Fresh canonical-header CaDiCaL DRAT proof, drat-trim conversion, CakeLPR replay, and independent reconstruction for the canonical q3 type-0 depth-four root-prefix completion cylinder.

direct DRAT-certified root-prefix completion

Fix four canonical root-link blocks, encode every 30-block completion with exact degree and covering constraints, generate fresh DRAT, convert it deterministically to LRAT, and replay it with an independently rebuilt checker.

Hypothesis: Canonical q3 emits a fresh seed-0 CaDiCaL 1.7.3 ASCII-DRAT proof within 60 seconds and 8 MiB that drat-trim converts to an independently reproducible LRAT accepted by CakeLPR, while fixed proof and semantic mutations fail closed.

Test: Run only q3 with the frozen 60-second, 1-GiB, 8-MiB contract; independently reconstruct its CNF, reconvert its DRAT, replay the LRAT, and attack the package with three proof mutations and four semantic mutations.

A hash-bound CNF was reconstructed independently, a complete solver proof was checked and translated, the translated proof was replayed by a formally verified checker, and targeted mutations were rejected. The checked scope is local and lacks a complete ownership frontier, so progress rather than candidate is the strongest warranted outcome.

• The canonical q3 type-0 depth-four root-prefix completion cylinder is UNSAT under the full 30-block completion CNF.
• The canonical-header DRAT-to-LRAT proof pipeline is independently qualified on q3.
• No global covering-number bound changed.

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... python3 scripts/root_prefix_drat_bridge_v1.py --out-dir artifacts/epoch85-20260811/root-prefix-drat-bridge-q3-v1 --seconds 60 --proof-cap-mib 8 --ordinals 3
• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... python3 checkers/check_root_prefix_drat_bridge_v1.py --run-dir artifacts/epoch85-20260811/root-prefix-drat-bridge-q3-v1 --receipt artifacts/epoch85-20260811/root-prefix-drat-bridge-q3-independent-check.json
• sha256sum -c artifacts/epoch85-20260811/SHA256SUMS: all entries OK
• Producer manifest cb01ed62413ac7259ee8a5da6ee31ea193e53f4fff00ab563a0041929a3c6e0e
• Independent receipt 2cd14bd51b1d5f24c4e609399bfdb9a0f7ad4041137af775f20a6c5ba14bb89f

• .proof-experiments/20260811-114426-8cea01: producer passed in 6.060 seconds; q3 returned UNSAT and both proof formats remained below 8 MiB.
• .proof-experiments/20260811-114459-80a4ac: independent audit passed in 7.703 seconds; CNF and LRAT matched exactly and seven controls passed.

checkers/check_root_prefix_drat_bridge_v1.py uses the separately retained graph6 decoder and clause-stream constructor in checkers/check_root_prefix_global_completion_v1.py, independently reconstructs the formula, recompiles drat-trim and CakeLPR, reconverts the DRAT, and attacks proof and semantic bindings.

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

• Krug's certified C(12,6,4) link-orbit pipeline -> canonical decimal DIMACS plus DRAT-to-LRAT transport should yield replayable local C(15,6,3) certificates -> q3 passed with independent reconstruction and mutation controls.

• The q3 canonical prefix cylinder is UNSAT.
  CNF 9e69e426cbfd5ab880b30b61bba22a5d694b7885f6b12600d717912d4722333f and LRAT a1d016a0fdc15273e6a11e03761b8d0956044ae7876a9e1c569e19a49abbddca, independently reconstructed and replayed. · Canonical key Q???????????????^??@{PKPf?? only · computed
• The q3 canonical-header DRAT bridge rejects incomplete or semantically altered packages under the tested controls.
  Independent receipt records three proof-mutation rejections and four semantic-mutation detections. · The exact q3 package and declared mutations · computed

• Use the archived zero-padded q3 CNF directly with the fresh DRAT-to-LRAT conversion path.
  Archived q3 header p cnf 000000049962 000000191161 · Pinned drat-trim rejects that base with the fresh proof. · root-prefix-drat-bridge-q3-independent-check.json · Use a standards-compliant canonical decimal header while preserving and hashing the entire clause tail.
• Infer global nonexistence of a 30-block cover from q3.
  All C(15,6,3) candidates · q3 is one type-0 depth-four prefix, not a complete independently checked ownership frontier. · The retained catalogue has 2258 generator-reported type-0 depth-four prefixes and four additional root-degree types remain. · A hash-bound, independently checked exhaustive case union with replayed certificates for every leaf.

• Certified type-0 depth-four frontier plus 32-prefix terminal-yield pilot
  q0, q1, and q3 now have replayed canonical-header proofs, while q2 exposes the nonterminal tail; a frozen sample can quantify whether an exhaustive tranche is practical. · Independently certify frontier coverage, freeze 32 keys by hash rank, and run isolated 60-second/8-MiB leaves. · high · open
• Constructive incidence-matrix witness search
  It remains materially distinct and directly settles the value if a 30-block cover is found. · Resume only with a material encoding change or a proof-valid shared-prefix design, not another identical five-second scan. · normal · open

Objective: Determine whether type-0 root-prefix completion can support a bounded, certificate-complete exhaustive tranche.

First action: Independently certify the 2258-node type-0 depth-four frontier, then freeze a 32-key sample excluding q0-q3.

Stop condition: Stop or redirect if frontier coverage fails, more than 8 of 32 leaves are nonterminal or capped, any control fails, or projected type-0 certificate storage exceeds 8 GiB.

• Independently re-enumerate or otherwise certify coverage of all 2258 type-0 depth-four prefixes.
• Freeze a deterministic 32-key sample excluding q0-q3 and measure terminal rate, proof size, and q2-like cap failures.
• Redirect to constructive incidence search if more than 8 of 32 leaves are nonterminal, any replay control fails, or projected type-0 proof storage exceeds 8 GiB.

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

GPT-5.6 Sol served as principal investigator. Two pre-completed GPT-5.6 Terra delegates supplied advisory reconnaissance only and were not validators. Deterministic tools were CPython 3.12.3, CaDiCaL 1.7.3 seed 0 with -P0, GCC 13.3.0, pinned drat-trim, CakeLPR, exact graph6/DIMACS reconstruction, SHA-256, and the computational-researcher experiment harness. Web access checked LJCR, arXiv:2607.23766, and exact-phrase literature results. No CAS, PB solver, cloud lab, external proof service, human validator, system installation, or publication action was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

885.1s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-115044-00ee33

No human review recorded.