Exhausted the first degree-feasible local exchange layer around Carmine Iorio's maintained 55-block cover: exactly three deletions and two additions.

degree-forced local exchange census

Final point degree 18 forces all three deletions through point 6 and both additions away from it; each feasible deletion triple determines a two-block incidence split which is checked against all 455 triples.

Hypothesis: At least one degree-compatible three-delete/two-add move from the maintained 55-cover is a 54-block C(15,5,3) cover.

Test: Enumerate the entire degree-compatible three-delete/two-add neighborhood and count candidates with zero uncovered triples.

The producer checks every candidate derived from the unconditional degree lemma. A materially different checker scans a broader deletion/addition representation, exactly matches the manifest and defects, and passes boundary and mutation controls.

• No 54-block C(15,5,3) cover lies at block-set symmetric-difference distance at most five from the displayed Iorio 55-cover.
• Exactly 15159 distinct degree-balanced candidates occur in the three-delete/two-add layer; the minimum uncovered-triple count is ten, attained by 88 candidates.

• python3 scripts/iorio_radius5_v1.py --cover sources/ljcr-c1553-55.txt --output-dir artifacts/iorio-radius5-20260809
• python3 scripts/check_iorio_radius5_v1.py --cover sources/ljcr-c1553-55.txt --manifest artifacts/iorio-radius5-20260809/candidate-manifest.jsonl --producer-result artifacts/iorio-radius5-20260809/result.json --output artifacts/iorio-radius5-20260809/independent-check.json --mutations-output artifacts/iorio-radius5-20260809/mutation-controls.json
• Experiment receipts 20260809-204706-cbf898 and 20260809-204716-536509.

• .proof-experiments/20260809-204706-cbf898: 684 feasible deletions, 15407 raw add-pairs, 15159 candidates, zero hits, minimum defect ten.
• .proof-experiments/20260809-204716-536509: exact manifest equality under independent reconstruction and four mutations rejected.

scripts/check_iorio_radius5_v1.py uses all C(55,3) deletion triples and all 3003 first-addition masks, unlike the producer's forced-pivot singleton split; it reconstructs the complete map and recomputes coverage by independent 455-bit OR.

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-pinnability -> local degree excess predicts the first feasible exchange layer -> the predicted three-delete/two-add layer was exactly enumerable but contained no cover.
• Certified covering searches -> finite negatives need independent coverage accounting -> the second encoding matched all 15159 candidates and rejected mutations.

• Any 54-cover is at symmetric-difference distance at least seven from the displayed Iorio 55-cover.
  Algebra excludes deletion layers one and two; artifacts/iorio-radius5-20260809/independent-check.json excludes layer three. · Simple block-set distance from sources/ljcr-c1553-55.txt only. · computed
• The exact minimum triple defect in the degree-balanced three-delete/two-add layer is ten, attained by 88 candidates.
  artifacts/iorio-radius5-20260809/result.json and independent-check.json · All 15159 distinct candidates in the checked layer. · computed

• Obtain a 54-cover from the displayed Iorio cover by at most three deletions and two additions.
  All simple 54-block families at symmetric-difference distance at most five from this exact source cover. · Layers one and two violate the forced point-6 degree change; every candidate in layer three misses at least ten triples. · artifacts/iorio-radius5-20260809/independent-check.json · A concrete producer/checker discrepancy or missing covering candidate.
• Scale directly to the four-delete/three-add layer solely because radius five failed.
  Campaign contribution allocation. · A larger arbitrary cutoff is not a contribution and no compression or acceptance path has been supplied. · The current result is only a local exclusion with minimum defect ten. · A proved bulk reduction, structural claim, information-rich pilot, or confirmed specialist interest.

• Cross-type native-PB robustness gate on common-family types 1-3.
  Type 4 showed a 64.897 percent PB-propagation reduction and the bounded protocol can test whether that signal generalizes. · Run six matched base/upper seed-0, 5000-conflict controls. · high · open
• Proof-capable globally complete pair-normalized decomposition.
  A complete negative is terminal, but only replayable per-leaf certificates count. · After the cross-type gate, verify one proof-producing UNSAT leaf end to end. · normal · open
• Use the 88 minimum-defect candidates as fixed regression controls.
  They are exact nearest local states but do not justify arbitrary neighborhood expansion. · Test whether a new structurally constrained trade reduces defect below ten. · low · open

Objective: Determine whether the compact native-PB pair strengthening is robust across the remaining three globally complete common-family types.

First action: Parameterize scripts/type4_native_pb_v1.py and its checker over canonical types 1, 2, and 3, preserving Z3 4.13.0, seed 0, and max_conflicts=5000.

Stop condition: Redirect if any semantic check fails, any type regresses in PB propagations, aggregate reduction is below 20 percent, or fewer than two types improve resource count or solver time by at least 20 percent.

• Parameterize the independently audited native-PB base/upper encoding over common-family types 1-3 and run the fixed 5000-conflict cross-type gate.
• Retain the radius-five manifest as a regression corpus; do not run radius seven without a proved compression, structural claim, or confirmed external interest.

• 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 ↗

GPT-5.6 Sol principal designed, audited, implemented, and interpreted the experiment. GPT-5.6 Terra delegates supplied advisory challenger and verification memos; model agreement was not counted as validation. Python 3.12.3 standard-library enumeration, integer bitsets, SHA-256, the project run_experiment.py harness, git metadata capture, and web search/open were used. No SAT solver, CAS, proof assistant, or lab compute was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1037.2s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260809-205543-990ea1

No human review recorded.