Complete minimum-unique-triple-loss deletion-class selection followed by exact incidence-profile enumeration of every defect-nine-relevant five-block completion.

minimum unique-triple-loss cell census

Order all five-block deletions by unavoidable unique-triple loss, select the complete singleton minimum class, and exhaust it using canonical missing-triple anchoring and one-plus-two-plus-two meet-in-the-middle.

Hypothesis: The unique strict-five deletion cell minimizing unavoidable unique-triple loss has an exact degree-preserving outside-seed five-block completion with defect at most nine.

Test: Select the entire minimum-loss class among all C(54,5) deletions and enumerate every exact-degree completion that could have defect at most nine.

Strict order statistics establish complete class selection, while the canonical-hitter lemma establishes enumeration completeness at the defect-nine threshold. Independent agreement supports the local exclusion, but its one-cell scope cannot change the global bound.

• Deletion cell [7,17,19,30,53] uniquely minimizes five-block unique-triple loss, with value 20.
• Exactly 6767836 threshold-relevant exact-degree completions occur in that cell.
• Their minimum defect is 11, attained twice; therefore the cell has no defect-at-most-nine completion.
• The maintained exact range remains 54 <= C(15,5,3) <= 55.

• Producer experiment 20260811-172443-325fec completed in 113.272 seconds and returned minimum defect 11.
• Independent experiment 20260811-172936-0753e6 completed in 105.625 seconds and returned valid=true.
• The first independent traversal timed out and supports no claim.
• Mutation experiment 20260811-173217-6ab4e6 rejected five decisive corruptions.
• sha256sum -c artifacts/degree18-min-unique-loss-cell-20260811/manifest.sha256 passes.

• .proof-experiments/20260811-172443-325fec: producer found minimum defect 11 among 6767836 candidates.
• .proof-experiments/20260811-172717-b20cf2: first independent traversal timed out and supports no claim.
• .proof-experiments/20260811-172936-0753e6: independent checker returned valid=true.
• .proof-experiments/20260811-173217-6ab4e6: five mutations rejected.

checkers/check_degree18_min_unique_loss_cell_v1.py imports no producer code. It selects the cell by strict order statistics, uses two 15-bit incidence planes instead of base-5 sums, reconstructs every decisive count and histogram bin, and directly verifies the saved best family.

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

• Loss-aware local repair -> minimum unavoidable outgoing loss was predicted to select the best repair cell -> the loss-20 cell has defect 11 while a loss-29 fixture has defect 10, so incoming recoverability must be modeled.

• The complete minimum unique-loss class is the singleton cell [7,17,19,30,53], with loss 20.
  Complete producer histogram and independent order-statistic proof. · The locked seed only. · computed
• The selected cell has no exact-degree outside-seed five-block completion with defect at most nine.
  Independent agreement on 6767836 completions and minimum defect 11. · Deletion cell [7,17,19,30,53] only. · computed

• Use the globally minimum unique-loss cell to obtain a defect-below-ten strict-five repair.
  The complete singleton minimum class under protocol v1. · Every threshold-relevant completion has defect at least 11. · result.json and independent-check.json · A demonstrated artifact error, different seed, or different move radius.
• Treat minimum outgoing unique loss as a sufficient repair-quality proxy.
  Comparison of the exact epoch-93 and epoch-87 cells. · Loss 20 yields defect 11 while loss 29 yields defect 10. · Both independently checked cell censuses. · Add a proved demand-aware recoverability term that correctly orders both controls.

• Demand-aware maximum-recovery bound.
  It directly models the failure signature omitted by unique-loss ordering. · Evaluate a matching, flow, or LP upper bound on only the epoch-87 and epoch-93 cells. · high · open
• Globally complete proof-producing pair-normalized SAT.
  It remains the terminal negative route but requires a measured encoding or decomposition improvement. · Run one matched branch pilot only after a nonzero semantic-delta audit and proof-smoke replay. · normal · open

Objective: Determine whether a demand-aware recovery bound can replace the falsified unique-loss proxy.

First action: Implement the smallest matching, flow, or LP upper bound on recoverable post-deletion losses and run it on the epoch-87 and epoch-93 calibration cells.

Stop condition: Redirect if the bound is unsound, the checker disagrees, or it fails to rank the known defect-10 fixture ahead of the defect-11 cell.

• Do not enumerate the next unique-loss class merely because it contains only 18 cells.
• Construct a provably one-sided demand-aware maximum-recovery bound.
• Calibrate it first on the exact epoch-87 and epoch-93 cells.
• Preserve globally complete proof-producing SAT as the alternative terminal route.

• 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 Sol principal investigator; two GPT-5.6 Terra delegates supplied advisory reconnaissance only, with stale skeleton advice rejected. Python 3.12.3 standard-library exact enumeration, arbitrary-precision bitsets, SHA-256, the computational-researcher harness, independent checker, mutation controls, and live maintained/primary-source searches were used. No SAT solver, CAS, proof assistant, lab job, package installation, system change, external write, publication, Git history change, or sub-agent spawning was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1799.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-174025-074a22

No human review recorded.