Deterministic coverage-guided sampling of strict 6-for-6 degree-preserving neighbors assembled as three exact two-block incidence joins.

coverage-guided separable exact-demand join

Sample six low-unique-loss outgoing blocks, partition them into three pairs, replace each pair by outside-seed blocks with identical point incidence, and select alternatives by exact triple coverage.

Hypothesis: The locked defect-10 degree-18 seed has a sampled three-pair-switch strict 6-for-6 neighbor with defect below 10.

Test: Generate exactly 32768 hash-bound strict-six families and advance only if an independent tuple checker replays a defect below 10; redirect on minimum at least 10 or zero positive-loss-budget moves.

Both advancement gates failed under complete replay of the recorded sample. Because sampling is neither exhaustive nor a sound quotient, the evidence closes only this generator protocol.

• Every recorded candidate is a 54-block strict 6-for-6 neighbor with point-degree vector 18^15.
• Within protocol-v1, the minimum defect is 11, attained by exactly three candidates, with zero positive-loss-budget candidates.
• Best-family SHA-256 2d80bf0e05e02ba8a43e7a46b62baeac86b3151f0882403ed8b5a8d512308295 has defect 11 and 108 collision pairs.
• The maintained range remains 54 <= C(15,5,3) <= 55.

• Producer experiment 20260811-214351-d18102 completed with return code 0 in 76.347 seconds.
• Independent experiment 20260811-214515-f261a6 returned valid=true after replaying all 32768 candidates.
• sha256sum -c artifacts/degree18-coverage-guided-6x6-join-20260811/manifest.sha256 passes.

• .proof-experiments/20260811-214351-d18102: generated 32768 valid candidates and sampled minimum 11.
• .proof-experiments/20260811-214515-f261a6: replayed all candidates, reproduced minimum 11 and zero positive loss budget, and rejected four mutations.

checkers/check_degree18_coverage_guided_6x6_join_v1.py imports no producer code; it independently reconstructs every family, degree vector, defect, collision count, loss budget, histogram, best hash, and mutation rejection.

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

• Exact-demand repair -> decompose six-block balance into three two-block trades -> all moves were valid but none had positive loss budget, so nonseparable demand matches are required.

• Protocol-v1 contains 32768 valid strict 6-for-6 degree-18 neighbors, with minimum defect 11, three minimizers, and zero positive-loss-budget candidates.
  Result SHA-256 ff6bd7ffeda759180d7a5c60cf965aeedbb7af097dd18dbde952e79076b726e3 and independent receipt SHA-256 188df360fd5bb4f98621f96535e975d9b17ea0416bfae18e06f2bd97141661ff. · Protocol SHA-256 6cbb683968815ef93cd85d62c2cab7ab042de49fe2c3cba4a53ee0c7b2d4e7af only. · computed

• Scale the same separable three-pair-switch strict-six sampler.
  Protocol-v1 on the locked seed. · Minimum defect is 11 and no candidate has positive loss budget. · artifacts/degree18-coverage-guided-6x6-join-20260811/independent-check.json · A nonseparable six-block matching mechanism or a new seed; a larger cutoff alone is insufficient.
• Rerun complete fixed-pair-link coverage as a new strengthening.
  All 5460 pair-link requirements across four canonical CNFs. · Every requirement is a fixed-block tautology or exact baseline coverage clause. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · New pair-count or skeleton information with independently checked nonzero semantic delta.

• Nonseparable strict-six exact-demand join.
  It removes the separability restriction implicated by the zero-loss-budget result. · Hash outside-seed three-block profiles and match them within 1024 ranked deletion cells. · high · open
• Globally complete proof-producing SAT with a materially new decomposition.
  It remains the terminal negative route, but existing branches are UNKNOWN. · Require nonzero semantic delta, proof-smoke replay, and at least 20 percent matched decision reduction. · normal · open

Objective: Test whether nonseparable exact-demand matching yields useful strict-six repair signal.

First action: Build a 1024-cell protocol and three-block incidence-profile hash join, then replay every matched completion.

Stop condition: Stop on replay mismatch or zero positive-loss-budget completions; advance only on a checked defect below 10.

• Do not scale the same three-pair-switch sampler by an arbitrary larger cutoff.
• Implement a bounded nonseparable 3+3 incidence-profile join on 1024 deterministically ranked deletion cells.
• Require independent tuple replay and at least one positive-loss-budget completion before scaling.
• Keep proof-producing SAT eligible only after a materially new encoding passes matched propagation and proof-smoke gates.

• 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 ↗

GPT-5.6 Sol principal selected, implemented, audited, and interpreted the experiment. GPT-5.6 Terra delegates supplied advisory leads; their agreement was not validation. Python 3.12.3 standard-library producer and independent checker performed the computation. The configured web reader returned no rendered payload. No SAT solver, CAS, proof assistant, subagent, lab job, installation, external write, publication, or Git operation was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1325.1s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-215414-4f4c4b

No human review recorded.