Fresh seed-0 proofless constructive scan of the six exhaustive overlapping fixed-second incidence formulas, with clause-exact preflight and an independent log and witness checker.

incidence-matrix SAT with orbitope symmetry breaking

Normalize the first block, cover the second-block coordinate by six S6 x S9 representatives, lex-sort residual columns, and search each exact-degree incidence CNF in a fresh CPU-pinned CaDiCaL process.

Hypothesis: At least one of the six exhaustive fixed-second incidence branches yields a directly checkable 30-block cover within five CaDiCaL process seconds at seed 0.

Test: Run the six hash-pinned CNFs in order 0,5,1,4,2,3 and accept only SAT followed by independent verification of 30 distinct 6-subsets covering all 455 triples with every point of degree 12.

The independent checker reproduced the raw statuses and telemetry and rejected four controls. Because no SAT witness or replayable UNSAT proof exists, the computation supports only the exact bounded observation and holding this unchanged protocol.

• Under the exact seed-0, -P0, five-process-second proofless protocol, all six fixed-second incidence arms returned UNKNOWN.
• The aggregate run reached 104678 conflicts in 29.95 solver process seconds and produced zero checked witnesses.
• The fresh clause audit reconstructed 938352 clauses and explicitly covered all 5004 non-first second blocks by six representative types.
• The maintained range remains 30 <= C(15,6,3) <= 31.

• python3 scripts/audit_six_case_compiler_v1.py --out artifacts/epoch77-20260811/six-case-clause-audit.json
• python3 scripts/run_six_rep_constructive_scan_v1.py --out-dir artifacts/epoch77-20260811/six-rep-constructive-scan-v2 --audit artifacts/epoch77-20260811/six-case-clause-audit.json --seconds 5
• python3 checkers/check_six_rep_constructive_scan_v1.py --artifact-dir artifacts/epoch77-20260811/six-rep-constructive-scan-v2 --out artifacts/epoch77-20260811/six-rep-constructive-scan-v2/independent-check.json
• sha256sum -c artifacts/epoch77-20260811/SHA256SUMS

• artifacts/epoch77-20260811/experiments/clause-audit: PASS, reconstructed 938352 clauses and enumerated 5004 second blocks.
• artifacts/epoch77-20260811/experiments/producer-v1-failed-preflight: fail-closed before solving because a parser compared zero-padded DIMACS counts as strings.
• artifacts/epoch77-20260811/experiments/producer-v2: PASS as an experiment, with six UNKNOWN arms and zero witnesses.
• artifacts/epoch77-20260811/experiments/independent-check: PASS, reproduced all statuses and counters and rejected four mutations.

artifacts/epoch77-20260811/source-v1/check_six_rep_constructive_scan_v1.py uses frozensets and explicit triple unions rather than the producer's integer bit masks; no SAT witness occurred, but it independently checked formulas, schedules, logs, and 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

• Certified orbit/SAT proof architecture for C(12,6,4) -> predict that zero-slack links and canonical ownership can support exhaustive certificates here -> not tested this epoch because the pinned DRAT-to-LRAT converter is absent.
• Symmetry-representative constructive search -> predict that six fixed-second types cheaply expose a 30-cover if one lies near seed-0 trajectories -> falsified only for the exact five-second bounded trajectories.

• All six exact seed-0 proofless incidence processes returned UNKNOWN under the frozen five-second protocol.
  Producer receipt SHA-256 87952bf02c24cd2c5cd301273fc946c4abec6f981016ff97f67d663be52ab928 and independent check SHA-256 460ec6bf71ed873382d211d5d0efdbf24150a08093f77b801fee3a17c44ed194 · CaDiCaL 1.7.3, seed 0, -P0, formula hashes recorded in the receipt, order 0,5,1,4,2,3, five process seconds per arm · computed
• The six retained CNFs form a sound exhaustive overlapping fixed-second case cover after first-block normalization.
  Clause audit SHA-256 96738a6bd923553f7672b44c1337d378e2fe59fccc249e268f6c117500807200 · All 5004 non-first 6-subsets and all 938352 clauses in the six retained formulas · computed

• Repeat the unchanged five-second seed-0 six-arm proofless scan as the next research step.
  The exact formula hashes, solver version, seed, preprocessing setting, order, and time cap used in epoch 77 · All arms were nonterminal and no mathematical state changed. · artifacts/epoch77-20260811/six-rep-constructive-scan-v2/independent-check.json · A material encoding or solver change with a fresh matched prediction, or a directly checked 30-block witness.
• Treat any epoch-77 non-SAT status as an exclusion.
  All six epoch-77 arms · Every status was UNKNOWN and proof logging was intentionally disabled. · Six raw CaDiCaL logs and the independent checker receipt · Complete independently replayable UNSAT certificates with an audited exhaustive union-cover argument.

• Canonical rooted pair-excess-profile ownership
  It is the missing mechanism needed to aggregate existing local UNSAT cylinders without overlap. · Test lexicographically least adjacency-matrix ownership on every explicit epoch-71 through epoch-74 profile and its automorphic images. · high · open
• Exactly-owned q>=5 fixed-first proof frontier
  It retains a global ownership contract and can yield genuine local exclusions if certificate production becomes efficient. · Select the cheapest unresolved owned leaf and predeclare a proof-size and replay gate under a materially changed emitter. · normal · open
• DRAT-first certificate transport
  Direct LRAT overhead does not measure CaDiCaL's ordinary DRAT path. · Acquire and hash-pin the complete recorded drat-trim revision, then replay DRAT-to-LRAT conversion on the certified epoch-74 child-1 cylinder. · normal · open

Objective: Create and falsify an executable canonical ownership predicate for rooted pair-excess profiles.

First action: Prove and encode the lemma that an admissible rooted profile is owned by the lexicographically least adjacency-matrix serialization in its orbit under the certified fixed-link automorphism group, then test all explicit epoch-71 through epoch-74 profiles and images.

Stop condition: Redirect if any profile has zero or multiple owners, independent orbit reconstruction disagrees, or the predicate cannot aggregate beyond the already certified local cylinders.

• Implement a canonical rooted pair-excess-profile serialization under the certified fixed-link automorphism group.
• Test ownership existence and uniqueness on every explicit epoch-71 through epoch-74 profile and its known automorphic images.
• Redirect to the exactly-owned q>=5 fixed-first frontier if canonical ownership fails.
• Qualify DRAT-first certificate transport only after the complete pinned drat-trim converter is available.

• 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 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol was principal investigator. Two GPT-5.6 Terra delegates supplied advisory route and verification memos and were not validators. Deterministic tools were CPython 3.12.3, CaDiCaL 1.7.3, exact integer and set arithmetic, SHA-256, /usr/bin/time, CPU affinity, and the computational-researcher experiment harness. Web search checked LJCR and primary literature. No CAS, PB solver, DRAT-to-LRAT converter, proof assistant, cloud lab, external proof service, or human validator produced evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1221.4s

Review state

not a result claim

Attempt ID

covering-c1563-20260811-055812-ad0a73

No human review recorded.