Complete coverage-aware enumeration of every strict degree-preserving 3-for-3 exchange from the hash-pinned degree-18 defect-nine family.

coverage-aware exact-degree local repair census

Generate incoming triples with exactly the deleted blocks' 15-coordinate incidence vector, reject seed blocks, and score the literal post-deletion 455-triple coverage mask; independently reconstruct the same space using a base-3 residual pair table.

Hypothesis: The pinned defect-nine family has a strict degree-preserving 3-for-3 exchange with final defect at most eight, or at least a defect-nine peer.

Test: Enumerate all legal exchanges and independently reproduce their exact minimum final defect; a minimum at most eight advances construction, nine falsifies strictness, and ten or more closes this neighborhood.

The producer and a materially different meet-in-the-middle checker independently audit the seed, cover every deletion header, reproduce the exact candidate count and minimum defect rowwise, emit byte-identical ledgers, and reject four integrity mutations. These checks support the local strict-minimum claim but cannot be extrapolated to other 54-block families.

• Family bcbf2effff530b2e6c7412bfbef22bc002ea2c66dd206b6a17a8eedf7bdecdad has 54 distinct blocks, point degrees 18, and defect nine.
• There are exactly 52,155,333 legal strict degree-preserving nonseed 3-for-3 exchanges from this family.
• Every such exchange has final defect at least ten.
• Therefore this family is a strict local minimum under the declared 3-for-3 move.

• artifacts/degree18-defect9-coverage-3for3-precount-20260812/producer artifacts/degree18-two-basin-crossover-20260812/best-certificate.json artifacts/degree18-defect9-coverage-3for3-precount-20260812/producer-ledger.jsonl artifacts/degree18-defect9-coverage-3for3-precount-20260812/producer-result.json
• artifacts/degree18-defect9-coverage-3for3-precount-20260812/checker artifacts/degree18-two-basin-crossover-20260812/best-certificate.json artifacts/degree18-defect9-coverage-3for3-precount-20260812/producer-ledger.jsonl artifacts/degree18-defect9-coverage-3for3-precount-20260812/checker-ledger.jsonl artifacts/degree18-defect9-coverage-3for3-precount-20260812/independent-check.json
• python3 checkers/test_degree18_defect9_coverage_3for3_mutations_v1.py --checker artifacts/degree18-defect9-coverage-3for3-precount-20260812/checker --seed artifacts/degree18-two-basin-crossover-20260812/best-certificate.json --ledger artifacts/degree18-defect9-coverage-3for3-precount-20260812/producer-ledger.jsonl --output artifacts/degree18-defect9-coverage-3for3-precount-20260812/mutation-controls.json
• sha256sum -c artifacts/degree18-defect9-coverage-3for3-precount-20260812/manifest.sha256

• .proof-experiments/20260812-195846-d0f02c: producer enumerated 52,155,333 legal exchanges and found exact minimum defect ten.
• .proof-experiments/20260812-195931-ff8869: independent checker indexed 4,507,503 block pairs, reconstructed every row, and reproduced minimum ten.
• .proof-experiments/20260812-195945-0c7788: four fail-closed mutations were rejected.
• .proof-experiments/20260812-200011-805313: the strict-local-minimum receipt and manifest were finalized and verified.

check_degree18_defect9_coverage_3for3_precount_v1.cpp does not use the producer's point-assignment recursion. It indexes all unordered pairs of the 3003 blocks by base-3 point-incidence sum, derives the residual pair demand for each possible third block, imposes a<b<c, rebuilds literal packed coverage, and compares all 24,804 producer rows.

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

• Exact local-search analysis -> fully classify the cheapest move before scaling -> the crossover seed has a one-unit barrier under both complete 2-for-2 and 3-for-3 moves.
• Meet-in-the-middle subset construction -> index pair incidence and derive the third component -> a 4,507,503-record pair table independently reproduced the 52,155,333-exchange census.

• The pinned family has 54 distinct blocks, degree vector 18^15, and defect nine.
  Hash-bound crossover certificate plus independent producer and checker seed audits. · The explicit labelled family. · computed
• Its complete strict degree-preserving 3-for-3 neighborhood contains exactly 52,155,333 legal nonseed exchanges.
  Byte-identical 24,804-row producer and checker ledgers. · The explicit family and its point-isomorphism class. · computed
• The exact minimum neighbor defect is ten.
  Point-assignment producer and residual-pair checker agree rowwise; receipt and manifest pass. · The complete declared 3-for-3 neighborhood. · computed

• Improve or preserve defect nine by one strict degree-preserving 3-for-3 exchange from bcbf2eff...
  All 52,155,333 legal exchanges from all C(54,3)=24,804 deletion headers. · The independently reproduced exact minimum final defect is ten. · artifacts/degree18-defect9-coverage-3for3-precount-20260812/receipt.json · Evidence invalidating the seed, coverage semantics, or either exhaustive encoding; otherwise use a different seed or move family.
• Use the injected simple-cycle two-link proposal as a new route without an overlap audit.
  The ordered-distinct-mark six-common-triple interface described in the delegate memo. · That mechanism overlaps the already completed 3,770-type two-link corpus and its 2,171 capacity survivors; it is not a fresh discriminator. · records/attempts/epoch-0120-two-link-local-completion-capacity-20260812.json and epoch-0121-two-link-point-capacity-prefilter-20260812.json · A genuinely new correlation or encoding that wins a matched pilot on an unresolved survivor.

• Relative-alignment quotient for the two parents that generated the defect-nine crossover child.
  The previous exact crossover covered only fixed stored labelled alignments; other relative point alignments may produce new degree-18 children while escaping the closed local neighborhoods. · Compute both parent automorphism groups and the exact or bounded double-coset alignment count before evaluating a child. · high · open
• Globally complete proof-producing normalized decomposition.
  It remains the only negative route capable of settling the value, but previous branches were UNKNOWN and require a materially new decomposition or measured propagation gain. · Design one new symmetry-disjoint cube family and run a matched proof-producing pilot with LRAT replay. · normal · open
• Coverage-aware move larger than three blocks from the defect-nine seed.
  A constructive hit is terminal, but the raw 4-for-4 space is enormous and must not be scaled without a sound header-level bulk filter. · Derive a one-sided deletion-header capacity bound and measure it on a deterministic sample before any exhaustive completion search. · low · open

Objective: Determine whether unexamined relative relabellings of the successful crossover parents form a tractable constructive quotient.

First action: Compute and independently verify the point-automorphism groups of plateau-new-19 and plateau-next-46, then estimate the exact double-coset alignment count.

Stop condition: Redirect if the stabilizers are trivial or too small, the canonical alignment universe exceeds the predeclared cap, or independent orbit accounting disagrees; directly validate any defect-below-nine child.

• Do not repeat or enlarge this exact 3-for-3 census; its finite neighborhood is closed.
• Compute and independently verify the automorphism groups of crossover parents plateau-new-19 and plateau-next-46.
• Estimate the resulting double-coset relative-alignment universe and proceed only under a predeclared tractability cap.
• Directly check any new defect-below-nine child against all 455 triples; otherwise redirect to a globally complete proof-producing decomposition.

• 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://central.bac-lac.gc.ca/.item?app=Library&id=nq24295&oclc_number=46548328&op=pdf ↗

GPT-5.6 Sol principal selected, designed, implemented, and interpreted the experiment. Two injected GPT-5.6 Terra delegates supplied bounded advisory reconnaissance; their agreement was not treated as validation, and their proposed simple-cycle route was rejected as overlapping prior completed work. C++20 standard-library producer and independent checker were compiled with g++ 13.3.0 using -O3 -DNDEBUG. Python 3.12.3 provided the experiment runner, mutation harness, receipt finalizer, and durable-state projection. The web reader checked the maintained repository and literature queries. No SAT/PB solver, CAS, proof assistant, cloud lab, package installation, external publication, Git commit, or remote write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1401.3s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-200454-133e4e

No human review recorded.