Tooling: replay balanced Fano 2.91× faster with identical exhaustive streams

[VictorLiwentao]

The historical balanced-Fano checker transposes a complete binary matrix at every meet-in-the-middle leaf. This tooling improvement propagates packed columns with exact Python integer operations and reconstructs a retained prefix matrix only when a witness is found. Both exhaustive streams, first-match behavior, witnesses, budgets and rejection checks are preserved. No new κ or search-domain claim.

Five sequential, alternating fresh-process pairs on CPython 3.13.2 / macOS arm64 measured median search time 5.969 → 2.051 seconds (2.91×) and peak process RSS 162,381,824 → 113,180,672 bytes (30.3% lower). Every sample matches every original result field. These measurements cover this fixed historical check, not the selected supplier replay or multiplication runtime.

Validation:

• Compare all 559,872 half assignments pointwise with the pinned original, retaining both original stream hashes and all 258,156 prefix keys. The covered full domain remains 6^14 = 78,364,164,096 local assignments via meet-in-the-middle.
• Add independent dense column controls, exact positive-witness/early-stop comparisons, and a missing-leaf mutation that preserves the negative Boolean but fails receipt equality. Input and budget failures retain their original exceptions.
• PYTHONDONTWRITEBYTECODE=1 make verify-tests: 555 tests in 85 isolated modules and 20 patch checks pass. The six new tests also pass under -O; the affected audit passes under -S; selected-record and whitespace checks pass.
• Regenerate only the historical certificate's changed source binding. A test restores that one binding and verifies the SHA256 of the entire original certificate. The selected frontier and upstream/ are unchanged.

Reproduce with standard-library Python 3.11+ (benchmark RSS reporting supports macOS/Linux):

python3 -B research/balanced-fano-performance/benchmark.py --rounds 5

Expected: PASS_IDENTICAL_COMPLETE_RESULTS. research/balanced-fano-performance/README.md contains the equivalence argument and review map; RESULT.json retains all samples and exact source pins; VALIDATION.json records coverage. Full make verify and the selected supplier cold replay were not rerun for this isolated historical-checker change. Remote CI is separate from local validation.

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. OS-random assignment seed 91, verification engineering. No pinned sprint issue existed, so the claim is local. Final overlap review covered 567 open PRs through #748; nearby algebra, geometry, footprint and streaming optimizations concern other checks and supply no code here.

Credit Douglas R. Colkitt's original balanced-Fano checker, scoped negative result and dense controls. Prepared by Wentao Li with substantial OpenAI Codex assistance, under Apache-2.0; Contributor profiles: GitHub: VictorLiwentao, X: @Is__Victor. Detailed predecessor attribution is in NOTICE.md. This changes no inherited mathematical assumptions and is not a formal proof of the full multiplication theorem.

[Mister-Meeseeks]

100-PR batch review at 4fad623a1e4ca06959f4326e221c2f8d9125c269.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Packed balanced-Fano enumeration: order-preserving column encoding and first-match reconstruction; complete half-stream differential tests plus dense independent controls.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.