Three-basin deterministic constructive search over exact point-degree-18 families using legal 2-for-2 incidence-preserving switches.

multi-basin exact-degree constructive repair

One verified defect-10 radius-five seed and two independently generated regular seeds undergo explicit SplitMix64-scheduled 2-for-2 trades; incremental triple multiplicities and an annealed collision/defect energy generate information.

Hypothesis: At least one of three deterministic degree-18 basins reaches a directly checkable defect below 10 within 2^18 proposals, with defect zero constituting a 54-block cover.

Test: Run exactly 262144 seeded legal-switch proposals per basin and independently replay every proposal and accepted move; accept the route only if the separately recomputed best defect is below 10.

The producer and separate checker agree exactly on hashes, telemetry, defects, degree vectors, and direct triple coverage, but the best verified family still misses ten triples. Because the trajectories are sampled and non-exhaustive, the only justified outcome is no_progress for the exact target and closure of this specific protocol.

• Exactly 786432 proposals were replayed across the three predeclared trajectories; 779613 were legal and 68396 were accepted.
• The independently checked best defects were 10, 27, and 26; no recorded best family covers all 455 triples.
• Every recorded best family has 54 distinct 5-subsets and point-degree vector 18^15.
• These claims apply only to the three deterministic trajectories and do not bound C(15,5,3).

• python3 scripts/degree18_multibasin_search_v1.py --cover sources/ljcr-c1553-55.txt --radius5-manifest artifacts/iorio-radius5-20260809/candidate-manifest.jsonl --protocol artifacts/degree18-multibasin-20260810/protocol.json --output-dir artifacts/degree18-multibasin-20260810
• python3 checkers/check_degree18_multibasin_search_v1.py --cover sources/ljcr-c1553-55.txt --radius5-manifest artifacts/iorio-radius5-20260809/candidate-manifest.jsonl --protocol artifacts/degree18-multibasin-20260810/protocol.json --artifact-dir artifacts/degree18-multibasin-20260810 --output artifacts/degree18-multibasin-20260810/independent-check.json --mutations-output artifacts/degree18-multibasin-20260810/mutation-controls.json
• sha256sum -c artifacts/degree18-multibasin-20260810/manifest.sha256
• Failed controls preserved: experiment 20260810-003624-7c4391 exposed comment-line parsing before any search; experiment 20260810-003901-31399a hit the checker cap before exact block-hit memoization.

• .proof-experiments/20260810-003624-7c4391: fail-closed parser control; exited before search on a comment line in the preserved source.
• .proof-experiments/20260810-003650-330ce2: successful producer; 786432 proposals, 68396 accepted moves, global best defect 10, no cover.
• .proof-experiments/20260810-003901-31399a: checker performance control; timed out before a receipt because block-to-triple maps were recomputed.
• .proof-experiments/20260810-004129-74498b: successful semantically identical cached replay; exact agreement and all mutations rejected.

checkers/check_degree18_multibasin_search_v1.py separately reconstructs the source and seeds, uses an independently written combinadic/replay implementation, full-recomputes 455 triple multiplicities periodically and finally, checks each best family by tuple/set and bitmask encodings, and rejects six trace 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 point-degree invariant without repair -> all 68396 accepted moves retained degree vector 18^15.
• Multi-start local optimization -> random regular basins should reveal whether the operator reaches useful regions -> both fell from defect 133 to the high twenties but did not beat the structured defect-10 seed.
• Collision-energy smoothing -> accept neutral structural rearrangements while tracking uncovered triples -> extensive motion occurred, but the strong basin did not improve, indicating an operator/guidance bottleneck.

• All three recorded seeds and best families are simple 54-block 5-uniform families with point degrees exactly 18.
  Independent seed reconstruction, replay, and direct best checks in artifacts/degree18-multibasin-20260810/independent-check.json. · The six recorded families only. · computed
• Protocol v1 has global best defect 10 across its three trajectories.
  Hash-exact independent replay of 786432 proposals and direct checking of all three best-state files. · Exactly protocol v1 with the recorded seeds and proposal budgets. · computed

• Scale the same three-basin 2-for-2 annealing protocol merely by increasing its proposal cutoff.
  The exact v1 seeds, energy, acceptance schedule, and move operator through 2^18 proposals per basin. · It failed the predeclared below-10 gate; more of the same would be an arbitrary cutoff extension with no contribution signal. · artifacts/degree18-multibasin-20260810/independent-check.json · A material mechanism change or a measured pilot that independently verifies defect below 10.

• Uncovered-triple-guided 3-for-3 or ejection-chain exact-degree trades.
  The v1 failure signature isolates reachability/guidance; a larger connected move can escape a 2-for-2 basin while preserving the forced degrees. · Run exactly 2^15 targeted proposals from the hash-bound defect-10 regression seed and independently replay them. · high · open
• Complete pair-excess cube-frontier construction before solver leaves.
  A hash-bound cube cover can convert pair-normalization into globally auditable proof branches and avoids another isolated UNKNOWN leaf. · Enumerate and independently reconstruct canonical cube headers and their union coverage without solving the leaves. · normal · open

Objective: Determine whether larger guided exact-degree trades can beat the defect-10 barrier before returning to proof-cube engineering.

First action: Specify a deterministic 3-for-3/ejection-chain generator that selects an uncovered triple, preserves all fifteen degrees, and records a replayable move trace; cap the first pilot at 2^15 proposals.

Stop condition: Stop and redirect to complete pair-excess cube-frontier enumeration if the independently checked pilot does not produce defect below 10 or if move legality/coverage replay disagrees.

• Do not extend the same 2-for-2 annealing cutoff.
• Run a 2^15-proposal uncovered-triple-guided 3-for-3/ejection-chain pilot from the defect-10 seed with the same direct acceptance gate and independent replay.
• If that pilot does not beat defect 10, redirect to a hash-bound complete pair-excess cube-frontier census before any proof-scale SAT run.

• 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, audited, implemented, and interpreted the epoch; two GPT-5.6 Terra delegates supplied advisory reconnaissance and experiment-design memos, promoted with provenance but not treated as evidence. Python 3.12.3 standard-library programs executed the deterministic search and independent replay through run_experiment.py. Web search/opening checked the maintained repository and primary construction paper. No CAS, SAT solver, proof assistant, sub-agent, or external human validator was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1492.2s

Review state

not a result claim

Attempt ID

covering-c1553-20260810-005024-4de0fa

No human review recorded.