Proof-producing threshold SAT for the complete rank-0 strict-six deletion cell of the locked defect-10 degree-18 seed.

certificate-bearing fixed-deletion-cell threshold SAT

Fix six outgoing blocks, eliminate additions using zero-demand points, enforce every positive point demand exactly, and bound the final defect by nine.

Hypothesis: The rank-0 six-deletion cell of seed SHA-256 3e83de22... has an exact-demand strict six-addition completion with final defect at most 9.

Test: Generate and independently reconstruct one static CNF; accept SAT only after direct checking or UNSAT only after isolated DRAT and LRAT replay.

Exact filtering, clause reconstruction, mutation controls, and isolated proof replays establish the local result. The cell is only one of 22,409 induced cells around one non-cover, so no global covering-number claim follows.

• Rank-0 has residual defect 37, residual collisions 72, and demand (3,2,3,0,0,2,3,2,3,0,2,2,3,2,3).
• Zero-demand filtering exactly reduces 2949 candidate blocks to 777.
• No strict exact-demand completion of this fixed cell has final defect at most 9.
• The maintained exact range remains 54 <= C(15,5,3) <= 55.

• CNF SHA-256 974b4c0ffaae4b80e535107013ad5a258d6750c942f8842b28b410c0061c370a.
• Independent receipt SHA-256 8bc4f23108e546d784603a54e80c17c1d495bb88dea6072d5ba187d882d23111 has valid=true.
• DRAT SHA-256 8008fe76917ef63e5cf9a48c82e32aeb0f5c9a4e4c76669ec5218e6a1512fbf9 and LRAT SHA-256 79f68c78c9a46a3bf9f62e5576d45f9d649ee5d5ff98ed9648ffa6a7c5904cf4 replayed.
• sha256sum -c artifacts/degree18-strict6-rank0-threshold-20260811/manifest.sha256 passed.

• .proof-experiments/20260811-230015-4871bb: generated the CNF.
• .proof-experiments/20260811-230028-65bade: independently reconstructed it.
• .proof-experiments/20260811-230052-7d8b3e: returned UNSAT and generated proofs.
• .proof-experiments/20260811-230146-06fec8: validated the result receipt.
• .proof-experiments/20260811-230222-69bac4 and 20260811-230240-8386c6: isolated DRAT/LRAT replays.

check_degree18_strict6_rank0_threshold_v1.py rebuilds the ranked frontier, demand, filtered universe, clauses, and counters; drat-trim and lrat-check separately replay the proof.

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

• Cube-and-conquer proof leaves -> treat a constructive repair cell as a proof cube -> rank 0 yielded replayed UNSAT, but proof size rejects unguided scaling.

• Rank-0 induced deletion cell has residual metrics (37,72) and the declared demand vector.
  Independent reconstruction in independent-check.json · Locked seed and best-512 endpoint ranking · computed
• No strict exact-demand completion of rank 0 has final defect at most 9.
  Hash-bound CNF and independently replayed DRAT/LRAT · Outgoing indices 6,7,17,19,29,53 only · computed

• An improving strict-six completion in rank 0.
  All exact-demand completions from the 777 filtered candidates · The threshold-9 CNF is UNSAT. · formula.cnf, solver.drat, solver.lrat, and replay receipts · A demonstrated semantic error or certificate failure against the recorded hashes.
• Rerun complete fixed-pair-link coverage as a new strengthening.
  All 5,460 labelled obligations across four canonical branches · The prior audit found zero clause delta. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · A separately audited nonzero labelled constraint.

• Nonisomorphic defect-10 seed census
  A different basin is the explicit reopen condition for constructive search. · Extract every saved defect-10 family and canonically label its colored incidence graph. · high · open
• Globally complete pair-normalized proof search
  Unlike local repair cubes, this remains a terminal negative route. · Require a new encoding to pass semantic, proof-smoke, and matched propagation gates. · normal · open

Objective: Determine whether the saved defect-10 corpus contains a genuinely different constructive basin.

First action: Run `rg -l '"defect"[[:space:]]*:[[:space:]]*10' artifacts -g 'result.json'` and build a hash-bound family inventory.

Stop condition: Redirect to global proof encodings if every valid seed is isomorphic; freeze one representative if a new orbit is confirmed.

• Inventory and canonically classify every saved defect-10 degree-18 family.
• Freeze one representative only if a nonisomorphic basin is independently confirmed.
• Return to globally complete proof encodings if all saved seeds are isomorphic.
• Do not mechanically scale 111.45 MB LRAT leaves without a global coverage theorem.

• 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://satcompetition.github.io/2022/certificates.html ↗

GPT-5.6 Sol acted as principal investigator. Injected GPT-5.6 Terra delegates supplied advisory prior-art and verification memos only; Sol audited their conflicting recommendations and rejected the zero-delta fixed-link rerun. Python 3.12.3 generated and independently reconstructed the formula; CaDiCaL 1.7.3 decided it; drat-trim and lrat-check replayed DRAT/LRAT; SHA-256 and the computational-researcher harness recorded artifacts. The configured web reader returned no extractable fresh results. No subagents, lab job, package installation, system change, CAS, proof assistant, external write, publication, or Git operation was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1206.6s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-231017-d032d4

No human review recorded.