Qualified canonical-header ASCII-DRAT to drat-trim to LRAT to CakeLPR transport on the predeclared q0 and q1 canonical root-prefix completion cylinders.

canonical-prefix completion with verified proof transport

Normalize only the DIMACS header, generate fresh bounded DRAT proofs, convert them to LRAT, replay them with CakeLPR, and independently reconstruct every CNF and repeat conversion and negative controls.

Hypothesis: Both retained q0 and q1 semantic cylinders admit fresh bounded canonical-header DRAT proofs that drat-trim verifies and converts to LRAT accepted by CakeLPR, while fixed 100-line prefixes fail closed.

Test: Run q0 and q1 with CaDiCaL 1.7.3, seed 0, -P0, 60-second solver limits, 1 GiB outer memory, and 8 MiB proof caps; require two drat-trim verifications, two CakeLPR acceptances, independent byte-identical formula reconstructions, deterministic LRAT reconversion, and six negative-control rejections.

The producer and independent checker agree through byte-level formula reconstruction, deterministic proof conversion, separate checking kernels, resource-bounded execution, hash binding, and negative controls. Their scope is only two sampled cylinders, so progress rather than candidate status is warranted.

• No 30-block cover extends canonical prefix Q???????????????OBsF_ow@{?? under the recorded global-completion encoding.
• No 30-block cover extends canonical prefix Q???????????????OO{BoO]@y?? under the recorded global-completion encoding.
• The canonical-header DRAT-to-LRAT proof pipeline is independently qualified on q0 and q1.
• The archived zero-padded q0 and q1 DIMACS bases are incompatible with the pinned drat-trim parser.
• The maintained range remains 30 <= C(15,6,3) <= 31.

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... scripts/root_prefix_drat_bridge_v1.py returned 0 in experiment 20260811-110821-86baf1.
• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... checkers/check_root_prefix_drat_bridge_v1.py returned 0 in experiment 20260811-110854-24727b.
• sha256sum -c artifacts/epoch84-20260811/hash-manifest.sha256 returned OK for every listed artifact.
• Independent receipt 4ffc8c93aee8275740c8ea5a4f99927faa3da79c709426acfb9d97d51632ae5b records two reconstructions, two reconversions, two CakeLPR acceptances, and six rejected controls.

• .proof-experiments/20260811-110821-86baf1: producer passed in 8.106 seconds; q0/q1 DRAT and LRAT chains verified.
• .proof-experiments/20260811-110854-24727b: independent audit passed in 7.871 seconds; formulas and LRATs matched and six controls were rejected.

checkers/check_root_prefix_drat_bridge_v1.py uses the separately written checkers/check_root_prefix_global_completion_v1.py clause-stream constructor, compiles fresh drat-trim and CakeLPR binaries, regenerates identical LRATs, and repeats prefix and padded-header controls.

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 C(12,6,4) DRAT-to-LRAT-to-CakeLPR chain -> canonical decimal headers should permit independently replayable C(15,6,3) local certificates -> q0 and q1 both passed.
• Parser interoperability diagnostics -> changing only a nonsemantic header representation should separate proof failure from formula failure -> canonical bases verified while otherwise identical padded bases were rejected.

• The maintained range is 30 <= C(15,6,3) <= 31.
  Maintained LJCR entry and its explicit 31-block construction, together with the retained lower-bound receipt. · Global C(15,6,3). · proved
• The q0 and q1 canonical prefix cylinders are unsatisfiable under the recorded full global-completion encoding.
  Independent CNF reconstruction, fresh DRAT verification, deterministic LRAT conversion, and CakeLPR replay. · Exactly Q???????????????OBsF_ow@{?? and Q???????????????OO{BoO]@y??. · computed
• Canonical decimal DIMACS headers repair the drat-trim transport failure for q0 and q1.
  Both canonical bases verified; both otherwise byte-identical zero-padded bases were rejected in the independent audit. · The two tested formulas and pinned drat-trim source. · computed

• Pass the archived zero-padded q0/q1 CNFs directly to drat-trim.
  The two epoch-83 bases with dimensions written as 000000049962 and 000000191161. · drat-trim does not parse those headers with the intended decimal semantics and rejected both bases. · artifacts/epoch84-20260811/root-prefix-drat-bridge-q01-independent-check.json · A pinned parser revision with explicit decimal parsing, source audit, and matched positive and negative replay controls.
• Scale immediately to a 32-prefix sample.
  Current accepted main-workspace proof-transport evidence. · Only q0 and q1 passed this exact bridge; q3 has not yet received an accepted Sol-run canonical-header DRAT receipt. · artifacts/epoch84-20260811/continuation-checkpoint.json · q3 passes the identical producer and independent-checker gates.

• Canonical-header DRAT bridge for q3.
  It is the smallest remaining test of whether the three terminal sampled cylinders share one accepted proof stack. · Run ordinal 3 with seed 0, -P0, 60 seconds, 1 GiB, 8 MiB proof caps, and the same independent audit. · high · open
• Frozen 32-prefix global-completion measurement.
  After q3 qualification, its terminal rate would estimate whether proof-producing prefix decomposition can remove uncertainty in bulk. · Hash-select the frozen 32 prefixes and require at least 29 independently certified terminal exclusions before further scale-up. · normal · open
• Materially different proof-producing encoding for unresolved q2.
  q2 was UNKNOWN under the direct-LRAT formula and can test whether the obstruction is encoding-specific. · Compile one alternate selector or incidence/PB encoding and compare preprocessing dimensions before solver search. · low · open

Objective: Qualify q3 under the same proof stack and decide whether the 32-prefix measurement is licensed.

First action: Extend scripts/root_prefix_drat_bridge_v1.py with an explicit ordinal selector while preserving q0/q1 behavior, then run ordinal 3 with the frozen limits.

Stop condition: Redirect on source or hash mismatch, UNKNOWN, proof cap, drat-trim failure, CakeLPR failure, non-deterministic reconstruction, or prefix acceptance.

• Add an explicit ordinal selector without changing the frozen q0/q1 producer semantics.
• Run q3 with the same seed, solver options, 60-second limit, 1 GiB memory, 8 MiB proof caps, and prefix controls.
• Independently reconstruct and replay q3 before considering the frozen 32-prefix measurement.
• Do not extrapolate the two certified cylinders to the 2,258-node type-0 frontier.

• 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/html/2607.23766v1 ↗
• https://github.com/marijnheule/drat-trim ↗
• https://github.com/tanyongkiam/cake_lpr ↗

GPT-5.6 Sol was principal investigator. Two GPT-5.6 Terra delegates supplied advisory reconnaissance only; Sol independently reran and audited every counted result, and their roles are recorded in artifacts/epoch84-20260811/terra-advisory-provenance.json. Python 3.12.3 implemented the producer and checker. CaDiCaL 1.7.3 generated ASCII DRAT. GCC 13.3.0 built pinned drat-trim and CakeLPR sources. The deterministic experiment harness recorded seeds, limits, logs, hashes, and memory. Web access rechecked LJCR, Krug 2026, and the checker repositories. No CAS, interactive proof assistant, cloud lab, external proof service, or human validator was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1085.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-111508-5ba63b

No human review recorded.