Deterministic nonseparable strict 6-for-6 search using arbitrary 2+2+2 incidence-profile decompositions over 1,024 ranked deletion cells of a fixed defect-10 degree-18 seed.

nonseparable exact-demand profile join

Rank six-block deletion cells, sample three realizable pair-incidence profiles whose coordinatewise sum equals the full deletion demand, realize each profile by outside-seed block pairs, and score compatible six-block additions with packed 455-bit coverage masks.

Hypothesis: The locked defect-10 degree-18 seed has a sampled nonseparable strict-six exact-demand neighbor with defect below 10.

Test: Search 1,024 deterministically ranked deletion cells with 128 arbitrary exact-demand profile splits per cell; advance only if an independently replayed winner has positive loss budget and defect below 10.

The checker independently reconstructed the frontier and every retained candidate, so the negative signal is reliable for the recorded sample. Sampling is neither exhaustive nor a safe quotient, so it cannot exclude a 54-cover or even a better completion in one retained cell.

• The checker independently reconstructed all 24,804 outgoing triples, 22,409 induced pre-cutoff deletion cells, and the retained 1,024-cell frontier.
• Every recorded winner is a distinct 54-block strict 6-for-6 neighbor with point-degree vector 18^15.
• Within the recorded winner corpus, the minimum defect is 11 and positive-loss-budget winners number zero.
• Best-family SHA-256 1716a0a4db9ab32b5ce052d7269ff5ad15d276e4ba24c21dc6801acaa5e04cc3 has defect 11 and 110 collision pairs.
• No 54-block cover or exclusion of 54 was obtained.

• Producer command recorded in experiment 20260811-222322-77f613 completed in 49.901 seconds with return code 0.
• Checker command recorded in experiment 20260811-222434-b3a5c5 completed in 4.225 seconds with return code 0.
• artifacts/degree18-nonseparable-6x6-profile-join-20260811/independent-check.json has valid=true and all five mutations rejected.
• sha256sum -c artifacts/degree18-nonseparable-6x6-profile-join-20260811/manifest.sha256 passed for every listed artifact.

• .proof-experiments/20260811-222322-77f613: 131,072 profile trials, 66,545 valid splits, 5,503,010 literal combinations, sampled minimum defect 11.
• .proof-experiments/20260811-222434-b3a5c5: independently rebuilt the frontier, replayed all 1,024 winners, reproduced minimum 11 and zero positive-loss-budget winners, and rejected five mutations.

checkers/check_degree18_nonseparable_6x6_profile_join_v1.py is separately written and uses literal set reconstruction and direct counting of all 455 triples. It does not reuse the producer's bitset scorer or profile sampler.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

no_progress

Public classification

no_progress

• Meet-in-the-middle exact-demand repair -> allow arbitrary complementary pair profiles instead of matching outgoing pairs -> the broader sample still produced zero positive-loss-budget winners, motivating exhaustive fixed-cell certification.

• The recorded corpus contains 1,024 valid strict 6-for-6 degree-18 neighbors with minimum defect 11 and zero positive-loss-budget winners.
  Result SHA-256 55adc6c7a651db149ed7ddeb8b476420e7a56cb6934acdd05663e68d17d35b5c and independent receipt SHA-256 4f94eebb06da4a668f93850232a1525f2c3adff3fe8ca5575e17d71304751f46. · Protocol SHA-256 d0b8d67833b9a57d9d9fe1f5b9a3092201e2b276d941d3ac4b228215084e232c only. · computed
• The independent reconstruction yields 22,409 distinct six-deletion cells induced by disjoint unions among the retained 512 three-deletion endpoints.
  Independent checker receipt and five fail-closed mutation controls. · The locked seed and declared endpoint ordering. · computed

• Scale protocol v1 solely by increasing its arbitrary profile or cell cutoff.
  The locked defect-10 seed and this coverage-ranked profile-sampling mechanism. · The broader nonseparable sample retained minimum defect 11 and produced zero positive-loss-budget winners. · artifacts/degree18-nonseparable-6x6-profile-join-20260811/independent-check.json · A new nonisomorphic defect-10 seed or an exhaustive realization method with replayable SAT/UNSAT certificates.
• Rerun complete fixed-pair-link coverage as a strengthening.
  All 5,460 labelled pair-link obligations across the four canonical branches. · Every obligation is a fixed-block tautology or an existing triple-coverage clause. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · Separately justified pair-count or skeleton constraints with independently checked nonzero semantic delta.
• Materialize the full joint type-4 header and weighted pair-skeleton quotient.
  The 91 surviving fixed-type-4 endpoint-header orbits. · The independently checked joint-orbit lower bound is 12,247,501, exceeding the 1,000,000-cell gate. · artifacts/type4-weighted-skeleton-frontier-gate-20260811/independent-check.json · A lazy encoding or new invariant that avoids materializing the joint orbit space.

• Proof-producing fixed-deletion-cell threshold SAT.
  It exhausts literal additions in one cell and can return a directly checked witness or a replayable local exclusion. · Encode deletion-cell rank 0 with exactly six additions, exact 15-point demand, and final defect at most nine; run one fixed CaDiCaL/DRAT pilot. · high · open
• Nonisomorphic defect-10 seed census.
  A genuinely different basin satisfies the constructive sampler's explicit reopen condition. · Collect saved defect-10 families and classify their colored incidence graphs before applying any further local search. · normal · open
• Globally complete proof-producing pair-normalized SAT.
  It remains the terminal negative route, but native PB proof tools are absent and prior CNF translations regressed. · Proceed only after a materially new encoding passes semantic, proof-smoke, and matched propagation gates. · low · open

Objective: Determine exhaustively whether retained deletion-cell rank 0 has a strict exact-demand completion with defect at most nine.

First action: Generate the static threshold CNF, its semantic manifest, and an independent assignment checker before invoking CaDiCaL with DRAT output.

Stop condition: Stop or redirect on semantic mismatch, proof replay failure, or UNKNOWN at the fixed cap; scale only after checked SAT or replayed UNSAT.

• Do not enlarge this sampler's cutoff on the same seed.
• Generate an independently audited defect-at-most-nine CNF for retained deletion-cell rank 0.
• Run CaDiCaL 1.7.3 with DRAT output and accept UNSAT only after drat-trim replay bound to the CNF hash.
• Accept SAT only after direct validation of six additions, degree 18, and all 455 triple multiplicities.
• Scale to further deletion cells only if the first leaf returns a checked status with tractable proof size.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗
• https://arxiv.org/abs/2607.23766 ↗
• https://central.bac-lac.gc.ca/.item?app=Library&id=nq24295&oclc_number=46548328&op=pdf ↗

OpenAI Codex, acting as the Sol principal, selected, implemented, ran, audited, and interpreted the epoch. The two user-supplied GPT-5.6 Terra delegate memos were advisory reconnaissance only and were not treated as evidence or independent validation. Python 3.12.3 standard-library code, exact enumeration, packed integer bitsets, SHA-256, the web reader/search, and a separately written deterministic checker were used. CaDiCaL 1.7.3 and project-scoped drat-trim were only availability-probed; no solver, CAS, or proof assistant was used in the decisive experiment. RoundingSat, VeriPB, and CakePB were absent. No external write, publication, Git operation, system installation, or lab job was performed.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1167.5s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-223106-bf56eb

No human review recorded.