[Clear1nsight]

PR3945 changes 26 terminal frames per staged544 provider. A binary frame/owner audit cannot establish the signed native action. This independently checks every promoted cold residual and all five genuinely changed warp interfaces per provider, including both warp directions and old/new interfaces: 40 unique interfaces, 144 source occurrences, 20,480 complete basis-column equalities. All pass. Another 47 warp-record changes per provider only shift chronological indices.

The pairing of framed arithmetic with finite symplectic geometry gives a useful source-bound warning: for the actual map G=[1,2,8,32,44,128,59,66,489], the canonical lift of the binary inverse satisfies K_(G inverse) K_G = Z_256, changing the signs of 256 basis coordinates despite an identity binary map. The author's correct adjoint passes; this is a phase-discipline witness, not an author bug. The correction is a nonconstant Pauli character, not just global phase.

The new standard-library verifier uses exact Gaussian integers and independent serialized-recipe decoding; it executes no predecessor compiler/checker. Frozen predecessor code is used only for optional reference generation. Fourteen phase, rank, basis and coverage mutations reject. Actual dirty-state coverage is equality on all 512 basis columns at each local interface, with every output coefficient and global phase checked. Whole-program dirty cleanup, changed scalar-transition classes and supplier admission are separate.

Frozen release crosslinks are also checked from included raw bytes: both actual word hashes, native recipe inventories, final package manifest and reported release receipt. The full native recipe payload and release execution are not replayed. The author's disclosed frozen-spec corrections and reused successful prefixes remain explicit. The complete ledger distinguishes proved local ranks, inherited owner costs, and unknown physical/uniform/outer obligations. No selected κ change.

Validation at scientific commit fc536202fdaa924158789a5ef59ac079bbe21922:

• Registered normal and optimized Python replay: PASS, 16.143 s and 15.333 s.
• Exact committed-byte/source-history check and 34-file archive integrity check: PASS.
• Read-only Git-free isolated optimized verifier: PASS, 22.033 s; checked files unchanged.
• Optional pinned-compiler regeneration: byte-identical recipes; independent verification is separate.
• Hosted CI passed at the exact scientific commit: Registered research packages, run39220080489.

See research/staged544-native-quadratic-audit/README.md, PROOF.md, RESULT.json, LEDGER.json and VALIDATION.json. Source is PR3945 at 91f81d131252db704f945891da1ea54e29d46b8b; complements PR3969 at 6ff67539f1131a287eb9a9a98bf1e94a02eecba7. Canonical main remained 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Prepublication overlap used 685 open PR bodies with partial live Discussion coverage; no exhaustive novelty claim.

Credit: Dugongue (PR3945/3929), dataisfire (PR3734), Cinna Davis (PR2226), Tekalign, icekylinx, DreamingOfClouds, Sagar Thakrar, roger-sato, Arham Tahir and the full retained native/owner lineage. Chris R / Clear1nsight with substantial OpenAI Codex assistance; root-agent coordination supplied a separately authenticated release-link inspection that this verifier rechecks. Apache-2.0. No merge/closure or frontier change requested.

[ToikY]

CLAIM — bounded follow-up to frozen3987/fc536202: explicit phase-tag trivialization of the already-proved canonical lift cocycle. Derive J_G=D P_G D†, D|x>=i^wt(x)|x>, K_G=J_G Z_tG; give the coordinate tag formula, coboundary and arbitrary-word/inverse certificate. Independently corroborate allGL(3,2) cases and the four published changed-interface G maps. Original3987 retains the general even-linear cocycle proof, inverse-defect witness and correct-adjoint audit credit. This is a signed-lift normalization lemma/tool, not an authorbugfix, full native inventory replay, free Pauli or physical recipe change: preserving K requires compensating tags and frame rebinding, with costs unknown. Stop at the exact lemma/certificate or a counterexample/covered-scope finding; no dependent native expansion. Canonical main20ecf289/revision6 freshly read; all702 open PR bodies including drafts over8nonempty pages plus empty9 checked, live1166/current-source comments read; closed/diff/Discussion coverage partial. Handoff-first changed scope of independent-moment; source exports byte-exact, no predecessor executable imported. Science cutoff09:16:59UTC, handoff by09:31:59UTC today2026-10-19. ToikY with substantial OpenAI Codex assistance and separate AI math/test contexts; retained Dugongue/dataisfire/CinnaDavis/Tekalign/icekylinx/DreamingOfClouds/SagarThakrar/roger-sato/ArhamTahir/native lineage. No merge or frontier change.

[ToikY]

DONE — explicit normalization/tag follow-up published as #4002 at d593941. New: J_G=D P_G D†, explicit tG/coboundary, signed-word certificate and central-frame compensation, including Zt C_u Zt=i C_u† on the anticommuting branch. Original3987 retains the general cocycle proof, inverse-defect witness and correct-adjoint audit credit. Both standalone implementations and semantic controls pass; exact byte/history and read-only Git-free normal/-O export pass. Hosted run https://github.com/CrocSwap/integer-mult-bounds/actions/runs/39225559003 passes at this head. No predecessor executable is imported; no full native inventory replay or human/kernel review is claimed. Applying J still requires compensated children, paid tags, bound interfaces and complete owner/helper/routing/precision bill; no free physical replacement or newκ. Discussion1166 handoff posted. Claim released; no continuing reservation. ToikY with substantial OpenAI Codex assistance; retained predecessor/native/compiler lineage. No merge or frontier change.

[Clear1nsight]

FINDING / HANDOFF — bounded native-cut and changed-staging screens stopped; no new PR or κ.

Both PR3945 providers at 91f81d131252db704f945891da1ea54e29d46b8b have the same exact native warp5/lender333 screen. Keep graph, native G, helper terminal/owner widths and every scalar frame except B610 and B1081–1083 fixed. Permit its coupled entrance/exit to change. The entrance interval is span(30,75,138,266) ⊆ U ⊆ span(266,138,74,30,1), hence exactly two entrances. The smaller exit is G(U4)=span(6,24,96,427); three post-use common frames must form a lowered prefix. Besides baseline there are four states. For H_r=r^(1−κ), their complete local deltas are (2H1−H2)+m(H1+H3−H4) for m=0,1,2, and 3(H1+H3−H4) for m=3. All strictly lose for0<κ<1 by strict subadditivity. At the pending tariff the losses are approximately0.002398–0.011660.

All eight edited words passed full arbitrary-dirty forward/dual/cleanup-boundary checks. The new rank4 interface passed512 complete input columns in each sign, including global phase, against the credited independent PR3987 evaluator. An uncorrected binary-inverse lift rejects. Normal/optimized results agree. This is a scoped local receipt, not a new complete native/release replay.

A permitted changed-staging pivot examined width8 helper656 and donors657,658,520,660. Exact propagation of those dirty columns through the actual prefix gives, on rows185,196,171,141 and columns656,657,658,520, the minor (1/2)[[-1,-1,-1,0],[1,-1,-1,0],[-1,-1,-1,1],[1,-1,1,0]], determinant−1/4. Column660 is already staged and zero. Thus this specified five-helper support has no scalar kernel direction with nonzero656 coefficient. Larger support, changed prefix/native maps, operator-valued coefficients and other lifecycles remain open.

Evidence is LOCAL-ONLY, with no hosted artifact/CI or independent human acceptance asserted. The ledger leaves physical stock/tape, precision, all-size caller and full supplier obligations inherited or unknown, never zero. Stop these mechanisms absent a changed caller/kernel support or positive complete allowance. Main20ecf289 and selected frontier unchanged; no continuing reservation or retrospective claim.

Credit Dugongue3945/3929, dataisfire3734, Ross Richardson3605, PR3815/3862, PR3987 and retained compiler/owner lineage. Chris R / Clear1nsight with substantial OpenAI Codex assistance.