + "modP2": 141 + }, + "residueModSquare": 100, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 30356863, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 2500, + "witnessOutsiderResidueModSquare": 2500, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 30356863, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 2500, + "witnessOutsiderResidueModSquare": 2500, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 30356863, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 2500, + "witnessOutsiderResidueModSquare": 2500, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 30356863, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 2500, + "witnessOutsiderResidueModSquare": 2500, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 30356863, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 2500, + "witnessOutsiderResidueModSquare": 2500, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 30356863, + "firstSquareDivisorWitness": { + "divisor": 53, + "square": 2809, + "quotient": 10807, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 2500, + "witnessOutsiderResidueModSquare": 2500, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 30356863, + "quotient": 10807 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 30356863, + "quotient": 10807 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 30356863, + "quotient": 10807 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 30356863, + "quotient": 10807 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 30356863, + "quotient": 10807 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 30356863, + "quotient": 10807 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.md new file mode 100644 index 0000000..97992d5 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500.md @@ -0,0 +1,42 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_2809_out_2500 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_2809_outsider_2500` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_2809_outsider_2500` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out2809=2500` +- Successor modulus: `11868025` +- Square witness: `2809` +- Required outsider residue: `2500` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `100 mod 2809` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out2809=2500, stabilize the 1 literal vertex-presence atoms whose first square witness is 2809. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 2500 (mod 2809) and vertex ≡ 100 (mod 2809), then outsider * vertex + 1 ≡ 0 (mod 2809). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V194.right_5718`: side=side18, value=5718, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.json new file mode 100644 index 0000000..46ccb5d --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.json @@ -0,0 +1,329 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.838Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_361_out_255", + "successorRank": 5, + "conditionId": "square_361_outsider_255", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out361=255", + "parentSplitModulus": 4225, + "successorSplitModulus": 1525225, + "square": 361, + "divisor": 19, + "requiredOutsiderResidueModSquare": 255, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_361_outsider_255_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 255 (mod 361) and vertex ≡ 235 (mod 361), then outsider * vertex + 1 ≡ 0 (mod 361).", + "outsiderResidueModSquare": 255, + "vertexResidueModSquare": 235, + "square": 361, + "affectedAtomCount": 2, + "verifiedAtomCount": 2, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V14.left_957", + "value": 957, + "residueModSquare": 235, + "expectedVertexResidueModSquare": 235, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V130.right_1318", + "value": 1318, + "residueModSquare": 235, + "expectedVertexResidueModSquare": 235, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out361=255, stabilize the 2 literal vertex-presence atoms whose first square witness is 361.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V14.left_957", + "side": "side7", + "value": 957, + "residues": { + "value": 957, + "mod25": 7, + "modP": 8, + "modP2": 112 + }, + "residueModSquare": 235, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 5080714, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 5080714, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 5080714, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 5080714, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 5080714, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 5080714, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 14074, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V130.right_1318", + "side": "side18", + "value": 1318, + "residues": { + "value": 1318, + "mod25": 18, + "modP": 5, + "modP2": 135 + }, + "residueModSquare": 235, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 6997263, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 6997263, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 6997263, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 6997263, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 6997263, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 6997263, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 19383, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 255, + "witnessOutsiderResidueModSquare": 255, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 2, + "stabilizedAtomCount": 2, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 5080714, + "quotient": 14074 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 5080714, + "quotient": 14074 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 5080714, + "quotient": 14074 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 5080714, + "quotient": 14074 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 5080714, + "quotient": 14074 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 5080714, + "quotient": 14074 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.md new file mode 100644 index 0000000..b4db1a9 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255.md @@ -0,0 +1,43 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_361_out_255 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_361_outsider_255` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_361_outsider_255` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out361=255` +- Successor modulus: `1525225` +- Square witness: `361` +- Required outsider residue: `255` +- Affected atoms: `2` +- Stabilized atoms: `2` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `235 mod 361` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out361=255, stabilize the 2 literal vertex-presence atoms whose first square witness is 361. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 255 (mod 361) and vertex ≡ 235 (mod 361), then outsider * vertex + 1 ≡ 0 (mod 361). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V14.left_957`: side=side7, value=957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V130.right_1318`: side=side18, value=1318, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.json new file mode 100644 index 0000000..5a8e662 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.json @@ -0,0 +1,1120 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.838Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_49_out_17", + "successorRank": 3, + "conditionId": "square_49_outsider_17", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out49=17", + "parentSplitModulus": 4225, + "successorSplitModulus": 207025, + "square": 49, + "divisor": 7, + "requiredOutsiderResidueModSquare": 17, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_49_outsider_17_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 17 (mod 49) and vertex ≡ 23 (mod 49), then outsider * vertex + 1 ≡ 0 (mod 49).", + "outsiderResidueModSquare": 17, + "vertexResidueModSquare": 23, + "square": 49, + "affectedAtomCount": 9, + "verifiedAtomCount": 9, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V31.left_2032", + "value": 2032, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V48.left_3257", + "value": 3257, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V66.left_4482", + "value": 4482, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V102.left_6932", + "value": 6932, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V113.right_268", + "value": 268, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V134.right_1493", + "value": 1493, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V152.right_2718", + "value": 2718, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V186.right_5168", + "value": 5168, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V204.right_6393", + "value": 6393, + "residueModSquare": 23, + "expectedVertexResidueModSquare": 23, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out49=17, stabilize the 9 literal vertex-presence atoms whose first square witness is 49.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V31.left_2032", + "side": "side7", + "value": 2032, + "residues": { + "value": 2032, + "mod25": 7, + "modP": 4, + "modP2": 4 + }, + "residueModSquare": 23, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 10787889, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220161, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 17, + "witnessOutsiderResidueModSquare": 17, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 10787889, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220161, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 17, + "witnessOutsiderResidueModSquare": 17, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 10787889, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220161, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 17, + "witnessOutsiderResidueModSquare": 17, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 10787889, + 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17, + "witnessOutsiderResidueModSquare": 17, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 33940438, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 17, + "witnessOutsiderResidueModSquare": 17, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 33940438, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 692662, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 17, + "witnessOutsiderResidueModSquare": 17, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 9, + "stabilizedAtomCount": 9, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 10787889, + "quotient": 220161 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 10787889, + "quotient": 220161 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 10787889, + "quotient": 220161 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 10787889, + "quotient": 220161 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 10787889, + "quotient": 220161 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 10787889, + "quotient": 220161 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.md new file mode 100644 index 0000000..71eb873 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17.md @@ -0,0 +1,50 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_49_out_17 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_49_outsider_17` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_49_outsider_17` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out49=17` +- Successor modulus: `207025` +- Square witness: `49` +- Required outsider residue: `17` +- Affected atoms: `9` +- Stabilized atoms: `9` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `23 mod 49` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out49=17, stabilize the 9 literal vertex-presence atoms whose first square witness is 49. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 17 (mod 49) and vertex ≡ 23 (mod 49), then outsider * vertex + 1 ≡ 0 (mod 49). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V31.left_2032`: side=side7, value=2032, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V48.left_3257`: side=side7, value=3257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V66.left_4482`: side=side7, value=4482, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V102.left_6932`: side=side7, value=6932, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V113.right_268`: side=side18, value=268, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V134.right_1493`: side=side18, value=1493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V152.right_2718`: side=side18, value=2718, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V186.right_5168`: side=side18, value=5168, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V204.right_6393`: side=side18, value=6393, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json new file mode 100644 index 0000000..f74b2ea --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.json @@ -0,0 +1,16488 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.834Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1", + "successorRank": 1, + "conditionId": "square_4_outsider_1", + "priority": "highest_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out4=1", + "parentSplitModulus": 4225, + "successorSplitModulus": 16900, + "square": 4, + "divisor": 2, + "requiredOutsiderResidueModSquare": 1, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_4_outsider_1_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 1 (mod 4) and vertex ≡ 3 (mod 4), then outsider * vertex + 1 ≡ 0 (mod 4).", + "outsiderResidueModSquare": 1, + "vertexResidueModSquare": 3, + "square": 4, + "affectedAtomCount": 145, + "verifiedAtomCount": 145, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V1.left_7", + "value": 7, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V3.left_107", + "value": 107, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V4.left_207", + "value": 207, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V5.left_307", + "value": 307, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V6.left_407", + "value": 407, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V7.left_507", + "value": 507, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V9.left_607", + "value": 607, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V10.left_707", + "value": 707, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V12.left_807", + "value": 807, + "residueModSquare": 3, + 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"D2.1_persist_outP2=70_out25=9_smaller=side7.V206.right_6443", + "value": 6443, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V207.right_6543", + "value": 6543, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V208.right_6643", + "value": 6643, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V209.right_6743", + "value": 6743, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V211.right_6843", + "value": 6843, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V213.right_6943", + "value": 6943, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V214.right_7043", + "value": 7043, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V215.right_7143", + "value": 7143, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out4=1, stabilize the 145 literal vertex-presence atoms whose first square witness is 4.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V1.left_7", + "side": "side7", + "value": 7, + "residues": { + "value": 7, + "mod25": 7, + "modP": 7, + "modP2": 7 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + 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"side": "side18", + "value": 7043, + "residues": { + "value": 7043, + "mod25": 18, + "modP": 10, + "modP2": 114 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 37391288, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9347822, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 37391288, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9347822, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 37391288, + 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true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 37391288, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9347822, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V215.right_7143", + "side": "side18", + "value": 7143, + "residues": { + "value": 7143, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 37922188, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 9480547, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + 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} + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 145, + "stabilizedAtomCount": 145, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 37164, + "quotient": 9291 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 37164, + "quotient": 9291 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 37164, + "quotient": 9291 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 37164, + "quotient": 9291 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 37164, + "quotient": 9291 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 37164, + "quotient": 9291 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md new file mode 100644 index 0000000..1ba2e3c --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1.md @@ -0,0 +1,186 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_4_out_1 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_4_outsider_1` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_4_outsider_1` +- Priority: `highest_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out4=1` +- Successor modulus: `16900` +- Square witness: `4` +- Required outsider residue: `1` +- Affected atoms: `145` +- Stabilized atoms: `145` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `3 mod 4` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out4=1, stabilize the 145 literal vertex-presence atoms whose first square witness is 4. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 1 (mod 4) and vertex ≡ 3 (mod 4), then outsider * vertex + 1 ≡ 0 (mod 4). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V1.left_7`: side=side7, value=7, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V3.left_107`: side=side7, value=107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V4.left_207`: side=side7, value=207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V5.left_307`: side=side7, value=307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V6.left_407`: side=side7, value=407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V7.left_507`: side=side7, value=507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V9.left_607`: side=side7, value=607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V10.left_707`: side=side7, value=707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V12.left_807`: side=side7, value=807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V13.left_907`: side=side7, value=907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V16.left_1007`: side=side7, value=1007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V17.left_1107`: side=side7, value=1107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V18.left_1207`: side=side7, value=1207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V19.left_1307`: side=side7, value=1307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V20.left_1407`: side=side7, value=1407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V22.left_1507`: side=side7, value=1507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V23.left_1607`: side=side7, value=1607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V25.left_1707`: side=side7, value=1707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V26.left_1807`: side=side7, value=1807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V28.left_1907`: side=side7, value=1907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V30.left_2007`: side=side7, value=2007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V32.left_2107`: side=side7, value=2107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V33.left_2207`: side=side7, value=2207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V34.left_2307`: side=side7, value=2307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V36.left_2407`: side=side7, value=2407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V37.left_2507`: side=side7, value=2507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V39.left_2607`: side=side7, value=2607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V40.left_2707`: side=side7, value=2707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V42.left_2807`: side=side7, value=2807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V43.left_2907`: side=side7, value=2907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V44.left_3007`: side=side7, value=3007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V45.left_3107`: side=side7, value=3107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V46.left_3207`: side=side7, value=3207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V49.left_3307`: side=side7, value=3307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V50.left_3407`: side=side7, value=3407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V52.left_3507`: side=side7, value=3507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V53.left_3607`: side=side7, value=3607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V55.left_3707`: side=side7, value=3707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V56.left_3807`: side=side7, value=3807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V57.left_3907`: side=side7, value=3907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V59.left_4007`: side=side7, value=4007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V60.left_4107`: side=side7, value=4107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V62.left_4207`: side=side7, value=4207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V63.left_4307`: side=side7, value=4307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V65.left_4407`: side=side7, value=4407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V67.left_4507`: side=side7, value=4507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V69.left_4607`: side=side7, value=4607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V70.left_4707`: side=side7, value=4707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V71.left_4807`: side=side7, value=4807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V73.left_4907`: side=side7, value=4907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V74.left_5007`: side=side7, value=5007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V76.left_5107`: side=side7, value=5107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V77.left_5207`: side=side7, value=5207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V79.left_5307`: side=side7, value=5307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V80.left_5407`: side=side7, value=5407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V83.left_5507`: side=side7, value=5507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V84.left_5607`: side=side7, value=5607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V85.left_5707`: side=side7, value=5707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V86.left_5807`: side=side7, value=5807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V87.left_5907`: side=side7, value=5907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V89.left_6007`: side=side7, value=6007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V90.left_6107`: side=side7, value=6107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V92.left_6207`: side=side7, value=6207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V93.left_6307`: side=side7, value=6307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V95.left_6407`: side=side7, value=6407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V96.left_6507`: side=side7, value=6507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V97.left_6607`: side=side7, value=6607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V98.left_6707`: side=side7, value=6707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V99.left_6807`: side=side7, value=6807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V101.left_6907`: side=side7, value=6907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V103.left_7007`: side=side7, value=7007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V105.left_7107`: side=side7, value=7107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V106.left_7207`: side=side7, value=7207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V108.left_7307`: side=side7, value=7307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V109.right_43`: side=side18, value=43, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V111.right_143`: side=side18, value=143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V112.right_243`: side=side18, value=243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V114.right_343`: side=side18, value=343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V116.right_443`: side=side18, value=443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V117.right_543`: side=side18, value=543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V119.right_643`: side=side18, value=643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V121.right_743`: side=side18, value=743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V123.right_843`: side=side18, value=843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V124.right_943`: side=side18, value=943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V126.right_1043`: side=side18, value=1043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V128.right_1143`: side=side18, value=1143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V129.right_1243`: side=side18, value=1243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V131.right_1343`: side=side18, value=1343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V132.right_1443`: side=side18, value=1443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V135.right_1543`: side=side18, value=1543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V137.right_1643`: side=side18, value=1643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V139.right_1743`: side=side18, value=1743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V140.right_1843`: side=side18, value=1843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V142.right_1943`: side=side18, value=1943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V143.right_2043`: side=side18, value=2043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V144.right_2143`: side=side18, value=2143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V145.right_2243`: side=side18, value=2243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V146.right_2343`: side=side18, value=2343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V148.right_2443`: side=side18, value=2443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V149.right_2543`: side=side18, value=2543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V151.right_2643`: side=side18, value=2643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V153.right_2743`: side=side18, value=2743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V155.right_2843`: side=side18, value=2843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V157.right_3043`: side=side18, value=3043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V158.right_3143`: side=side18, value=3143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V159.right_3243`: side=side18, value=3243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V161.right_3343`: side=side18, value=3343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V162.right_3443`: side=side18, value=3443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V164.right_3543`: side=side18, value=3543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V165.right_3643`: side=side18, value=3643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V167.right_3743`: side=side18, value=3743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V168.right_3843`: side=side18, value=3843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V169.right_3943`: side=side18, value=3943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V170.right_4043`: side=side18, value=4043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V171.right_4143`: side=side18, value=4143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V173.right_4243`: side=side18, value=4243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V174.right_4343`: side=side18, value=4343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V176.right_4443`: side=side18, value=4443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V177.right_4543`: side=side18, value=4543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V179.right_4643`: side=side18, value=4643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V180.right_4743`: side=side18, value=4743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V181.right_4843`: side=side18, value=4843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V182.right_4943`: side=side18, value=4943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V183.right_5043`: side=side18, value=5043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V185.right_5143`: side=side18, value=5143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V187.right_5243`: side=side18, value=5243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V189.right_5343`: side=side18, value=5343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V190.right_5443`: side=side18, value=5443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V192.right_5543`: side=side18, value=5543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V193.right_5643`: side=side18, value=5643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V195.right_5743`: side=side18, value=5743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V196.right_5843`: side=side18, value=5843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V197.right_5943`: side=side18, value=5943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V199.right_6043`: side=side18, value=6043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V200.right_6143`: side=side18, value=6143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V202.right_6243`: side=side18, value=6243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V203.right_6343`: side=side18, value=6343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V206.right_6443`: side=side18, value=6443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V207.right_6543`: side=side18, value=6543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V208.right_6643`: side=side18, value=6643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V209.right_6743`: side=side18, value=6743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V211.right_6843`: side=side18, value=6843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V213.right_6943`: side=side18, value=6943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V214.right_7043`: side=side18, value=7043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V215.right_7143`: side=side18, value=7143, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.json new file mode 100644 index 0000000..66c6012 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.json @@ -0,0 +1,216 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.839Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_529_out_19", + "successorRank": 6, + "conditionId": "square_529_outsider_19", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out529=19", + "parentSplitModulus": 4225, + "successorSplitModulus": 2235025, + "square": 529, + "divisor": 23, + "requiredOutsiderResidueModSquare": 19, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_529_outsider_19_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 19 (mod 529) and vertex ≡ 167 (mod 529), then outsider * vertex + 1 ≡ 0 (mod 529).", + "outsiderResidueModSquare": 19, + "vertexResidueModSquare": 167, + "square": 529, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V81.left_5457", + "value": 5457, + "residueModSquare": 167, + "expectedVertexResidueModSquare": 167, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out529=19, stabilize the 1 literal vertex-presence atoms whose first square witness is 529.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V81.left_5457", + "side": "side7", + "value": 5457, + "residues": { + "value": 5457, + "mod25": 7, + "modP": 10, + "modP2": 49 + }, + "residueModSquare": 167, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 28971214, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 54766, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 19, + "witnessOutsiderResidueModSquare": 19, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 28971214, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 54766, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 19, + "witnessOutsiderResidueModSquare": 19, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 28971214, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 54766, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 19, + "witnessOutsiderResidueModSquare": 19, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 28971214, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 54766, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 19, + "witnessOutsiderResidueModSquare": 19, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 28971214, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 54766, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 19, + "witnessOutsiderResidueModSquare": 19, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 28971214, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 54766, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 19, + "witnessOutsiderResidueModSquare": 19, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 28971214, + "quotient": 54766 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 28971214, + "quotient": 54766 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 28971214, + "quotient": 54766 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 28971214, + "quotient": 54766 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 28971214, + "quotient": 54766 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 28971214, + "quotient": 54766 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.md new file mode 100644 index 0000000..bb1e3bd --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19.md @@ -0,0 +1,42 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_529_out_19 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_529_outsider_19` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_529_outsider_19` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out529=19` +- Successor modulus: `2235025` +- Square witness: `529` +- Required outsider residue: `19` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `167 mod 529` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out529=19, stabilize the 1 literal vertex-presence atoms whose first square witness is 529. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 19 (mod 529) and vertex ≡ 167 (mod 529), then outsider * vertex + 1 ≡ 0 (mod 529). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V81.left_5457`: side=side7, value=5457, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.json new file mode 100644 index 0000000..f9f6511 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.json @@ -0,0 +1,216 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.839Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_841_out_263", + "successorRank": 7, + "conditionId": "square_841_outsider_263", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out841=263", + "parentSplitModulus": 4225, + "successorSplitModulus": 3553225, + "square": 841, + "divisor": 29, + "requiredOutsiderResidueModSquare": 263, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_841_outsider_263_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 263 (mod 841) and vertex ≡ 275 (mod 841), then outsider * vertex + 1 ≡ 0 (mod 841).", + "outsiderResidueModSquare": 263, + "vertexResidueModSquare": 275, + "square": 841, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V29.left_1957", + "value": 1957, + "residueModSquare": 275, + "expectedVertexResidueModSquare": 275, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out841=263, stabilize the 1 literal vertex-presence atoms whose first square witness is 841.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V29.left_1957", + "side": "side7", + "value": 1957, + "residues": { + "value": 1957, + "mod25": 7, + "modP": 7, + "modP2": 98 + }, + "residueModSquare": 275, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 10389714, + "firstSquareDivisorWitness": { + "divisor": 29, + "square": 841, + "quotient": 12354, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 263, + "witnessOutsiderResidueModSquare": 263, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 10389714, + "firstSquareDivisorWitness": { + "divisor": 29, + "square": 841, + "quotient": 12354, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 263, + "witnessOutsiderResidueModSquare": 263, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 10389714, + "firstSquareDivisorWitness": { + "divisor": 29, + "square": 841, + "quotient": 12354, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 263, + "witnessOutsiderResidueModSquare": 263, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 10389714, + "firstSquareDivisorWitness": { + "divisor": 29, + "square": 841, + "quotient": 12354, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 263, + "witnessOutsiderResidueModSquare": 263, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 10389714, + "firstSquareDivisorWitness": { + "divisor": 29, + "square": 841, + "quotient": 12354, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 263, + "witnessOutsiderResidueModSquare": 263, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 10389714, + "firstSquareDivisorWitness": { + "divisor": 29, + "square": 841, + "quotient": 12354, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 263, + "witnessOutsiderResidueModSquare": 263, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 10389714, + "quotient": 12354 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 10389714, + "quotient": 12354 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 10389714, + "quotient": 12354 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 10389714, + "quotient": 12354 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 10389714, + "quotient": 12354 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 10389714, + "quotient": 12354 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.md new file mode 100644 index 0000000..4f5f99f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263.md @@ -0,0 +1,42 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_841_out_263 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_841_outsider_263` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_841_outsider_263` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out841=263` +- Successor modulus: `3553225` +- Square witness: `841` +- Required outsider residue: `263` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `275 mod 841` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out841=263, stabilize the 1 literal vertex-presence atoms whose first square witness is 841. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 263 (mod 841) and vertex ≡ 275 (mod 841), then outsider * vertex + 1 ≡ 0 (mod 841). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V29.left_1957`: side=side7, value=1957, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.json new file mode 100644 index 0000000..924259e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.json @@ -0,0 +1,216 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.839Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_961_out_504", + "successorRank": 8, + "conditionId": "square_961_outsider_504", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out961=504", + "parentSplitModulus": 4225, + "successorSplitModulus": 4060225, + "square": 961, + "divisor": 31, + "requiredOutsiderResidueModSquare": 504, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_961_outsider_504_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 504 (mod 961) and vertex ≡ 368 (mod 961), then outsider * vertex + 1 ≡ 0 (mod 961).", + "outsiderResidueModSquare": 504, + "vertexResidueModSquare": 368, + "square": 961, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V115.right_368", + "value": 368, + "residueModSquare": 368, + "expectedVertexResidueModSquare": 368, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out961=504, stabilize the 1 literal vertex-presence atoms whose first square witness is 961.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V115.right_368", + "side": "side18", + "value": 368, + "residues": { + "value": 368, + "mod25": 18, + "modP": 4, + "modP2": 30 + }, + "residueModSquare": 368, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 1953713, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 504, + "witnessOutsiderResidueModSquare": 504, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 1953713, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 504, + "witnessOutsiderResidueModSquare": 504, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 1953713, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 504, + "witnessOutsiderResidueModSquare": 504, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 1953713, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 504, + "witnessOutsiderResidueModSquare": 504, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 1953713, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 504, + "witnessOutsiderResidueModSquare": 504, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 1953713, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 2033, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 504, + "witnessOutsiderResidueModSquare": 504, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 1953713, + "quotient": 2033 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 1953713, + "quotient": 2033 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 1953713, + "quotient": 2033 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 1953713, + "quotient": 2033 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 1953713, + "quotient": 2033 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 1953713, + "quotient": 2033 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.md new file mode 100644 index 0000000..7008b6f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504.md @@ -0,0 +1,42 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_961_out_504 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_961_outsider_504` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_961_outsider_504` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out961=504` +- Successor modulus: `4060225` +- Square witness: `961` +- Required outsider residue: `504` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `368 mod 961` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out961=504, stabilize the 1 literal vertex-presence atoms whose first square witness is 961. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 504 (mod 961) and vertex ≡ 368 (mod 961), then outsider * vertex + 1 ≡ 0 (mod 961). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V115.right_368`: side=side18, value=368, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.json new file mode 100644 index 0000000..3054380 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.json @@ -0,0 +1,5527 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.836Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8", + "parentPacketId": "p848_split_atom_packet_D2_1_persist_outP2_70_out25_9_smaller_side7", + "parentAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7", + "successorAtomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.square_9_out_8", + "successorRank": 2, + "conditionId": "square_9_outsider_8", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=70|out25=9|smaller=side7", + "successorSplitKey": "outP2=70|out25=9|smaller=side7|out9=8", + "parentSplitModulus": 4225, + "successorSplitModulus": 38025, + "square": 9, + "divisor": 3, + "requiredOutsiderResidueModSquare": 8, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_9_outsider_8_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 8 (mod 9) and vertex ≡ 1 (mod 9), then outsider * vertex + 1 ≡ 0 (mod 9).", + "outsiderResidueModSquare": 8, + "vertexResidueModSquare": 1, + "square": 9, + "affectedAtomCount": 48, + "verifiedAtomCount": 48, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V2.left_82", + "value": 82, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V8.left_532", + "value": 532, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V11.left_757", + "value": 757, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + 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"D2.1_persist_outP2=70_out25=9_smaller=side7.V191.right_5518", + "value": 5518, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V198.right_5968", + "value": 5968, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V201.right_6193", + "value": 6193, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V205.right_6418", + "value": 6418, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V212.right_6868", + "value": 6868, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=70|out25=9|smaller=side7|out9=8, stabilize the 48 literal vertex-presence atoms whose first square witness is 9.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { 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"side": "side18", + "value": 6418, + "residues": { + "value": 6418, + "mod25": 18, + "modP": 9, + "modP2": 165 + }, + "residueModSquare": 1, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 34073163, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 34073163, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 34073163, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 34073163, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 34073163, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 34073163, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 3785907, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.1_persist_outP2=70_out25=9_smaller=side7.V212.right_6868", + "side": "side18", + "value": 6868, + "residues": { + "value": 6868, + "mod25": 18, + "modP": 4, + "modP2": 108 + }, + "residueModSquare": 1, + "successorChecks": [ + { + "N": 7343, + "outsider": 5309, + "productPlusOne": 36462213, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 5309, + "productPlusOne": 36462213, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 5309, + "productPlusOne": 36462213, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 5309, + "productPlusOne": 36462213, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7366, + "outsider": 5309, + "productPlusOne": 36462213, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7368, + "outsider": 5309, + "productPlusOne": 36462213, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 4051357, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 8, + "witnessOutsiderResidueModSquare": 8, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 48, + "stabilizedAtomCount": 48, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 6, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 5309, + "productPlusOne": 435339, + "quotient": 48371 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 5309, + "productPlusOne": 435339, + "quotient": 48371 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 5309, + "productPlusOne": 435339, + "quotient": 48371 + }, + { + "witnessIndex": 3, + "N": 7357, + "outsider": 5309, + "productPlusOne": 435339, + "quotient": 48371 + }, + { + "witnessIndex": 4, + "N": 7366, + "outsider": 5309, + "productPlusOne": 435339, + "quotient": 48371 + }, + { + "witnessIndex": 5, + "N": 7368, + "outsider": 5309, + "productPlusOne": 435339, + "quotient": 48371 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.md new file mode 100644 index 0000000..1f96134 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8.md @@ -0,0 +1,89 @@ +# D2.1_persist_outP2=70_out25=9_smaller=side7.square_9_out_8 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_1_persist_outP2_70_out25_9_smaller_side7_square_9_outsider_8` +- Parent atom: `D2.1_persist_outP2=70_out25=9_smaller=side7` +- Condition: `square_9_outsider_8` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=70|out25=9|smaller=side7|out9=8` +- Successor modulus: `38025` +- Square witness: `9` +- Required outsider residue: `8` +- Affected atoms: `48` +- Stabilized atoms: `48` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `1 mod 9` + +## Theorem Obligation + +Under outP2=70|out25=9|smaller=side7|out9=8, stabilize the 48 literal vertex-presence atoms whose first square witness is 9. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 8 (mod 9) and vertex ≡ 1 (mod 9), then outsider * vertex + 1 ≡ 0 (mod 9). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V2.left_82`: side=side7, value=82, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V8.left_532`: side=side7, value=532, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V11.left_757`: side=side7, value=757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V15.left_982`: side=side7, value=982, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V21.left_1432`: side=side7, value=1432, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V24.left_1657`: side=side7, value=1657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V27.left_1882`: side=side7, value=1882, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V35.left_2332`: side=side7, value=2332, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V38.left_2557`: side=side7, value=2557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V41.left_2782`: side=side7, value=2782, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V47.left_3232`: side=side7, value=3232, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V51.left_3457`: side=side7, value=3457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V54.left_3682`: side=side7, value=3682, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V61.left_4132`: side=side7, value=4132, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V64.left_4357`: side=side7, value=4357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V68.left_4582`: side=side7, value=4582, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V75.left_5032`: side=side7, value=5032, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V78.left_5257`: side=side7, value=5257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V82.left_5482`: side=side7, value=5482, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V88.left_5932`: side=side7, value=5932, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V91.left_6157`: side=side7, value=6157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V94.left_6382`: side=side7, value=6382, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V100.left_6832`: side=side7, value=6832, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V104.left_7057`: side=side7, value=7057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V107.left_7282`: side=side7, value=7282, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V110.right_118`: side=side18, value=118, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V118.right_568`: side=side18, value=568, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V122.right_793`: side=side18, value=793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V125.right_1018`: side=side18, value=1018, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V133.right_1468`: side=side18, value=1468, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V138.right_1693`: side=side18, value=1693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V141.right_1918`: side=side18, value=1918, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V147.right_2368`: side=side18, value=2368, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V150.right_2593`: side=side18, value=2593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V154.right_2818`: side=side18, value=2818, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V160.right_3268`: side=side18, value=3268, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V163.right_3493`: side=side18, value=3493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V166.right_3718`: side=side18, value=3718, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V172.right_4168`: side=side18, value=4168, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V175.right_4393`: side=side18, value=4393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V178.right_4618`: side=side18, value=4618, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V184.right_5068`: side=side18, value=5068, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V188.right_5293`: side=side18, value=5293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V191.right_5518`: side=side18, value=5518, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V198.right_5968`: side=side18, value=5968, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V201.right_6193`: side=side18, value=6193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V205.right_6418`: side=side18, value=6418, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.1_persist_outP2=70_out25=9_smaller=side7.V212.right_6868`: side=side18, value=6868, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.json new file mode 100644 index 0000000..d42d2be --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.json @@ -0,0 +1,390 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_121_out_112", + "successorRank": 4, + "conditionId": "square_121_outsider_112", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out121=112", + "parentSplitModulus": 4225, + "successorSplitModulus": 511225, + "square": 121, + "divisor": 11, + "requiredOutsiderResidueModSquare": 112, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_121_outsider_112_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 112 (mod 121) and vertex ≡ 27 (mod 121), then outsider * vertex + 1 ≡ 0 (mod 121).", + "outsiderResidueModSquare": 112, + "vertexResidueModSquare": 27, + "square": 121, + "affectedAtomCount": 3, + "verifiedAtomCount": 3, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V9.left_632", + "value": 632, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V101.left_6682", + "value": 6682, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V142.right_2568", + "value": 2568, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out121=112, stabilize the 3 literal vertex-presence atoms whose first square witness is 121.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V9.left_632", + "side": "side7", + "value": 632, + "residues": { + "value": 632, + "mod25": 7, + "modP": 8, + "modP2": 125 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 3053193, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 3053193, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 3053193, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 3053193, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 3053193, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 25233, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V101.left_6682", + "side": "side7", + "value": 6682, + "residues": { + "value": 6682, + "mod25": 7, + "modP": 0, + "modP2": 91 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 32280743, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 32280743, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 32280743, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 32280743, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 32280743, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 266783, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V142.right_2568", + "side": "side18", + "value": 2568, + "residues": { + "value": 2568, + "mod25": 18, + "modP": 7, + "modP2": 33 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 12406009, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 12406009, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 12406009, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 12406009, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 12406009, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 102529, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 112, + "witnessOutsiderResidueModSquare": 112, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 3, + "stabilizedAtomCount": 3, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 3053193, + "quotient": 25233 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 3053193, + "quotient": 25233 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 3053193, + "quotient": 25233 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 3053193, + "quotient": 25233 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 3053193, + "quotient": 25233 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.md new file mode 100644 index 0000000..76fa242 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112.md @@ -0,0 +1,44 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_121_out_112 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_121_outsider_112` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_121_outsider_112` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out121=112` +- Successor modulus: `511225` +- Square witness: `121` +- Required outsider residue: `112` +- Affected atoms: `3` +- Stabilized atoms: `3` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `27 mod 121` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out121=112, stabilize the 3 literal vertex-presence atoms whose first square witness is 121. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 112 (mod 121) and vertex ≡ 27 (mod 121), then outsider * vertex + 1 ≡ 0 (mod 121). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V9.left_632`: side=side7, value=632, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V101.left_6682`: side=side7, value=6682, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V142.right_2568`: side=side18, value=2568, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.json new file mode 100644 index 0000000..b2be9f0 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.json @@ -0,0 +1,194 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_1849_out_1133", + "successorRank": 8, + "conditionId": "square_1849_outsider_1133", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out1849=1133", + "parentSplitModulus": 4225, + "successorSplitModulus": 7812025, + "square": 1849, + "divisor": 43, + "requiredOutsiderResidueModSquare": 1133, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_1849_outsider_1133_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 1133 (mod 1849) and vertex ≡ 235 (mod 1849), then outsider * vertex + 1 ≡ 0 (mod 1849).", + "outsiderResidueModSquare": 1133, + "vertexResidueModSquare": 235, + "square": 1849, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V86.left_5782", + "value": 5782, + "residueModSquare": 235, + "expectedVertexResidueModSquare": 235, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out1849=1133, stabilize the 1 literal vertex-presence atoms whose first square witness is 1849.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V86.left_5782", + "side": "side7", + "value": 5782, + "residues": { + "value": 5782, + "mod25": 7, + "modP": 10, + "modP2": 36 + }, + "residueModSquare": 235, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 27932843, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1133, + "witnessOutsiderResidueModSquare": 1133, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 27932843, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1133, + "witnessOutsiderResidueModSquare": 1133, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 27932843, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1133, + "witnessOutsiderResidueModSquare": 1133, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 27932843, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1133, + "witnessOutsiderResidueModSquare": 1133, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 27932843, + "firstSquareDivisorWitness": { + "divisor": 43, + "square": 1849, + "quotient": 15107, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1133, + "witnessOutsiderResidueModSquare": 1133, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 27932843, + "quotient": 15107 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 27932843, + "quotient": 15107 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 27932843, + "quotient": 15107 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 27932843, + "quotient": 15107 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 27932843, + "quotient": 15107 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.md new file mode 100644 index 0000000..2052766 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133.md @@ -0,0 +1,42 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_1849_out_1133 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_1849_outsider_1133` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_1849_outsider_1133` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out1849=1133` +- Successor modulus: `7812025` +- Square witness: `1849` +- Required outsider residue: `1133` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `235 mod 1849` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out1849=1133, stabilize the 1 literal vertex-presence atoms whose first square witness is 1849. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 1133 (mod 1849) and vertex ≡ 235 (mod 1849), then outsider * vertex + 1 ≡ 0 (mod 1849). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V86.left_5782`: side=side7, value=5782, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.json new file mode 100644 index 0000000..0c6c42a --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.json @@ -0,0 +1,194 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_289_out_207", + "successorRank": 6, + "conditionId": "square_289_outsider_207", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out289=207", + "parentSplitModulus": 4225, + "successorSplitModulus": 1221025, + "square": 289, + "divisor": 17, + "requiredOutsiderResidueModSquare": 207, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_289_outsider_207_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 207 (mod 289) and vertex ≡ 215 (mod 289), then outsider * vertex + 1 ≡ 0 (mod 289).", + "outsiderResidueModSquare": 207, + "vertexResidueModSquare": 215, + "square": 289, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V18.left_1082", + "value": 1082, + "residueModSquare": 215, + "expectedVertexResidueModSquare": 215, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out289=207, stabilize the 1 literal vertex-presence atoms whose first square witness is 289.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V18.left_1082", + "side": "side7", + "value": 1082, + "residues": { + "value": 1082, + "mod25": 7, + "modP": 3, + "modP2": 68 + }, + "residueModSquare": 215, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 5227143, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 207, + "witnessOutsiderResidueModSquare": 207, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 5227143, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 207, + "witnessOutsiderResidueModSquare": 207, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 5227143, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 207, + "witnessOutsiderResidueModSquare": 207, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 5227143, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 207, + "witnessOutsiderResidueModSquare": 207, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 5227143, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 18087, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 207, + "witnessOutsiderResidueModSquare": 207, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 5227143, + "quotient": 18087 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 5227143, + "quotient": 18087 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 5227143, + "quotient": 18087 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 5227143, + "quotient": 18087 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 5227143, + "quotient": 18087 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.md new file mode 100644 index 0000000..6906073 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207.md @@ -0,0 +1,42 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_289_out_207 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_289_outsider_207` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_289_outsider_207` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out289=207` +- Successor modulus: `1221025` +- Square witness: `289` +- Required outsider residue: `207` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `215 mod 289` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out289=207, stabilize the 1 literal vertex-presence atoms whose first square witness is 289. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 207 (mod 289) and vertex ≡ 215 (mod 289), then outsider * vertex + 1 ≡ 0 (mod 289). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V18.left_1082`: side=side7, value=1082, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.json new file mode 100644 index 0000000..64571a4 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.json @@ -0,0 +1,194 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_361_out_138", + "successorRank": 7, + "conditionId": "square_361_outsider_138", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out361=138", + "parentSplitModulus": 4225, + "successorSplitModulus": 1525225, + "square": 361, + "divisor": 19, + "requiredOutsiderResidueModSquare": 138, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_361_outsider_138_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 138 (mod 361) and vertex ≡ 34 (mod 361), then outsider * vertex + 1 ≡ 0 (mod 361).", + "outsiderResidueModSquare": 138, + "vertexResidueModSquare": 34, + "square": 361, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V98.left_6532", + "value": 6532, + "residueModSquare": 34, + "expectedVertexResidueModSquare": 34, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out361=138, stabilize the 1 literal vertex-presence atoms whose first square witness is 361.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V98.left_6532", + "side": "side7", + "value": 6532, + "residues": { + "value": 6532, + "mod25": 7, + "modP": 6, + "modP2": 110 + }, + "residueModSquare": 34, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 31556093, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 138, + "witnessOutsiderResidueModSquare": 138, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 31556093, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 138, + "witnessOutsiderResidueModSquare": 138, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 31556093, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 138, + "witnessOutsiderResidueModSquare": 138, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 31556093, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 138, + "witnessOutsiderResidueModSquare": 138, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 31556093, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 87413, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 138, + "witnessOutsiderResidueModSquare": 138, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 31556093, + "quotient": 87413 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 31556093, + "quotient": 87413 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 31556093, + "quotient": 87413 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 31556093, + "quotient": 87413 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 31556093, + "quotient": 87413 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.md new file mode 100644 index 0000000..b1dbc63 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138.md @@ -0,0 +1,42 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_361_out_138 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_361_outsider_138` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_361_outsider_138` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out361=138` +- Successor modulus: `1525225` +- Square witness: `361` +- Required outsider residue: `138` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `34 mod 361` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out361=138, stabilize the 1 literal vertex-presence atoms whose first square witness is 361. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 138 (mod 361) and vertex ≡ 34 (mod 361), then outsider * vertex + 1 ≡ 0 (mod 361). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V98.left_6532`: side=side7, value=6532, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.json new file mode 100644 index 0000000..32e74e6 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.json @@ -0,0 +1,880 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_49_out_29", + "successorRank": 3, + "conditionId": "square_49_outsider_29", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out49=29", + "parentSplitModulus": 4225, + "successorSplitModulus": 207025, + "square": 49, + "divisor": 7, + "requiredOutsiderResidueModSquare": 29, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_49_outsider_29_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 29 (mod 49) and vertex ≡ 27 (mod 49), then outsider * vertex + 1 ≡ 0 (mod 49).", + "outsiderResidueModSquare": 29, + "vertexResidueModSquare": 27, + "square": 49, + "affectedAtomCount": 8, + "verifiedAtomCount": 8, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V16.left_1007", + "value": 1007, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V34.left_2232", + "value": 2232, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V70.left_4682", + "value": 4682, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V89.left_5907", + "value": 5907, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V112.right_468", + "value": 468, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V148.right_2918", + "value": 2918, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V165.right_4143", + "value": 4143, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V183.right_5368", + "value": 5368, + "residueModSquare": 27, + "expectedVertexResidueModSquare": 27, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out49=29, stabilize the 8 literal vertex-presence atoms whose first square witness is 49.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V16.left_1007", + "side": "side7", + "value": 1007, + "residues": { + "value": 1007, + "mod25": 7, + "modP": 6, + "modP2": 162 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 4864818, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 4864818, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 4864818, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 4864818, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 4864818, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 99282, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V34.left_2232", + "side": "side7", + "value": 2232, + "residues": { + "value": 2232, + "mod25": 7, + "modP": 9, + "modP2": 35 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 10782793, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 10782793, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 10782793, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 10782793, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 10782793, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 220057, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V70.left_4682", + "side": "side7", + "value": 4682, + "residues": { + "value": 4682, + "mod25": 7, + "modP": 2, + "modP2": 119 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 22618743, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 22618743, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 22618743, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 22618743, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 22618743, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 461607, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V89.left_5907", + "side": "side7", + "value": 5907, + "residues": { + "value": 5907, + "mod25": 7, + "modP": 5, + "modP2": 161 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 28536718, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 28536718, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 28536718, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 28536718, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 28536718, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 582382, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V112.right_468", + "side": "side18", + "value": 468, + "residues": { + "value": 468, + "mod25": 18, + "modP": 0, + "modP2": 130 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 2260909, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 2260909, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 2260909, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 2260909, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 2260909, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 46141, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V148.right_2918", + "side": "side18", + "value": 2918, + "residues": { + "value": 2918, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 14096859, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 14096859, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 14096859, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 14096859, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 14096859, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 287691, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V165.right_4143", + "side": "side18", + "value": 4143, + "residues": { + "value": 4143, + "mod25": 18, + "modP": 9, + "modP2": 87 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 20014834, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 20014834, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 20014834, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 20014834, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 20014834, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 408466, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V183.right_5368", + "side": "side18", + "value": 5368, + "residues": { + "value": 5368, + "mod25": 18, + "modP": 12, + "modP2": 129 + }, + "residueModSquare": 27, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 25932809, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 25932809, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 25932809, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 25932809, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 25932809, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 529241, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 29, + "witnessOutsiderResidueModSquare": 29, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 8, + "stabilizedAtomCount": 8, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 4864818, + "quotient": 99282 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 4864818, + "quotient": 99282 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 4864818, + "quotient": 99282 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 4864818, + "quotient": 99282 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 4864818, + "quotient": 99282 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.md new file mode 100644 index 0000000..fce09b4 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29.md @@ -0,0 +1,49 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_49_out_29 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_49_outsider_29` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_49_outsider_29` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out49=29` +- Successor modulus: `207025` +- Square witness: `49` +- Required outsider residue: `29` +- Affected atoms: `8` +- Stabilized atoms: `8` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `27 mod 49` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out49=29, stabilize the 8 literal vertex-presence atoms whose first square witness is 49. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 29 (mod 49) and vertex ≡ 27 (mod 49), then outsider * vertex + 1 ≡ 0 (mod 49). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V16.left_1007`: side=side7, value=1007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V34.left_2232`: side=side7, value=2232, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V70.left_4682`: side=side7, value=4682, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V89.left_5907`: side=side7, value=5907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V112.right_468`: side=side18, value=468, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V148.right_2918`: side=side18, value=2918, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V165.right_4143`: side=side18, value=4143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V183.right_5368`: side=side18, value=5368, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.json new file mode 100644 index 0000000..e1e9cf3 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.json @@ -0,0 +1,14012 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_4_out_3", + "successorRank": 1, + "conditionId": "square_4_outsider_3", + "priority": "highest_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out4=3", + "parentSplitModulus": 4225, + "successorSplitModulus": 16900, + "square": 4, + "divisor": 2, + "requiredOutsiderResidueModSquare": 3, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_4_outsider_3_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 3 (mod 4) and vertex ≡ 1 (mod 4), then outsider * vertex + 1 ≡ 0 (mod 4).", + "outsiderResidueModSquare": 3, + "vertexResidueModSquare": 1, + "square": 4, + "affectedAtomCount": 142, + "verifiedAtomCount": 142, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V2.left_57", + "value": 57, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V3.left_157", + "value": 157, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V4.left_257", + "value": 257, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + 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"D2.2_persist_outP2=99_out25=6_smaller=side18.V201.right_6693", + "value": 6693, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V202.right_6793", + "value": 6793, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V204.right_6893", + "value": 6893, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V205.right_6993", + "value": 6993, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V207.right_7093", + "value": 7093, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V208.right_7193", + "value": 7193, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V210.right_7293", + "value": 7293, + "residueModSquare": 1, + "expectedVertexResidueModSquare": 1, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out4=3, stabilize the 142 literal vertex-presence atoms whose first square witness is 4.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V2.left_57", + "side": "side7", + "value": 57, + "residues": { + "value": 57, + "mod25": 7, + "modP": 5, + "modP2": 57 + }, + "residueModSquare": 1, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 275368, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 68842, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 3, + "witnessOutsiderResidueModSquare": 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"N": 7307, + "outsider": 4831, + "productPlusOne": 275368, + "quotient": 68842 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 275368, + "quotient": 68842 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 275368, + "quotient": 68842 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 275368, + "quotient": 68842 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 275368, + "quotient": 68842 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.md new file mode 100644 index 0000000..fb6fc10 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3.md @@ -0,0 +1,183 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_4_out_3 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_4_outsider_3` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_4_outsider_3` +- Priority: `highest_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out4=3` +- Successor modulus: `16900` +- Square witness: `4` +- Required outsider residue: `3` +- Affected atoms: `142` +- Stabilized atoms: `142` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `1 mod 4` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out4=3, stabilize the 142 literal vertex-presence atoms whose first square witness is 4. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 3 (mod 4) and vertex ≡ 1 (mod 4), then outsider * vertex + 1 ≡ 0 (mod 4). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V2.left_57`: side=side7, value=57, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V3.left_157`: side=side7, value=157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V4.left_257`: side=side7, value=257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V5.left_357`: side=side7, value=357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V6.left_457`: side=side7, value=457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V8.left_557`: side=side7, value=557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V10.left_657`: side=side7, value=657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V12.left_757`: side=side7, value=757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V13.left_857`: side=side7, value=857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V15.left_957`: side=side7, value=957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V17.left_1057`: side=side7, value=1057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V19.left_1157`: side=side7, value=1157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V20.left_1257`: side=side7, value=1257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V22.left_1357`: side=side7, value=1357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V24.left_1457`: side=side7, value=1457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V25.left_1557`: side=side7, value=1557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V27.left_1657`: side=side7, value=1657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V28.left_1757`: side=side7, value=1757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V30.left_1857`: side=side7, value=1857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V31.left_1957`: side=side7, value=1957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V32.left_2057`: side=side7, value=2057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V33.left_2157`: side=side7, value=2157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V35.left_2257`: side=side7, value=2257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V37.left_2357`: side=side7, value=2357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V38.left_2457`: side=side7, value=2457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V40.left_2557`: side=side7, value=2557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V41.left_2657`: side=side7, value=2657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V43.left_2757`: side=side7, value=2757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V44.left_2857`: side=side7, value=2857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V45.left_2957`: side=side7, value=2957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V46.left_3057`: side=side7, value=3057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V47.left_3157`: side=side7, value=3157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V49.left_3257`: side=side7, value=3257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V50.left_3357`: side=side7, value=3357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V52.left_3457`: side=side7, value=3457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V53.left_3557`: side=side7, value=3557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V55.left_3657`: side=side7, value=3657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V56.left_3757`: side=side7, value=3757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V58.left_3857`: side=side7, value=3857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V59.left_3957`: side=side7, value=3957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V60.left_4057`: side=side7, value=4057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V62.left_4157`: side=side7, value=4157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V63.left_4257`: side=side7, value=4257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V65.left_4357`: side=side7, value=4357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V66.left_4457`: side=side7, value=4457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V68.left_4557`: side=side7, value=4557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V69.left_4657`: side=side7, value=4657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V71.left_4757`: side=side7, value=4757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V72.left_4857`: side=side7, value=4857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V73.left_4957`: side=side7, value=4957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V75.left_5057`: side=side7, value=5057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V76.left_5157`: side=side7, value=5157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V78.left_5257`: side=side7, value=5257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V79.left_5357`: side=side7, value=5357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V81.left_5457`: side=side7, value=5457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V83.left_5557`: side=side7, value=5557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V84.left_5657`: side=side7, value=5657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V85.left_5757`: side=side7, value=5757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V87.left_5857`: side=side7, value=5857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V90.left_5957`: side=side7, value=5957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V91.left_6057`: side=side7, value=6057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V93.left_6157`: side=side7, value=6157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V94.left_6257`: side=side7, value=6257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V96.left_6357`: side=side7, value=6357, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V97.left_6457`: side=side7, value=6457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V99.left_6557`: side=side7, value=6557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V100.left_6657`: side=side7, value=6657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V102.left_6757`: side=side7, value=6757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V104.left_6857`: side=side7, value=6857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V105.left_6957`: side=side7, value=6957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V107.right_93`: side=side18, value=93, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V108.right_193`: side=side18, value=193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V110.right_293`: side=side18, value=293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V111.right_393`: side=side18, value=393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V113.right_493`: side=side18, value=493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V115.right_593`: side=side18, value=593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V116.right_693`: side=side18, value=693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V118.right_793`: side=side18, value=793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V119.right_893`: side=side18, value=893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V121.right_993`: side=side18, value=993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V122.right_1093`: side=side18, value=1093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V123.right_1193`: side=side18, value=1193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V124.right_1293`: side=side18, value=1293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V125.right_1393`: side=side18, value=1393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V127.right_1493`: side=side18, value=1493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V128.right_1593`: side=side18, value=1593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V130.right_1693`: side=side18, value=1693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V131.right_1793`: side=side18, value=1793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V133.right_1893`: side=side18, value=1893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V134.right_1993`: side=side18, value=1993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V135.right_2093`: side=side18, value=2093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V136.right_2193`: side=side18, value=2193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V137.right_2293`: side=side18, value=2293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V139.right_2393`: side=side18, value=2393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V140.right_2493`: side=side18, value=2493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V143.right_2593`: side=side18, value=2593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V144.right_2693`: side=side18, value=2693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V146.right_2793`: side=side18, value=2793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V147.right_2893`: side=side18, value=2893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V149.right_2993`: side=side18, value=2993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V150.right_3093`: side=side18, value=3093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V151.right_3193`: side=side18, value=3193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V153.right_3293`: side=side18, value=3293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V154.right_3393`: side=side18, value=3393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V156.right_3493`: side=side18, value=3493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V157.right_3593`: side=side18, value=3593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V159.right_3693`: side=side18, value=3693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V160.right_3793`: side=side18, value=3793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V161.right_3893`: side=side18, value=3893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V162.right_3993`: side=side18, value=3993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V163.right_4093`: side=side18, value=4093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V166.right_4193`: side=side18, value=4193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V167.right_4293`: side=side18, value=4293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V169.right_4393`: side=side18, value=4393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V172.right_4593`: side=side18, value=4593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V173.right_4693`: side=side18, value=4693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V175.right_4793`: side=side18, value=4793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V176.right_4893`: side=side18, value=4893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V177.right_4993`: side=side18, value=4993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V179.right_5093`: side=side18, value=5093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V180.right_5193`: side=side18, value=5193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V182.right_5293`: side=side18, value=5293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V184.right_5393`: side=side18, value=5393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V186.right_5493`: side=side18, value=5493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V187.right_5593`: side=side18, value=5593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V188.right_5693`: side=side18, value=5693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V189.right_5793`: side=side18, value=5793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V190.right_5893`: side=side18, value=5893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V192.right_5993`: side=side18, value=5993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V193.right_6093`: side=side18, value=6093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V195.right_6193`: side=side18, value=6193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V196.right_6293`: side=side18, value=6293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V198.right_6393`: side=side18, value=6393, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V199.right_6493`: side=side18, value=6493, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V200.right_6593`: side=side18, value=6593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V201.right_6693`: side=side18, value=6693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V202.right_6793`: side=side18, value=6793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V204.right_6893`: side=side18, value=6893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V205.right_6993`: side=side18, value=6993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V207.right_7093`: side=side18, value=7093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V208.right_7193`: side=side18, value=7193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V210.right_7293`: side=side18, value=7293, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.json new file mode 100644 index 0000000..d79a3c3 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.json @@ -0,0 +1,292 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_961_out_26", + "successorRank": 5, + "conditionId": "square_961_outsider_26", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out961=26", + "parentSplitModulus": 4225, + "successorSplitModulus": 4060225, + "square": 961, + "divisor": 31, + "requiredOutsiderResidueModSquare": 26, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_961_outsider_26_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 26 (mod 961) and vertex ≡ 924 (mod 961), then outsider * vertex + 1 ≡ 0 (mod 961).", + "outsiderResidueModSquare": 26, + "vertexResidueModSquare": 924, + "square": 961, + "affectedAtomCount": 2, + "verifiedAtomCount": 2, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V57.left_3807", + "value": 3807, + "residueModSquare": 924, + "expectedVertexResidueModSquare": 924, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V174.right_4768", + "value": 4768, + "residueModSquare": 924, + "expectedVertexResidueModSquare": 924, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out961=26, stabilize the 2 literal vertex-presence atoms whose first square witness is 961.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V57.left_3807", + "side": "side7", + "value": 3807, + "residues": { + "value": 3807, + "mod25": 7, + "modP": 11, + "modP2": 89 + }, + "residueModSquare": 924, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 18391618, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 18391618, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 18391618, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 18391618, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 18391618, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 19138, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V174.right_4768", + "side": "side18", + "value": 4768, + "residues": { + "value": 4768, + "mod25": 18, + "modP": 10, + "modP2": 36 + }, + "residueModSquare": 924, + "successorChecks": [ + { + "N": 7307, + "outsider": 4831, + "productPlusOne": 23034209, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7318, + "outsider": 4831, + "productPlusOne": 23034209, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7337, + "outsider": 4831, + "productPlusOne": 23034209, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7343, + "outsider": 4831, + "productPlusOne": 23034209, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + }, + { + "N": 7357, + "outsider": 4831, + "productPlusOne": 23034209, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 23969, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 26, + "witnessOutsiderResidueModSquare": 26, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 2, + "stabilizedAtomCount": 2, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 18391618, + "quotient": 19138 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 18391618, + "quotient": 19138 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 18391618, + "quotient": 19138 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 18391618, + "quotient": 19138 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 18391618, + "quotient": 19138 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.md new file mode 100644 index 0000000..69a11af --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26.md @@ -0,0 +1,43 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_961_out_26 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_961_outsider_26` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_961_outsider_26` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out961=26` +- Successor modulus: `4060225` +- Square witness: `961` +- Required outsider residue: `26` +- Affected atoms: `2` +- Stabilized atoms: `2` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `924 mod 961` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out961=26, stabilize the 2 literal vertex-presence atoms whose first square witness is 961. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 26 (mod 961) and vertex ≡ 924 (mod 961), then outsider * vertex + 1 ≡ 0 (mod 961). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V57.left_3807`: side=side7, value=3807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V174.right_4768`: side=side18, value=4768, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.json new file mode 100644 index 0000000..6df3cc9 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.json @@ -0,0 +1,4800 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.842Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7", + "parentPacketId": "p848_split_atom_packet_D2_2_persist_outP2_99_out25_6_smaller_side18", + "parentAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18", + "successorAtomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.square_9_out_7", + "successorRank": 2, + "conditionId": "square_9_outsider_7", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=6|smaller=side18", + "successorSplitKey": "outP2=99|out25=6|smaller=side18|out9=7", + "parentSplitModulus": 4225, + "successorSplitModulus": 38025, + "square": 9, + "divisor": 3, + "requiredOutsiderResidueModSquare": 7, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_9_outsider_7_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 7 (mod 9) and vertex ≡ 5 (mod 9), then outsider * vertex + 1 ≡ 0 (mod 9).", + "outsiderResidueModSquare": 7, + "vertexResidueModSquare": 5, + "square": 9, + "affectedAtomCount": 48, + "verifiedAtomCount": 48, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V1.left_32", + "value": 32, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V7.left_482", + "value": 482, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V11.left_707", + "value": 707, + "residueModSquare": 5, + 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"D2.2_persist_outP2=99_out25=6_smaller=side18.V194.right_6143", + "value": 6143, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V197.right_6368", + "value": 6368, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V203.right_6818", + "value": 6818, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V206.right_7043", + "value": 7043, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.2_persist_outP2=99_out25=6_smaller=side18.V209.right_7268", + "value": 7268, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=6|smaller=side18|out9=7, stabilize the 48 literal vertex-presence atoms whose first square witness is 9.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + 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"witnessRowCount": 5, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7307, + "outsider": 4831, + "productPlusOne": 154593, + "quotient": 17177 + }, + { + "witnessIndex": 1, + "N": 7318, + "outsider": 4831, + "productPlusOne": 154593, + "quotient": 17177 + }, + { + "witnessIndex": 2, + "N": 7337, + "outsider": 4831, + "productPlusOne": 154593, + "quotient": 17177 + }, + { + "witnessIndex": 3, + "N": 7343, + "outsider": 4831, + "productPlusOne": 154593, + "quotient": 17177 + }, + { + "witnessIndex": 4, + "N": 7357, + "outsider": 4831, + "productPlusOne": 154593, + "quotient": 17177 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.md new file mode 100644 index 0000000..5db8a41 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7.md @@ -0,0 +1,89 @@ +# D2.2_persist_outP2=99_out25=6_smaller=side18.square_9_out_7 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_2_persist_outP2_99_out25_6_smaller_side18_square_9_outsider_7` +- Parent atom: `D2.2_persist_outP2=99_out25=6_smaller=side18` +- Condition: `square_9_outsider_7` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=6|smaller=side18|out9=7` +- Successor modulus: `38025` +- Square witness: `9` +- Required outsider residue: `7` +- Affected atoms: `48` +- Stabilized atoms: `48` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `5 mod 9` + +## Theorem Obligation + +Under outP2=99|out25=6|smaller=side18|out9=7, stabilize the 48 literal vertex-presence atoms whose first square witness is 9. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 7 (mod 9) and vertex ≡ 5 (mod 9), then outsider * vertex + 1 ≡ 0 (mod 9). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V1.left_32`: side=side7, value=32, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V7.left_482`: side=side7, value=482, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V11.left_707`: side=side7, value=707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V14.left_932`: side=side7, value=932, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V23.left_1382`: side=side7, value=1382, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V26.left_1607`: side=side7, value=1607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V29.left_1832`: side=side7, value=1832, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V36.left_2282`: side=side7, value=2282, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V39.left_2507`: side=side7, value=2507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V42.left_2732`: side=side7, value=2732, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V48.left_3182`: side=side7, value=3182, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V51.left_3407`: side=side7, value=3407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V54.left_3632`: side=side7, value=3632, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V61.left_4082`: side=side7, value=4082, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V64.left_4307`: side=side7, value=4307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V67.left_4532`: side=side7, value=4532, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V74.left_4982`: side=side7, value=4982, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V77.left_5207`: side=side7, value=5207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V80.left_5432`: side=side7, value=5432, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V88.left_5882`: side=side7, value=5882, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V92.left_6107`: side=side7, value=6107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V95.left_6332`: side=side7, value=6332, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V103.left_6782`: side=side7, value=6782, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V106.right_68`: side=side18, value=68, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V114.right_518`: side=side18, value=518, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V117.right_743`: side=side18, value=743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V120.right_968`: side=side18, value=968, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V126.right_1418`: side=side18, value=1418, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V129.right_1643`: side=side18, value=1643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V132.right_1868`: side=side18, value=1868, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V138.right_2318`: side=side18, value=2318, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V141.right_2543`: side=side18, value=2543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V145.right_2768`: side=side18, value=2768, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V152.right_3218`: side=side18, value=3218, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V155.right_3443`: side=side18, value=3443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V158.right_3668`: side=side18, value=3668, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V164.right_4118`: side=side18, value=4118, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V168.right_4343`: side=side18, value=4343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V171.right_4568`: side=side18, value=4568, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V178.right_5018`: side=side18, value=5018, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V181.right_5243`: side=side18, value=5243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V185.right_5468`: side=side18, value=5468, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V191.right_5918`: side=side18, value=5918, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V194.right_6143`: side=side18, value=6143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V197.right_6368`: side=side18, value=6368, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V203.right_6818`: side=side18, value=6818, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V206.right_7043`: side=side18, value=7043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.2_persist_outP2=99_out25=6_smaller=side18.V209.right_7268`: side=side18, value=7268, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.json new file mode 100644 index 0000000..6da40a7 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.json @@ -0,0 +1,182 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_121_out_95", + "successorRank": 4, + "conditionId": "square_121_outsider_95", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out121=95", + "parentSplitModulus": 4225, + "successorSplitModulus": 511225, + "square": 121, + "divisor": 11, + "requiredOutsiderResidueModSquare": 95, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_121_outsider_95_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 95 (mod 121) and vertex ≡ 14 (mod 121), then outsider * vertex + 1 ≡ 0 (mod 121).", + "outsiderResidueModSquare": 95, + "vertexResidueModSquare": 14, + "square": 121, + "affectedAtomCount": 3, + "verifiedAtomCount": 3, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V16.left_982", + "value": 982, + "residueModSquare": 14, + "expectedVertexResidueModSquare": 14, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V104.left_7032", + "value": 7032, + "residueModSquare": 14, + "expectedVertexResidueModSquare": 14, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V151.right_2918", + "value": 2918, + "residueModSquare": 14, + "expectedVertexResidueModSquare": 14, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out121=95, stabilize the 3 literal vertex-presence atoms whose first square witness is 121.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V16.left_982", + "side": "side7", + "value": 982, + "residues": { + "value": 982, + "mod25": 7, + "modP": 7, + "modP2": 137 + }, + "residueModSquare": 14, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1756799, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 14519, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 95, + "witnessOutsiderResidueModSquare": 95, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V104.left_7032", + "side": "side7", + "value": 7032, + "residues": { + "value": 7032, + "mod25": 7, + "modP": 12, + "modP2": 103 + }, + "residueModSquare": 14, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12580249, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 103969, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 95, + "witnessOutsiderResidueModSquare": 95, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V151.right_2918", + "side": "side18", + "value": 2918, + "residues": { + "value": 2918, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "residueModSquare": 14, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5220303, + "firstSquareDivisorWitness": { + "divisor": 11, + "square": 121, + "quotient": 43143, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 95, + "witnessOutsiderResidueModSquare": 95, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 3, + "stabilizedAtomCount": 3, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 1756799, + "quotient": 14519 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.md new file mode 100644 index 0000000..1384263 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95.md @@ -0,0 +1,44 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_121_out_95 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_121_outsider_95` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_121_outsider_95` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out121=95` +- Successor modulus: `511225` +- Square witness: `121` +- Required outsider residue: `95` +- Affected atoms: `3` +- Stabilized atoms: `3` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `14 mod 121` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out121=95, stabilize the 3 literal vertex-presence atoms whose first square witness is 121. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 95 (mod 121) and vertex ≡ 14 (mod 121), then outsider * vertex + 1 ≡ 0 (mod 121). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V16.left_982`: side=side7, value=982, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V104.left_7032`: side=side7, value=7032, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V151.right_2918`: side=side18, value=2918, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.json new file mode 100644 index 0000000..3d91df1 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.json @@ -0,0 +1,106 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_1369_out_420", + "successorRank": 9, + "conditionId": "square_1369_outsider_420", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out1369=420", + "parentSplitModulus": 4225, + "successorSplitModulus": 5784025, + "square": 1369, + "divisor": 37, + "requiredOutsiderResidueModSquare": 420, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_1369_outsider_420_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 420 (mod 1369) and vertex ≡ 942 (mod 1369), then outsider * vertex + 1 ≡ 0 (mod 1369).", + "outsiderResidueModSquare": 420, + "vertexResidueModSquare": 942, + "square": 1369, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V205.right_6418", + "value": 6418, + "residueModSquare": 942, + "expectedVertexResidueModSquare": 942, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out1369=420, stabilize the 1 literal vertex-presence atoms whose first square witness is 1369.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V205.right_6418", + "side": "side18", + "value": 6418, + "residues": { + "value": 6418, + "mod25": 18, + "modP": 9, + "modP2": 165 + }, + "residueModSquare": 942, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11481803, + "firstSquareDivisorWitness": { + "divisor": 37, + "square": 1369, + "quotient": 8387, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 420, + "witnessOutsiderResidueModSquare": 420, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 11481803, + "quotient": 8387 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.md new file mode 100644 index 0000000..7f89b8e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420.md @@ -0,0 +1,42 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_1369_out_420 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_1369_outsider_420` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_1369_outsider_420` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out1369=420` +- Successor modulus: `5784025` +- Square witness: `1369` +- Required outsider residue: `420` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `942 mod 1369` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out1369=420, stabilize the 1 literal vertex-presence atoms whose first square witness is 1369. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 420 (mod 1369) and vertex ≡ 942 (mod 1369), then outsider * vertex + 1 ≡ 0 (mod 1369). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V205.right_6418`: side=side18, value=6418, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.json new file mode 100644 index 0000000..f357e2f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.json @@ -0,0 +1,144 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_289_out_55", + "successorRank": 5, + "conditionId": "square_289_outsider_55", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out289=55", + "parentSplitModulus": 4225, + "successorSplitModulus": 1221025, + "square": 289, + "divisor": 17, + "requiredOutsiderResidueModSquare": 55, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_289_outsider_55_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 55 (mod 289) and vertex ≡ 21 (mod 289), then outsider * vertex + 1 ≡ 0 (mod 289).", + "outsiderResidueModSquare": 55, + "vertexResidueModSquare": 21, + "square": 289, + "affectedAtomCount": 2, + "verifiedAtomCount": 2, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V102.left_6957", + "value": 6957, + "residueModSquare": 21, + "expectedVertexResidueModSquare": 21, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V210.right_6668", + "value": 6668, + "residueModSquare": 21, + "expectedVertexResidueModSquare": 21, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out289=55, stabilize the 2 literal vertex-presence atoms whose first square witness is 289.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V102.left_6957", + "side": "side7", + "value": 6957, + "residues": { + "value": 6957, + "mod25": 7, + "modP": 2, + "modP2": 28 + }, + "residueModSquare": 21, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12446074, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 43066, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 55, + "witnessOutsiderResidueModSquare": 55, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V210.right_6668", + "side": "side18", + "value": 6668, + "residues": { + "value": 6668, + "mod25": 18, + "modP": 12, + "modP2": 77 + }, + "residueModSquare": 21, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11929053, + "firstSquareDivisorWitness": { + "divisor": 17, + "square": 289, + "quotient": 41277, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 55, + "witnessOutsiderResidueModSquare": 55, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 2, + "stabilizedAtomCount": 2, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 12446074, + "quotient": 43066 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.md new file mode 100644 index 0000000..36a5477 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55.md @@ -0,0 +1,43 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_289_out_55 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_289_outsider_55` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_289_outsider_55` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out289=55` +- Successor modulus: `1221025` +- Square witness: `289` +- Required outsider residue: `55` +- Affected atoms: `2` +- Stabilized atoms: `2` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `21 mod 289` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out289=55, stabilize the 2 literal vertex-presence atoms whose first square witness is 289. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 55 (mod 289) and vertex ≡ 21 (mod 289), then outsider * vertex + 1 ≡ 0 (mod 289). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V102.left_6957`: side=side7, value=6957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V210.right_6668`: side=side18, value=6668, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.json new file mode 100644 index 0000000..4f2e5b8 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.json @@ -0,0 +1,106 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_361_out_345", + "successorRank": 7, + "conditionId": "square_361_outsider_345", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out361=345", + "parentSplitModulus": 4225, + "successorSplitModulus": 1525225, + "square": 361, + "divisor": 19, + "requiredOutsiderResidueModSquare": 345, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_361_outsider_345_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 345 (mod 361) and vertex ≡ 158 (mod 361), then outsider * vertex + 1 ≡ 0 (mod 361).", + "outsiderResidueModSquare": 345, + "vertexResidueModSquare": 158, + "square": 361, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V164.right_3768", + "value": 3768, + "residueModSquare": 158, + "expectedVertexResidueModSquare": 158, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out361=345, stabilize the 1 literal vertex-presence atoms whose first square witness is 361.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V164.right_3768", + "side": "side18", + "value": 3768, + "residues": { + "value": 3768, + "mod25": 18, + "modP": 11, + "modP2": 50 + }, + "residueModSquare": 158, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 6740953, + "firstSquareDivisorWitness": { + "divisor": 19, + "square": 361, + "quotient": 18673, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 345, + "witnessOutsiderResidueModSquare": 345, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 6740953, + "quotient": 18673 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.md new file mode 100644 index 0000000..588059f --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345.md @@ -0,0 +1,42 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_361_out_345 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_361_outsider_345` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_361_outsider_345` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out361=345` +- Successor modulus: `1525225` +- Square witness: `361` +- Required outsider residue: `345` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `158 mod 361` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out361=345, stabilize the 1 literal vertex-presence atoms whose first square witness is 361. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 345 (mod 361) and vertex ≡ 158 (mod 361), then outsider * vertex + 1 ≡ 0 (mod 361). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V164.right_3768`: side=side18, value=3768, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.json new file mode 100644 index 0000000..ae96e77 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.json @@ -0,0 +1,334 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_49_out_25", + "successorRank": 3, + "conditionId": "square_49_outsider_25", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out49=25", + "parentSplitModulus": 4225, + "successorSplitModulus": 207025, + "square": 49, + "divisor": 7, + "requiredOutsiderResidueModSquare": 25, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_49_outsider_25_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 25 (mod 49) and vertex ≡ 47 (mod 49), then outsider * vertex + 1 ≡ 0 (mod 49).", + "outsiderResidueModSquare": 25, + "vertexResidueModSquare": 47, + "square": 49, + "affectedAtomCount": 7, + "verifiedAtomCount": 7, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V12.left_782", + "value": 782, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V50.left_3232", + "value": 3232, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V66.left_4457", + "value": 4457, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V84.left_5682", + "value": 5682, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V131.right_1468", + "value": 1468, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V147.right_2693", + "value": 2693, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V167.right_3918", + "value": 3918, + "residueModSquare": 47, + "expectedVertexResidueModSquare": 47, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out49=25, stabilize the 7 literal vertex-presence atoms whose first square witness is 49.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V12.left_782", + "side": "side7", + "value": 782, + "residues": { + "value": 782, + "mod25": 7, + "modP": 2, + "modP2": 106 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 1398999, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 28551, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V50.left_3232", + "side": "side7", + "value": 3232, + "residues": { + "value": 3232, + "mod25": 7, + "modP": 8, + "modP2": 21 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 5782049, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 118001, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V66.left_4457", + "side": "side7", + "value": 4457, + "residues": { + "value": 4457, + "mod25": 7, + "modP": 11, + "modP2": 63 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7973574, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 162726, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V84.left_5682", + "side": "side7", + "value": 5682, + "residues": { + "value": 5682, + "mod25": 7, + "modP": 1, + "modP2": 105 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10165099, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 207451, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V131.right_1468", + "side": "side18", + "value": 1468, + "residues": { + "value": 1468, + "mod25": 18, + "modP": 12, + "modP2": 116 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2626253, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 53597, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V147.right_2693", + "side": "side18", + "value": 2693, + "residues": { + "value": 2693, + "mod25": 18, + "modP": 2, + "modP2": 158 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 4817778, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 98322, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V167.right_3918", + "side": "side18", + "value": 3918, + "residues": { + "value": 3918, + "mod25": 18, + "modP": 5, + "modP2": 31 + }, + "residueModSquare": 47, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7009303, + "firstSquareDivisorWitness": { + "divisor": 7, + "square": 49, + "quotient": 143047, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 25, + "witnessOutsiderResidueModSquare": 25, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 7, + "stabilizedAtomCount": 7, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 1398999, + "quotient": 28551 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.md new file mode 100644 index 0000000..c1e815e --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25.md @@ -0,0 +1,48 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_49_out_25 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_49_outsider_25` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_49_outsider_25` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out49=25` +- Successor modulus: `207025` +- Square witness: `49` +- Required outsider residue: `25` +- Affected atoms: `7` +- Stabilized atoms: `7` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `47 mod 49` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out49=25, stabilize the 7 literal vertex-presence atoms whose first square witness is 49. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 25 (mod 49) and vertex ≡ 47 (mod 49), then outsider * vertex + 1 ≡ 0 (mod 49). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V12.left_782`: side=side7, value=782, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V50.left_3232`: side=side7, value=3232, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V66.left_4457`: side=side7, value=4457, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V84.left_5682`: side=side7, value=5682, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V131.right_1468`: side=side18, value=1468, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V147.right_2693`: side=side18, value=2693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V167.right_3918`: side=side18, value=3918, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.json new file mode 100644 index 0000000..7e60fb3 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.json @@ -0,0 +1,5578 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_4_out_1", + "successorRank": 1, + "conditionId": "square_4_outsider_1", + "priority": "highest_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out4=1", + "parentSplitModulus": 4225, + "successorSplitModulus": 16900, + "square": 4, + "divisor": 2, + "requiredOutsiderResidueModSquare": 1, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_4_outsider_1_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 1 (mod 4) and vertex ≡ 3 (mod 4), then outsider * vertex + 1 ≡ 0 (mod 4).", + "outsiderResidueModSquare": 1, + "vertexResidueModSquare": 3, + "square": 4, + "affectedAtomCount": 145, + "verifiedAtomCount": 145, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V1.left_7", + "value": 7, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V3.left_107", + "value": 107, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V4.left_207", + "value": 207, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V6.left_307", + "value": 307, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V7.left_407", + "value": 407, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V9.left_507", + "value": 507, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V10.left_607", + "value": 607, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V11.left_707", + "value": 707, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V13.left_807", + "value": 807, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": 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"D2.3_persist_outP2=99_out25=14_smaller=side7.V213.right_6843", + "value": 6843, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V214.right_6943", + "value": 6943, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V215.right_7043", + "value": 7043, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V216.right_7143", + "value": 7143, + "residueModSquare": 3, + "expectedVertexResidueModSquare": 3, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out4=1, stabilize the 145 literal vertex-presence atoms whose first square witness is 4.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V1.left_7", + "side": "side7", + "value": 7, + "residues": { + "value": 7, + "mod25": 7, + "modP": 7, + "modP2": 7 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, 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3060532, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V214.right_6943", + "side": "side18", + "value": 6943, + "residues": { + "value": 6943, + "mod25": 18, + "modP": 1, + "modP2": 14 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12421028, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3105257, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V215.right_7043", + "side": "side18", + "value": 7043, + "residues": { + "value": 7043, + "mod25": 18, + "modP": 10, + "modP2": 114 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12599928, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3149982, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V216.right_7143", + "side": "side18", + "value": 7143, + "residues": { + "value": 7143, + "mod25": 18, + "modP": 6, + "modP2": 45 + }, + "residueModSquare": 3, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12778828, + "firstSquareDivisorWitness": { + "divisor": 2, + "square": 4, + "quotient": 3194707, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1, + "witnessOutsiderResidueModSquare": 1, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 145, + "stabilizedAtomCount": 145, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 12524, + "quotient": 3131 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.md new file mode 100644 index 0000000..7a743f1 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1.md @@ -0,0 +1,186 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_4_out_1 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_4_outsider_1` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_4_outsider_1` +- Priority: `highest_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out4=1` +- Successor modulus: `16900` +- Square witness: `4` +- Required outsider residue: `1` +- Affected atoms: `145` +- Stabilized atoms: `145` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `3 mod 4` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out4=1, stabilize the 145 literal vertex-presence atoms whose first square witness is 4. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 1 (mod 4) and vertex ≡ 3 (mod 4), then outsider * vertex + 1 ≡ 0 (mod 4). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V1.left_7`: side=side7, value=7, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V3.left_107`: side=side7, value=107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V4.left_207`: side=side7, value=207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V6.left_307`: side=side7, value=307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V7.left_407`: side=side7, value=407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V9.left_507`: side=side7, value=507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V10.left_607`: side=side7, value=607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V11.left_707`: side=side7, value=707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V13.left_807`: side=side7, value=807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V14.left_907`: side=side7, value=907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V17.left_1007`: side=side7, value=1007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V18.left_1107`: side=side7, value=1107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V20.left_1207`: side=side7, value=1207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V22.left_1307`: side=side7, value=1307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V24.left_1407`: side=side7, value=1407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V25.left_1507`: side=side7, value=1507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V27.left_1607`: side=side7, value=1607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V28.left_1707`: side=side7, value=1707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V29.left_1807`: side=side7, value=1807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V31.left_1907`: side=side7, value=1907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V32.left_2007`: side=side7, value=2007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V34.left_2107`: side=side7, value=2107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V35.left_2207`: side=side7, value=2207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V37.left_2307`: side=side7, value=2307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V38.left_2407`: side=side7, value=2407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V39.left_2507`: side=side7, value=2507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V40.left_2607`: side=side7, value=2607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V41.left_2707`: side=side7, value=2707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V43.left_2807`: side=side7, value=2807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V44.left_2907`: side=side7, value=2907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V46.left_3007`: side=side7, value=3007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V47.left_3107`: side=side7, value=3107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V49.left_3207`: side=side7, value=3207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V51.left_3307`: side=side7, value=3307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V52.left_3407`: side=side7, value=3407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V53.left_3507`: side=side7, value=3507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V54.left_3607`: side=side7, value=3607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V56.left_3707`: side=side7, value=3707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V57.left_3807`: side=side7, value=3807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V59.left_3907`: side=side7, value=3907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V60.left_4007`: side=side7, value=4007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V62.left_4107`: side=side7, value=4107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V63.left_4207`: side=side7, value=4207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V64.left_4307`: side=side7, value=4307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V65.left_4407`: side=side7, value=4407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V67.left_4507`: side=side7, value=4507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V69.left_4607`: side=side7, value=4607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V70.left_4707`: side=side7, value=4707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V72.left_4807`: side=side7, value=4807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V73.left_4907`: side=side7, value=4907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V75.left_5007`: side=side7, value=5007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V76.left_5107`: side=side7, value=5107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V77.left_5207`: side=side7, value=5207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V78.left_5307`: side=side7, value=5307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V79.left_5407`: side=side7, value=5407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V82.left_5607`: side=side7, value=5607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V85.left_5707`: side=side7, value=5707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V86.left_5807`: side=side7, value=5807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V88.left_5907`: side=side7, value=5907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V89.left_6007`: side=side7, value=6007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V90.left_6107`: side=side7, value=6107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V91.left_6207`: side=side7, value=6207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V92.left_6307`: side=side7, value=6307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V94.left_6407`: side=side7, value=6407, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V95.left_6507`: side=side7, value=6507, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V97.left_6607`: side=side7, value=6607, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V98.left_6707`: side=side7, value=6707, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V100.left_6807`: side=side7, value=6807, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V101.left_6907`: side=side7, value=6907, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V103.left_7007`: side=side7, value=7007, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V105.left_7107`: side=side7, value=7107, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V106.left_7207`: side=side7, value=7207, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V108.left_7307`: side=side7, value=7307, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V109.right_43`: side=side18, value=43, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V111.right_143`: side=side18, value=143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V112.right_243`: side=side18, value=243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V115.right_343`: side=side18, value=343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V116.right_443`: side=side18, value=443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V118.right_543`: side=side18, value=543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V119.right_643`: side=side18, value=643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V120.right_743`: side=side18, value=743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V121.right_843`: side=side18, value=843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V122.right_943`: side=side18, value=943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V124.right_1043`: side=side18, value=1043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V125.right_1143`: side=side18, value=1143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V127.right_1243`: side=side18, value=1243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V128.right_1343`: side=side18, value=1343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V130.right_1443`: side=side18, value=1443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V132.right_1543`: side=side18, value=1543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V133.right_1643`: side=side18, value=1643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V134.right_1743`: side=side18, value=1743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V135.right_1843`: side=side18, value=1843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V137.right_1943`: side=side18, value=1943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V138.right_2043`: side=side18, value=2043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V140.right_2143`: side=side18, value=2143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V141.right_2243`: side=side18, value=2243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V143.right_2343`: side=side18, value=2343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V144.right_2443`: side=side18, value=2443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V145.right_2543`: side=side18, value=2543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V146.right_2643`: side=side18, value=2643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V148.right_2743`: side=side18, value=2743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V150.right_2843`: side=side18, value=2843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V152.right_2943`: side=side18, value=2943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V154.right_3043`: side=side18, value=3043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V155.right_3143`: side=side18, value=3143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V157.right_3243`: side=side18, value=3243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V158.right_3343`: side=side18, value=3343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V159.right_3443`: side=side18, value=3443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V160.right_3543`: side=side18, value=3543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V161.right_3643`: side=side18, value=3643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V163.right_3743`: side=side18, value=3743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V165.right_3843`: side=side18, value=3843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V168.right_3943`: side=side18, value=3943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V169.right_4043`: side=side18, value=4043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V172.right_4143`: side=side18, value=4143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V173.right_4243`: side=side18, value=4243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V174.right_4343`: side=side18, value=4343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V175.right_4443`: side=side18, value=4443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V177.right_4543`: side=side18, value=4543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V180.right_4643`: side=side18, value=4643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V181.right_4743`: side=side18, value=4743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V183.right_4843`: side=side18, value=4843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V184.right_4943`: side=side18, value=4943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V186.right_5043`: side=side18, value=5043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V187.right_5143`: side=side18, value=5143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V188.right_5243`: side=side18, value=5243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V189.right_5343`: side=side18, value=5343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V190.right_5443`: side=side18, value=5443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V192.right_5543`: side=side18, value=5543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V193.right_5643`: side=side18, value=5643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V195.right_5743`: side=side18, value=5743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V196.right_5843`: side=side18, value=5843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V198.right_5943`: side=side18, value=5943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V199.right_6043`: side=side18, value=6043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V200.right_6143`: side=side18, value=6143, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V201.right_6243`: side=side18, value=6243, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V203.right_6343`: side=side18, value=6343, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V206.right_6443`: side=side18, value=6443, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V207.right_6543`: side=side18, value=6543, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V209.right_6643`: side=side18, value=6643, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V211.right_6743`: side=side18, value=6743, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V213.right_6843`: side=side18, value=6843, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V214.right_6943`: side=side18, value=6943, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V215.right_7043`: side=side18, value=7043, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V216.right_7143`: side=side18, value=7143, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.json new file mode 100644 index 0000000..204d415 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.json @@ -0,0 +1,144 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_529_out_202", + "successorRank": 6, + "conditionId": "square_529_outsider_202", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out529=202", + "parentSplitModulus": 4225, + "successorSplitModulus": 2235025, + "square": 529, + "divisor": 23, + "requiredOutsiderResidueModSquare": 202, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_529_outsider_202_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 202 (mod 529) and vertex ≡ 474 (mod 529), then outsider * vertex + 1 ≡ 0 (mod 529).", + "outsiderResidueModSquare": 202, + "vertexResidueModSquare": 474, + "square": 529, + "affectedAtomCount": 2, + "verifiedAtomCount": 2, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V26.left_1532", + "value": 1532, + "residueModSquare": 474, + "expectedVertexResidueModSquare": 474, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V202.right_6293", + "value": 6293, + "residueModSquare": 474, + "expectedVertexResidueModSquare": 474, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out529=202, stabilize the 2 literal vertex-presence atoms whose first square witness is 529.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V26.left_1532", + "side": "side7", + "value": 1532, + "residues": { + "value": 1532, + "mod25": 7, + "modP": 11, + "modP2": 11 + }, + "residueModSquare": 474, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 2740749, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 5181, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 202, + "witnessOutsiderResidueModSquare": 202, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V202.right_6293", + "side": "side18", + "value": 6293, + "residues": { + "value": 6293, + "mod25": 18, + "modP": 1, + "modP2": 40 + }, + "residueModSquare": 474, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11258178, + "firstSquareDivisorWitness": { + "divisor": 23, + "square": 529, + "quotient": 21282, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 202, + "witnessOutsiderResidueModSquare": 202, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 2, + "stabilizedAtomCount": 2, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 2740749, + "quotient": 5181 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.md new file mode 100644 index 0000000..0320d11 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202.md @@ -0,0 +1,43 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_529_out_202 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_529_outsider_202` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_529_outsider_202` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out529=202` +- Successor modulus: `2235025` +- Square witness: `529` +- Required outsider residue: `202` +- Affected atoms: `2` +- Stabilized atoms: `2` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `474 mod 529` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out529=202, stabilize the 2 literal vertex-presence atoms whose first square witness is 529. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 202 (mod 529) and vertex ≡ 474 (mod 529), then outsider * vertex + 1 ≡ 0 (mod 529). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V26.left_1532`: side=side7, value=1532, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V202.right_6293`: side=side18, value=6293, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.json new file mode 100644 index 0000000..6170529 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.json @@ -0,0 +1,106 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_7921_out_1789", + "successorRank": 10, + "conditionId": "square_7921_outsider_1789", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out7921=1789", + "parentSplitModulus": 4225, + "successorSplitModulus": 33466225, + "square": 7921, + "divisor": 89, + "requiredOutsiderResidueModSquare": 1789, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_7921_outsider_1789_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 1789 (mod 7921) and vertex ≡ 4618 (mod 7921), then outsider * vertex + 1 ≡ 0 (mod 7921).", + "outsiderResidueModSquare": 1789, + "vertexResidueModSquare": 4618, + "square": 7921, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V179.right_4618", + "value": 4618, + "residueModSquare": 4618, + "expectedVertexResidueModSquare": 4618, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out7921=1789, stabilize the 1 literal vertex-presence atoms whose first square witness is 7921.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V179.right_4618", + "side": "side18", + "value": 4618, + "residues": { + "value": 4618, + "mod25": 18, + "modP": 3, + "modP2": 55 + }, + "residueModSquare": 4618, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 8261603, + "firstSquareDivisorWitness": { + "divisor": 89, + "square": 7921, + "quotient": 1043, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 1789, + "witnessOutsiderResidueModSquare": 1789, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 8261603, + "quotient": 1043 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.md new file mode 100644 index 0000000..4160d30 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789.md @@ -0,0 +1,42 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_7921_out_1789 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_7921_outsider_1789` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_7921_outsider_1789` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out7921=1789` +- Successor modulus: `33466225` +- Square witness: `7921` +- Required outsider residue: `1789` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `4618 mod 7921` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out7921=1789, stabilize the 1 literal vertex-presence atoms whose first square witness is 7921. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 1789 (mod 7921) and vertex ≡ 4618 (mod 7921), then outsider * vertex + 1 ≡ 0 (mod 7921). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V179.right_4618`: side=side18, value=4618, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.json new file mode 100644 index 0000000..9b81bbd --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.json @@ -0,0 +1,106 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_961_out_828", + "successorRank": 8, + "conditionId": "square_961_outsider_828", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out961=828", + "parentSplitModulus": 4225, + "successorSplitModulus": 4060225, + "square": 961, + "divisor": 31, + "requiredOutsiderResidueModSquare": 828, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_961_outsider_828_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 828 (mod 961) and vertex ≡ 224 (mod 961), then outsider * vertex + 1 ≡ 0 (mod 961).", + "outsiderResidueModSquare": 828, + "vertexResidueModSquare": 224, + "square": 961, + "affectedAtomCount": 1, + "verifiedAtomCount": 1, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V170.right_4068", + "value": 4068, + "residueModSquare": 224, + "expectedVertexResidueModSquare": 224, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out961=828, stabilize the 1 literal vertex-presence atoms whose first square witness is 961.", + "proofBoundary": "This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too." + }, + "affectedVertexPresenceAtoms": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V170.right_4068", + "side": "side18", + "value": 4068, + "residues": { + "value": 4068, + "mod25": 18, + "modP": 12, + "modP2": 12 + }, + "residueModSquare": 224, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 7277653, + "firstSquareDivisorWitness": { + "divisor": 31, + "square": 961, + "quotient": 7573, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 828, + "witnessOutsiderResidueModSquare": 828, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 1, + "stabilizedAtomCount": 1, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 7277653, + "quotient": 7573 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.md new file mode 100644 index 0000000..c755166 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828.md @@ -0,0 +1,42 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_961_out_828 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_961_outsider_828` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_961_outsider_828` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out961=828` +- Successor modulus: `4060225` +- Square witness: `961` +- Required outsider residue: `828` +- Affected atoms: `1` +- Stabilized atoms: `1` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `224 mod 961` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out961=828, stabilize the 1 literal vertex-presence atoms whose first square witness is 961. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 828 (mod 961) and vertex ≡ 224 (mod 961), then outsider * vertex + 1 ≡ 0 (mod 961). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V170.right_4068`: side=side18, value=4068, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.json b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.json new file mode 100644 index 0000000..b60bd51 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.json @@ -0,0 +1,1930 @@ +{ + "schema": "erdos.p848_split_atom_successor_packet/1", + "generatedAt": "2026-04-14T11:46:09.844Z", + "problemId": "848", + "packetId": "p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7", + "parentPacketId": "p848_split_atom_packet_D2_3_persist_outP2_99_out25_14_smaller_side7", + "parentAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7", + "successorAtomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.square_9_out_7", + "successorRank": 2, + "conditionId": "square_9_outsider_7", + "priority": "dominant_refinement_successor", + "status": "candidate_successor_obligation_verified", + "splitRefinement": { + "parentSplitKey": "outP2=99|out25=14|smaller=side7", + "successorSplitKey": "outP2=99|out25=14|smaller=side7|out9=7", + "parentSplitModulus": 4225, + "successorSplitModulus": 38025, + "square": 9, + "divisor": 3, + "requiredOutsiderResidueModSquare": 7, + "compatibleWithCurrentSplit": true + }, + "symbolicVertexFamilyLemma": { + "lemmaId": "square_9_outsider_7_vertex_family", + "status": "symbolic_vertex_family_lemma_verified", + "statement": "If outsider ≡ 7 (mod 9) and vertex ≡ 5 (mod 9), then outsider * vertex + 1 ≡ 0 (mod 9).", + "outsiderResidueModSquare": 7, + "vertexResidueModSquare": 5, + "square": 9, + "affectedAtomCount": 49, + "verifiedAtomCount": 49, + "failedAtomCount": 0, + "checks": [ + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V2.left_32", + "value": 32, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V5.left_257", + "value": 257, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V8.left_482", + "value": 482, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V15.left_932", + "value": 932, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V19.left_1157", + "value": 1157, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V23.left_1382", + "value": 1382, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V30.left_1832", + "value": 1832, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V33.left_2057", + "value": 2057, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V36.left_2282", + "value": 2282, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V42.left_2732", + "value": 2732, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V45.left_2957", + "value": 2957, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V48.left_3182", + "value": 3182, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V55.left_3632", + "value": 3632, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V58.left_3857", + "value": 3857, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V61.left_4082", + "value": 4082, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, 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"D2.3_persist_outP2=99_out25=14_smaller=side7.V191.right_5468", + "value": 5468, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V194.right_5693", + "value": 5693, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V197.right_5918", + "value": 5918, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V204.right_6368", + "value": 6368, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V208.right_6593", + "value": 6593, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V212.right_6818", + "value": 6818, + "residueModSquare": 5, + "expectedVertexResidueModSquare": 5, + "vertexMatchesResidueFamily": true, + "productPlusOneResidueModSquare": 0 + } + ], + "proofBoundary": "This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas." + }, + "theoremObligation": { + "kind": "square_residue_vertex_presence_subobligation", + "parentObligationId": "D2_p13_matching_lower_bound", + "targetObligationId": "D4_matching_bound_implies_sMaxMixed_bound", + "statement": "Under outP2=99|out25=14|smaller=side7|out9=7, stabilize the 49 literal vertex-presence atoms whose first square witness is 9.", + 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"firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 997467, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V191.right_5468", + "side": "side18", + "value": 5468, + "residues": { + "value": 5468, + "mod25": 18, + "modP": 8, + "modP2": 60 + }, + "residueModSquare": 5, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 9782253, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1086917, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V194.right_5693", + "side": "side18", + "value": 5693, + "residues": { + "value": 5693, + "mod25": 18, + "modP": 12, + "modP2": 116 + }, + "residueModSquare": 5, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10184778, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1131642, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V197.right_5918", + "side": "side18", + "value": 5918, + "residues": { + "value": 5918, + "mod25": 18, + "modP": 3, + "modP2": 3 + }, + "residueModSquare": 5, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 10587303, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1176367, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V204.right_6368", + "side": "side18", + "value": 6368, + "residues": { + "value": 6368, + "mod25": 18, + "modP": 11, + "modP2": 115 + }, + "residueModSquare": 5, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11392353, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1265817, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V208.right_6593", + "side": "side18", + "value": 6593, + "residues": { + "value": 6593, + "mod25": 18, + "modP": 2, + "modP2": 2 + }, + "residueModSquare": 5, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 11794878, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1310542, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + }, + { + "atomId": "D2.3_persist_outP2=99_out25=14_smaller=side7.V212.right_6818", + "side": "side18", + "value": 6818, + "residues": { + "value": 6818, + "mod25": 18, + "modP": 6, + "modP2": 58 + }, + "residueModSquare": 5, + "successorChecks": [ + { + "N": 7343, + "outsider": 1789, + "productPlusOne": 12197403, + "firstSquareDivisorWitness": { + "divisor": 3, + "square": 9, + "quotient": 1355267, + "stableUnderCurrentSplitModulus": false + }, + "requiredOutsiderResidueModSquare": 7, + "witnessOutsiderResidueModSquare": 7, + "witnessSatisfiesSuccessorResidue": true, + "stableUnderSuccessorSplitModulus": true + } + ], + "status": "bounded_presence_stabilized_by_successor_square_residue" + } + ], + "checks": { + "affectedAtomCount": 49, + "stabilizedAtomCount": 49, + "failedAtomCount": 0, + "allAffectedAtomsPresent": true, + "allAffectedAtomsStabilized": true, + "witnessRowCount": 1, + "witnessRows": [ + { + "witnessIndex": 0, + "N": 7343, + "outsider": 1789, + "productPlusOne": 57249, + "quotient": 6361 + } + ] + }, + "nextTheoremActions": [ + "Promote this square-residue successor into a symbolic vertex-family lemma.", + "After this condition is proved, attack the next sibling square-residue successor condition.", + "Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled." + ] +} diff --git a/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.md b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.md new file mode 100644 index 0000000..5cf9a39 --- /dev/null +++ b/packs/number-theory/problems/848/SPLIT_ATOM_PACKETS/SUCCESSORS/D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7.md @@ -0,0 +1,90 @@ +# D2.3_persist_outP2=99_out25=14_smaller=side7.square_9_out_7 + +This is a focused successor packet emitted from a Problem 848 split atom refinement condition. + +## Summary + +- Packet id: `p848_split_atom_successor_packet_D2_3_persist_outP2_99_out25_14_smaller_side7_square_9_outsider_7` +- Parent atom: `D2.3_persist_outP2=99_out25=14_smaller=side7` +- Condition: `square_9_outsider_7` +- Priority: `dominant_refinement_successor` +- Status: `candidate_successor_obligation_verified` +- Successor split: `outP2=99|out25=14|smaller=side7|out9=7` +- Successor modulus: `38025` +- Square witness: `9` +- Required outsider residue: `7` +- Affected atoms: `49` +- Stabilized atoms: `49` +- Failed atoms: `0` +- Symbolic family lemma: `symbolic_vertex_family_lemma_verified` +- Vertex residue family: `5 mod 9` + +## Theorem Obligation + +Under outP2=99|out25=14|smaller=side7|out9=7, stabilize the 49 literal vertex-presence atoms whose first square witness is 9. + +Boundary: This successor packet stabilizes one vertex-presence subfamily only; it is not a full split lemma until the sibling refinement conditions and matching/edge obligations are promoted too. + +## Symbolic Vertex-Family Lemma + +If outsider ≡ 7 (mod 9) and vertex ≡ 5 (mod 9), then outsider * vertex + 1 ≡ 0 (mod 9). + +Boundary: This proves the square-residue vertex-presence family for this successor condition only; sibling conditions still need their own family lemmas. + +## Next Theorem Actions + +- Promote this square-residue successor into a symbolic vertex-family lemma. +- After this condition is proved, attack the next sibling square-residue successor condition. +- Do not treat this sub-obligation as a full split proof until all sibling vertex conditions and edge obstructions are handled. + +## Affected Vertex Atoms + +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V2.left_32`: side=side7, value=32, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V5.left_257`: side=side7, value=257, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V8.left_482`: side=side7, value=482, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V15.left_932`: side=side7, value=932, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V19.left_1157`: side=side7, value=1157, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V23.left_1382`: side=side7, value=1382, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V30.left_1832`: side=side7, value=1832, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V33.left_2057`: side=side7, value=2057, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V36.left_2282`: side=side7, value=2282, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V42.left_2732`: side=side7, value=2732, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V45.left_2957`: side=side7, value=2957, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V48.left_3182`: side=side7, value=3182, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V55.left_3632`: side=side7, value=3632, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V58.left_3857`: side=side7, value=3857, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V61.left_4082`: side=side7, value=4082, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V68.left_4532`: side=side7, value=4532, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V71.left_4757`: side=side7, value=4757, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V74.left_4982`: side=side7, value=4982, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V80.left_5432`: side=side7, value=5432, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V83.left_5657`: side=side7, value=5657, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V87.left_5882`: side=side7, value=5882, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V93.left_6332`: side=side7, value=6332, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V96.left_6557`: side=side7, value=6557, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V99.left_6782`: side=side7, value=6782, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V107.left_7232`: side=side7, value=7232, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V110.right_68`: side=side18, value=68, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V114.right_293`: side=side18, value=293, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V117.right_518`: side=side18, value=518, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V123.right_968`: side=side18, value=968, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V126.right_1193`: side=side18, value=1193, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V129.right_1418`: side=side18, value=1418, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V136.right_1868`: side=side18, value=1868, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V139.right_2093`: side=side18, value=2093, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V142.right_2318`: side=side18, value=2318, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V149.right_2768`: side=side18, value=2768, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V153.right_2993`: side=side18, value=2993, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V156.right_3218`: side=side18, value=3218, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V162.right_3668`: side=side18, value=3668, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V166.right_3893`: side=side18, value=3893, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V171.right_4118`: side=side18, value=4118, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V178.right_4568`: side=side18, value=4568, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V182.right_4793`: side=side18, value=4793, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V185.right_5018`: side=side18, value=5018, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V191.right_5468`: side=side18, value=5468, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V194.right_5693`: side=side18, value=5693, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V197.right_5918`: side=side18, value=5918, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V204.right_6368`: side=side18, value=6368, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V208.right_6593`: side=side18, value=6593, status=`bounded_presence_stabilized_by_successor_square_residue` +- `D2.3_persist_outP2=99_out25=14_smaller=side7.V212.right_6818`: side=side18, value=6818, status=`bounded_presence_stabilized_by_successor_square_residue` diff --git a/research/frontier-engine/.npmignore b/research/frontier-engine/.npmignore new file mode 100644 index 0000000..da404ca --- /dev/null +++ b/research/frontier-engine/.npmignore @@ -0,0 +1,4 @@ +artifacts/ +build/ +src/*.egg-info/ +experiments/**/live-frontier-sync/