Exhaustively classify the two-delete/one-insert neighbourhood of the hash-bound archival 31-block cover using independent bitmask and direct-set implementations.

degree-aware 31-to-30 constructive local repair

Delete each pair of archival blocks, compute the triples losing their final covering occurrence, and test every one of the 5005 possible inserted 6-blocks; independently repeat without the pruning rule.

Hypothesis: Not recorded.

Test: Not recorded.

Every possible pair of deleted archival blocks and every possible inserted 6-block was covered by the unpruned computation. The independent bitmask computation obtained the same result using a proved one-sided filter, the source cover passed Python and C validators with negative controls, and the final receipt checker bound all decisive hashes and outputs.

• For the archival 31-block cover with SHA-256 289eed03daa87839214706723ff94bbf615f248044ef5591553daf89e120050a, no family formed by deleting two distinct blocks and inserting one 6-subset is a 30-block C(15,6,3) cover.
• Exactly 165 of its 465 deletion pairs leave at most 20 triples uncovered.
• The greater-than-20 prefilter reduces the insertion kernel from 2,327,325 to 825,825 checks without losing a possible one-block repair.

• python3 checkers/two_for_one_compression_bitmask_v1.py -> PASS pairs=465, survivors=165, checks=825825, repairs=0
• python3 checkers/two_for_one_compression_sets_v1.py -> PASS checks=2327325, repairs=0
• sh scripts/run_cover_controls_v1.sh -> both validators accepted the source and rejected duplicate/corruption controls
• python3 checkers/verify_two_for_one_receipt_v1.py -> PASS receipt hash-bound

• .proof-experiments/20260808-174819-8f69cf: bitmask enumeration, 825,825 retained checks, zero repairs
• .proof-experiments/20260808-174819-1f2d1d: independent unpruned set enumeration, 2,327,325 checks, zero repairs
• .proof-experiments/20260808-174840-ff5bdf: Python and C source-cover validation with duplicate and corruption controls
• .proof-experiments/20260808-175153-c27e91: final receipt and hash consistency check passed
• .proof-experiments/20260808-175447-d7954e: lab registration failed before job creation; no SAT computation ran

not provided

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

• C(12,6,4) certificate discipline -> require independent encodings and hash-bound receipts for finite exclusions -> the local exchange claim passed this discipline, while no parameter-specific global rigidity was imported.

• The fixed archival 31-cover has no two-delete/one-insert repair to a 30-block cover.
  artifacts/epoch4-20260808/two_for_one_compression_receipt.json and .proof-experiments/20260808-175153-c27e91 · All 2,327,325 deletion-pair/insertion representations around the exact hash-bound source cover. · computed
• A deletion pair leaving more than 20 uncovered triples cannot be repaired by one inserted 6-block.
  A 6-block contains exactly 20 triples; independently guarded by the unpruned enumerator. · Any two-delete/one-insert covering repair problem. · proved
• The archival 31-block input covers all 455 triples.
  .proof-experiments/20260808-174840-ff5bdf, using Python-set and C direct-incidence validators. · The exact file with SHA-256 289eed03daa87839214706723ff94bbf615f248044ef5591553daf89e120050a. · computed

• A two-delete/one-insert repair of the fixed archival 31-cover.
  Every pair of distinct archival blocks and all 5005 possible inserted 6-subsets. · Both exhaustive implementations found zero repairs. · artifacts/epoch4-20260808/two_for_one_compression_receipt.json · A demonstrated source-hash, enumeration, or receipt-checker defect; a larger exchange is a different route.
• Treat this local exclusion as evidence that no arbitrary 30-cover exists.
  The global C(15,6,3) decision problem. · Only families in one fixed 31-cover's exchange neighbourhood were enumerated. · The receipt's explicit scope and represented-space calculation. · A proved theorem showing every 30-cover must occur in this neighbourhood.

• Matched 3-for-2 repair pilot from the 165 viable deletion pairs.
  These are exactly the deletion pairs closest to one-block repair, and a larger exchange can be tested with incremental masks under a small matched budget. · Implement deterministic seeded 3-for-2 moves and compare them with equal-budget unconstrained deletion starts. · high · open
• Five-seed matched pair-propagation confirmation.
  The complete packet remains the smallest discriminator for the structural SAT route. · Run bash scripts/submit_pair_multiseed_lab_v1.sh only when registration can return a durable job ID. · normal · open

Objective: Determine whether the 165 closest deletion pairs provide superior starts for degree-aware 3-for-2 constructive repair.

First action: Implement a deterministic matched pilot with predeclared seeds, move budget, incremental triple masks, point-degree deltas, and an equal-budget unconstrained control.

Stop condition: A 30-cover stops for dual validation; failure to beat the control redirects away from archival-cover local repair; successful lab registration switches back to the exact 20-cell SAT gate.

• Implement a deterministic 3-for-2 exchange pilot using the 165 surviving deletion pairs as degree-aware starts.
• Run equal-budget unconstrained starts as a control and compare best uncovered-triple count plus point-degree deviation.
• Stop immediately on a 30-block hit and validate it with both direct cover checkers.
• Retry the hash-bound 20-cell SAT lab packet only after registration returns a durable job ID.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=6&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/abs/1706.06825 ↗
• https://arxiv.org/abs/2607.23766 ↗

orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1052.0s

Review state

not a result claim

Attempt ID

covering-c1563-20260808-175948-a18f71

No human review recorded.