Applied an orbit-size lower bound to a sound 15-cycle subset before attempting the proposed joint pair-type/exact-skeleton header census.

pair-type and exact-skeleton header census

Count compatible labelled 15-cycle excess skeletons and divide by each canonical common-family stabilizer order.

Hypothesis: The complete joint pair-family/exact-skeleton frontier has fewer than 2145 canonical headers.

Test: Redirect if simple 15-cycle skeletons with the normalized pair as a nonedge already yield at least 2145 stabilizer orbits.

A compatible simple 15-cycle is a valid syntactic weighted-degree-two skeleton header. The invariant subset has 14!/2-13! labelled members per type, and an orbit has size at most the relevant stabilizer order. Every resulting type-specific lower bound exceeds 2145.

• The type 1 through 4 compatible-cycle header-orbit lower bounds are 5,405,400, 24,324,300, 32,432,400, and 3,603,600.
• The four-type syntactic header frontier has at least 65,765,700 orbits from simple 15-cycle skeletons alone.
• This is exactly 30,660 times the 2145-cube baseline.
• No 54-cover, exact-skeleton feasibility class, or SAT branch is excluded.

• python3 scripts/pair_type_skeleton_header_gate_v1.py --protocol protocols/pair-type-skeleton-header-gate-v1.json --output artifacts/pair-type-skeleton-header-gate-20260810/result.json
• python3 checkers/check_pair_type_skeleton_header_gate_v1.py --protocol protocols/pair-type-skeleton-header-gate-v1.json --result artifacts/pair-type-skeleton-header-gate-20260810/result.json --output artifacts/pair-type-skeleton-header-gate-20260810/independent-check.json
• python3 checkers/test_pair_type_skeleton_header_gate_mutations_v1.py --protocol protocols/pair-type-skeleton-header-gate-v1.json --result artifacts/pair-type-skeleton-header-gate-20260810/result.json --output artifacts/pair-type-skeleton-header-gate-20260810/mutation-controls.json
• sha256sum -c artifacts/pair-type-skeleton-header-gate-20260810/manifest.sha256

• .proof-experiments/20260810-013100-ba7aa7: final producer; lower bound 65,765,700.
• .proof-experiments/20260810-013100-601b1b: independent explicit-group checker passed.
• .proof-experiments/20260810-013101-ac4ba9: six semantic mutations rejected.
• .proof-experiments/20260810-013119-490486: byte-identical regeneration passed.

check_pair_type_skeleton_header_gate_v1.py explicitly generates and closes each permutation group, verifies its family action, and independently double-counts fixed-edge Hamilton cycles.

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

• Certified cube decomposition -> stronger literal headers should shrink the frontier -> fixing five blocks instead caused at least 65,765,700 orbits.
• Orbit-stabilizer screening -> test a countable invariant subset before enumeration -> rejected the route with subsecond decisive compute.

• The four full canonical-family stabilizer orders are 6912, 1536, 1152, and 10368.
  artifacts/pair-type-skeleton-header-gate-20260810/independent-check.json · The four fixed representatives in protocol v1. · computed
• The four-type simple-15-cycle header subset has at least 65,765,700 orbits.
  Exact orbit inequalities in result.json, independently reconstructed in independent-check.json. · Syntactic headers only; no feasibility assertion. · proved

• Create one proof leaf for every joint canonical pair type and complete exact pair-excess skeleton.
  The syntactic header scheme tested by protocol v1. · A sound subset already requires at least 65,765,700 orbits. · artifacts/pair-type-skeleton-header-gate-20260810/manifest.sha256 · A proved pre-leaf aggregation or feasibility filter removing or merging at least 30,660x, with an independently checked complete union map.

• Uncovered-triple-guided 3-for-3/ejection-chain exact-degree trades.
  This is the cheapest direct-witness route after the 2-for-2 defect-10 plateau. · Run exactly 32768 deterministic proposals with independent replay. · high · open
• Symbolic exact-pair aggregation without explicit skeleton headers.
  It may retain the native-PB propagation benefit without destroying skeleton symmetry. · Build one independently reconstructed proof-producing type-2 symbolic-skeleton pilot. · normal · open

Objective: Test whether larger guided exact-degree moves beat the verified defect-10 barrier.

First action: Create protocols/degree18-guided-3x3-v1.json specifying 32768 proposals from artifacts/degree18-multibasin-20260810/best-radius5-regression.txt, seed 0, exact degree preservation, replayable traces, and a below-10 advance gate.

Stop condition: Redirect on checker disagreement, failure to beat defect 10, or inability to define a deterministic degree-preserving move without repair.

• Do not enumerate explicit joint pair-type/exact-skeleton headers.
• Run the 32768-proposal guided 3-for-3/ejection-chain pilot from the defect-10 seed.
• Retain a negative route only if skeleton targets remain symbolically aggregated with proof-producing independent replay.

• 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 ↗

GPT-5.6 Sol was principal investigator. GPT-5.6 Terra delegates supplied advisory reconnaissance only; the relied-on memo was promoted with provenance and was not counted as validation. Deterministic Python 3.12.3 performed exact counting, permutation-group closure, regeneration, and mutation tests. No CAS, solver, proof assistant, or lab job was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1083.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260810-013935-4956f1

No human review recorded.