[d6g8k5htny-coder]

This supplies a constructive low-mode coupling for a new finite-word sampler of the planar side24 Gaussian field. Independent uniform128-bit input words, a clipped inverse-normal map, dyadic64 quantiles and dyadic128 Fourier weights give a low-mode error below 1.47e-18 at cutoffs24 and32. The proof covers every word, including CDF interval ambiguity and algorithm termination.

The source-bound certificate composes this error with #220's infinite spectral tail and normalization correction. At cutoff32, the ideal-field supremum error is at most 0.000000386931068362268551 outside a failure budget of 0.000000000007008709160237. This is an unconditional statement under the declared IID input model. No actual RNG law, historical PCG64 coupling, Gaussian barcode, lifetime-law confirmation, or independent human review is inferred.

The implementation replays a nine-word deterministic cutoff1 fixture. A future experiment must construct and separately certify its new polynomial, nodes and barcode. Frozen C39/C40 sources are byte-identical.

Validation: complete 20-stage local master passed on the unchanged tree; 88 experiment tests pass normally and under -O. Fresh nonauthor mathematical review and integration review pass on this exact commit without findings. All six current hosted checks passed, Codex review completed without findings, and original formal ZIP custody was verified: run36798912522 tested merge79d135e896fb1379d95ff02131d7978810693d4c, SHA25653e9155fc1ec7fe5f56e85de459762d24f06c46d53436708c869ff5cec796ea0. Formal alignment remains pending; no scientific promotion.

Current disposition:

• Head: 6f7da57f94777a25784b32ab62a4f2809d5ecd8f; tree: d43a10cd09602c06d4374ea7a4e97c016149557f; base: ece4f01ef0bc435babd159a39c94e3a07eaf8786.
• Integration owner: OpenAI/Codex root session01a0bbb5-2fcb-77f0-b78b-4d220ddd7ab2.
• R17 claim 94b525e1-1e79-47f1-a11a-3eb9cb27c1d5, Work Events392; pickup on Bound ideal Gaussian spectral tails and preserve the open coupling #220 comment5922321922; expiry2026-10-01T02:35:29Z.
• No unresolved candidate finding. Separate Math#205 reporting AMEND is retained at reviewed head b875a467; its author’s successor01d09e9 awaits a fresh bounded review.
• Completed: merged 8ed4e73bafb3c9fd97a439b2e30e4a795a567a4f, identical reviewed tree; all eight landed checks passed. Original landed formal ZIP run36799654218 SHA25603d041cb2c0d84fa68a3b0fbaf6d0ed2df2e23d3167d41ccda565b0e7903e9af verified.
• One private C41 archive SHA256d4b5e9120d73a3c2145480b93682c68f6605b2c5476789de57de84f97cc84cef, 5,229,433 bytes, raw readback identical. Registered Artifact Index835, Evidence Lineage557, Review Queue78–82; Work Events396–399 PUBLISH /400–403 RELEASE. Claim RELEASED.
• Next: certify a new polynomial/barcode under the declared coupling model, and separately review the newly amended Math#205 reporting bytes under a fresh claim.

Reviews are “Dylan Roy — delegated AI review,” with actual AI executor disclosed, personal reading PENDING and zero organizational-independence credit. Scientific gates stay unchanged.

[chatgpt-codex-connector]

Codex Review Summary

This comment shows the latest Codex review activity on this pull request.

Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-01T01:02:55.504373Z	6f7da57	PR opened

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[d6g8k5htny-coder]

Dylan Roy — delegated AI review. Actual performer: OpenAI / Codex agent /root/c41_remainder_algebra, fresh nonauthor for this candidate; Dylan’s personal reading PENDING; zero organizational-independence credit. Scientific effect NONE.

PASS_TECHNICAL, integration/custody scope only. Reviewed the exact 12-file C41 candidate and now bind this verdict to published PR221 head 6f7da57f94777a25784b32ab62a4f2809d5ecd8f, tree d43a10cd09602c06d4374ea7a4e97c016149557f, parent ece4f01ef0bc435babd159a39c94e3a07eaf8786. Candidate inventory SHA256 b6a3adc1b0450c04ec8918249360bc5a8617989f988bef37d0a524246ef5bd02; delivery source inventory SHA256 22a28d80829fce74febe8bb978287857ced9b8ae3467433930af682a87ab9c1b. Exact Git-blob comparisons verify all 40 delivery-source files against the commit and current checkout, including all 12 originally reviewed candidate files and all 28 consumed-source bindings. Changed paths are exactly the candidate paths; reviewed bytes are unchanged.

All 28 consumed source identities match; 25 inherited sources and all eight frozen C39/C40 packet files are byte-identical to base. Original certificates and receipts remain intact. Strict C41 directory replay passes normally and under -O. A separate reviewer script exercises 38 actual integration cases in each mode: original replay and produce/verify positives, plus 36 intended refusals, including nine false certificates with fully rebound output/receipt/report identities, malformed receipt/schema cases, duplicate/nonfinite JSON, source/output substitutions, report alteration, frozen C40 rebinding and output overwrite. No replay function was mocked.

All 47 local links across the changed reader pages resolve. The public decimal bound agrees with the exact certificate, IID inputs remain a premise, historical rho/full-field diagram bounds remain null, and new Gaussian barcode count stays zero. Workflow change is exactly one added replay step; required aggregate/formal/public workflow bytes are unchanged. Local CLI replay cost 23.38s/24.90s; focused controls 28.58s/28.79s. Full master and final tested-commit hosted checks remain separate, including the five-minute hosted runtime.

No actionable integration finding. This review excludes the full coupling proof (separate reviewer), whole imported theorem acceptance, actual input-source law, new Gaussian observations, lifetime-law or expected-count confirmation, scientific promotion and human/organizational independence. Detailed source assertions, exposure, scripts, stdout/stderr and receipts are retained in continuation41/evidence/coupling-integration-review.

Append-only publication attestation: published-commit-attestation.json, SHA256 10b531e1c465230ad7845394103bc495d9ab948957e69dbcdaaf9b6670377fe8; original REVIEW.md remains SHA256 5595df8ee8d67843a76748c0d4b75d11fb65d87643a086f84ce332f78719cffc. This is unchanged-source transfer of the existing scoped review, not a repeated proof or test run. Root reports the separate 20-stage master passed in 65.56s with 88 experiment tests in each mode; that report was not rerun here. Hosted required checks remain pending and are not discharged by this attestation.

[d6g8k5htny-coder]

Dylan Roy — delegated AI review. Actual performer: OpenAI / Codex, agent /root/c41_coupling_review, fresh nonauthor review of the prospective finite-bit Gaussian coupling proof, arithmetic implementation and certificate. Dylan's personal reading remains PENDING; organizational-independence credit is zero.

Technical verdict: PASS_TECHNICAL — ACCEPT for the stated prospective coupling scope, with findings [], bound to exact commit 6f7da57f94777a25784b32ab62a4f2809d5ecd8f (tree d43a10cd09602c06d4374ea7a4e97c016149557f, parent ece4f01ef0bc435babd159a39c94e3a07eaf8786).

I reconstructed the clipped quantile-bin Lipschitz argument, Mills bound and every-real-coordinate count, positive integral series with directed rounding, uniform every-input CDF precision and every-word bisection termination, weight multiplicities and coefficient error, and composition with the frozen tail contract. The source review recorded 8 passing focused tests, exact directory replay, and 8 reviewer-authored check groups: 69 independent rational CDF probes, 26 quantile words including clipping-threshold bins, coefficient bookkeeping through cutoff64, global precision witnesses, and substantive arithmetic/multiplicity negative controls. These finite checks provide implementation coverage; the all-input statement was also reviewed analytically.

The bounded commit attestation compared all 12 candidate paths, all 40 root inventory paths and all 42 original review inventory paths against both current files and exact Git objects (45 paths in their union). All identities match. Original reports were preserved; no tests were repeated to transfer the unchanged review. Candidate inventory SHA-256: b6a3adc1b0450c04ec8918249360bc5a8617989f988bef37d0a524246ef5bd02; source inventory: 22a28d80829fce74febe8bb978287857ced9b8ae3467433930af682a87ab9c1b; technical report: dd3db71eaee8ba412b49f301532c3f721e6334c537a1391b8e51aeea911036a7.

This statement assumes the declared IID uniform-word input law. It does not certify an RNG or physical source, the historical polynomial's coupling, any new Gaussian barcode, lifetime law, exceptional expected-count bound, formal-kernel evidence or independent-human review. Historical coupling and infinite-field diagram errors remain null. This is a technical source review, not whole scientific acceptance; integration/custody and hosted checks remain separately recorded. Author proof/source exposure and the full evidence are in the original review and appended commit attestation.

[d6g8k5htny-coder]

C42 complete: PR #222 merged at 3b242e76, with exact polynomial/grid/barcode bridge and one deterministic smooth-polynomial bin count. Two source-bound nonauthor reviews, one stable 21-stage master, current hosted checks and original pre/landed formal artifacts passed. One private immutable delivery was byte-verified, registered and read back; claim a808ae9d-f56a-4c7f-934e-178652927acb released. C41 source objects remain unchanged. Gaussian input law, expected counts, infinite-field observation, lifetime-law and scientific independence predicates remain separate.