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

research/central-factor-packed/BENCHMARK.json

@@ -0,0 +1,185 @@
+{
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+  "clock": "time.perf_counter",
+  "fresh_processes": true,
+  "implementation_sha256": {
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+  "note": "Descriptive local timing; no performance pass/fail threshold. Complete audit includes source admission and full certificate comparison.",
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+}

research/central-factor-packed/CLAIM.md

@@ -0,0 +1,66 @@
+# Seed 93: exact central-factor verification
+
+- Track: verification engineering; OS assignment seed **93** from
+  `secrets.randbelow(100)` at 2026-10-13 14:01:44 UTC.
+- Base: `47481c89fd30a43f8f882eb4b391e89c29273fd0` (`origin/main`, fetched).
+- Local claim: 2026-10-13 14:05 UTC. Expected finish: 14:33 UTC
+  (01:33 AEDT on October 14); final eight minutes reserved for verification
+  and handoff. No pinned issue or open sprint coordination issue was present.
+- Object: `scripts/experiments/complex_centers.py::verify_factor`, especially
+  the historical h=26 dyadic central factor's 6,760,000 integer coefficients.
+- Hypothesis/method: injectively encode complete coefficient rows in integers
+  using a proved input-dependent radix, retaining every supplied gather/scatter
+  entry and all original structural and scalar-charge checks. Compare the full
+  original receipt and benchmark the same factor and complete historical audit.
+- Deliverable: opt-in source-pinned accelerator, radix argument, differential
+  and corruption controls, reproducible before/after timings, and a focused PR.
+  No new kappa, construction, search or impossibility claim.
+
+## Selection and overlap
+
+Three candidates considered: historical scratch-pooling interval bounds,
+historical disjoint-tensor frame traversal, and historical dyadic central
+factor coefficient checking. The first already intersects pending
+logarithm/interval accelerators #667/#672; the second would require broader
+graph changes. The central factor has a small complete exact oracle,
+and the original h=26 check measured 3.495 seconds on this host.
+The assignment seed also fixes the alternative-basis permutations and the
+64 large signed-entry cases, including first/last/random row selection and
+parameter choices h=8,10,12,14. Scope diversity comes from the different
+verified product, not from rerunning an existing search with a new seed.
+
+The 717-open-PR snapshot and focused all-state/current searches were checked.
+#809 changes this historical factor by a basis shear; this work changes only
+verification of supplied factors. #898/#752/#778 use related exact integer
+packing for other matrices. Their technique is credited, with no pending code
+import. #849 changes a selected scalar replay, #818 changes R420 RREF, #921
+schedules test modules, and #946 handles byte/container portability. None
+reserves this coefficient verifier. Closed negative results are not reopened.
+
+The selected base record is PR890's conditional
+`1661957774647029/10^18`, with PR869/870, Hao Yan's PR858 T16 construction,
+and PR589 on PR555. It was traced through `selected-result.json`, the current
+status/review ledger, `community-frontier890-review.md`, and the literal T21
+construction/proof. Earlier local checkout material described PR799; the new
+worktree and exact-base records supersede that initial reading.
+
+## Result
+
+Completed: [source, proof and reproduction](README.md),
+[exact timings](BENCHMARK.json), and [validation](VALIDATION.md).
+The complete historical audit's median fell from 5.629786 s to 3.489217 s
+(1.613481x), with byte-identical certificates in all six complete-audit timed
+runs. Factor-only median improved 18.332397x. Eleven test groups pass on
+Python 3.14.6 normally and under `-O`, and on Python 3.12.12. A minimal offline
+relocation and selected-record integrity check pass. No kappa change.
+
+The final complete snapshot contains 701 open PRs through #948. An immediate
+pre-submission refresh also found #949's distinct factory-scale optimum.
+New #947 and predecessor
+#937 concern changed historical factors/shear optimality, not this verifier;
+their exact heads and distinction are credited in NOTICE.md. #809/#898 heads
+remain unchanged. No coordination issue is pinned. Main advanced to
+`007664306fff84fbb1c9a1b4053b69f439764034`; all 43 inherited pins still match its
+Git blobs and PR890 remains selected. The branch keeps its exact starting base.
+The implementation was frozen before the final verification phase; no further
+investigation or delegated work was launched.

research/central-factor-packed/NOTICE.md

@@ -0,0 +1,47 @@
+# Attribution and license
+
+Prepared by **Ross Richardson (@RossRichardson)** with substantial
+**OpenAI Codex assistance**, including design, implementation, mathematical
+analysis, tests, documentation and automated verification. No independent human
+peer review is claimed. This contribution is under the repository's
+Apache-2.0 license; see the root `LICENSE`.
+
+The original dyadic factor, structural validation, receipt schema, side circuit,
+phase argument and cost ledger are by **Douglas R. Colkitt**, retained at
+`d55bcd62ceb8f322bcf311a5a66e94c3ac7724f0`. The structural/charge checks in
+`packed.py` are adapted from his `scripts/experiments/complex_centers.py`;
+the baseline and proof sources are retained unchanged and pinned in
+`SOURCES.json`. Upstream material retains its own source notices and license.
+
+Related exact integer-packing verification work, inspected before this change:
+
+- Curtis Dransfield / @Curtis-D,
+  [PR752](https://github.com/CrocSwap/integer-mult-bounds/pull/752),
+  `3603d8d9184995ae1cc67c0f5e01f02f3a1d634e`: quadratic-affine witness replay.
+- @merramil, [PR778](https://github.com/CrocSwap/integer-mult-bounds/pull/778),
+  `f015b04c74801fa330f818d178e809c760fb5469`: single-intersection Gram replay.
+- @CubeJerry, [PR898](https://github.com/CrocSwap/integer-mult-bounds/pull/898),
+  `521c86e7fd4d0fbd1ed4e0524aa26a1e45861477`: Leech-minor byte lanes.
+
+This contribution applies the related injective-encoding principle to a
+different exact obligation: the complete rectangular sparse gather/scatter
+product against triple incidence, with an input-dependent signed radix.
+No pending PR implementation is imported and no novelty claim is made for
+integer packing itself.
+
+Curtis Dransfield's [PR809](https://github.com/CrocSwap/integer-mult-bounds/pull/809),
+`66cabb478385fbaa1a8060123cd57545d703d84e`, researches a basis shear of the same
+historical center. It is a construction contribution; this verifier retains
+the baseline factor and does not import or certify that PR's changed invoice.
+The final overlap check also inspected Ross Richardson's
+[PR937](https://github.com/CrocSwap/integer-mult-bounds/pull/937)
+(`b303fed6dfe2066dcd78c0d8ed74d2a3b153ba72`) and
+[PR947](https://github.com/CrocSwap/integer-mult-bounds/pull/947)
+(`b6f6418bdcae748b267cea72a5949d551feb7bb2`). These change the historical
+factor and classify a shear family, respectively; their construction/proof
+code is not imported or replayed here.
+
+The accepted frontier is credited in `community-frontier890-review.md`:
+Chafik Boukhalfa's T21 composition, Jeremy Kothe's U8 work, Hao Yan's T16
+mechanism, DreamingOfClouds' PR589 on eumemic's PR555, and their predecessors.
+This package does not alter their result or establish new source priority.