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Proved: five-label length-twelve high-weight pruning is sound #4903
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DONE — PR #4992 proves the sharp high-weight cap 11, including the missing nonplanar (8,4) case. This closes Open next question 1 of PR #4907. The claim is released. Exact head: Scope: simple restored universal length-twelve singleton-prefix walks on F2^5, with functionals of weight four or five. Universality forces a repeated minority projection in an (8,4) split. The cycle needs at least five neighbor incidences; the complementary translation permits four. This excludes every minority shape. Small support bounds then give cap 11 for (6,6) and (7,5), with equality witnesses at both weights. The observed cap and absence of (8,4) words were already in PR #4907; the contribution is their proof. Checks passed: all 23,816 small support sets; all 127,400 invariant-majority set pairs; a separately implemented literal graph search on all 13,664 universal sets; both equality witnesses; 12 semantic controls; eight actual code mutations; normal/optimized Python 3.12 replay; committed-byte and export checks; Git-free read-only optimized replay; proof/receipt corruption controls. The optional full-history wrapper could not run in the shallow checkout; all four pins were checked against the base and its explicit ancestry instead. The PR body and rendered HTML were read back and matched the reviewed draft. Hosted CI was pending at publication. No new kappa, selected-frontier change, engine integration, seven-label exclusion, supplier admission or full multiplication theorem follows. Independent human and proof-kernel review remain open. The next useful task is a partial-prefix completion contract before any engine change or runtime claim. Credit Mihir Srivastava (@mihir-s-05) for PR #4907, Nick Petalas (@petalas) for PR #4894, and the earlier lineage credited and linked in the package. Prepared for Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"census-pruning-audit","scope":"Sharp cap 11 and structural exclusion of all (8,4) splits for universal five-label length-twelve walks; PR4907 open question 1","base":"b91956876e5b4122fd89179f1b57557ff8378f15","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/4992"} |
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DONE — PR #5001, head The proof counts unused matching edges and endpoint capacity for a simple cube path. Every completion satisfies an even crossing-count interval, with the final closing edge included. This holds for all n>=2 and even 4<=L<=2^n; no universality assumption is needed. The bounded verifier checks 110,655 prefix/functional cases and all 3,838 closed cycles in four domains, plus a separate literal-word enumeration in two domains. It finds 704 strict prefix rejections relative to matching balance and return distance. Five actual code mutations fail; normal/optimized, exact-pin, committed-byte and Git-free read-only export checks pass. The PR body and rendered HTML were read back. Hosted registered-package CI passed at the published head. No maintained engine, seven-label exclusion, performance gain or new kappa is claimed. Next step: measure an opt-in engine integration against unchanged leaf receipts. No integration claim is held. Base {
"schema": "integer-mult-coordination/v1",
"kind": "DONE",
"task": "census-pruning-audit",
"scope": "Sound partial-prefix matching capacity for simple hypercube cycle completion",
"base": "bee95ce88f9f19802f0613f92838895cd0e14a1f",
"expiry": null,
"artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5001"
} |
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DONE (scoped result) / 2026-10-23T07:14:31.732132+00:00 / priority revision 7 The actual union-census successor now offers an opt-in matching-capacity predicate behind a proved simple-prefix caller gate. Complete restored/hit multisets agree in five bounded domains. At n=5,L=12 nodes fall 3.43%, but local process-inclusive median rises about 50%, so the predicate remains off by default. Public artifact: #5033, exact head Evidence status: author-checked with a separate AI-assisted read-only source/logic review; normal and optimized registered checks, source pins, committed bytes/history and package export checks pass. Exact commands, environments and unrun obligations are in the package. Hosted CI status is separate and is not implied by DONE. Scope: Integrate PR5001's proved matching-capacity completion test as an opt-in prune into one existing maintained simple-cube-walk census, preserving the complete accepted/restored leaf multiset and reports. Measure both node reduction and end-to-end runtime in bounded n<=5,L<=12 domains; a slowdown or redundant predicate is a valid decision, not a speedup claim. Next work: see the package's Open next questions and explicit remaining contracts. No new selected frontier, complete multiplication theorem, independent human review or proof-kernel acceptance is asserted. This claim is released. Credit: Ali Romman PR5001/PR4992; Nick Petalas PR4894 matching balance; Mihir Srivastava PR4907 handoff; Ross Richardson PR943; Nicholas Stone PR2973 parity correction. New work substantial OpenAI Codex assistance. Prepared by JoyboyBrian with substantial OpenAI Codex assistance. {
"schema": "integer-mult-coordination/v1",
"kind": "DONE",
"task": "census-pruning-audit",
"scope": "Integrate PR5001's proved matching-capacity completion test as an opt-in prune into one existing maintained simple-cube-walk census, preserving the complete accepted/restored leaf multiset and reports. Measure both node reduction and end-to-end runtime in bounded n<=5,L<=12 domains; a slowdown or redundant predicate is a valid decision, not a speedup claim.",
"base": "f259dabc7d70e0db8d6d36bfda888f008bbfecc1",
"expiry": null,
"artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5033"
} |
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DONE — PR #5044, exact head The new generator checks all 51,975 coordinate-normalized multiplicity words before geometric filtering: 3,381 simple walks, 828 universal walks and 4,968 high-weight cases. Review and completeness argument; exact receipt. Normal/optimized registered replay, the predecessor's registered replay, eight receipt-independent semantic mutations, committed bytes and official export integrity pass. Fresh Git-free, read-only optimized export replay/mutations preserve all eight files. Hosted run39917060220 was queued at publication; no hosted pass is claimed here. Export SHA256: The concurrent six-plus-six path-join audit is credited as a separate oracle. PR5001 engine integration remains its existing claimant's task; no claim is held here. This contribution does not change the selected frontier, central acceptance ledger or complete kappa calculation. No independent human/proof-kernel acceptance, seven-label census, supplier admission, selected cold replay or optional full-history preflight is claimed. Prepared by Mihir Srivastava with substantial OpenAI Codex assistance. The account's predecessor #4907 authorship is disclosed. Credit Ali Romman #4992, Nick Petalas #4894, unpaidmoon #4148, Nicholas Stone #2973, James Reed #3096 and Ross Richardson #943. Apache-2.0. Original advance claim, retained as history and superseded by the DONE status above: CLAIM / 2026-10-23 07:08 UTC / priority revision 7 I take the independent-review portion of Ali Romman's PR #4992 handoff (#1166 (comment)). Canonical base: Question: does the written sharp-cap argument cover every minority shape, and does an independently implemented complete-word oracle corroborate cap 11 and absence of (8,4) splits? I will review the alternating-level/repeated-projection implication and support classification, and enumerate the 51,975 normalized words with multiplicities (4,2,2,2,2), retaining all words until literal closing/simplicity and universality checks. No excess, support, matching-balance or quotient prune will select the candidates. Separate-class support accounting, sharp witnesses and deliberate failure controls will be checked. This is an explicit independent audit, not a new bound. It is separate from JoyboyBrian's active PR5001 engine-integration claim. The ledger currently records #4992 as archive-only/partially reviewed, with scientific review and source-bound replay open. My own prior #4907 result is a credited predecessor, so this is a new solo agent/code check of Ali Romman's successor, not an independent human or proof-kernel acceptance. Overlap: 323 open PRs and 4,134 Discussion records, complete remote pagination at 2026-10-23 07:04 UTC; relevant #4903 comments and the ledger were read. Sparse local coverage initially included 7 of 6,710 note records; omitted notes, arbitrary diffs and unpublished work remain limits. Selected-baseline source bindings pass. Expected artifact: a focused independent-check package and proof-review note, or a precise counterexample. Stop after this bounded check; no engine change, larger census, supplier admission or new kappa. LOCAL-ONLY until publication. Claim expires 2026-10-23T09:08:00Z. Credit Ali Romman (#4992), Mihir Srivastava (#4907), Nick Petalas (#4894), unpaidmoon (#4148), Nicholas Stone (#2973), James Reed (#3096), and Ross Richardson (#943). Prepared by Mihir Srivastava with substantial OpenAI Codex assistance. Apache-2.0. {
"schema": "integer-mult-coordination/v1",
"kind": "DONE",
"task": "census-pruning-audit",
"scope": "Independent proof review and complete position/perfect-matching word oracle for PR4992 sharp cap11",
"base": "f259dabc7d70e0db8d6d36bfda888f008bbfecc1",
"expiry": null,
"artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5044"
} |
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DONE — PR #5049, head d51e570. This completes the independent-review part of Ali Romman's PR4992 handoff. Claim released; no new kappa. Written proof audit and independent completeness argument and exact receipt. The independent six-plus-six path join checks 221,700 rooted length-twelve cycles up to reversal, including 49,680 universal cycles and 298,080 high-weight functional cases. Every mask has maximum excess 11; no universal weight-four (8,4) split exists. The full histogram matches PR4907 after the exact factor 60. The theorem and earlier measurements remain predecessor results. The written review finds no blocking gap, explicitly checking repeated minority projections, y=w, and the affine-basis reduction. No predecessor executable is imported, and no audited bound is used to prune generation. Evidence: Windows 11 / CPython 3.12.0 normal and optimized registered audits pass. Six small literal-word domains cover all 77,019 words and exactly agree with the joined cycle sets. Eight semantic rejections, both sharp witnesses, six actual code mutations with receipt comparison bypassed, and two private source/typed-receipt corruptions pass. Original PR4992 normal/optimized registered replay also passes separately. Metadata/pins, all 11 committed package/input files and official export integrity pass. All three direct commands pass in a fresh Git-free export with empty PATH; all 12 exported files stay unchanged. Export SHA-256: 390f02f42b334ad4c4eec372f1648a65a03d96e9a62850c7b14c8a7f0585d6dd. Hosted plan was in progress at publication; local checks do not imply hosted success. Reproduce with Python 3.12: python3.12 -B scripts/research_package.py --package research/f7-sharp-cap-independent-auditScope and remaining obligations: AI-assisted independent implementation and proof review, not independent human or proof-kernel acceptance. Full-history ancestry preflight was not run in the shallow checkout. No engine integration, seven-label census, supplier admission, selected cold replay or complete multiplication theorem is claimed. The selected kappa remains 60403/20000000. PR5001 and JoyboyBrian's active prefix-engine integration remain separate. The next review is the four-block contradiction and support reduction by an independent human or proof assistant; no larger census is proposed. Freshness: priority revision 7; source base f259dab; audited PR4992 head 12a0105. Canonical main refreshed to 4c0a359 with governing guidance, selected record and audited inputs unchanged. Final advisory overlap: 304 open PRs at 07:19:57 UTC, 4,153 Discussion records at 07:21:20 UTC, 103 local records; 6,609 tracked notes omitted. Arbitrary diffs and unpublished work remain limits. Credit Ali Romman/#4992, Mihir Srivastava/#4907, Nick Petalas/#4894, unpaidmoon, Nicholas Stone, James Reed and Ross Richardson. Original sources/notices unchanged. Prepared by Mihir Srivastava with substantial OpenAI Codex assistance, solo; not a blinded or human review. Apache-2.0. Original advance scope: independently review PR4992 and join two six-edge paths to audit the complete finite domain; no engine integration. The original claim was scheduled to expire at 09:15 UTC and is now released early. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"census-pruning-audit","scope":"Independent proof and six-plus-six path-join audit corroborates PR4992 sharp cap 11; separate from PR5001 engine integration","base":"f259dabc7d70e0db8d6d36bfda888f008bbfecc1","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5049"} |
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Coordination after the pre-submission overlap refresh: the position/perfect-matching audit is complete locally. It generates all 51,975 multiplicity words before literal simplicity/universality filtering and obtains 3,381 simple / 828 universal walks, 4,968 high-weight cases, cap11, and no universal (8,4). Eight semantic code mutations fail with receipt comparison disabled. The proof review found no gap in the scoped argument. The six-plus-six path join in this claim is a different oracle; my package does not implement or reserve that method or PR5001 engine integration. I am acknowledging this concurrent claim in the focused PR and retaining the position/matching implementation with its completeness argument. Published in PR #5044, head |
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DONE — scoped proof and package published, 2026-10-22, priority revision 7.
PR #4907, head
faf51ea356b9b5d5ce00c141124e4fc3fcefce73, proves that every simple restored universal length-twelve walk on F2^5 has excess at most 15 for each weight-four or weight-five functional. The new quotient-cycle argument excludes the planar minority in the (8,4) case. This answers #4148's remaining (5,12) proof question and #4894's handoff.Author-checked evidence: all 828 universal words / 4,968 functionals; 127,400 set pairs / 224 planar obstructions; 120 cube neighbor pairs; normal and optimized registered replay, committed-byte/source-history checks, export integrity and Git-free replay. Corrupted proof and receipt bytes are rejected. The measured maximum 11 remains finite evidence. Both hosted checks passed on this exact head in CI run 39872913962: planning and the registered normal/optimized package replay. No independent human or formal proof-kernel review, seven-label exclusion, engine integration or new kappa is claimed. The claim is released.
Next bounded question: prove the sharper cap 11 and exclusion of universal (8,4) walks, starting with nonplanar minority configurations. Exact source pins, commands, limitations and predecessor credit are in the PR and package. Prepared by Mihir Srivastava with substantial OpenAI Codex assistance.
Pre-submission main was unchanged at
624de9dc66858af0945e5f8a0942488d62280d43. Refreshed overlap covered 425 open PRs and 3,957 Discussion records, with 51 of 6,319 local notes searched plus relevant direct reads. No competing scoped proof was found within that coverage.Original advance claim, retained as historical coordination evidence (its in-progress status and expiry are superseded above):
CLAIM / 2026-10-22 / priority revision 7
I take the remaining
(n,L)=(5,12)high-weight pruning question in unpaidmoon's #4148 Open next question 3 and Nick Petalas's #4894 handoff. The question is whether every simple restored universal singleton-prefix walk on F2^5 obeys the fixed excess budget 15 for every functional of weight at least four.Base: canonical main
624de9dc66858af0945e5f8a0942488d62280d43. Predecessor #4894 is pinned at2e95d12a8f1557a90102314a773c74420bcbd4fe. I will use its credited matching-balance observation, analyze the(8,4)quotient-cycle case, and seek a structural proof with a separately implemented bounded finite check. Stop at a proof, counterexample or exact missing implication; no seven-label census or engine integration.This changes the
census-pruning-auditcard to a scoped proof question. #3699/#3733/#4148 and the later five-label census already supply measured evidence; repeating their table is not the intended contribution. Credit Nicholas Stone #2973 for the corrected excess boundary, James Reed #3096, Ross Richardson #943, unpaidmoon and Nick Petalas for the cited model, question and prior evidence.Overlap: fresh helper snapshot contains 424 open PRs and 3,950 Discussion records with complete remote pagination. The sparse local scan initially covered 5 of 6,319 notes; relevant f7 successor notes were then materialized and read. Live #4894 and latest handoffs were checked. Arbitrary diffs, omitted notes and unpublished work remain limits. No competing claim for this exact proof was found.
Expected artifact: one isolated package, written proof and exact verifier. Evidence is LOCAL-ONLY until linked. Claim expires 2026-10-23T01:30:00Z. Prepared by Mihir Srivastava with substantial OpenAI Codex assistance. No new kappa or selected-frontier change.
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