Joint sparse binary-MILP optimization over the complete strict five-deletion/five-addition, point-degree-preserving neighborhood of the newest verified defect-10 seed.

joint exact-degree constructive repair

Choose all five deleted seed blocks and five added non-seed blocks simultaneously, preserve all fifteen point degrees, and minimize binary indicators for uncovered triples.

Hypothesis: Within 90 seconds, the joint model returns a strict 5-for-5 neighbor with fewer than ten uncovered triples.

Test: Run the complete joint local model once under a fixed 90-second cap and independently recompute the returned family, degrees, and all 455 triple multiplicities.

The direct checker establishes the returned positive data only. The failed advance gate, nonzero MIP gap, and absence of an optimality or UNSAT certificate prevent promotion beyond no_progress.

• Candidate SHA-256 7486273dcebac2f74f3637da714e10aebd3a41ceaf5b823564cbcd6f8c3821ca contains 54 distinct 5-subsets, has all point degrees 18, and covers exactly 445 of 455 triples.
• The candidate differs from seed 3e83de22... by exactly five deleted and five added blocks.
• The solver stopped at its time limit with objective 10; its reported dual bound 5 and relative gap 0.5 are telemetry, not independently certified mathematical bounds.

• Producer: python3 scripts/degree18_joint_milp_5x5_v1.py --protocol protocols/degree18-joint-milp-5x5-v1.json --output-dir artifacts/degree18-joint-milp-5x5-20260811
• Checker: python3 checkers/check_degree18_joint_milp_5x5_v1.py --protocol protocols/degree18-joint-milp-5x5-v1.json --result artifacts/degree18-joint-milp-5x5-20260811/result.json --output artifacts/degree18-joint-milp-5x5-20260811/independent-check.json
• sha256sum -c artifacts/degree18-joint-milp-5x5-20260811/manifest.sha256 passed.

• .proof-experiments/20260811-104640-8f3b90: 90.73-second harness run; HiGHS timed out with checked defect-10 incumbent, reported dual bound 5, and no optimality certificate.
• .proof-experiments/20260811-104827-ca1bfc: independent checker passed in 0.126 seconds and rejected four mutations.

checkers/check_degree18_joint_milp_5x5_v1.py independently parses block sets, reconstructs the five deletions and additions, counts all fifteen point degrees and all 455 triple multiplicities, checks hashes and flags, and rejects four mutations. It deliberately does not certify the MILP lower bound.

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

• Endpoint-by-endpoint completion -> joint sparse optimization should remove arbitrary prefix bias -> the model covered the complete local move universe but still returned defect ten.
• Optimization timeout -> threshold feasibility can avoid spending search on defect-ten incumbents -> next test should impose defect <= 9 and use a proof-capable encoding.

• The recorded candidate is a strict 5-for-5, degree-18 family with defect ten and 110 collision pairs.
  artifacts/degree18-joint-milp-5x5-20260811/independent-check.json · Candidate SHA-256 7486273dcebac2f74f3637da714e10aebd3a41ceaf5b823564cbcd6f8c3821ca only. · computed
• The joint model has 3,458 binary variables, 472 constraints, and 48,503 sparse nonzeros.
  artifacts/degree18-joint-milp-5x5-20260811/result.json and generator source · Protocol degree18-joint-milp-5x5-v1 only. · computed

• Treat the complete fixed-pair-link rerun as a new strengthening.
  All 5,460 labelled pair-link requirements in the four canonical degree-18 CNFs. · Every requirement is either fixed-block true or exactly an existing baseline coverage clause, giving zero logical clause delta. · artifacts/pair-link-cnf-delta-audit-20260811/result.json and independent-check.json · A separately proved pair-count or skeleton constraint with a concrete non-subsumption witness.
• Restart the raw point-link census under its original 120-class capacity budget.
  The q=6 bin of degree-profile 6,6,5^12 optimal C(14,4,2) links. · At least 121 pairwise nonisomorphic classes were already independently checked, crossing the saved stop threshold. · artifacts/q6-frontier-capacity-20260809-v3/representatives.txt and independent-check.json · A proved stronger whole-bin quotient or decomposition producing a manageable globally coupled frontier.
• Scale the same joint MILP solely by extending its wall-clock limit.
  Protocol degree18-joint-milp-5x5-v1 on seed 3e83de22... · The fixed gate failed, the incumbent did not beat defect ten, and the timeout supplied no certificate. · .proof-experiments/20260811-104640-8f3b90/experiment.json and independent-check.json · A proof-capable defect-at-most-nine threshold encoding, a material decomposition, or a directly checked better incumbent from a changed mechanism.

• Owner-approved radius-five selector stratum.
  Its 288-cell predecessor is proof-replayed and its 3,072-cell map is independently hash-bound, but the protocol requires explicit human approval. · After approval of map SHA-256 7fcfd2d9..., generate exactly the first 256-cell selector union and require complete proof replay. · high · open
• Proof-capable joint 5-for-5 defect-at-most-nine feasibility.
  The optimization model left the exact local threshold unresolved; a threshold CNF can yield a checked witness or replayable negative certificate. · Generate and independently reconstruct the full strict 5-for-5 CNF with total uncovered indicators at most nine, then run one fixed proof-producing cap. · normal · open

Objective: Resolve selector authorization or decide the strict 5-for-5 defect-at-most-nine threshold proof-capably.

First action: Request approval or rejection of selector map SHA-256 7fcfd2d9b429c02d3c968921155f1384343ba5bde865d7f0d9c59aab0f59a403; absent approval, draft the immutable defect-at-most-nine CNF protocol.

Stop condition: Stop on withheld selector approval, semantic mismatch, fixed-cap UNKNOWN, or proof-replay failure; promote immediately on a directly checked defect-below-10 family.

• Do not extend the same MILP wall cutoff.
• Request explicit approval or rejection of selector map SHA-256 7fcfd2d9b429c02d3c968921155f1384343ba5bde865d7f0d9c59aab0f59a403.
• Absent selector approval, encode the full joint 5-for-5 condition with total defect at most nine in proof-capable CNF and independently reconstruct its semantics before solving.
• For SAT, directly check the returned 54-block family; for UNSAT, require complete DRAT-to-LRAT replay before excluding this local neighborhood.

• 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 ↗

Codex GPT-5 served as Sol principal, audited the supplied GPT-5.6 Terra delegate memos as advisory leads, and relied only on primary sources or deterministic workspace artifacts. Python 3.12.3, SciPy 1.11.4 scipy.optimize.milp with HiGHS, standard-library checking code, SHA-256, and the computational-researcher experiment harness were used. No new sub-agent was spawned, no solver-reported lower bound was promoted as proof, and the Terra memos were not treated as independent validation.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1100.8s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-105612-9d5424

No human review recorded.