Exhaustive coverage-pruned exact-degree three-block replacement search around the hash-bound seed-6 U=2 anchor, followed by a materially different labelled ternary-incidence replay.

coverage-pruned three-slot exact replacement

Delete three anchor blocks, reject deletion triples whose union cannot contain both original missing triples, enumerate all point-multiplicity-preserving replacement triples modulo slot permutations, and score coverage with exact 455-bit masks.

Hypothesis: The complete exact-degree three-block replacement shell of the fixed seed-6 U=2 anchor is tractable and contains either a verified 30-block cover or a finite independently checked zero-cover result.

Test: Enumerate every cover-eligible deletion and require two different encodings to match all 836 per-deletion candidate/score digests; stop on any cover or mismatch.

The union argument safely excludes every omitted deletion from forming a cover. The primary enumerator covers every incidence-balanced replacement of each survivor exactly once, and the independent labelled-slot recursion reproduces every per-case candidate/score digest. Therefore the zero-cover conclusion is exhaustive for the stated local scope.

• The fixed seed-6 U=2 anchor has no covering exact-degree replacement obtained by deleting and replacing three selected blocks.
• For the 836 cover-eligible deletions there are exactly 8,484,420 canonical distinct replacement triples, of which 8,414,065 yield valid 30-distinct-block families.
• Among those valid operations the minimum deficit is 2 and the number of covers is zero.
• The score histogram does not cover the 3,224 union-eliminated deletions and therefore does not establish full radius-three local optimality.

• python3 scripts/audit_degree_u2_delete3_v1.py --result artifacts/epoch24-20260809/fresh_nonisomorphic_starts_result.json --seed 6 --closed-two-block-receipt artifacts/epoch24-20260809/degree_u2_q1_checker_receipt.json --closed-two-block-receipt artifacts/epoch24-20260809/degree_u2_q2_checker_receipt.json --closed-two-block-receipt artifacts/epoch25-20260809/degree_u2_q3_checker_receipt.json --receipt artifacts/epoch26-20260809/degree_u2_delete3_primary_receipt.json
• Primary receipt SHA-256 666d09268eba5673a28b376d213d21a0799ea9d5d10b2166da624f82da03294c.
• python3 checkers/check_degree_u2_delete3_v1.py --result artifacts/epoch24-20260809/fresh_nonisomorphic_starts_result.json --primary artifacts/epoch26-20260809/degree_u2_delete3_primary_receipt.json --receipt artifacts/epoch26-20260809/degree_u2_delete3_checker_receipt.json
• Checker receipt SHA-256 3eee151a6c1c21b27f20cd47127b878e32341571178eb224872edff1b586dd9a.
• Fail-closed controls rejected a corrupted source binding and a corrupted first-surviving-row digest.

• .proof-experiments/20260809-092825-0923f0: optimized primary completed in 84.346 seconds with 8,414,065 valid operations and zero covers.
• .proof-experiments/20260809-093032-ccef5b: independent checker completed in 157.740 seconds and matched all 836 per-deletion digests.
• .proof-experiments/20260809-093418-248572: source-binding and row-digest mutations were both rejected.

checkers/check_degree_u2_delete3_v1.py uses labelled ternary point-to-slot recursion rather than the primary first-block/forced-completion formulation; it matched all 836 candidate/score digests and aggregate counts.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

None recorded.

• The fixed seed-6 anchor has point degree 12 and exactly two uncovered triples, {4,13,15} and {5,11,12}.
  Anchor SHA-256 bbcd920a469fc4015612f837adf1d73e7784f0e794cfaa4f0693ddd43c39d6b9 and two independent reconstructions. · The fixed labelled seed-6 anchor. · computed
• Exactly 836 of 4,060 deletion triples can possibly cover both original missing triples under exact degree preservation.
  Primary and independent union reconstruction agree. · Three-block deletions of the fixed anchor. · computed
• No exact-degree three-block replacement of the fixed anchor forms a cover.
  3,224 deletion triples eliminated by proof; 8,414,065 valid operations across the remaining 836 independently exhaustively scored with zero covers. · All three-block exact-degree replacements of the fixed labelled anchor. · computed
• Returning one deleted block reduces the remaining exact-degree move to support at most two.
  Pointwise incidence cancellation; checked for all 122,563 one-return operations. · Returned-block operations in the enumerated cover-eligible shell. · proved

• Repair the fixed seed-6 anchor into a cover by an exact-degree replacement supported on three selected blocks.
  All 4,060 deleted-block triples and every distinct valid replacement triple. · 3,224 deletion choices leave an original missing triple impossible to cover; exhaustive scoring of all valid replacements in the other 836 found zero covers. · artifacts/epoch26-20260809/degree_u2_delete3_primary_receipt.json and artifacts/epoch26-20260809/degree_u2_delete3_checker_receipt.json · A source-binding, union-filter, enumeration, scoring, or checker defect.
• Use the 17 point-capacity profiles as a complete symmetry quotient.
  The 836 cover-eligible deletion triples. · Equal capacity counts do not establish colored residual-hypergraph isomorphism or equivalent candidate coverage masks. · All 836 deletions were retained and independently checked rather than represented by 17 samples. · A proved canonical colored-residual isomorphism classification with independently checked orbit coverage.

• Proof-producing incidence/PB search over six proved second-block representatives.
  It addresses the global 30-block existence question and retains the exact-degree and symmetry reductions. · Pin a proof emitter/replayer, compile the six variants, and replay a bounded UNSAT control before solver scale-up. · high · open
• Materially changed constructive witness search using exact three-block moves as escape operators.
  A cover directly settles C(15,6,3)=30, while the completed shell identifies what a successful move cannot look like near the best anchor. · Implement a deterministic multi-anchor search whose state transition permits accepted support-three non-cover moves, and compare against the frozen fresh-start baseline under matched proposals. · normal · open
• Full radius-three local-optimum classification of the seed-6 anchor.
  Only 22,217,114 canonical allocations are bounded across all deletions; completing them could certify absence or exhibit a deficit-one neighbor. · Add checkpointed score-all-deletions mode and an independent segmented replay; stop immediately on a U=1 family. · normal · open

Objective: Test whether a proof-producing global incidence/PB decomposition can generate independently replayable terminal evidence.

First action: Audit pinned proof-emitter and proof-replayer availability, then compile one smallest six-representative incidence/PB calibration cube with exact degree-12 constraints.

Stop condition: Redirect on proof-format replay failure, source/hash mismatch, or preprocessing growth that projects beyond the declared certificate budget; promote only on a verified witness or replayed proof.

• Require a pinned proof-producing PB/SAT emitter and independent proof replayer before scaling the six second-block incidence representatives.
• Retain materially changed constructive witness search as a symmetric alternative; do not merely add arbitrary random seeds.
• Optionally submit a checkpointed 22,217,114-canonical-case extension to score all 4,060 deletions and test full radius-three local optimality, while labeling it local.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://www.coveringrepository.com/default.aspx ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=6&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol principal designed, implemented, audited, and interpreted the epoch. GPT-5.6 Terra delegates supplied advisory workload and prior-art reconnaissance; their agreement was not treated as validation, and relied-on artifacts were promoted with provenance. Deterministic computation used CPython 3.12.3, exact Python integers, SHA-256, GNU/Linux, and the project run_experiment harness. No CAS, SAT solver, proof assistant, or external proof service was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1631.6s

Review state

not a result claim

Attempt ID

covering-c1563-20260809-094129-5e45b6

No human review recorded.