Tooling: 1.13x faster exact stage-pair audit with identical receipts

[navinor]

The historical stage-pair audit spends most of its runtime in exact rational arithmetic. This replaces two wasteful patterns with identical operations, preserving every receipt and rejection check. Tooling improvement; no new kappa.

Changes

1. scripts/audit_fused_block.py — rational_rank skips redundant Q(x) construction when an entry is already a Fraction. Q(Q) returns the same value after needless normalization.
2. scripts/audit_stage_pair.py — modular_rank converts denominators through a cached _mod_inv(d, prime) helper (same pow(d, -1, prime) call) instead of one fresh pow() per matrix entry. lru_cache does not cache exceptions, so a non-invertible denominator raises the same ValueError.

No matrix, pivot order, stopping rule, candidate list, or rejection predicate was touched.

Measurements

Fresh-process timings of certificate() (compute only), CPython 3.12.14 / Windows, stdlib only. OS caches not flushed; host not isolated. Timing is descriptive, not a pass threshold.

run	original (s)	optimized (s)
1	16.63	14.31
2	15.79	13.96
3	15.57	13.64
median	15.79	13.96

Median 15.79 s to 13.96 s: 1.13x faster, 11.6% less wall time. Microbenchmarks: rational_rank 3.05x on 50 sampled frames; modular conversion 1.42x on 20 sampled matrices.

python3 -B research/stage-pair-performance/benchmark.py --rounds 3

Expected: PASS_IDENTICAL_STAGE_PAIR_RECEIPTS.

Validation

• Full certificate() output identical to certificates/stage-pair-audit.json in every field except the single expected source_sha256 entry for the edited audit_stage_pair.py (rank sum 8684, 64 candidates, 6 local improvements).
• audit_fused_block and audit_joint_frames certificates regenerate byte-identical.
• New tests/test_stage_pair_performance.py: 6 tests compare optimized helpers against verbatim base-commit references on edge cases (empty, zero, singular, non-square, ints vs Fractions, 30-digit numerators, primes 101/103), including the ValueError path. Existing suites pass: test_stage_pair (8), test_fused_block (7), test_joint_frames (8), test_quadratic_affine (4).
• Full make verify and the selected-supplier cold replay were not rerun for this isolated historical-checker change. upstream/ untouched; selected frontier unchanged.

Provenance

• Contributor: Aaron Wang (navinor).
• Prepared with substantial AI assistance (Muse Spark via OpenCode). No independent human peer review claimed.
• Base: 7ee02b7c96d85f22b38d28bd7ed49bb8c1aeb261. OS-random assignment seed 92, verification-engineering track. Claim, candidates, and overlap review in research/stage-pair-performance/SELECTION.json. No open PR covers the stage-pair audit (checked through PR 823).

[Mister-Meeseeks]

100-PR batch review at 2b342526350a3c36936feb7f3f50669fad2770b1.

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

Reviewed scope: Fraction reuse and modular-inverse caching in two rank checkers; focused reference-equivalence and failure regressions.

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.