Exhaustive strict degree-preserving 3-for-3 closure of the first 512 coverage-ranked deletion endpoints from the verified defect-10 seed.

coverage-aware exact local closure

Rank all 24,804 three-block deletions by residual defect, collision count, and lexicographic order; exhaust every strict incidence-matched three-block insertion for ranks 0 through 511.

Hypothesis: At least one strict incidence-matched completion among the first 512 coverage-ranked endpoints has fewer than ten uncovered triples.

Test: Exhaustively score all strict completions of the hash-bound 512-endpoint prefix and independently reconstruct their minimum defect.

The gapless checker union agrees with every endpoint row, total, and optimum; regeneration is byte-identical and direct coverage confirms ten missing triples. These facts support only the stated local negative.

• Every strict incidence-matched completion in the declared 512-endpoint prefix has at least ten uncovered triples.
• The checked prefix contains exactly 1,191,854 neighbors.
• The best checked family has defect 10, 107 collision pairs, and point degrees 18^15.

• sha256sum -c artifacts/degree18-3x3-closure512-20260811/manifest.sha256
• Union receipt reconstructs shard ranges [0,128), [128,256), [256,320), [320,384), and [384,512).
• Independent global tuple/set checker reports 54 distinct blocks, 445 covered triples, ten missing triples, and valid=false.

• .proof-experiments/20260811-025003-ca0d01: canonical producer completed 512 endpoints and 1,191,854 neighbors.
• .proof-experiments/20260811-025212-e3547d: byte-identical producer regeneration.
• .proof-experiments/20260811-030507-5ff44a and 20260811-030644-04305a: independent ranks 0 through 255.
• .proof-experiments/20260811-031149-0f2ef0, 20260811-031213-5f0b44, and 20260811-031213-c5526f: independent ranks 256 through 511.
• .proof-experiments/20260811-031234-6f09b8: gapless union receipt.
• .proof-experiments/20260811-031302-d86a62: separate global negative control.

Five separately executed endpoint shards reconstructed all ranks and completions; a union checker verified contiguous coverage, exact totals, the global optimum, regeneration, and 30 mutations. The pre-existing tuple/set global checker independently confirmed ten missing triples.

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

• Local-search exchange neighborhoods -> coverage-ranked deletions should concentrate repairable states -> exhaustive selected closure improved collisions but did not reduce defect.

• All 1,191,854 neighbors in the declared prefix have defect at least ten.
  artifacts/degree18-3x3-closure512-20260811/independent-check.json · The hash-bound 512-endpoint prefix only. · computed
• The best checked family has 54 distinct blocks, point degrees 18^15, and covers 445 triples.
  .proof-experiments/20260811-031302-d86a62/stdout.txt · Best family SHA-256 3e83de2272aaf5fa18b6167ba384ac6722bd4f03d49c6b1ca3979e98c3f80462. · computed

• Advance the defect-10 seed using exhaustive strict 3-for-3 completion of the first 512 residual-defect/collision/lex-ranked endpoints.
  Exactly 1,191,854 neighbors; no claim about other endpoints or families. · The independently reconstructed minimum defect is ten. · artifacts/degree18-3x3-closure512-20260811/independent-check.json · A materially different bulk ordering or multi-step closure mechanism with an independently checked below-ten signal.

• Type-4 skeleton-link interface lift-map audit.
  It restores labelled boundary correlations absent from the failed local closure prefix. · Define the complete boundary map and independently census its lifts before generating SAT leaves. · high · open
• Multi-step degree-preserving closure with exact beam certificates.
  A second exchange may cross the defect-ten barrier that every single checked exchange retained. · Only after specifying a non-arbitrary canonical beam and a complete independently checkable endpoint certificate. · low · open

Objective: Determine whether type-4 skeleton signatures admit complete labelled link-interface lifts.

First action: Create protocols/type4-skeleton-link-interface-v1.json defining the exact domain, codomain, lift invariants, coverage count, and stop gates.

Stop condition: Stop or redirect on universal survival, checker disagreement, or a complete lift universe exceeding the declared bounded capacity.

• Specify and audit the exact domain, codomain, boundary invariants, and complete labelled lift map for the type-4 skeleton-link interface.

• 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 ↗

GPT-5.6 Sol served as principal investigator. GPT-5.6 Terra delegates supplied bounded advisory reconnaissance and stale-route challenges; their agreement was not validation. Python 3.12.3 standard-library exact enumeration, SHA-256, the computational-researcher harness, and deterministic local checkers were used. No SAT solver, CAS, proof assistant, package installation, publication, external write, or Git operation was used. A checkpointed-lab submission was attempted after a checker exceeded two minutes, but sandbox permissions prevented creation of any lab job; validation was instead decomposed into bounded gapless shards.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

2570.4s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-031942-744f1b

No human review recorded.