Erdos1038: assimilate R19-R23 PC salvo and playback updates

.github/workflows/erdos1038-agent-work.yml

@@ -19,15 +19,15 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Check out repository
-        uses: actions/checkout@v4
+        uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683  # v4.2.2
 
       - name: Set up Python
-        uses: actions/setup-python@v5
+        uses: actions/setup-python@0b93645e9fea7318ecaed2b359559ac225c90a2b  # v5.3.0
         with:
           python-version: "3.11"
 
       - name: Set up Rust
-        uses: dtolnay/rust-toolchain@stable
+        uses: dtolnay/rust-toolchain@29eef336d9b2848a0b548edc03f92a220660cdb8  # stable @ 2025
 
       - name: Compile Python runners
         run: |

Erdos1038/agent-work/MANIFEST.sha256

@@ -1,7 +1,7 @@
 786629101c2b52a7a64d88879b2ff9f1fb66b1bc8536e576109fd676580211e5  Erdos1038/agent-work/.gitignore
 c7cca5ba0c8dd85f05028e2be9bcef3220f637e1b9555cf97b749ea9e1102378  Erdos1038/agent-work/CURRENT_FRONTIER.md
 7efaa1855ad3e87579d337dd321e10780e2b0dd2bfbb44672108796d6e638959  Erdos1038/agent-work/EVEREST_ROUTE_FRAME.md
-75cecbc3ec7b8920963aa69469b1bcd405e12185042f5844f496c57cb4660413  Erdos1038/agent-work/EVEREST_ROUTE_PLAYBACK.jsonl
+d9a601000e91771719e42bf8fb2ee94b7e3c8b84e766fc8e8710731aa9ff2319  Erdos1038/agent-work/EVEREST_ROUTE_PLAYBACK.jsonl
 ad206fde9b683936339ed7d4674badf9be7bc14adb56d95432696c06c996a10b  Erdos1038/agent-work/MODE2_GIT_HANDOFF.md
 d5e2985caf54a66ba3a5ab258065e9d1c51fa797589cf9dbd612440ecc3bb598  Erdos1038/agent-work/PR_REVIEW_PROTOCOL.md
 424110ead03f6c808bd1450dac45fb18590158832c809ac1ca465b3b3c1c0237  Erdos1038/agent-work/PUBLIC_CONTEXT.json

Erdos1038/agent-work/problem-at-hand/EXTERNAL-REVIEW-ASSIMILATION-ROUND_19/MANIFEST.json

@@ -0,0 +1,43 @@
+{
+  "packet_id": "EXTERNAL-REVIEW-ASSIMILATION-ROUND_19",
+  "round_id": "ROUND_19",
+  "created_utc": "2026-05-28T03:50:00Z",
+  "external_agent": "perplexity-computer",
+  "external_dispatch": {
+    "linear_comment_id": "348613ea-3a75-44bd-9a68-84cbf391113a",
+    "linear_issue": "KEN-5",
+    "dispatched_utc": "2026-05-28T03:31:02Z",
+    "mode": "MODE_2_INTENSE_SOLVE_END_TO_END",
+    "tracks": ["Track B (primary): canonical hyperelliptic basis seed", "Track A (adversarial parallel): falsifier hunt"]
+  },
+  "bundle_provenance": {
+    "source_path": "/Users/kenbengoetxea/Downloads/jobs/ROUND_19/",
+    "substrate_path": "Research-Hub/perplexity-substrate/projects/erdos-1038/jobs/ROUND_19/",
+    "bundle_manifest": "Research-Hub/perplexity-substrate/projects/erdos-1038/jobs/ROUND_19/BUNDLE.sha256",
+    "files": [
+      {"name": "CANONICAL_BASIS_SEED.md", "sha256": "9248f3f25248ea8ab140ebc59c34d9dc58e72fbe37325d43201f04f156eec6f8"},
+      {"name": "FALSIFIER_SWEEP_DESIGN.md", "sha256": "e26cbf4242e9f8335f81cafc64de74b3b4dba5855dc980d15387c5294ee3d848"},
+      {"name": "NULL_FALSIFIER_REPORT.json", "sha256": "a0c8f0c467b6d55b6e2e05fc65066ae07f3132b63fb92196553dd4efebd03187"},
+      {"name": "round19_canonical_falsifier_sweep.py", "sha256": "71b99628f1b33f610e5f743998009b47e9d5c01da3ad142504a94f24b7fd9a25"}
+    ]
+  },
+  "verdicts": {
+    "CANONICAL_BASIS_SEED.md": "ACCEPT_AS_STARTING_PROPOSAL",
+    "FALSIFIER_SWEEP_DESIGN.md": "ACCEPT_SCOPE_LIMITED",
+    "NULL_FALSIFIER_REPORT.json": "ACCEPT_SCOPE_LIMITED",
+    "round19_canonical_falsifier_sweep.py": "ACCEPT_AS_F64_SCAFFOLD"
+  },
+  "status": "ASSIMILATED",
+  "claim_level_at_assimilation": 0,
+  "claim_ceiling": "Route proposal only; no #1038 theorem advance; six receipts still absent.",
+  "scope_tags": ["F64_SAMPLED_ONLY", "SCAFFOLD_ONLY"],
+  "forbidden_claims_confirmed": [
+    "Does not claim #1038 solved",
+    "Does not claim altitude movement",
+    "Does not treat external prose as evidence",
+    "Does not turn synthetic fixtures into theorem pass",
+    "Does not promote claim level"
+  ],
+  "playback_event_id": "evt-20260528-round-19-complete",
+  "next_local_gate": "EXP-MATH-ERDOS1038-PHI-K-HYPERELLIPTIC-CANONICAL-BASIS-INTERVAL-SEED-20260527-01"
+}

Erdos1038/agent-work/problem-at-hand/EXTERNAL-REVIEW-ASSIMILATION-ROUND_19/METHODOLOGY_NOTES.md

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+# Round 19 — Methodology Notes
+
+Two issues surfaced during assimilation that affect interpretation of the null falsifier result. Neither is fatal to Round 19's work product — both are gaps that the next-local-gate or Round 20 should close.
+
+## Flag 1 — The "transform-condition" diagnostic is tautological
+
+The script computes a "weighted-QR-style transform diagnostic" as `cond(R)` where `R` comes from `QR(M)`. This is intended to play the role weighted-QR's coordinate transform played when it produced the 4.7e16 conditioning that triggered the demote.
+
+For real square matrices M, the QR decomposition has Q orthogonal and R upper-triangular with `M = QR`. Since Q is orthogonal it preserves all singular values: `cond(R) = cond(QR) = cond(M)` exactly.
+
+This is confirmed empirically in the report itself: `max_condition = 20.81295453370498` vs. `max_transform_condition = 20.81295453370497`. The two values agree to last-digit roundoff. Independent verification (random 5×5 example): `cond(R)/cond(M) = 1.000000000000`, `||Q^T Q - I|| ≈ 9e-16`.
+
+**Implication:** the "transform stress" diagnostic in this sweep is not actually a separate check — it tests the same quantity as `cond(M)`. PC's null falsifier therefore tests one thing (conditioning of the canonical gap matrix at small genus under endpoint clustering), not two.
+
+This does **not** invalidate the Track B canonical-basis seed proposal. It does narrow the evidence Track A actually provides: the route survives small-genus toy conditioning, full stop. The route's behavior under the kind of weighted-coordinate-transform that destroyed weighted-QR has not been tested by this sweep.
+
+**Next-local-gate must include:** a transform diagnostic that is NOT a tautology — e.g., apply a weighted-coordinate transform analogous to the weighted-QR setup that produced 4.7e16, then compare conditioning before and after. Or compute condition of an explicit basis-change matrix (e.g., from monomials to Chebyshev rescaled, or from canonical to row-space/cycle-space coordinates) and check whether that transform is itself well-conditioned.
+
+## Flag 2 — Genus range stops at 4; the real concern is genus 24
+
+PC's risk section names the central concern correctly: "The monomial canonical basis may itself be ill-conditioned at genus 24." The Vandermonde-like structure of `[x^0, x^1, ..., x^{n-1}]` is famously ill-conditioned at high degree — condition number grows roughly exponentially in n on equispaced nodes, and even on Chebyshev nodes the situation degrades at degree ~20+.
+
+The sweep tests g=2, 3, 4. Nothing about g=24 is established. The toy null result is consistent with both "the canonical basis works at high genus" and "the canonical basis catastrophically fails at high genus" — the sweep simply doesn't probe the regime where the question matters.
+
+This is an honest, named gap (PC flagged it in the risk section), not a failure of Round 19. But it is the question that determines whether the canonical-basis primary parallel route is viable at all.
+
+**Next-local-gate must include:** a direct conditioning probe at g=24, or at least a continuation of the sweep through g=8, 12, 16, 20, 24 to characterize the conditioning growth curve. If the curve crosses 1e10 well below g=24, the route needs the Chebyshev-rescaled or row-space-equivalence variant PC named as defensive alternatives.
+
+## Other notes (minor)
+
+- f64 sampling without interval arithmetic means the entire sweep is `F64_SAMPLED_ONLY` per the public scope tags. Even if Flag 1 and Flag 2 were addressed, the sweep would not produce a route certificate — only an f64 sanity check that informs whether to invest in an interval-arithmetic re-implementation.
+- The `cluster_eps` minimum of 1e-4 is reasonable for f64 (well above the ~1e-16 round-off floor). For interval re-implementation, smaller clustering can be probed without precision concerns.
+- The sweep uses 160 Legendre quadrature nodes per integral. Quadrature error is not measured. For interval certification, error bounds on the quadrature are required.
+
+## Scope of these flags
+
+These are gaps in what Round 19's evidence supports, not flaws in PC's output. PC was honest about every limitation (claim_level 0, scope statements throughout, risk section naming the genus-24 issue). The flags belong on the **route's evidence record**, not on PC's adherence to the dispatch.
+
+Round 19 advances the canonical-basis route from "named primary parallel" to "starting proposal with toy-scale null check." It does not yet provide a route certificate. The next-local-gate document specifies what it would take to do so.

Erdos1038/agent-work/problem-at-hand/EXTERNAL-REVIEW-ASSIMILATION-ROUND_19/NEXT_LOCAL_GATE.md

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+# Round 19 — Next Local Gate
+
+Recommended next-local-gate packet ID (matches PC's recommendation):
+
+```
+EXP-MATH-ERDOS1038-PHI-K-HYPERELLIPTIC-CANONICAL-BASIS-INTERVAL-SEED-20260527-01
+```
+
+This is local work — not a PC dispatch. The receipts and conditioning evidence the gate produces must come from local interval-certified compute against the real 25-component private payload.
+
+## Gate requirements (must all PASS to promote canonical-basis route to receipt-backed level)
+
+### G1. Genus-growth conditioning probe (f64 sufficient at first)
+
+Extend Round 19's sweep through `genus ∈ {2, 4, 8, 12, 16, 20, 24}`. Same endpoint-clustering stressor. Plot `cond(M)` vs genus. Report the genus at which `cond(M)` crosses `1e10`.
+
+- If crossover happens at g ≤ 24: the unrescaled monomial canonical basis fails for #1038. Pivot to PC's defensive alternatives — Chebyshev-rescaled numerators or row-space/cycle-space equivalence.
+- If crossover happens at g > 24: proceed to G2 with the unrescaled monomial basis.
+
+This is f64-sufficient because we're triaging, not certifying. The interval re-implementation comes at G3.
+
+### G2. Non-tautological transform diagnostic
+
+Replace `cond(R) from QR(M)` (tautological with `cond(M)`) with a real transform stressor. Options:
+
+- **(a) Weighted-coordinate transform.** Apply the same kind of weighted coordinate transform that produced weighted-QR's 4.7e16 — but using the canonical basis as the underlying matrix. Compute the transform's own condition. If the transform is well-conditioned (≪ 1e10), the route survives the same stressor that demoted weighted-QR.
+- **(b) Basis-change matrix.** Compute `cond(P)` where `P` is the change-of-basis matrix from monomials `{x^{j-1}}` to Chebyshev-rescaled `{T_{j-1}(scaled_x)}`. If `cond(P) ≪ 1e10`, the two basis families are numerically interchangeable.
+- **(c) Cycle-space equivalence test.** Verify that two different choices of certified gap rows yield matrices related by a well-conditioned similarity — i.e., the row-space invariant PC named is preserved.
+
+Any of (a)/(b)/(c) is a real diagnostic. The current QR-from-M is not.
+
+### G3. Interval-arithmetic re-implementation
+
+Convert the sweep from f64 to interval arithmetic. The existing endpoint-safe Chebyshev quadrature scheme (`x = mid + half · cos(θ)` with square-root endpoint factored) translates directly. Required additions:
+- Outward-rounded interval enclosures on every quadrature node
+- Bounded quadrature truncation error
+- Verified condition number bounds (not just point estimates)
+
+Output the three files PC recommended:
+
+```
+CANONICAL_PERIOD_MATRIX_INTERVALS.json
+CANONICAL_BASIS_CONDITION_CERTIFICATE.json
+CANONICAL_BASIS_SEED_RESULTS.json
+```
+
+Once these exist with interval-certified bounds, the scope tag advances from `F64_SAMPLED_ONLY` to `F64_INTERVAL_CONSTRAINED` (or further).
+
+### G4. Endpoint-limit source vector expression
+
+PC's accept criteria include "endpoint-limit source vector expressed in same basis." This is not yet specified. The local gate must produce the explicit construction: given the canonical basis on the 24-row scaffold, how does the endpoint-limit source kernel project onto it? Without this, the route cannot connect to the endpoint-limit gate (Task C from the dispatch — deferred from Round 19 but still a real future blocker).
+
+## What stays absent
+
+- Six private receipts (ROOT_BOX.json etc.) remain absent. Nothing in this local gate changes that. They are still a future-round local-agent deliverable for the dependent-Vieta consumer path, independent of the canonical-basis route work above.
+- No theorem advance is implied by completing G1-G4. The receipt would promote the canonical-basis route from "starting proposal" to "interval-certified seed." It does NOT prove #1038 or compose into the global reduction.
+
+## If this gate completes cleanly
+
+Route status becomes:
+
+- **canonical_hyperelliptic_basis**: PRIMARY PARALLEL with receipt-backed seed (claim level ≤ 2 depending on what scope-tag is reached)
+- **weighted_qr_basis**: stays DEMOTED to diagnostic
+- **dependent_vieta_consumer**: still BLOCKED on six absent receipts (unchanged)
+- Open summit-level blockers (endpoint-limit kernel, KKT/strict-slack, global reduction): unchanged
+
+## Round 20 dispatch question
+
+Whether Round 20 goes back to PC depends on whether G1-G4 are PC-shaped or local-shaped:
+
+- G1 is PC-shaped (literature-curated decision on rescaling vs. unrescaled, plus extended sweep). Could dispatch.
+- G2 is borderline PC-shaped. The diagnostic-design question can be PC; the implementation is local.
+- G3 is local-shaped. Interval arithmetic against private endpoint payload — PC cannot access private receipts.
+- G4 is local-shaped (algebraic derivation on private structure).
+
+A reasonable Round 20 dispatch would be: PC produces G1 (conditioning growth curve at genus 8–24 in f64) and G2 (real transform diagnostic design), leaving G3 and G4 for local Codex/Claude work. That's a tight, well-scoped follow-up that builds directly on Round 19 without re-derivation.

Erdos1038/agent-work/problem-at-hand/EXTERNAL-REVIEW-ASSIMILATION-ROUND_19/README.md

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+# EXTERNAL-REVIEW-ASSIMILATION-ROUND_19
+
+Local assimilation packet for Perplexity Computer's Round 19 work product on Erdős #1038.
+
+## Files
+
+- `MANIFEST.json` — packet metadata, bundle provenance, per-artifact verdicts, status, scope tags, forbidden-claims confirmation.
+- `VERDICT_LEDGER.md` — per-artifact accept/reject reasoning. Aggregate verdict.
+- `REPRODUCIBILITY_CHECK.md` — local rerun of `round19_canonical_falsifier_sweep.py`; structural identity + f64 last-bit numerical agreement.
+- `METHODOLOGY_NOTES.md` — two flags surfaced during assimilation: (1) QR-transform diagnostic is tautological with cond(M), (2) genus-24 conditioning unprobed.
+- `NEXT_LOCAL_GATE.md` — four-gate ladder (G1–G4) for promoting canonical-basis route from "starting proposal" to "interval-certified seed." Round 20 dispatch question addressed.
+
+## Status
+
+`ASSIMILATED` at claim level 0. PC's Round 19 output was honest, well-scoped, and respected every constraint in the dispatch. Two methodology gaps named for the next gate to close.
+
+## Bundle source
+
+PC bundle lives at `Research-Hub/perplexity-substrate/projects/erdos-1038/jobs/ROUND_19/` (with `BUNDLE.sha256` for provenance). The bundle itself is referenced by SHA from `MANIFEST.json` in this packet — no copies of PC's files are duplicated here.
+
+## Playback
+
+`evt-20260528-round-19-complete` event logged in `Erdos1038/agent-work/EVEREST_ROUTE_PLAYBACK.jsonl`.

Erdos1038/agent-work/problem-at-hand/EXTERNAL-REVIEW-ASSIMILATION-ROUND_19/REPRODUCIBILITY_CHECK.md

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+# Round 19 — Reproducibility Check
+
+## Method
+
+Copied `round19_canonical_falsifier_sweep.py` from the PC bundle into a clean temp directory (`/tmp/round19-repro/`). Ran with local Python 3.9.6 / numpy 2.0.2. Compared resulting `NULL_FALSIFIER_REPORT.json` against PC's submitted version.
+
+## Result
+
+Structural identity:
+- `status`: NO_FALSIFIER_FOUND_IN_TOY_RANGE (match)
+- `trial_count`: 63 (match)
+- `coverage`: identical (match)
+- `claim_level`: 0 (match)
+- `claim_scope`: identical text (match)
+
+Numerical values:
+
+| Field | PC value | Local rerun value | Delta |
+|---|---|---|---|
+| `max_condition` | 20.81295453370498 | 20.812954533704993 | ~1e-14 |
+| `max_transform_condition` | 20.81295453370497 | 20.812954533704982 | ~1e-14 |
+| `min_singular_min` | 1.7326932764839196 | 1.7326932764839196 | 0 |
+
+The two condition values differ from PC's only in the last digit. This is consistent with f64 last-bit roundoff arising from different BLAS backend implementations of QR/SVD (Accelerate on macOS vs. whichever backend PC's sandbox used). Structural and quantitative agreement to ~14 significant digits.
+
+**Verdict: REPRODUCIBLE at f64 precision.** No discrepancy beyond float roundoff noise.
+
+## What reproducibility does NOT establish
+
+- Reproducibility verifies the script faithfully implements what PC claims; it does not validate the scientific claim about #1038.
+- The script is f64-sampled only. Re-running yields the same f64 numbers but does not produce an interval certificate.
+- The script tests genus 2-4 only. Re-running cannot extrapolate to genus 24.
+- Reproducibility of a null falsification result does not constitute proof of anything; null result remains scope-limited evidence per PC's own claim_scope.