Tooling: 4.78x faster exact bounded quadratic-code replay

[RossRichardson]

The historical quadratic-code rank checker rebuilds large XOR-permutation masks for every row. This tooling improvement adds an opt-in per-replay geometry-mask cache. The original benchmark at d84d3b950127ff9252e5c059a629bb654500192a measured the unchanged 4,096-row t=6 workload at 87.66 s → 18.36 s (4.78×) on macOS arm64 / CPython 3.14.6: three alternating fresh-process pairs, with all six complete receipts byte-identical. This is historical workload timing, not a new measurement of the refreshed dependency closure or integer multiplication.

Only research/cube-xor-replay/ and its focused Linux workflow are added relative to current main. The source generators, elimination, row order, stopping rule, certificates, selected frontier and upstream/ retain their current-main state. No new kappa or impossibility result: the t=6 rank lower bound is 3,088 and positive deficit remains not excluded.

Reproduce

python3.12 -I -O -B research/cube-xor-replay/verify.py

Python 3.10+, standard library only, in a fresh process/checkout without .pyc files. -B prevents cache writes but does not disable cache reads. Expected:

PASS_CUBE_XOR_VERIFICATION rows=4324 coefficients=8596927616 t6_rank=3088 t6_excluded=false

For the accelerated workload alone: python3 -I -B research/cube-xor-replay/replay.py --case t6. Full differential verification also executes the original permutation, so its runtime differs from accelerated replay.

Review continuation and compatibility

The requested full differential/certificate comparison now completes at both the reviewed original head and current head 4ba229532a76516e5f6f5befc1d6d9dc4834f6f9. Exact local CPython 3.12.12 runs took 118.575 s and 105.254 s respectively; each completed both cases and all 17 tests. Current-head validation also passes all nine inherited cube tests with the cached backend, all 38 effective Git/SHA256 pins, selected-record integrity, and whitespace checks. Separate AI-assisted source/coverage review found no substantive issue and checked sensitivity of the source and compatibility guards.

The branch incorporates canonical main ffbd90dd90dbe0055464f3a1411b25a3a4fdc6b8, priority revision 5. Three changed transitive imports would otherwise reject the integration. A separately authenticated COMPATIBILITY.json records exactly those three versions with an explicit path allowlist and predecessor binding. Their changed methods are outside this replay's called path. Original SOURCES.json, EXPECTED-T6.json, BENCHMARK.json, VALIDATION.json, CLAIM.json, cached permutation and coverage verifier remain unchanged. The complete post-integration replay preserves the scientific receipts.

Detailed delta and scope · Canonical continuation. The linked PR follow-up comment records exact logs and live CI status. The historical Linux job passed the complete command on its historical PR merge ref; it is separate from CI for the updated head.

Evidence and limits

Direct old/new integer equality covers every generated row, including dependent rows: 4,324 rows / 8,596,927,616 binary coefficients. Both the complete historical t=3,4,5 certificate and full bounded t=6 receipt remain byte-identical. Only geometry masks are cached; input guards still run on warm hits. The written equivalence argument covers every valid power-of-two row width.

The 17 tests include exhaustive small rows, basis/index pairs, seed-94 dense controls, high coordinates, incomplete screens, source/fixture/manifest corruption, and offline relocation. A common column permutation preserves rank and independent-row indices but changes the witness stream; complete receipt comparison rejects it. Dropped rows and corrupt masks are detected.

No new benchmark, full make verify, selected native cold replay, supplier admission, Lean or full multiplication theorem is claimed. Generic Python-loader hardening is an explicitly separate next question. Maintainer incorporation and review-ledger disposition remain separate actions.

Historical research base: 2921874911956718fcaaaf9396fe8267b3cfa9f0; original submission base: abdc6a7002abdbcd9e21bfc5e1a795784deacfdf; cube source: d55bcd62ceb8f322bcf311a5a66e94c3ac7724f0. OS seed 94, verification-engineering track. Current overlap refresh covers 491 open PRs and 1,535 Discussion records with complete pagination and no warnings at 2026-10-16 07:21–07:22 UTC; this continues the existing contribution. PR667 logarithms, PR752 quadratic-affine products, PR898 Leech lanes and PR976 joint-frame rank remain distinct and credited.

Credit Douglas R. Colkitt for the original family, permutation, audit and certificate. Contribution and follow-up by Ross Richardson with substantial OpenAI Codex assistance, including implementation, mathematical/source audit and testing; no independent human review claimed. Apache-2.0. Inherited mathematical/compiler/hosting/precision/tape/analytic assumptions retain their scope.

[Mister-Meeseeks]

100-PR batch review at d84d3b950127ff9252e5c059a629bb654500192a.

This remains open after scoped triage. Next review step: The historical cube-XOR differential case passed, but the whole command reached 180 seconds before the larger declared coverage completed. Finish the remaining differential/certificate comparison.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

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

[RossRichardson]

Completed the requested differential/certificate continuation and pushed the current-main compatibility follow-up at 4ba229532a76516e5f6f5befc1d6d9dc4834f6f9.

The complete unchanged command now passes at reviewed head d84d3b950127ff9252e5c059a629bb654500192a (118.575 s), and the same full command passes after the integration refresh at the new head (105.254 s). Both runs used macOS arm64 / CPython 3.12.12, fresh isolated processes and no preexisting bytecode caches, with a 900-second cap rather than the review's 180-second cap.

python3.12 -I -O -B research/cube-xor-replay/verify.py

Current-head output:

PASS_CUBE_XOR_DIFFERENTIAL case=historical
PASS_CUBE_XOR_DIFFERENTIAL case=t6
.................
----------------------------------------------------------------------
Ran 17 tests in 2.230s

OK
PASS_CUBE_XOR_VERIFICATION rows=4324 coefficients=8596927616 t6_rank=3088 t6_excluded=false

Coverage includes every complete row before elimination, including dependent rows. Historical and bounded t=6 receipts remain byte-identical. Current-head log SHA256: 808532dbbdd094dc9d75cf5c4a15451579e8d79bbdcadb5b4784fb667bde13eb; reviewed-head log SHA256: 2673a033caa449e61e7013040d09aa3a84db0ddfb74c83ac6a3239c87954de3d.

The compatibility check found three changed transitive imports on current canonical main ffbd90dd.... The follow-up preserves the original manifest and all scientific/benchmark evidence, and authenticates exactly those three dependency versions in a separate allowlisted overlay. Their changed methods are not called by this replay. The nine inherited cube tests, all 38 effective SHA256/Git-blob pins, selected-record integrity and git diff --check also pass. Separate AI-assisted audit found no substantive issue; deleting either relevant source/compatibility guard makes its control fail.

Delta, frozen evidence and open questions · Canonical discussion.

CI status: the historical focused Linux job has the complete pass marker and all 17 tests on its historical merge ref. The new focused job was queued when first checked; its result is separate from these completed local checks.

The requested finite comparison is complete. Maintainer incorporation/ledger reconciliation remains open. No new benchmark, kappa, t=6 exclusion, supplier admission, formal-kernel proof or independent human review is claimed. Original cube work: Douglas R. Colkitt; adapter and follow-up: Ross Richardson with substantial OpenAI Codex assistance, Apache-2.0.