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Independent verification: Bernstein certificates for all 47 outer inequalities #813

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Merged
Mister-Meeseeks merged 2 commits into from
Oct 13, 2026
Merged

Independent verification: Bernstein certificates for all 47 outer inequalities #813

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71ba81c
Independent verification: certify all 47 outer inequalities with Bern…
bitplane Oct 13, 2026
5d3b961
Record seed-79 result and PR link
bitplane Oct 13, 2026
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42 changes: 42 additions & 0 deletions research/outer-bernstein-certificate/CLAIM.json
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Original file line number Diff line number Diff line change
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{
"assignment_seed": 79,
"drawn_at_utc": "2026-10-13T05:38:49.180785+00:00",
"track": "Independent verification or formalization",
"base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
"candidates": [
"Independent quadratic-phase verification of selected cold wrappers; overlap PR702/712",
"Algebraic positivity certificates for all 47 selected outer-assembly inequalities, plus both exact selected witnesses",
"Reverse scalar/dirty-centre restoration verification; overlap PR745"
],
"selection": "79 mod 3 = 1; choose the second candidate",
"scope": "Independently certify the retained 47-row outer arithmetic on its admitted parameter domain using exact multivariate Bernstein coefficients; bind the equations to the selected source and match native/conservative PR626 receipts. No supplier or all-size theorem claim.",
"method": "Sparse rational polynomials, denominator clearing, exact Bernstein conversion, independently interpreted source expressions and exact rational witness comparisons",
"expected_deliverable": "Written positivity argument, source-bound algebraic certificate, standard-library replay and mathematical controls; at most one focused PR",
"expected_finish_utc": "2026-10-13T06:25:00Z",
"coordination": "No pinned sprint issue exists; issue 650 requests Discussions. Local claim.",
"overlap_snapshot": {
"open_prs": 611,
"through_pr": 791,
"related_prs": [
183,
294,
701,
706,
678,
771,
766
]
},
"status": "completed; submitted as one focused PR",
"attribution": "Prepared for Gareth Davidson (@bitplane) with substantial OpenAI Codex assistance; Apache-2.0",
"completed_at_utc": "2026-10-13T06:08:19Z",
"result": "README.md",
"reproduce": "python3 -B -I research/outer-bernstein-certificate/verify.py",
"result_summary": "All 47 admitted outer inequalities receive exact positive Bernstein certificates; 57 polynomial records, 2586 coefficients and all 94 selected native/conservative slacks verified. No new kappa.",
"overlap_refresh_through": 810,
"validation": "24 built-in controls, 12 tests, independent SymPy coefficient replay, Python 3.12/3.14, optimized/isolated/relocated/no-site replay and selected-record integrity pass.",
"scope_note": "The closed-form ceiling and written reduction are credited to PR183; the contribution is independent complete coefficient evidence and exact selected-instance binding.",
"submission_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/813",
"validated_code_commit": "71ba81c628ec1d80383f131b0735b18f34d254cf",
"publication_check": "PR813 is open, non-draft, against main; only this ten-file package is added. A committed minimal export passed the main verifier, all 12 tests and the independent SymPy replay. The immediate queue check also inspected distinct PR811."
}
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