Deterministic uncovered-triple-guided strict 3-for-3 local search on exact point-degree-18 54-block families, starting from the independently verified defect-10 seed.

uncovered-triple-guided exact-degree local repair

Choose an uncovered triple, select three low-unique-load incident blocks, repartition their exact 15-point incidence multiset into three absent blocks containing the target triple, and accept using exact incremental defect/collision energy.

Hypothesis: The guided strict 3-for-3 trajectory reaches an independently checked defect below 10 within exactly 32,768 proposals; defect zero would be a 54-block cover.

Test: Replay all 32,768 deterministic proposals independently and advance only if the separately recomputed best family misses fewer than 10 of the 455 triples.

Producer and checker agree exactly on proposal telemetry, hashes, rejection classes, accepted records, point degrees, and direct triple coverage. Because the best is the input seed and the trajectory is sampled rather than exhaustive, the justified outcome is no_progress and closure only of this exact protocol.

• Exactly 32,768 proposals were replayed; 30,123 were legal strict 3-for-3 moves and 1,591 were accepted.
• The independently checked best family covers exactly 445 of 455 triples, has defect 10, and is byte-identical to the input seed.
• Every accepted state preserves 54 distinct blocks and point-degree vector 18^15.
• These claims apply only to the recorded deterministic trajectory and do not bound C(15,5,3).

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... -- python3 scripts/degree18_guided_3x3_search_v1.py --protocol artifacts/degree18-guided-3x3-20260810/protocol.json --output-dir artifacts/degree18-guided-3x3-20260810
• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... -- python3 checkers/check_degree18_guided_3x3_search_v1.py --protocol artifacts/degree18-guided-3x3-20260810/protocol.json --artifact-dir artifacts/degree18-guided-3x3-20260810 --output artifacts/degree18-guided-3x3-20260810/independent-check.json --mutations-output artifacts/degree18-guided-3x3-20260810/mutation-controls.json
• sha256sum -c artifacts/degree18-guided-3x3-20260810/manifest.sha256

• .proof-experiments/20260810-021254-dae460: producer completed in 10.446 s; 32,768 proposals, best defect 10, no cover.
• .proof-experiments/20260810-021316-afb8e6: independent replay completed in 14.996 s; exact agreement and all five mutations rejected.

checkers/check_degree18_guided_3x3_search_v1.py independently implements RNG, proposal construction, combinadic unranking, incremental counts, acceptance, and best tracking; it periodically recomputes all 455 counts, verifies tuple and bitmask coverage, and rejects five mutations.

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 combinatorial trades -> preserve the slack-zero degree equations automatically -> every accepted strict 3-for-3 move retained degree vector 18^15.
• Constraint-guided local search -> force a currently uncovered triple while minimizing outgoing unique-load -> 30,123 legal proposals still failed to improve defect 10.
• Independent deterministic replay -> treat stochastic-looking search as an exact finite trajectory -> producer/checker hashes and telemetry agreed on all 32,768 proposals.

• Protocol degree18-guided-3x3-v1 has best defect 10 and covers 445 triples.
  Hash-exact independent replay and direct tuple/bitmask checks in artifacts/degree18-guided-3x3-20260810/independent-check.json. · Exactly seed 1553301 and 32,768 proposals under protocol v1. · computed
• All 1,591 accepted transitions preserve 54 distinct blocks and point-degree vector 18^15.
  Independent proposal regeneration, incidence-multiset equality, and periodic full recomputation. · The accepted trace records in protocol v1 only. · computed

• Scale this exact sampled guided 3-for-3 protocol solely by increasing its proposal cutoff.
  Seed SHA-256 138e85fe..., RNG seed 1553301, four-draw low-unique-load selection, energy 16*defect+collisions, and the first 32,768 proposals. · It failed the predeclared below-10 advancement gate and produced no improvement of the seed. · artifacts/degree18-guided-3x3-20260810/independent-check.json · A materially changed move/objective, an exhaustive neighborhood certificate, or an independently checked defect below 10 from a different bounded mechanism.

• Complete strict 3-for-3 neighborhood capacity census.
  It separates true local optimality from proposal bias and can yield an exact local structural certificate if the count is affordable. · Count all incidence-preserving incoming families for each of C(54,3)=24,804 outgoing triples and independently reproduce the total/histogram without scoring neighbors. · high · open
• SAT-guided ejection-chain repair from the defect-10 family.
  If the complete 3-for-3 neighborhood is too large or has minimum defect 10, a variable-length exact-degree completion can cross the sampled trade barrier. · Encode a bounded remove-r/add-r degree-preserving completion with all ten missing triples forced, starting at r=4 and requiring a direct witness or replayable UNSAT local proof. · normal · open
• Shared symbolic pair-excess proof encoding.
  It avoids the epoch-39 explosion from explicit type/skeleton headers while retaining globally sound pair-excess information. · Calibrate one proof-producing shared-skeleton encoding against the best audited pair-upper PB baseline at a matched cap. · normal · open

Objective: Determine whether the verified defect-10 seed is exhaustively tractable under strict 3-for-3 trades before investing in a larger constructive or proof route.

First action: Enumerate the incoming-family count for every one of the 24,804 outgoing block triples, write a hash-bound histogram/total, and independently reproduce it with a separate recurrence.

Stop condition: Stop or redirect on checker disagreement or when the measured neighbor count and projected exact scoring traffic exceed the predeclared capacity; do not score a partial neighborhood as an exclusion.

• Do not extend the same sampled 3-for-3 cutoff.
• Count the complete strict incidence-preserving 3-for-3 neighborhood over all 24,804 outgoing triples, with a separate counting implementation.
• Only if that capacity gate is affordable, exhaustively score the neighborhood and certify its minimum defect; otherwise redirect to SAT-guided ejection chains or a symbolic shared pair-excess proof encoding.

• 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 principal designed, implemented, and interpreted the epoch. Two GPT-5.6 Terra delegates supplied advisory reconnaissance only; their memos were audited, not treated as evidence or votes, and no delegate artifact was claimed. Deterministic evidence used Python 3.12.3 standard-library code with exact integer arithmetic and the computational-researcher experiment runner; web search refreshed source status and prior art. No CAS, SAT solver, proof assistant, or external lab was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1222.9s

Review state

not a result claim

Attempt ID

covering-c1553-20260810-022232-82b1d2

No human review recorded.