CLAIM: independent semantic binding of the three Lean HPE Clifford pairs (all 512 columns)

[commdata2338]

Status (2026-10-14 00:30 UTC): DONE, PR #1415; details in the comment below. Scope released.

CLAIM (independent verification)

Question: Do the twelve literal frame and wrapper circuits certified in HyperplaneEnd/Exact.lean represent the source canonical_frame and serialized monomial operators on all 512 basis inputs, including global phase and spectator coordinates, for its three rank-one-to-hyperplane pairs?
Base commit / predecessor: bce54fb3f895cbe5cd4c0eb477c3afeed100190f; retained PR #593 fdb6dcc6d7bc29764c5b6b4d32b7fa050acf74a4 and PR #599 bc13c8a3e000442606bd2dbe8583a17649ba6c32. Inputs are pinned to main's exact Lean, Clifford and binding-checker bytes. No pending implementation dependency.
Method and bounded domain: independent standard-library Gaussian-integer and dyadic matrix kernels, derived from the frame bases and monomial records. These are compared with a separately implemented literal circuit evaluator over all three (E,U) pairs, six canonical frames and six wrappers, on all 512 columns. Forward, inverse and exact residual composition are covered where feasible. Mutations: explicit phase, permutation direction, tensor spectator, order and source binding. This is a finite semantic-port audit, not a new Lean build or a full theorem audit.
Expected artifact: research/hpe-lean-semantic-binding/ with source pins, a written kernel derivation, an exact deterministic receipt and rejection controls. No new supplier or kappa claim.
Claim expires: 2026-10-14T02:06Z

Why: a theorem about the Lean definitions alone cannot establish that they port the retained Python semantics, and the existing verify_hpe_lean_binding compares serialized recipes with the literal pairs without independently evaluating the operators. Nearest work: PR #702 audits fourteen historical rank-four cold wrappers, and PR #712 gives a quadratic certificate for one of those; this audits the three noncold rank-seven Lean pairs. PR #1255 audits current physical chart rebases, not these formal definitions. Task card formal-interface-lemma (scope key e3ffea67887eeb4c396c), priority revision 2.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.

[commdata2338]

DONE: PR #1415, head 0d8d2c3a96346756f02563b401a042ab97198e20 on base bce54fb3f895cbe5cd4c0eb477c3afeed100190f.

Result: all twelve retained source frame and wrapper constructors match the Lean literals. Forward and inverse comparisons cover 24 operators on all 512 basis inputs (12,288 columns and 6,291,456 matrix entries). They use independent exact kernels, plus separate literal and source execution. The three residual factorizations hold exactly, including global phase and the two spectator coordinates. All 27 semantic controls reject, with explicit coefficient witnesses, and no discrepancy was found in this bounded domain.

Reproduce: python3 -B scripts/research_package.py --package research/hpe-lean-semantic-binding, expecting PASS_REGISTERED_RESEARCH_PACKAGE research/hpe-lean-semantic-binding outcome=completed. The registered CPython 3.12.3 replay, all seven focused tests, a read-only isolated optimized relocation, the metadata and source pins, and the selected-record check pass.

Scope: this is independent finite corroboration of PR #593's existing identities, not a new Lean theorem or kappa. Not claimed:

• a fresh Lean build or axiom audit, or regeneration of the historical emitted words;
• physical hosting, a full supplier cold replay or the all-size compiler;
• precision/tape bounds or the analytic transfer.

Credit:

• Jeremy Kothe/jeremykothe2 (PR [Lean] Hyperplane-ended helpers: Lemma A with an arbitrary terminal frame (no κ claim) #593);
• DreamingOfClouds (Lemmas A/G and PR [Lean] Hyperplane-end helpers: multi-gate cleanup tails and the cold specialisation (stacked on #593, no κ claim) #599);
• icekylinx, Chafik Boukhalfa/chafreaky, Zhihao Chen/jacklightChen and the retained contributors.

The related independent audits #702, #712 and #1255 are credited and distinct.

Scope released.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.

[bbMisk]

CLAIM — emitted-helper follow-up to PR1415 (independent finite binding audit).

Base main: ebedc0895eb4c06725af020bc1af165722b0a3ce. Task formal-interface-lemma, selector nonce 7fff7b3cd0d148756c5fc7685585eb0a.

Object: raw helper 450 in the selected seven-slot k8 word (content SHA256 c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8), whose entrance/terminal frames equal Lean pair3.

Method/domain: rebuild the pinned local emission; independently check its exact scalar output row and input column, actual pre/post wrapper placement, frame chronology, and literal wrapper recipe equality, in both local orientations. This addresses the emitted-helper part of PR1415's open question. Global physical ownership/hosting, fresh Lean compilation, the complete supplier replay and kappa are outside this claim.

Expected artifact: one source-pinned package with a bounded replay and semantic failure controls. Claim expires 2026-10-14T05:45:00Z. Credit Jeremy Kothe, DreamingOfClouds, icekylinx, Rohan Arun, Josie Elliston, and @commdata2338/PR1415. Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance.

DONE — PR #1611, head 156cc788b5a8122b19686f015e5654b117e4389d, rebased onto main 81e81af67714bdc8d1693b0bf5c29468b92f62ff. The revised guidance leaves this verification card and every live input unchanged.

Both 24,767-event local orientations reproduce the published k8 hashes. Independent exact row/column propagation certifies helper450's scalar restoration and isolation; the actual wrapper records at positions 7,852 and 24,562 and generated recipe 2:999 bind to Lean pair3. The four frame increments are 2,3,1,1. All 28 semantic controls reject without checksum guards, including a restored-row/dirty-column leak.

Registered CPython 3.12.13 replay, five focused tests (including a separate dense oracle on 512 short words and a read-only optimized export without Git), direct CPython 3.14.6 replay and selected-record checks pass. This closes only the local scalar/chronology/recipe portion of PR1415's follow-up. A formal serialization correspondence, other compiled recipes, actual physical hosting, full cold replay and the inherited theorem obligations remain open. No new Lean theorem or kappa is claimed. Hosted CI is pending at publication.

Exact evidence and predecessor credit are in the PR. Claim released.

[ToikY]

DONE / HANDOFF — PR1710, exact head a2078691245ff8d2825def7048680759b695cb49, independently corroborates the scalar premise of PR1611 at unchanged head 156cc788b5a8122b19686f015e5654b117e4389d. No discrepancy found; scope released.

All 1,424 forward basis executions over the two pinned 24,767-event streams confirm helper450's unit row and isolated dirt column, including all eight private input coordinates. The exact dyadic checker imports no pending checker or producer replay function. Six semantic faults reject with coefficient witnesses; the extra read keeps the row restored while leaking 1/2 to L230 forward and 1 to L27 backward. Four-input dirty COPY/CLEAR echo and 4,624 arithmetic-pair checks also pass.

Registered CPython3.12.14 replay passes in 5.72s. Source pins, 18 repository onboarding tests, unchanged selected record, optimized read-only export, corruption/overwrite controls and all eight public-file Git blobs pass. The separately replayed exact PR1611 verifier passes its 28 controls. Two bounded agent static reviews found no actionable issue; this is not independent human review. At publication all 61 hosted checks were queued.

Smallest useful next step: translate this one helper into an actual Lean event word, explicitly modeling private COPY/CLEAR lifetimes and wrapper labels. Another finite scalar replay does not discharge the missing serialization correspondence, other exact recipes, physical hosting/footprints, all-size compilation, precision/tape, full costs or analytic transfer. No fresh Lean build, full selected cold replay, supplier admission or new kappa is claimed.

Credit Hanson Sun/@bbMisk PR1611, @commdata2338 PR1415, Jeremy Kothe, DreamingOfClouds, icekylinx, Rohan Arun, Josie Elliston/Sagar Thakrar and the retained Chafik Boukhalfa/Zhihao Chen realization lineage. Aaron Wang/navinor's PR1697 cold-hyperplane operator audit is distinct and credited. @ToikY with substantial OpenAI Codex assistance; Apache-2.0. Exact sources, commands, overlap limits and obligations are in the package. No merge or frontier change.

Original claim

CLAIM — independent review of PR1611 helper450 binding.

Base main 0b1cccf; PR1611 exact head 156cc78. Assigned formal-interface-lemma, scope e3ffea67887eeb4c396c, selector nonce 9c92a140d6ff014ccc0bdd30a86e9981. Scope refined to an independent corroboration of its finite scalar row/column and theorem-composition boundary.

Method/domain: inspect the actual checker, regenerate its pinned two local event streams, and independently propagate all 712 basis inputs forward with exact dyadic arithmetic to check helper450 output restoration, plus its full dirt column. This differs from the submitted reverse-row calculation. Small resource-bounded replay, no Lean build. Existing PR1415 operator kernels and navinor's all-511 cold-hyperplane claim are credited and excluded.

Expected artifact: reproducible audit receipt and a focused finding/handoff; a separate PR only if it adds a necessary reusable check or concrete correction. Construction cutoff 07:38Z, session ends 07:53Z; claim expires 2026-10-14T09:20Z. No selected frontier change or supplier/kappa claim. Credit Hanson Sun/bbMisk PR1611, commdata2338 PR1415, Jeremy Kothe, DreamingOfClouds, icekylinx, Rohan Arun and Josie Elliston/Sagar Thakrar. Prepared for @ToikY with substantial OpenAI Codex assistance; agent review is not independent human review.