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Scoped negative result: 72/77 copy-cost lower bounds for two masked Walsh P112 totals #1689

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Merged
Mister-Meeseeks merged 3 commits into from
Oct 14, 2026
Merged

Scoped negative result: 72/77 copy-cost lower bounds for two masked Walsh P112 totals #1689

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d57696c
Preserve pinned PR845 geometry and attribution [skip ci]
just-mn Oct 13, 2026
efeb7a1
Research: exclude two masked Walsh P112 totals
just-mn Oct 13, 2026
f877240
Document current P112 overlap and open questions
just-mn Oct 14, 2026
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35 changes: 35 additions & 0 deletions research/p112-masked-walsh/CLAIM.json
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{
"track": "structural decoder research",
"seed": 48,
"seed_source": "secrets.randbelow(100), operating-system randomness",
"base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
"claimed_at": "2026-10-13T11:43:53.824293+00:00",
"expected_finish": "2026-10-13T13:00:00Z",
"candidates": [
"Two additional P112 decoder totals",
"Asymmetric higher-dimensional cube decoder",
"Restored-total reuse across decoder stages"
],
"choice": "Two masked Walsh totals; seed 48 selects the P112 branch from the three candidates (48 mod 3 = 0).",
"object": "P112 exact 2G factorization retaining all eight coordinate reader columns, adding two cut-supported Walsh sources and two unimodular mixed readers.",
"domain": "28 coordinate pairs \u00d7 511 nonzero F2^9 label functionals \u00d7 40 matrices in {-1,0,1}^{2x2} with determinant +/-1",
"method": "Exact pairing ranks; seed-shuffled cut order; exhaust all 572320 cases, no early success stop.",
"deliverable": "Scoped complete finite cost census, deterministic certificate, exact endpoint identity, negative controls and independent replay. No new kappa.",
"coordination": "REST search returned only open issue 650 (Discussions), so no open sprint issue exists; local claim.",
"overlap": "695 open PRs inspected through #904; #845 covers one total; #717 covers in-column-space/gauge families and reports unfinished mixed-beta searches; #669 and #772 already cover asymmetric proper-star geometry; #848 covers restored R439 sharing. None covers the declared masked-Walsh family.",
"revised_expected_finish": "2026-10-13T19:30:00Z",
"refinement": "The finite census revealed a support-cell reduction: additionally certify an optimistic lower bound for arbitrary real coefficient matrices with both columns nonzero, using six scalar and five reader-support representatives.",
"continuation_recorded_at": "2026-10-13T18:46:49Z",
"outcome": {
"status": "completed scoped negative result",
"result": "README.md",
"certificate": "RESULT.json",
"all_real_copy_lower_bound": 72,
"all_real_nonzero_sources_lower_bound": 77,
"finite_cases": 572320,
"finite_minimum": 72,
"finite_nonzero_sources_minimum": 78,
"independent_replay": "passed; direct binary pairing matrices match all histograms",
"publication_branch": "https://github.com/just-mn/integer-mult-bounds/tree/codex/p112-masked-walsh/research/p112-masked-walsh"
}
}
1 change: 1 addition & 0 deletions research/p112-masked-walsh/GEOMETRY.json
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24 changes: 24 additions & 0 deletions research/p112-masked-walsh/NOTICE.md
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# Attribution and license

Prepared for Denis (@just-mn), with substantial OpenAI Codex assistance in
research, proof development, implementation, verification and documentation.
An economical separate Codex worker implemented the independent pairing-matrix
replay. This is AI-assisted independent implementation, not human peer review.

New files are under the repository's Apache-2.0 license.
`vendor/pr845-geometry.py`, `vendor/pr845-PROOF.md` and `vendor/pr845-NOTICE.md`
are unchanged copies from Mihir Srivastava (@mihir-s-05), PR845 at
125ce25bdae421627b56077adc14940c2d0aa52f. Their original notice is retained.
They credit DreamingOfClouds' PR717 model and PR446 copy interpretation and
Joel Pulikkan / GamingPuzzled's PR620 baseline. All remain predecessor work.
GEOMETRY.json is generated from that exact geometry implementation.

The context of the selected construction retains Jeremy Kothe's PR799,
Chafik Boukhalfa's PR741, DreamingOfClouds' PR589, eumemic's PR555 and the
repository's cumulative contributor lineage. No priority for their results,
or a new selected kappa, is claimed here.

The final overlap review also credits concurrent work by Philipp / @mightyOil
(PR1191 and PR1197), @thakrarsagar (PR1327), and the free-rectangle work in
PR1375, PR1460 and PR1473. Their statements are compared in README.md and
heads recorded in OVERLAP.json; their implementations are not imported.
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