Extract and occurrence-map the verified radius-0-through-4 DRAT input core, then independently reconstruct its clause semantics from the fixed seed.

proof-core-guided layer-five filtering

Use the replayed local proof to select source rows in bulk, transferring only independently necessary coverage and degree conditions to a future count-five filter.

Hypothesis: The verified local proof core contains radius-invariant coverage or point-degree rows that justify a sound early layer-five filter.

Test: Run drat-trim -c on the hash-locked CNF/DRAT pair, map every canonical clause multiset to a unique source occurrence, independently rebuild all 379377 source clauses from the seed, and require at least one portable coverage or degree row.

The discriminator’s success condition was independently met, so core-guided count-five filtering remains technically justified. Proof relevance alone supplies no new covering theorem, hence the outcome is progress rather than candidate.

• The checked local proof input core contains exactly 80527 unique source-clause occurrences.
• It includes 326 distinct coverage rows and degree-equivalence clauses for 9 distinct points.
• The occurrence map passes complete independent reconstruction and four mutation controls.
• No layer-five repair or global 54-block family was excluded.

• drat-trim returned VERIFIED and reported 80527 of 379377 clauses in core.
• The semantic producer generated core-map SHA-256 88c39e059c853a71d9477816277d9cd05b515d85c33f9de1ef053ef0e5f81dc3.
• The independent checker returned valid=true with all four mutation_rejections=true.
• sha256sum -c artifacts/radius-le4-proof-core-map-20260810/manifest.sha256 passed.

• .proof-experiments/20260810-042124-ca30c8: proof replay and 80527-clause core extraction passed.
• .proof-experiments/20260810-042507-0d04c9: strict literal-order mapping failed closed.
• .proof-experiments/20260810-042608-42a913: canonical occurrence mapping passed.
• .proof-experiments/20260810-042645-6ad44d: independent reconstruction and mutations passed.

scripts/check_radius_le4_core_map_v1.py independently rebuilds the complete formula from the seed, verifies every canonical core/source occurrence and semantic label, and rejects altered-hash, duplicate-occurrence, altered-row, and false-invariance 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

• Proof minimization -> select potentially informative necessary rows before larger search -> 80527 of 379377 clauses retained and 335 portable semantic rows identified.
• Compiler-style canonicalization -> treat clause literal order as presentation rather than identity -> all 66423 reordered clauses mapped without ambiguity.
• Meet-in-the-middle repair search -> reuse only invariant degree and coverage signatures -> discriminator passed, but count-five pruning remains unmeasured.

• The locked proof core contains 326 coverage rows and point-degree-equivalence rows for 9 points.
  artifacts/radius-le4-proof-core-map-20260810/result.json and independent-check.json · One radius-0-through-4 proof around the fixed defect-10 seed. · computed
• All 80527 core clauses have unique canonical source occurrences.
  core-map.jsonl plus independent reconstruction and duplicate controls · Locked CNF SHA-256 0ea6467682f81c99328a721041dbf1466a885cfdd2750975edd6cbe3e0e18c6c. · computed

• Map drat-trim core clauses as byte-identical ordered DIMACS tuples.
  The locked 80527-clause extracted core. · 66423 emitted clauses have reordered literals, although their canonical literal multisets map uniquely. · .proof-experiments/20260810-042507-0d04c9 and the checked canonical map · Use an extractor preserving literal order, or retain canonical multiset matching with duplicate fail-closed guards.

• Six-state count-five filter from the selected invariant rows.
  The underlying 326 coverage and 9 point-degree conditions are necessary for valid repairs. · Run exact feasibility on a deterministic stratified deletion-signature pilot with independent reconstruction. · high · open
• Globally complete pair-normalized proof-producing SAT.
  It retains terminal global scope and is the immediate redirect if local filter retention is high. · Test one proof-preserving encoding change under matched telemetry. · normal · open
• Variable-length exact-degree ejection chains.
  A checked defect below 10 would reopen the constructive route. · Specify a materially new move generator before another bounded pilot. · low · open

Objective: Measure whether the portable core-selected rows remove enough exact count-five signatures to justify a complete partition.

First action: Implement a six-state producer and independent checker using exactly the selected rows in artifacts/radius-le4-proof-core-map-20260810/core-map.jsonl, then run a deterministic stratified pilot.

Stop condition: Redirect on checker disagreement, use of any nonportable auxiliary clause, high exact retention, or unacceptable per-cell cost.

• Parse the exact 326 triples and 9 points from core-map.jsonl.
• Build a six-state count-five necessary-condition producer and separately implemented checker.
• Run only a deterministic stratified deletion-signature pilot and measure exact retention and cost.
• Redirect to globally complete pair-normalized SAT if the filter retains nearly all pilot cells.

• 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://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol acted as principal investigator, selected and implemented the discriminator, executed the tools, and interpreted the result. GPT-5.6 Terra challenger-prior-art and experiment-verification delegates supplied advisory reconnaissance only; model agreement was not validation. Python 3.12.3 implemented the producer and independent checker. drat-trim SHA-256 92f0aa9575ed519d66a99b8b1b3dde6ece4618ae4c202a3a4b200265dda0aa7a replayed the locked DRAT proof and extracted the core. SHA-256 bound all decisive artifacts.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1051.5s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260810-043328-3e8e26

No human review recorded.