Fix #548: [Model] CosineProductIntegration

[GiggleLiu]

Summary

• add an implementation plan for CosineProductIntegration
• document the witness-free evaluation approach and follow-up implementation batches

Fixes #548

[codecov]

Codecov Report

❌ Patch coverage is 99.50980% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 97.87%. Comparing base (e067f91) to head (b74600d).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
..._tests/rules/partition_cosineproductintegration.rs	98.57%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff            @@
##             main     #684    +/-   ##
========================================
  Coverage   97.86%   97.87%            
========================================
  Files         627      631     +4     
  Lines       68842    69046   +204     
========================================
+ Hits        67374    67577   +203     
- Misses       1468     1469     +1     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[GiggleLiu]

Implemented CosineProductIntegration in this PR.

Summary:

• added the new misc model, registry exports, CLI pred create support, paper entry, tests, and canonical example-db fixture
• model configs are explicit sign assignments (0 => +a_i, 1 => -a_i), so a satisfying config witnesses sum_i epsilon_i a_i = 0
• during implementation I corrected the ticket's predicate after review and a literature cross-check: the witness-bearing NP-complete form is the integral != 0 decision / balanced-sign-assignment existence. The original = 0 phrasing is the complement problem and does not fit the repo's closed-loop witness semantics

Verification:

• cargo test cosine_product_integration --lib
• cargo test --features "ilp-highs example-db" verify_model_fixtures_match_computed --lib
• cargo run -p problemreductions-cli --bin pred -- create CosineProductIntegration --coefficients 2,3,5
• make paper
• make clippy
• make test

[Copilot]

Pull request overview

This PR adds a new CosineProductIntegration model implementing the Cosine Product Integration decision problem (Garey & Johnson A7 AN14). The problem asks whether ∫₀²π ∏ᵢcos(aᵢθ)dθ ≠ 0, which is equivalent to checking whether a balanced sign assignment exists for the given integer coefficients. The implementation uses a pseudo-polynomial DP approach for the has_balanced_sign_assignment helper and brute-force sign enumeration for the core evaluate method.

Changes:

• Added CosineProductIntegration model with schema, Problem/SatisfactionProblem trait implementations, signed-sum evaluation, DP-based balanced-sum check, and declare_variants complexity annotation
• Added CLI pred create support with --coefficients flag and comprehensive unit tests
• Added mathematical documentation in the paper and a canonical example in the example DB

Reviewed changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
src/models/misc/cosine_product_integration.rs	Core model: struct, schema, signed_sum, has_balanced_sign_assignment DP, Problem/SatisfactionProblem impls, variants, example spec
src/unit_tests/models/misc/cosine_product_integration.rs	Tests covering creation, signed sum, evaluate, solver, empty/zero/negative cases, serialization
src/models/misc/mod.rs	Register new module, re-export, add to canonical example specs
src/models/mod.rs	Re-export CosineProductIntegration
src/lib.rs	Add to prelude
problemreductions-cli/src/commands/create.rs	CLI create handler for CosineProductIntegration, import, flag check, format hint cleanup
problemreductions-cli/src/cli.rs	Add --coefficients flag, help text, and example
docs/paper/reductions.typ	Mathematical definition and explanation in the paper
src/example_db/fixtures/examples.json	Canonical example instance and updated existing example solutions

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[GiggleLiu]

Review Pipeline Report

Check	Result
Copilot comments	0 fixed
Issue/human comments	1 checked, 0 fixed
Structural review	16/16 passed
CI	green
Agentic test	passed
Needs human decision	none
Board	Review pool -> Under review -> Final review

Remaining issues for final review

• None.

🤖 Generated by review-pipeline

[isPANN]

On Hold: The reduction from Partition is completely trivial. The problem is essentially Partition in disguise, so it doesn't add meaningful value to the reduction graph.