Emit and independently replay a bounded canonical-header ASCII-DRAT certificate for the frozen q0-m0 type-0 depth-four root-link completion cylinder.

proof-producing root-link completion decomposition

Fix one canonical four-block root-link prefix, encode every normalized 30-block completion with exact degree-12 incidence constraints, and use proof-producing SAT plus independent reconstruction and replay to decide the cylinder.

Hypothesis: The frozen q0-m0 CNF emits a complete CaDiCaL 1.7.3 ASCII-DRAT proof within 60 seconds and 16777216 bytes, convertible to LRAT within the same cap and independently replayable.

Test: Run one seed-0, -P0 CaDiCaL process with a 16 MiB proof cap, then require drat-trim verification, byte-identical independent LRAT reconversion, qualified lrat-check and CakeLPR replay, and fail-closed truncation controls.

The solver's UNSAT output is supported by a complete DRAT verified by drat-trim and an LRAT accepted by CakeLPR and qualified lrat-check. A materially different formula constructor reproduced the base exactly, and proof truncations failed closed. These checks justify the exact local exclusion but not any broader ownership claim.

• The q0-m0 cylinder with graph6 key Q???????????????OK[CwB@ooX? is UNSAT under the frozen 30-block completion encoding.
• Its complete DRAT has SHA-256 e87026fa9a16614904de48b17d46dc48325993889483a44dbce53efeb93dcbc3 and size 8757790 bytes.
• Its converted LRAT has SHA-256 bc1df8123ce77e87b9e8aad3372a663968aad19f48e6147e6da440643a5dcb79 and size 4537565 bytes.
• The global maintained range remains 30 <= C(15,6,3) <= 31.

• Producer: python3 scripts/q0_m0_drat16_v1.py --out-dir artifacts/epoch89-20260811/q0-m0-drat16-v1 --seconds 60 --proof-cap-bytes 16777216.
• Checker: python3 checkers/check_q0_m0_drat16_v1.py --run-dir artifacts/epoch89-20260811/q0-m0-drat16-v1 --out artifacts/epoch89-20260811/q0-m0-drat16-independent-check.json.
• CaDiCaL exit 20 at 9310 conflicts; drat-trim reported VERIFIED; CakeLPR reported VERIFIED UNSAT.
• Independent receipt status PASS, no failures, decision CERTIFIED_LOCAL_Q0_M0_UNSAT.

• .proof-experiments/20260811-144829-22e37d: producer completed in 8.256 seconds; UNSAT, 8757790-byte DRAT and 4537565-byte LRAT.
• .proof-experiments/20260811-144903-833c87: independent audit completed in 8.905 seconds; PASS with nine controls.

checkers/check_q0_m0_drat16_v1.py uses a separate graph6 decoder and formula constructor, freshly compiles drat-trim, lrat-check, and CakeLPR, qualifies the LRAT replayers on a known-good full q3 proof, reconstructs q0-m0 byte-for-byte, reconverts the DRAT, and tests nine mutations.

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

• Certified C(12,6,4) link-orbit decomposition -> predict that a fixed C(15,6,3) root-link cylinder can carry a compact replayable proof -> q0-m0 passed locally, but the required complete global orbit union is still absent.

• No normalized 30-block cover extends the q0-m0 labelled canonical four-block type-0 root-link prefix.
  Complete DRAT/LRAT package and independent PASS receipt. · Graph6 key Q???????????????OK[CwB@ooX? under the frozen 49962-variable, 191161-clause encoding. · computed
• The type-0 depth-four frontier contains exactly 2258 canonical prefix families.
  Epoch-86 clean-room orbit closure and independent frontier audit. · Root-link degree type (8,4^13) through depth four under the declared hereditary filters. · computed
• Every putative 30-block cover has every point in exactly 12 blocks.
  Slack-zero incidence count 6*30 = 15*12 together with the point-degree lower bound. · Any 30-block C(15,6,3) covering. · proved

• A 30-block completion of q0-m0.
  The exact frozen labelled prefix cylinder. · The independently reconstructed CNF is UNSAT. · DRAT e87026fa9a16614904de48b17d46dc48325993889483a44dbce53efeb93dcbc3; LRAT bc1df8123ce77e87b9e8aad3372a663968aad19f48e6147e6da440643a5dcb79; independent receipt PASS. · A demonstrated checker, formula-semantics, or certificate defect.
• Promote q0-m0 UNSAT to a global exclusion.
  All putative 30-block covers. · q0-m0 is one overlapping type-0 prefix cylinder; 2253 other type-0 cylinders and four other root-degree types remain. · The frozen manifest and clean-room frontier scope. · A complete independently checked coverage union across all five root-degree types with replayed terminal certificates.

• Materially strengthened constructive exact-degree-12 incidence search.
  A single directly checked 30-block cover settles the target without proof-frontier ownership. · Add one new sound global structural constraint to a frozen incidence branch and compare it with a matched control under a short predeclared gate. · high · open
• Hash-ranked proof-yield and storage pilot.
  q0-m0 shows that 16 MiB ASCII-DRAT transport can terminate and replay, but representative yield and aggregate storage remain unknown. · After human approval, freeze a small sample disjoint from the five certified keys and replay every terminal leaf. · normal · open
• Complete five-type root-link coverage bridge.
  This is necessary before local cylinder certificates can support a global negative result. · Specify owner predicates and independently enumerate the first missing root-degree type under a bounded frontier cap. · low · open

Objective: Choose between a materially new constructive incidence discriminator and an owner-approved proof-yield pilot without overstating the local exclusion.

First action: Ask the human owner to approve the exact proof-pilot scope; absent approval, identify and compile one new sound global incidence constraint with a matched control.

Stop condition: Redirect on hash drift, cap or replay failure, missing ownership, or lack of a material encoding delta.

• Do not dispatch a larger proof pilot until the human owner approves its exact population, caps, aggregate storage gate, and stopping rule.
• Prefer a materially strengthened constructive exact-degree-12 incidence experiment because one checked 30-block witness bypasses the ownership bottleneck.
• For any negative scale-up, build independently checked coverage across all five root-degree types and replay every terminal leaf.

• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol served as principal investigator. Two pre-completed GPT-5.6 Terra delegates supplied advisory prior-art and experiment-design memos; Sol audited their relied-on claims and model agreement was not validation. Deterministic work used CPython 3.12.3, CaDiCaL 1.7.3 seed 0, GCC 13.3.0, drat-trim, lrat-check, CakeLPR, SHA-256, exact graph6/CNF reconstruction, and the computational-researcher experiment harness. Web retrieval checked LJCR, the Covering Repository context, arXiv:2607.23766, and exact-phrase searches. No CAS, PB solver, proof assistant beyond CakeLPR's verified kernel, cloud lab, external proof service, human validator, system installation, publication action, or successor job dispatch was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1134.3s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-145816-dd25f9

No human review recorded.