Four deterministic strict exact-degree ejection-chain arms of lengths 4, 5, 6, and 7 from the verified defect-10 seed, followed by a complete pre-acceptance proposal audit.

variable-length exact-degree ejection chains

Target an uncovered triple, select outgoing blocks by dynamic unique-coverage-loss tournaments, preserve their complete point-incidence multiset, and close the incoming family by randomized-tie bipartite Havel-Hakimi construction.

Hypothesis: At least one of four 8192-proposal arms produces a directly checked 54-block family with fewer than ten uncovered triples.

Test: Audit all legal proposed replacements before acceptance and advance only if an independently checked proposed family has defect below 10.

The producer, repeated regeneration, and direct family checkers agree on the saved minima and invariants. Because the search is sampled and non-exhaustive, it supports closure only of protocol v1, not any mathematical exclusion.

• Every recorded accepted arm best is byte-identical to the defect-10 input seed.
• The accepted global best has 54 distinct blocks, point degrees 18^15, and covers exactly 445 triples.
• The deterministic audit reported no defect-improving proposal among its 32750 legal sampled replacements.
• The saved best-proposed families have independently checked defects 13, 17, 18, and 22 for lengths 4, 5, 6, and 7.

• Producer experiment 20260810-065309-818bda completed 32768 proposals.
• Independent accepted-best check 20260810-065428-4014c5 passed with four rejected mutations.
• Regeneration experiment 20260810-065509-799008 reproduced all trace and best files.
• Proposal audit 20260810-065848-66cd0e found zero improving sampled proposals.
• Direct proposed-minimum check 20260810-065920-8569cc passed.
• Repeated audit 20260810-065939-302891 reproduced the identical stdout hash.
• sha256sum -c artifacts/degree18-ejection-chain-20260810/manifest.sha256 passed.

• .proof-experiments/20260810-065309-818bda: producer; 32768 proposals, zero accepted moves, best defect 10.
• .proof-experiments/20260810-065428-4014c5: independent accepted-best check; direct coverage agreement and four mutations rejected.
• .proof-experiments/20260810-065509-799008: fresh regeneration; all traces and best files reproduced.
• .proof-experiments/20260810-065848-66cd0e: complete pre-acceptance proposal audit; zero improving sampled proposals.
• .proof-experiments/20260810-065920-8569cc: independent direct checks of four proposed minima.
• .proof-experiments/20260810-065939-302891: repeated proposal audit with identical output hash.

check_degree18_ejection_chain_v1.py directly checks accepted best families, and check_degree18_ejection_proposal_audit_v1.py independently recomputes each saved proposed minimum using tuple counters and a 455-bit mask. Full proposal-stream enumeration was deterministically regenerated but not independently reimplemented.

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 bipartite degree realization -> predicted cheap variable-length closure -> 32750 of 32768 proposals closed successfully.
• Uncovered-triple-guided local search -> predicted coverage improvement -> every sampled proposal instead increased defect, with best increase from 10 to 13.
• Pre-acceptance auditing -> predicted separation of proposal and annealing failures -> showed proposal geometry itself was already inadequate.

• Protocol v1's accepted best is the hash-bound defect-10 input seed.
  Independent tuple/bit-mask checks and byte-identical regeneration · The four recorded protocol-v1 arms only · computed
• The deterministic proposal audit's saved per-arm minima have defects 13, 17, 18, and 22.
  proposal-audit.json, direct independent checks of all four saved families, and repeated deterministic audit · The 32750 legal proposals generated in the four recorded streams · computed

• Scale protocol v1 solely by increasing its cutoff, changing its seed, or raising its acceptance temperature.
  The saved outgoing tournament, Havel-Hakimi closure, energy, and four arm definitions · No sampled legal proposal improved defect before acceptance; the best proposed defect was 13. · artifacts/degree18-ejection-chain-20260810/proposal-audit.json and proposal-audit-independent-check.json · Materially new coverage-aware proposal geometry that independently verifies defect below 10

• Proof-replayed layer-five successor
  Its 288-cell predecessor passed pruning and complete proof-replay gates. · After explicit owner approval, freeze and run the 12-by-256 selector-union protocol. · high · open
• Proof-preserving globally complete encoding improvement
  It remains unblocked and can affect the exact target rather than one sampled basin. · Independently reconstruct one materially changed canonical branch encoding and compare at a matched cap. · normal · open
• Coverage-aware exact closure
  Degree closure is cheap, but outgoing/incoming choices must explicitly preserve singleton-covered triples. · Before another search, solve a 256-proposal matched pilot whose closure objective lexicographically minimizes lost singleton triples and then defect. · low · open

Objective: Resolve the authorization gate for the proof-replayed layer-five successor; otherwise improve a globally complete proof encoding.

First action: Present the exact 3072-cell layer-five scope and predecessor receipt for explicit owner approval; do not dispatch without it.

Stop condition: Stop on absent approval, proof/formula reconstruction disagreement, or failure of the matched global encoding improvement gate.

• Do not increase protocol-v1 cutoff, change only its seed, or raise its acceptance temperature.
• Obtain explicit owner approval before dispatching the 12-by-256 proof-replayed layer-five successor.
• Absent approval, test one materially new proof-preserving globally complete encoding with independent formula reconstruction and a matched improvement gate.
• Reopen constructive chains only with materially new coverage-aware proposal geometry and a directly checked defect below 10.

• 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 ↗

GPT-5.6 Sol was principal investigator. GPT-5.6 Terra delegates supplied advisory reconnaissance only; their stale fixed-pair suggestion was rejected, and the constructive fallback was independently specified and executed. Python 3.12.3 performed deterministic proposal generation, exact integer counting, tuple and 455-bit coverage checks, mutation tests, regeneration, SHA-256 hashing, and computational-researcher experiment capture. No sub-agent was spawned in this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1473.7s

Review state

not a result claim

Attempt ID

covering-c1553-20260810-070644-0afa58

No human review recorded.