Redefine BMF as exact factorization; fix BicliqueCover semantics; add BMF → BicliqueCover

[GiggleLiu]

Summary

Two aligned changes; the second only works after the first.

Change 1 — Redefine BMF from approximate factorization (minimize Hamming distance, every config feasible) to exact factorization: infeasible when B ⊙ C ≠ A, else minimize |B|_1 + |C|_1 (total factor size). Matches the classical problem (Monson–Pullman–Rees 1995) and restores the Boolean-rank interpretation.

• Update BMF → ILP to the equality-constrained formulation: drop error variables e_{i,j}, pin w_{i,j} = A_{i,j}, change objective to min Σ b_{i,r} + Σ c_{r,j}. Overhead shrinks by m·n variables and m·n constraints.
• Fix the pre-existing BMF canonical example: the committed optimal_config was not actually an exact factorization (verified by hand: Hamming distance 2). Replaced with a genuine exact factorization that makes test_bmf_paper_example and model_specs_are_optimal consistent.

Change 2 — Fix BicliqueCover semantics to the classical sub-biclique form, then add the trivial BMF → BicliqueCover reduction.

• is_valid_cover now also requires every biclique's L_b × R_b ⊆ E(G). Previously the code only checked edge coverage — the OR-cover variant — which disagreed with the struct's docstring and with the paper's ILP constraint x_{l,b} + y_{r,b} ≤ 1 for non-edges (the paper was already describing the stronger form; the code was underconstrained).
• BicliqueCover → ILP now emits the matching non-edge constraint.
• Canonical BicliqueCover example switched from the OR-cover optimum (total size 5) to the correct sub-biclique optimum (total size 6), matching the paper's worked example.
• New BMF → BicliqueCover reduction: matrix-to-biadjacency + rank passthrough, with extract_solution transposing the right-vertex half from vertex-major to biclique-row-major. Trivial under the fixed semantics.
• Paper updated: BicliqueCover problem-def now states the sub-biclique requirement explicitly; new reduction-rule("BMF", "BicliqueCover") entry added.

Julia parity fixtures dropped for both BMF (old Hamming-distance semantics) and BicliqueCover (Julia ProblemReductions package has the same OR-cover bug — its is_biclique only checks non-emptiness). The corresponding Rust parity tests are removed and the Julia generator has notes explaining the divergence. The upstream Julia package will need the same fix separately.

Test plan

• cargo build --lib clean
• cargo clippy --all-targets -- -D warnings clean
• cargo test --lib — 4951 pass
• cargo test --lib --features example-db — 5050 pass (includes model_specs_are_self_consistent and model_specs_are_optimal for the updated canonical specs)
• cargo test --test main — 75 integration tests pass
• make export-schemas and make paper rebuild cleanly
• End-to-end: pred path BMF BicliqueCover returns a 1-hop path; pred create --example BMF → pred evaluate gives Min(8) for the exact config and Min(None) for infeasible configs

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.92%. Comparing base (ff8ae70) to head (3a37e70).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1056   +/-   ##
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  Coverage   97.92%   97.92%           
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  Files         964      966    +2     
  Lines       99872    99933   +61     
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+ Hits        97796    97857   +61     
  Misses       2076     2076           

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