[ToikY]

Change and mathematical scope

Adds an external written review of Nick Petalas #6574, pinned to 48e312ff18d5b66b0969148f615fdf5ce0f92edd. No material theorem or kernel gap was found in the conditional implication from its finite correction predicates to the all-integer bijection, both inverse compositions, exact complex sum and local error bound.

The review binds complete Walsh quotient coverage, offset congruences, the complete target permutation, target-indexed inverse partners, weighted sums and norm/zero conditions to the actual kernel. It keeps the two diagonal phases and global sign in the correct nonlinear inverse order. The all-integer map is distinguished from the4096-bit entry guard and4090-bit round-trip headroom; outputs are not recapped and the bounded admitted set is not a register permutation.

A minor prose clarification follows from the fixture expression: a shift parameter B in(128,1024,4090) constructs some B+1-bit components, so the last fixture reaches4091 bits. No fixture ran; this is not a theorem, API or headroom failure. The source retains its codec, matching,64-row certificate, table, sharp constant and all finite outcomes, none newly established or replayed here.

Task and overlap

Advance claim and handoff. Canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a, eight guidance pins, revision8 and selected6030 were refreshed for the round and before publication. The full formal-interface card is retained with changed written-review scope; its formal/kernel gate remains unmet.

Checked the live Hub/index,704 complete open/draft bodies and heads across eight pages, targeted all-state searches and the source's empty timeline. Final refresh: no metadata/head/body changes, source unchanged. #6536's three-axis contract, #6573's stochastic prefix variance, #6585's phase isolation, #6619's added norm premise, #6146's shear and the earlier retained-record reviews address different interfaces. Sparse local, hidden and unindexed coverage remains unknown; search absence is not a novelty proof. Prior results are excluded.

Validation

Exact review, inert source texts and sealed roles. REVIEW13,882bytes, SHA256 d346f62f9f2d5d145682d1cb62ba53cc4420f9e3e072a13627ca4f0145fe24eb. Target-known abstract and source-aware code drafts were sealed before peer reading, then source cross-binding and exact-version assessment passed. Historical source/preclaim exposure is disclosed; first drafts remain unchanged. Nine/nine overlapping written controls are UNEXECUTED, not18 experiments. Actual table existence and source finite outcomes remain conditional and unreplayed.

All25 files froze at02:03:11.278644UTC. Ten exact source objects total65,198bytes; actual foreign Git custody is separated from ten canonical provenance pins. The full original card, sole canonical parent, package-only change and unchanged selected record passed. All25 public files match frozen bytes/modes/sizes. A separate byte role passed31 checks, SHA2562f0b08f2c57a076d6535f2d57bb2401178d1811bd5c4b996a0074cb6ef9732ec, with prior abstract/cross involvement disclosed. The complete26-member194,560-byte manual export passed full readback, SHA256 f3c3889ae73b4e5284a9bb9c614843b8e6a2d83a379dfad011be2dd245793fef. Upstream path/blob/mode locators and two plaintext hashes were checked; the consumer-construction body and foreign ORIGIN context body were not read. This inert subset has no scientific VERIFY hook and is not an original runnable-suite assertion.

Original CI run42148118686, attempt1, passed711 helper tests/24 skips on Python3.12.16. Scientific replay was skipped with zero commands. Exact synthetic checkout62bcd9497d9f1bf75d346f080fd87d43eba7776d has the public tree and canonical/public parents; this is not a repository merge or mathematical acceptance. The170,625-byte plan log was downloaded once and fully reread, SHA25657168ab547637770b2669aae7688f49a673049ee812c2f5b4392375276368380. At least15 minutes of verification precede handoff. No source imports, constructor, matching, class enumeration, certificate, endpoint fixture, fault campaign, NumPy/native operator or proof kernel ran.

Credit

Nick Petalas #6574 retains the codec, matching, certificate, sharpness, table and original finite evidence. Credit Ali Romman #6536/#6534/#5821, David Ganz/Dugongue #5815, Brian/JoyboyBrian #5485, #4743 and every retained Gaussian/native/compiler/NOTICE contributor. Walsh orthogonality, quotient algebra and matching are classical. ToikY used substantial OpenAI Codex with separate abstract, code, metadata and byte roles. Attribution/license is retained; no blind, human, kernel acceptance or endorsement is claimed.

Open next questions

Formalize the complete certificate-to-lattice/kernel implication; separately bind a literal caller's charts, adjoint/group order, dirty banks, precision and full transform/classification/table-access/restoration invoice. Phase covariance, exact fourth power, inward norm and predecessor ports are not inherited. Full supplier/outer admission and all five selected assumptions remain open. See TASK for first steps and blockers. No κ/frontier/adoption change or merge; maintainer edits and auto-merge disabled.