A deterministic 256-pair comparison of proof-core-weighted versus singleton-loss-only immediate strict 3-for-3 exact-degree repairs from the verified defect-10 seed.

proof-core-weighted exact-degree local repair

Pair two outgoing-block selectors on identical deterministic word schedules, preserve point degree 18 by exact incidence-multiset repartitioning, and directly score the resulting 54-block candidates.

Hypothesis: Within 256 matched proposals, the proof-core-weighted arm reaches defect below 10 and records more strict paired defect/collision wins than the singleton-loss-only arm.

Test: Generate both arms from the same fixed seed and fifteen-word schedule per pair, then independently reconstruct every proposal and require proof-core best defect below 10 plus a positive matched-win balance.

The producer and materially different checker agree on every schedule, proposal, candidate metric, best result, and matched comparison. Because the experiment samples only 256 immediate repairs and its advancement gates failed, it supports closure only of this exact heuristic, not a mathematical exclusion.

• Exactly 256 paired schedules were reconstructed; the baseline arm produced 237 legal proposals and the proof-core arm produced 239.
• Both arms had independently checked best defect 13, while the fixed seed has defect 10.
• Among 228 jointly legal pairs, baseline won 88, proof-core won 58, and 82 tied under lexicographic defect/collision comparison.
• The empty-core weighted selector reproduced baseline selection on all 256 schedules.
• These claims exclude no unvisited local neighbor and do not change 54 <= C(15,5,3) <= 55.

• sha256sum -c artifacts/proof-core-paired-repair-256-20260811/manifest.sha256 passed for every listed artifact.
• python3 scripts/proof_core_paired_repair_v1.py --protocol protocols/proof-core-paired-repair-256-v1.json --output-dir artifacts/proof-core-paired-repair-256-20260811
• python3 checkers/check_proof_core_paired_repair_v1.py --protocol protocols/proof-core-paired-repair-256-v1.json --artifact-dir artifacts/proof-core-paired-repair-256-20260811 --output /tmp/check.json --mutations-output /tmp/mutations.json
• The independent checker reported 256 reconstructed pairs, 476 full candidate recomputations, 256 zero-core matches, and all mutations rejected.

• .proof-experiments/20260811-013229-2ec7f8: producer completed in 1.481 seconds; 256 pairs, best defect 13 in both arms, no cover.
• .proof-experiments/20260811-013230-b0df4e: checker completed in 1.532 seconds; 256 pairs reconstructed, 476 legal candidates full-recomputed, 256 zero-core controls passed, four mutations rejected.

checkers/check_proof_core_paired_repair_v1.py independently implements the RNG stream, selector tournaments, combination enumeration, incidence repartitioning, candidate construction, full 455-triple counts, matched summaries, zero-core control, and mutation rejection.

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

• Local UNSAT proof cores -> weight losses on proof-used coverage rows -> predicted better immediate constructive repair -> observed no defect improvement and a 58-to-88 matched loss.

• Protocol proof-core-paired-repair-v1 has best defect 13 in both selector arms.
  Hash-bound result plus independent full reconstruction in artifacts/proof-core-paired-repair-256-20260811/independent-check.json. · Exactly 256 schedules from RNG seed 15537201 and the fixed defect-10 seed. · computed
• The proof-core selector loses the matched defect/collision comparison 58 to 88, with 82 ties.
  Independent reconstruction of all 228 jointly legal pairs. · Jointly legal pairs in protocol v1 only. · computed
• Every legal recorded candidate is a simple 54-block family with point-degree vector 18^15.
  Independent candidate reconstruction and validation for all 476 legal arm proposals. · Recorded legal proposals only. · computed

• Scale the exact proof-core weighting used in protocol v1 solely by increasing its proposal cutoff.
  Fixed defect-10 seed, immediate strict 3-for-3 moves, weight equal to total singleton loss plus proof-core singleton loss, and the matched schedule design. · It failed to beat defect 10 and lost the matched comparison against singleton-loss-only selection. · artifacts/proof-core-paired-repair-256-20260811/independent-check.json · A theorem relating proof-core row frequency to repair potential, or an independently checked materially changed weighting that first beats defect 10 under a matched pilot.

• Certificate-first 3,072-cell radius-five closure tranche.
  It reuses a checked local proof pipeline and can produce replayable local exclusions or a directly checked repair, with a clear stop gate. · Audit the twelve deterministic strata and hash-bound cell map, obtain human scope approval, then generate and replay the selector-union proofs. · high · open
• Measured global pair-normalized proof encoding.
  It retains terminal global scope but prior formulas remained solver-UNKNOWN. · Design one proof-preserving encoding change and run a matched pilot requiring at least 20% fewer decisions. · normal · open
• Materially different constructive repair mechanism.
  A direct 54-cover remains terminal and the current weighting failure does not test longer ejection chains or exact five-for-five completion. · Predeclare a small matched test whose accepted signal is independently checked defect below 10, not merely a larger proposal cutoff. · normal · open

Objective: Prepare the exact 3,072-cell certificate-first radius-five protocol for owner review without dispatching it.

First action: Audit protocols/core-guided-layer5-filter-pilot-v1.json, scripts/core_guided_layer5_filter_v1.py, the twelve-stratum map, and the hash-bound selector-union replay contract; present the exact scope for human approval.

Stop condition: Do not dispatch without approval; after approval, redirect on any cell-map disagreement, retained cell, failed LRAT replay, or unacceptable throughput.

• Do not extend the exact proof-core weight or proposal cutoff used here.
• Audit the exact twelve-stratum, 3,072-cell radius-five protocol without dispatching it.
• Obtain human approval for that precise local scope before running it.
• If approved, require per-cell reconstruction and LRAT replay of the hash-bound selector union; stop on any disagreement, retained cell, or poor throughput.
• Keep global pair-normalized SAT on hold until a proof-capable encoding demonstrates at least a 20% matched decision reduction.

• 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/math/9502238 ↗
• https://doi.org/10.1002/jcd.3180030404 ↗

GPT-5.6 Sol acted as principal investigator, audited the injected packet, specified and implemented the experiment, and interpreted the result. GPT-5.6 Terra challenger-prior-art and experiment-verification delegates supplied advisory reconnaissance only; their agreement was not validation, and the relied-on recommendation was promoted with provenance. Python 3.12.3 performed exact enumeration and checking; SHA-256 bound artifacts; the computational-researcher harness captured commands, limits, logs, versions, and hashes; web search checked current status and prior art. No SAT solver, CAS, proof assistant, new subagent, lab job, installation, system change, external write, or publication was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1271.7s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-013913-020ceb

No human review recorded.