Independent verification: quadratic-phase certificate for a selected cold wrapper

research/cold-wrapper-quadratic81/CLAIM.md

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+# Sprint claim
+
+- Track: independent verification; fresh OS-random seed **81**, drawn with
+  `secrets.randbelow(100)` on 2026-10-13.
+- Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60` (freshly fetched main).
+- Object: the selected #626 cold-helper pair `E = []`,
+  `U = [268, 140, 45, 30]`, width 4; helper register 442 in both providers.
+  This is recipe `0:429` in CK and `0:413` in JP8. Among each provider's 14
+  lexicographically sorted rank-4 cold recipes, seed `81 % 14 = 11` selects it.
+- Method: independent closed matrix-entry formulas over Gaussian integers,
+  checking every one of the 512 basis inputs and all 512 output coordinates.
+  No imports from the Clifford tableau/compiler or existing state evaluator.
+- Deliverable: pinned instance, exact full-operator check, meaningful wrong
+  phase/geometry/monomial controls, and a proof of the kernel formula's scope.
+  No new kappa and no full formal multiplication theorem.
+- Claim time: 2026-10-13 04:25 UTC; expected finish: 04:50 UTC.
+  Final quarter reserved for verification and handoff.
+- Three candidates: prime-power cyclic inverse identity (already two engines,
+  plus #668/#666), entering-helper wrapper (literal proofs in #593 and #581),
+  and this rank-4 cold wrapper. The third has no selected literal Lean theorem
+  and benefits from a different all-basis matrix-entry implementation.
+- Overlap: #662 accelerates the existing tableau/zero-state checker and compares
+  circuit-prefix states; this is an independent closed-kernel calculation.
+  #680 studies fixed register words, not this supplier wrapper. #675 audits
+  owner boundaries. Current negative results and review scope remain intact.
+- No pinned coordination issue exists; Discussions remains disabled and #650
+  asks for a channel. This local claim avoids opening a reservation issue.
+
+Joshua Snider (`jsnider3`), with substantial OpenAI Codex assistance. Apache-2.0.
+
+## Evidence-driven scope refinement — 04:30 UTC
+
+PR #702 at `27db45ac6befa99d6c06be920a93845023e81937` appeared at
+04:26:49 UTC while this work was in progress. It covers all 14 cold frames
+using direct matrix entries, including this pair. The initial one-pair replay
+here passed, but would duplicate that method. The single pivot keeps the same
+helper and replaces the deliverable with an affine-support certificate and
+coefficient-wise quadratic-phase identity over 13 Boolean variables. This
+independently corroborates #702 by symbolic algebra rather than a second
+all-column enumerator. No #702 implementation or result is imported.
+
+## Result — 2026-10-13 04:39 UTC
+
+Submitted [PR #712](https://github.com/CrocSwap/integer-mult-bounds/pull/712).
+The affine support map is bijective and the quadratic phase residual vanishes
+at all 92 coefficient positions. Thirteen rejection controls pass; five test
+groups include direct checks of all six phase components on all 8,192 Boolean
+assignments. Normal and optimized isolated runs from a separate committed-files-only
+worktree reproduce the exact saved certificate. Selected-record and whitespace
+checks passed. No new kappa or full theorem is claimed.
+
+Final overlap refresh through #711 found #702 as the related amplitude audit,
+credited for its broader frame coverage. The symbolic method is distinct and
+upstream main remains at the recorded base. No pinned sprint issue exists, so
+this is the local result update and handoff link. The source contribution is
+commit `634026a`; this follow-up changes only the claim's handoff record.