Tooling: 1.61x faster exact historical central-factor audit (no new kappa)

[RossRichardson]

The historical h=26 dyadic central-factor audit checks 6,760,000 exact coefficients with Python-level sparse products. This opt-in, source-pinned adapter packs complete rows into exact integers using a proved input-dependent radix. It preserves every coefficient obligation, structural/charge check, and the complete historical certificate. Tooling improvement; no new kappa or construction.

Three alternating fresh-process pairs on macOS arm64 / CPython 3.14.6 measured median complete-audit wall time 5.629786 → 3.489217 seconds (1.613481×). Factor-only runs, including admission, generation and receipt comparison, improved 18.332397×. Both engines use identical inputs, and all complete receipts retain SHA256 ffae0f0a22863718e3134a924592dcf4b05e919223323ba536c587c592bfe6a1. Raw samples, environment and implementation hashes are retained; these are descriptive timings without a performance gate.

Reproduce from the repository root with Python 3.11+ standard library:

python3 -I -B research/central-factor-packed/verify.py
python3 -I -B research/central-factor-packed/test_packed.py

Expected verification status: PASS_CENTRAL_FACTOR_PACKED, coefficients_checked: 6760000, and the complete receipt hash above.

Validation completed:

• Eleven package test groups pass on Python 3.14.6, also under -O, and Python 3.12.12. The original four dirty-interface/factor tests run with each engine. The full inherited audit deliberately rejects -O because it relies on assertions.
• Complete original-verifier comparisons at h=8,10,12,18,26; equivalent factors accepted; all 1,806 single-entry/sign/deletion corruptions at h=8 rejected. Additional controls cover large signed values, endpoints, malformed factors, wrong scalar charges, stale-input reuse, missing/altered sources and adapter, incomplete receipts and output preservation. A deliberately faulty radix accepts a swapped-column factor that the proper radix rejects.
• Complete packed replay on Python 3.12 and minimal offline relocation to a path containing spaces reproduce the same certificate. Selected-record integrity and staged whitespace checks pass. All 43 inherited pins match both base Git objects and refreshed main.

Only research/central-factor-packed/ is added. The original sources, default verification commands, selected frontier and upstream/ are unchanged. Full make verify, selected cold replay, Lean and hosted CI were not run locally; no claim is made that those gates passed. The radix argument is written mathematics, and finite checks do not prove the full multiplication theorem or discharge its inherited hypotheses.

Base: 47481c89fd30a43f8f882eb4b391e89c29273fd0. OS assignment seed 93, verification engineering; three candidates, exact scope, stopping rule and completed local claim are recorded. No pinned coordination issue exists. The final complete overlap snapshot covered 701 open PRs through #948, followed by a refresh through #949. PR809/937/947 concern changed historical factors or shear optimality; this package preserves the baseline factor and does not import their code. Refreshed main 007664306fff84fbb1c9a1b4053b69f439764034 retains every input pin and PR890's selected conditional κ = 0.001661957774647029.

Credit Douglas R. Colkitt for the original factor/audit, Curtis Dransfield's PR752, merramil's PR778 and CubeJerry's PR898 for related exact packing techniques, and PR809/937/947 for distinct center research. Exact heads and licenses are recorded in NOTICE.md. Prepared by Ross Richardson (@RossRichardson) with substantial OpenAI Codex assistance, under Apache-2.0; no independent human review claimed.