Tooling: 4.75× faster production P112 free-sink audit via signed modular determinants with identical receipts

[VictorLiwentao]

Change and scope

At base 0b1cccf86e2f5132ed286a26ef0a681a495740ea, production research/p112-free-sink-audit97/independent.py still computed every signed minor with rational Fraction elimination. woklerx’s opt-in adapter research/p112-signed-modular86/ (incorporated #1144) already proved a modulo-521 kernel that recovers each full signed determinant inside a checked Hadamard envelope, with identical complete audit receipts. This PR wires that equivalent rewrite into the production independent checker.

The original rational elimination is retained as rational_determinant and as the fallback for rows outside the envelope. Pairwise Fraction-only bytes are vendored in baseline.py. The opt-in package vendors the same baseline for its reference engine. Leave-alone tooling through #2431 and deferred ck-dyadic-replay-production / scalar-fused-dyadic-production were not reopened.

No certificate κ pins change.

Tooling improvement; no new kappa. Selected frontier untouched.

Result

On Linux / CPython 3.12.3 with taskset -c 0, five alternating in-process pairs over the complete 28,560-case / 4,030-minor audit gave median wall time 0.681 → 0.143 s (4.754×) with per-round ratios 4.618–4.880×. Timing is host-descriptive and is not a correctness gate. Every audit receipt matches the pairwise baseline.

Package: research/p112-signed-modular-production/.
Tip: d688ec0ff64f300c3ff124a60893c5c8c5e4f1c4.

Validation

python3.12 -I -B research/p112-signed-modular-production/verify.py
python3.12 -I -O -B research/p112-signed-modular-production/verify.py
python3.12 -B scripts/research_package.py --package research/p112-signed-modular-production
python3.12 -B -m unittest tests.test_p112_signed_modular_production
taskset -c 0 python3.12 -I -B research/p112-signed-modular-production/benchmark.py --rounds 5

Expected:

PASS_P112_SIGNED_MODULAR_PRODUCTION cases=28560 minors=4030 signed_matrices=19767 controls=10 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/p112-signed-modular-production outcome=completed
PASS_IDENTICAL_P112_SIGNED_MODULAR_PRODUCTION_RECEIPTS

Default verify is read-only. Temp-copy certificate determinant-flip foil rejects via audit failure. Package gates under -O still load checkers with compile(..., optimize=0). Full make verify, selected cold replay, Lean, and multiplication-theorem obligations were not rerun for this isolated historical-checker change.

Why the modular path is equivalent

Every frozen square minor has dimension at most eight and integer rows of squared Euclidean norm at most four. Hadamard’s inequality gives |det A| ≤ 2^n ≤ 256. Modulus 521 is prime and greater than twice 256, so the unique representative in (-260, 260) recovers the exact signed determinant whenever the modular path fires. See research/p112-signed-modular86/.

Overlap and credit

Closest priors (different delivery): woklerx’s research/p112-signed-modular86/ / #1144 (opt-in modular dets; this is the production wiring), CrocSwap/integer-mult-bounds#756. Leave-alone tooling through #2431 was not reopened. No competing open PR on production p112-free-sink-audit97/independent.py at refresh.

Credit woklerx and the retained P112 free-sink lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.