Independently audit HPE energy-radix full matrices

[RossRichardson]

Independently corroborates Arham Tahir’s PR #1906 at 788848032c16bbe0a543c1186c6691c66131c090. A separately written closed literal parser and direct integer realification reconstruct all six pinned HPE matrices, without importing the predecessor parser/interpreter, using adjoints, or accepting a packed fingerprint. All 3,072 complex rows and 6,291,456 real entries agree across the three normalized pairs; the complete row digests and energies match the predecessor receipt. This closes the finite forward/adjoint independence gap left by its sampled correspondence check. No discrepancy or new radix bound is claimed.

Only research/hpe-energy-independent-audit/ is added. It includes exact source pins, the unmodified attributed PR1906 receipt, a deterministic audit receipt, a task card and a registered replay. A separate exact-circuit specialist reviewed the all-dimension energy/sharpness argument, valid-gate unitarity, normalization and the new code. This is independent AI review, not human or Lean review.

Validation: CPython 3.12.12 on macOS arm64 registered replay passes, including seven test groups, 585 complete short-word comparisons against dense Gaussian-rational matrices, phase/character/scale controls, equivalent presentations, seven checksum-free receipt corruptions, detector-removal sensitivity, missing evidence, explicit regeneration and optimized read-only relocation. The direct oracle also passes under optimized CPython 3.14.6. The pinned predecessor’s direct verifier, selected-record integrity and whitespace checks pass. Hosted CI is separate.

Reproduce: python3.12 -I -B scripts/research_package.py --package research/hpe-energy-independent-audit.

Scope: written proof review plus finite literal-matrix verification. No new Lean proof/build, supplier cold replay, canonical-frame derivation, physical hosting, precision/tape cost, full multiplication theorem, or new kappa. The source-specific parser is not a general Lean parser; source authentication is material. Formalize the energy-kernel lemma and guarded-gate row norms before adopting the reduced-radix checker.

Credit PR1906/Arham Tahir, PR1859/woklerx, PR593/Jeremy Kothe, commdata2338’s earlier semantic-binding work, PR1781/Sagar Thakrar’s distinct recipe census, and the retained Clifford/Lemma A/G lineage. Prepared for Ross with substantial OpenAI Codex assistance, Apache-2.0. Current-main base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selector nonce cfbe139628a1920458d65ac59391c82d, independent-verification / refined formal-interface-lemma. Claim and audit discussion.

Final overlap refresh: 582 open PRs (including drafts) and 563 Discussion/comment/reply records, complete pagination and no warnings at 2026-10-14 14:20–14:22 UTC. The nearest results are the deliberately audited PR1906, predecessor PR1859 and their coordination thread. Titles/bodies and indexed local notes are covered, not every diff or nested source; no novelty proof is claimed. PR1906 and main remained at their pinned heads.

[Mister-Meeseeks]

Batch review at a055aaf34b012e04714066aafbfc7057ee1f3e9f.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent closed parser and direct realification check all6291456 entries of six retained matrices, all3072 row energies and1906 row digests. Seven tests include585 small dense words and nonunitary countercontrol. Corroborates1906 without importing its interpreter; no new bound, Lean build or selected supplier replay.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.