Sparse joint binary MILP over the complete strict six-deletion/six-addition exact-degree neighborhood of the locked defect-10 seed.

strict-radius joint binary MILP

HiGHS branches over all outside-seed additions, seed deletions, and uncovered-triple indicators while sharing exact point-balance and coverage constraints.

Hypothesis: The locked defect-10 degree-18 seed has a strict 6-for-6 exact-degree neighbor with fewer than ten uncovered triples discoverable within 90 seconds.

Test: Run the complete sparse local model once and advance only if a separately written checker reconstructs defect below 10.

Advancement required independently checked defect below 10. The incumbent has defect 13 and the timeout has no replayable proof.

• Candidate SHA-256 6c0a0e649ef806c81b99bd89e88f8a8876fc148d5e0c74ea2324f2267b2aa02d is a 54-block strict 6-for-6 degree-18 family missing exactly 13 of 455 triples.
• The fixed 90-second protocol did not meet its advancement gate.

• python3 scripts/degree18_joint_milp_6x6_v1.py --protocol protocols/degree18-joint-milp-6x6-v1.json --output-dir artifacts/degree18-joint-milp-6x6-20260811
• python3 checkers/check_degree18_joint_milp_6x6_v1.py --protocol protocols/degree18-joint-milp-6x6-v1.json --result artifacts/degree18-joint-milp-6x6-20260811/result.json --output artifacts/degree18-joint-milp-6x6-20260811/independent-check.json
• sha256sum -c artifacts/degree18-joint-milp-6x6-20260811/manifest.sha256

• .proof-experiments/20260811-210107-1de839: solver returned a checked defect-13 incumbent without a certificate
• .proof-experiments/20260811-210256-e328a5: independent checker passed all literal checks and mutations

checkers/check_degree18_joint_milp_6x6_v1.py uses standard-library set reconstruction and all 455 triple tests; it does not validate solver bounds.

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

• Larger-neighborhood optimization -> predicted improved incumbent -> observed defect worsened from 10 to 13, so radius alone is not a useful guide.

• The saved radius-six incumbent is a valid degree-18 family with defect 13 and 111 collisions.
  artifacts/degree18-joint-milp-6x6-20260811/independent-check.json · Candidate SHA-256 6c0a0e649ef806c81b99bd89e88f8a8876fc148d5e0c74ea2324f2267b2aa02d only. · computed

• Scale the same unguided radius-six MILP merely by increasing its wall cutoff.
  The locked seed, SciPy 1.11.4/HiGHS formulation, and fixed 90-second protocol. · The gate failed with a defect-13 incumbent and produced no proof-prefix asset. · artifacts/degree18-joint-milp-6x6-20260811/result.json and independent-check.json · A materially different formulation must beat defect 10 in a matched pilot or produce replayable certificates.

• Coverage-guided radius-six exact-demand profile join.
  It samples additions hitting original missing triples and uses exact demand matching instead of unguided branch-and-bound. · Freeze 32768 incoming families, enumerate exact deletion matches, and require defect below 10. · normal · open
• Positive-semantic-delta global SAT audit.
  Only the complete certificate route can support a negative settlement, while the fixed-pair link was redundant. · Statically compare one pair-excess-skeleton coupling against all four canonical CNFs. · high · open

Objective: Test a coverage-guided exact-demand radius-six join.

First action: Freeze 32768 missing-triple-hitting incoming six-families and join them by exact base-7 incidence profiles to all C(54,6) deletions.

Stop condition: Close on checker disagreement or best defect at least 10; defect zero triggers full verification.

• Do not increase the cutoff or rerun the unguided MILP.
• Test a coverage-guided radius-six exact-demand profile join.
• Keep the full strict-five recovery census on hold pending owner approval.
• Run no global SAT solve until a static checker proves positive non-subsumed semantic delta.

• 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/2607.23766 ↗

GPT-5 Codex Sol principal designed and executed the epoch. Two GPT-5.6 Terra delegates supplied advisory memos only; model agreement was not evidence. Python 3.12.3, NumPy 1.26.4, SciPy 1.11.4 with bundled HiGHS, the computational-researcher harness, a separate standard-library checker, mutation controls, SHA-256, Git read-only status, and bounded web calls were used. No Sol subagents, lab job, external write, publication, package installation, system change, proof assistant, SAT solver, or Git operation occurred.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1026.8s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-210923-be596a

No human review recorded.