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Independent verification: bind all 511 cold hyperplane operators with phase and spectator - #1697
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Batch review at Merged to Reviewed scope: Independent exact semantic binding of all511 cold hyperplane terminals with global phase and chart spectator retained. Packed-basis evaluation is justified by explicit coefficient/radix bounds; external finite evidence, not Lean instantiation or emitted-helper admission. 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).
2 participants
Result and scope
Independent finite semantic binding for empty entrance E=0 and all 511
hyperplane terminals U in F2^9: the actual canonical-frame circuit and
serialized child wrappers satisfy
L^-1 T_U R^-1 = C_[8] tensor I_2, exactlyincluding global phase and the wrapped coordinate chart's one spectator.
The retained HPE proof note records a local all-511 cold check but says its
checking script was not shipped. This package makes that source-side premise
reproducible; the original finding retains credit. No new Lean theorem,
kernel execution, emitted-word replay, supplier adoption, invoice or kappa.
Assignment, source binding and overlap
formal-interface-lemma, refined tothe independent theorem-to-certificate binding method.
3b261ab51d51856a178fbaca68514f8a; catalogue scope keye3ffea67887eeb4c396c.d78fe4bbb6f6b769e39586f8bb3ba8c31a31fd3a.exact_cold/cold_hyperplane_widthinHyperplaneEnd/Multi.lean, zero entrance, normals 1..511, sourcecanonical_frame(9,U)and serializedlower_childmonomials.last-change commit
1db1fbe68cb5186899cf1fd691bc92056a845e49; compilerlast-change commit
e07a8a3f9f79c22113398a0c5dbbc7601f489b3e.computation. Final refresh at 2026-10-14T07:13Z covered 385 open PRs and
337 discussions with complete pagination, plus local notes/ledger.
non-cold C7/two-spectator pairs. Existing cold14 packages check fourteen
rank-four endpoints. Neither supplies this all-511 rank-eight audit.
No competing concrete binding was found; no novelty certificate claimed.
Evidence and independent method
Every annihilator kernel has 256 elements and an independently constructed
eight-vector basis. Every producer child reports rank eight and the zero
entrance has an empty circuit. Candidate constructors internally use their
tableau/zero-state machinery; neither is the independent acceptance oracle.
A separately written Gaussian-integer literal evaluator and serialized inverse
monomial evaluator compare the wrapped operation against the closed-form C8
kernel
16*(-i)^popcount(delta)at common denominator256, with cross-spectatorzeros. The encoded input uses radix2^18. A proved numerator coefficient bound
4^8 plus reference bound16 gives difference digits <=65552 < radix-1, so exact
packed equality forces all matrix entries to agree. This logically covers
261632 complex-linear columns / 133955584 entries without storing those matrices.
It is not a claim that equality on an arbitrary single input proves equality.
Five circuit faults reject, plus the unsafe-radix alias control. Optimized CLI
tests reject omitted-hyperplane/unsafe-radix receipts and int/float or int/Boolean
receipt aliases with explicit diagnostics. The type-alias edge case was found
in separate AI review, reproduced by failing tests and fixed by type-preserving
canonical JSON comparison. Fresh registered replay passed afterward.
The separate read-only AI mathematical/code reviews found no critical or
important issue. The code reviewer independently expanded ordinary basis
columns 0,1,255,256,511 at normals 1,257,511 using Gaussian/Fraction arithmetic:
30 physical/wrapped equations and 15360 row entries agreed, including global
phase and spectator identity. That review is not human or kernel review.
Files and reproduction
Adds only
research/cold-hyperplane-semantic-binding/:README.md,TASK.json,SOURCES.json,VERIFY.json,RESULT.json,verify.py,test_verify.py. Predecessor sources and selected record untouched.Observed on Windows/Python3.12: metadata/pins PASS; two unittest groups PASS
(79.309s); full registered replay PASS.
Remaining obligations and credit
This supplies external finite evidence for hE/hU in the stated operator model,
not a numeric-mask-to-Lean adapter or a proof term. Actual helper unit rows/
zero columns, tails, recipes, chronology, footprints, whole-call hosting,
precision/tape, all-size compiler and analytic obligations are not rechecked.
No new moment or a<D/E improvement is claimed: the conditional width-eight
operator interface is checked, not a new fully priced physical supplier.
The bounded next question in README/TASK is a formal normal-1 cold instance
followed by a generic canonical-frame semantic bridge. No full cold replay or
hosted-CI success is claimed.
Credit Jeremy Kothe / jeremykothe2
(#593), DreamingOfClouds
(#599 and Lemma A/G/compiler
lineage), commdata2338's independent non-cold binding
(#1415), icekylinx's retained
compiler package and the original cold14 source checks. No predecessor files
are copied or edited. Prepared by Aaron Wang / navinor, with help from
chatgpt, including substantial research, implementation, writing and separate
read-only AI reviews. Apache-2.0.
Workflow feedback: the formal-pair survey prevented repeating a saturated
non-cold audit. The smallest/mixed probes succeeded before the complete family.
No directly fitting open handoff was found; the chosen card's source-binding
route was retained. No dependencies were installed. At the donor's request,
the temporary custom-location worktree will be cleaned after publication.