Complete exact enumeration of every legal degree-preserving 2-for-2 neighbor of the hash-pinned degree-18 defect-nine seed.

complete exact-degree local repair census

Partition each deleted block pair's symmetric difference into equal-incidence replacement pairs, collision-filter them, and score exact triple coverage; independently recover pairs by scanning all 3003 possible first blocks.

Hypothesis: The validated defect-nine seed has a legal degree-preserving 2-for-2 neighbor with at most eight uncovered triples.

Test: Enumerate all incidence-compatible cells for all 1431 deletion pairs and independently recompute the minimum defect; defect at most eight advances and defect zero is terminal.

The producer and a materially different exhaustive checker agree row-for-row and on all aggregate counts. Direct tuple and bitmask audits agree on the best endpoint, four mutations fail closed, and decisive outputs regenerate byte-identically. This supports the exact local claim but no global extrapolation.

• Seed bcbf2effff530b2e6c7412bfbef22bc002ea2c66dd206b6a17a8eedf7bdecdad has 54 distinct blocks, point degrees 18, and defect nine.
• Its complete legal nonidentity degree-preserving 2-for-2 neighborhood has 38,941 exchange occurrences and minimum defect ten.
• Therefore the seed is a strict local minimum for the declared move.

• python3 scripts/degree18_defect9_2for2_neighborhood_v1.py --protocol protocols/degree18-defect9-2for2-neighborhood-v1.json --output-dir artifacts/degree18-defect9-2for2-neighborhood-20260812
• python3 checkers/check_degree18_defect9_2for2_neighborhood_v1.py --protocol protocols/degree18-defect9-2for2-neighborhood-v1.json --artifact-dir artifacts/degree18-defect9-2for2-neighborhood-20260812 --output artifacts/degree18-defect9-2for2-neighborhood-20260812/independent-check.json
• python3 checkers/audit_degree18_defect9_2for2_best_v1.py --protocol protocols/degree18-defect9-2for2-neighborhood-v1.json --artifact-dir artifacts/degree18-defect9-2for2-neighborhood-20260812 --output artifacts/degree18-defect9-2for2-neighborhood-20260812/direct-audit.json
• sha256sum -c artifacts/degree18-defect9-2for2-neighborhood-20260812/manifest.sha256

• .proof-experiments/20260812-124119-f2e764: producer completed with minimum defect ten
• .proof-experiments/20260812-124146-765844: independent checker completed 4,297,293 first-block scans
• .proof-experiments/20260812-124153-494189: direct endpoint audit passed
• .proof-experiments/20260812-124153-ff84ee: four mutations were rejected
• .proof-experiments/20260812-124153-74aeb6: decisive outputs regenerated byte-identically

check_degree18_defect9_2for2_neighborhood_v1.py does not use the producer's symmetric-difference generator: it scans all 3003 first blocks for each deletion, derives the complement by bit incidence, and recomputes full-family 455-bit coverage and fifteen degrees. A separate auditor uses explicit tuple containment and another coverage union.

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-trade local search -> measure the full neighborhood before scaling -> the new seed is a strict 2-for-2 local minimum.
• Certified covering proofs -> separate compressed production from a deliberately less compressed checker -> 40,809 direct cells and 4,297,293 scans agreed exactly.

• The pinned family bcbf2eff... has 54 distinct blocks, point degrees 18, and exactly nine uncovered triples.
  Input certificate plus independent checker seed audit · The explicit labelled family · computed
• Every legal nonidentity degree-preserving 2-for-2 neighbor of the pinned seed has defect at least ten.
  Complete ledger and independent reconstruction · The pinned seed's one-step 2-for-2 neighborhood · computed

• Improve or preserve defect nine by one legal nonidentity degree-preserving 2-for-2 move.
  All 39,378 nonidentity incidence-compatible attempts, of which 437 collide and 38,941 are legal · The exact minimum legal-neighbor defect is ten. · artifacts/degree18-defect9-2for2-neighborhood-20260812/receipt.json · Use a different move family or produce evidence invalidating the seed/census semantics.

• Two-link exact local-completion prefilter on canonical marked shared-triple families
  It restores two compatible optimal point links and has global structural reach. · Positive-control the residual formulas, then canonically count (H,a,b) types under a 100,000-type cap. · high · open
• Proof-producing PB/SAT calibration on one globally complete normalized branch
  It remains globally decisive but should scale only after measured proof throughput and independent replay. · Run one fixed-cap proof-producing pilot and replay any emitted proof. · normal · open

Objective: Measure whether two exact optimal point-link completions prune canonical marked shared-triple families for the 15-cycle skeleton branch.

First action: Reconstruct Iorio's control links and verify d^a_z = 5 + [z=a] - h_z and d^b_z = 5 + [z=b] - h_z.

Stop condition: Stop or redirect on control failure, incomplete canonical action, more than 100,000 marked types, or universal survival.

• Do not repeat or enlarge the same 2-for-2 census.
• Verify the two residual-link degree formulas on Iorio's 55-cover.
• Canonically count marked six-triple families (H,a,b) under the full S13 action with a 100,000-type stop.

• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗

Codex (GPT-5), acting as Sol principal, selected the route, audited the Terra memos, designed and interpreted the experiment, and rejected the stale fixed-pair rerun. GPT-5.6 Terra delegates supplied advisory prior-art and verification memos only; model agreement was not counted as validation. CPython 3.12.3 standard-library programs performed deterministic enumeration, independent reconstruction, direct auditing, mutation tests, and regeneration. No SAT solver, CAS, proof assistant, or lab job was used. Web search checked the maintained LJCR record and primary arXiv sources.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1464.5s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-125210-dff608

No human review recorded.