Optimize 24 residual-defect-ranked strict 4-for-4 repairs of an independently checked defect-10 degree-18 seed using sparse binary MILP, then reconstruct every endpoint and returned family independently.

exact-degree local MILP repair

Exhaustively rank all outgoing four-block sets by residual defect, collision count, and lexicographic order; optimize point-balanced incoming blocks with binary MILP.

Hypothesis: At least one of the 24 minimum-residual-defect outgoing four-sets from seed SHA-256 3e83de2272aaf5fa18b6167ba384ac6722bd4f03d49c6b1ca3979e98c3f80462 has a strict point-balanced completion with fewer than ten uncovered triples.

Test: Return and directly check the minimum-defect family produced across the frozen 24 endpoints; advance only below defect 10.

The advancement observable was a directly checked defect below 10. The independently checked minimum returned defect was exactly 10, so the gate failed. The computation sampled only 24 endpoints and cannot support a broader negative claim.

• The frozen endpoint ordering contains 316251 labelled outgoing four-sets, and the independent checker reconstructed its first 24 exactly.
• All 24 returned families were directly checked; their defect histogram is {10:1, 11:9, 12:10, 13:3, 14:1}.
• The best checked family remains the incumbent seed with defect 10, collision count 107, and SHA-256 3e83de2272aaf5fa18b6167ba384ac6722bd4f03d49c6b1ca3979e98c3f80462.
• The fixed-pair-link-only strengthening has independently audited logical CNF delta zero across 5460 labelled requirements.

• Producer experiment 20260811-095646-bd4d23 completed in 26.379 seconds.
• Checker experiment 20260811-095732-e8349f reconstructed 316251 endpoints, checked 24 candidates, and rejected four mutations.
• A second producer run regenerated result.json, endpoints.jsonl, and best.txt byte-identically.
• sha256sum -c artifacts/degree18-milp-4x4-repair-20260811/manifest.sha256 passed.

• 20260811-095646-bd4d23: 24 MILPs completed; minimum returned defect 10.
• 20260811-095732-e8349f: all endpoints and candidates reconstructed; four mutations rejected.
• Temporary deterministic regeneration: result, endpoints, and best files were byte-identical.

scripts/check_degree18_milp_4x4_repair_v1.py independently re-enumerates all 316251 outgoing sets and directly verifies every candidate using tuple-key triple counts. It does not independently certify the HiGHS optimality claims, so no local UNSAT theorem is asserted.

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 completion -> binary MILP predicts stronger repair than randomized Havel-Hakimi closure -> all selected endpoints still returned defect at least 10.

• The selected endpoint order is exactly the first 24 of 316251 outgoing four-sets under the frozen key.
  Independent full re-enumeration in independent-check.json. · Seed SHA-256 3e83de22... and protocol SHA-256 17aa9e57.... · computed
• Every returned candidate has 54 distinct blocks, degree vector 18^15, and the recorded directly recomputed defect.
  Twenty-four direct checks and four rejected mutations. · The 24 returned candidates only. · computed
• Complete fixed-pair-link coverage adds zero clauses beyond fixed-block tautologies and baseline triple-coverage clauses.
  artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · All 5460 labelled link requirements in the four canonical baseline CNFs. · computed

• Scale the first-prefix 4-for-4 MILP protocol as an advance route.
  The exact 24-endpoint protocol only. · The predeclared below-10 signal failed, and larger arbitrary cutoffs are not contributions. · Independent checker reports best defect 10. · A materially different conditioned endpoint rule with a justified information advantage.
• Run complete fixed-pair-link coverage as a strengthening.
  Link-only constraints across all four canonical degree-18 baselines. · Logical CNF delta is zero. · 5460 reconstructed requirements and five rejected mutations. · A separately justified non-link constraint with independently checked nonzero semantic or propagation delta.

• Owner-approved radius-five selector stratum.
  A 288-cell predecessor is replay-certified and the 3072-cell map is independently reconstructed. · After explicit approval of map hash 7fcfd2d9..., generate exactly the first 256-cell selector union. · high · open
• Missing-triple-conditioned exact repair.
  Residual-defect ordering alone failed; conditioning the outgoing demand on the ten missing triples may alter the realizable incoming coverage geometry. · Define and independently audit a bounded endpoint rule before running any optimizer. · normal · open
• Materially new proof-producing conditioned global encoding.
  A complete replayed exclusion remains terminal, but prior generic cardinality compilers missed their gates. · Require a nonzero semantic delta and at least 20 percent matched decision improvement on one canonical leaf. · low · open

Objective: Resolve the owner gate for the hash-bound selector map.

First action: Obtain explicit approval or rejection of SHA-256 7fcfd2d9b429c02d3c968921155f1384343ba5bde865d7f0d9c59aab0f59a403.

Stop condition: Hold without approval; after approval stop on map mismatch, UNKNOWN, failed SAT decoding, failed DRAT/LRAT replay, or throughput below the frozen gate.

• Request explicit owner approval or rejection of selector map SHA-256 7fcfd2d9b429c02d3c968921155f1384343ba5bde865d7f0d9c59aab0f59a403.
• If approved, freeze only the first 256-cell selector stratum and apply the existing DRAT-to-LRAT replay contract.
• If approval is unavailable, design a non-prefix repair family conditioned on missing-triple structure and require a directly checked defect below 10 before scale-up.
• Do not rerun the zero-delta fixed-pair-link route or enlarge the 24-endpoint prefix.

• 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 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol principal audited the Terra memos, selected and implemented the discriminator, executed and interpreted the experiments, and updated the durable state. GPT-5.6 Terra delegates supplied prior-art and verification reconnaissance only; their agreement was not used as validation. Python 3.12.3, NumPy 1.26.4, SciPy 1.11.4 with scipy.optimize.milp/HiGHS, deterministic tuple-based Python checking, SHA-256, and the computational-researcher experiment harness were used. No lab job, proof assistant, SAT proof, or external publication action was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1118.2s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-100617-779162

No human review recorded.