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Bind emitted k8 helper 450 to the retained Lean wrapper pair - #1611
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Batch review at Merged to Reviewed scope: Exact regeneration binds both complete k8 event streams and helper450's scalar row, column, frames and wrapper monomials to the retained pair3 literal. This is a finite theorem-to-emission binding; Lean event serialization and full hosted supplier realization remain open. 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. |
…kernel A - The certificate's fresh invoice pins WRAPPER-CHECKS.json's bytes (now bound and recorded); the gap is that no chain code reads its status, and exactness comes only from the producer's own generation and decoding (re-run in the cold replay, verify_slots.py:103). - Overlap: CrocSwap#1697 covers 0:1000..0:1003 as hyperplane cases, CrocSwap#1611 tied 2:999 to Exact.lean pair 3; only the 22 FULL-ended records were producer-only. Byte-identical example corrected. - Kernel B's monomial and F_w are checked against kernel A on every column before evaluation; RESULT records per-kernel counts; dead adjoint removed. - Controls: width -1 and +1; residual events must be pre/post only; exact record field sets. 17 tests. - Credits: Lemma A (CrocSwap#516), producer hpe_adapters_local.py (DreamingOfClouds), PR425 (jacklightChen).
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Change and mathematical scope
This finite audit connects helper 450 in the selected seven-slot k8 word to the retained Lean
pair3wrapper identity. It checks the actual emitted pre/post positions and frame path, exact scalar restoration and isolation, and both regenerated wrapper monomials. Onlyresearch/k8-hpe450-binding/is added.Both local orientations have 24,767 events and 19,693 scalar operations. Independent exact rational propagation gives a unit output row and isolated input column for helper 450, including the eight private center coordinates. The recipe
2:999equals Leanpair3, including both global phases. Its pre/post wrappers occur at zero-based positions 7,852 and 24,562; its four frame increments are 2, 3, 1, 1.This is a partial theorem-to-emission binding, with no new Lean theorem, supplier admission or kappa claim. Exact lowering of other events, a formal JSON-to-Lean correspondence, physical hosting/footprints, all-size compilation, precision/tape, full costs and analytic transfer remain separate. No fresh Lean build or full selected cold replay was run.
Task and overlap
formal-interface-lemma, refined tok8-seven-slot/raw-helper450/pair3/emitted-boundary. Selector nonce7fff7b3cd0d148756c5fc7685585eb0a; full card inTASK.json.ebedc0895eb4c06725af020bc1af165722b0a3ce; rebased onto81e81af67714bdc8d1693b0bf5c29468b92f62ff. Revision-3 guidance was reread: this card, all live inputs and the selected result were unchanged.156cc788b5a8122b19686f015e5654b117e4389d.c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8. The selected source manifest binds the slot pins; fresh canonical and forward/backward event payloads match those pins.0d8d2c3a96346756f02563b401a042ab97198e20, already audits the fixed operator kernels. This addresses its explicit emitted-helper follow-up. No pending PR implementation is imported or executed.Validation
Registered replay passes on CPython 3.12.13/macOS. The direct replay also passes on CPython 3.14.6. All 28 semantic mutations are rejected without checksum guards. One control preserves the helper row but leaks its dirt elsewhere: coefficient 1/2 at L230 forward and 1 at L27 backward, rejected by the column check.
Five tests cover a separate dense-matrix oracle on all 512 three-operation words at three local coordinates, structural errors, source tampering, receipt tampering, and an optimized read-only source export without Git. The selected-record check and whitespace check pass. Hosted CI is not claimed.
Deterministic receipt SHA256:
1a343f661c9a47c9a5aa5ad5a4308c9f56d10c5a1934542bb5e6cbf889c8ad71. Sources and CI invalidation inputs are explicit; regeneration uses temporary directories and compares decompressed payloads.Credit
Jeremy Kothe (formalization/k8), DreamingOfClouds (wrappers and Lemmas A/G), icekylinx (compiler), Rohan Arun (selected packing), Josie Elliston and Sagar Thakrar (retained word/audits), @commdata2338 (PR1415), and the credited Chafik Boukhalfa/Zhihao Chen realization lineage. Original notices remain unchanged; new work is Apache-2.0.
Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in analysis, implementation, validation and writing. No independent human review is claimed.
Open next questions
The README and
TASK.jsonidentify two remaining connections: an explicit Lean event translation for this local certificate, and helper450's actual T16 physical invocations. The first is blocked on the serialization correspondence; the second on chart/route, compiled-recipe and footprint evidence beyond this audit.