Coupled saved triple-excess witnesses for all 41 pair-excess skeleton types to four global block-intersection moments, the root skeleton moment, and block-pair parity using exact profile-histogram feasibility.

global block-intersection moment envelope

Double-count triple excess against block intersection sizes, then solve one compressed 96-profile integer histogram for each skeleton type.

Hypothesis: At least one of the 41 saved triple-excess witnesses cannot extend to a 54-root histogram satisfying all four global block-intersection excess moments.

Test: Solve the 41 compressed integer histogram systems and directly check every positive witness; retaining all 41 closes this projection as a type-pruning route.

An explicit positive necessary-projection witness for each skeleton type proves that this envelope cannot eliminate any type at the tested scope. Independent arithmetic checking and byte-identical regeneration exclude solver-output or transcription errors, but the projection deliberately omits common labelled block realization.

• In any hypothetical 54-block cover, the four block-intersection counts for a triple T are determined by e_T and s(T) through the stated formulas.
• Each of the 41 saved triple-excess witnesses has a checked 54-root histogram satisfying all tested global moment constraints.
• The global aggregate moment envelope eliminates zero pair-excess skeleton types.
• The exact covering number remains in the maintained range 54 to 55.

• Producer: python3 scripts/global_intersection_moment_envelope_v1.py --manifest artifacts/joint-orbit-census-20260808/manifest.json --triple-witnesses artifacts/triple-excess-prefilter-20260808/result.json --output artifacts/global-intersection-moment-envelope-20260810/result.json
• Result SHA-256: 78a4a73531c9fe274856fb80fcf1d852eb0c0e6d087d12b824ab854998f45c28
• Independent checker: 41 skeletons, 4,305 pair equations, and 2,214 profile occurrences passed.
• Five fail-closed mutations were rejected.
• Regeneration produced the identical result SHA-256.
• sha256sum -c artifacts/global-intersection-moment-envelope-20260810/manifest.sha256 passed all 19 entries.

• .proof-experiments/20260810-060935-7b9a11: all 41 histogram systems SAT
• .proof-experiments/20260810-061116-0c946c: independent checker PASS
• .proof-experiments/20260810-061124-0909a1: five mutations rejected
• .proof-experiments/20260810-061026-d1e70d: byte-identical regeneration

scripts/check_global_intersection_moment_envelope_v1.py reconstructs skeletons and the 96 profiles independently and checks witnesses using direct integer arithmetic without Z3.

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

None recorded.

• For any triple T in a hypothetical 54-cover, N0=14+s(T)-e_T, N1=27-2s(T)+3e_T, N2=12+s(T)-3e_T, and N3=1+e_T.
  Double-counting derivation and independently reconstructed arithmetic checker. · Any hypothetical 54-block C(15,5,3) cover. · proved
• All 41 saved triple-excess witnesses extend to the tested global profile-histogram envelope.
  Explicit sparse histograms in result.json, checked independently. · The necessary aggregate projection using the certified 96 local profiles. · computed

• Use the complete fixed-pair link alone as the next discriminator.
  The previous full 754-target fixed-pair-link run. · Every target already survived; repeating it is stale. · artifacts/type4-complete-pair-link-gate-20260809/independent-check.json · Couple it to genuinely new labelled information and predeclare a distinct pruning or propagation gate.
• Use the global aggregate block-intersection moment envelope to eliminate a pair-excess skeleton type.
  All 41 skeleton types with one checked triple-excess witness each and all four aggregate moments. · Every type has an independently checked positive histogram witness. · artifacts/global-intersection-moment-envelope-20260810/certified-result.json · Provide a stronger labelled compatibility constraint not implied by the current histograms, or demonstrate a material proof-search propagation improvement.

• Proof-replayed layer-five repair validation.
  The 288-cell predecessor passed its pruning and proof-replay gates. · After explicit owner approval, freeze a 12-by-256 stratified protocol with selector-union proof replay and fail-closed reconstruction. · high · open
• Variable-length exact-degree constructive ejection chains.
  This restores larger moves around the verified defect-10 seed and is materially distinct from the exhausted 2-for-2 tranche. · Run a deterministic matched-budget chain-length pilot and accept only a directly checked defect below 10. · normal · open
• Proof-preserving globally complete encoding improvement.
  Only a global witness or replayed exclusion settles the target. · Require a matched-cap propagation or decision improvement before another proof-scale run. · normal · open

Objective: Choose between the independently validated layer-five successor and a distinct constructive ejection-chain pilot without repeating exhausted aggregate projections.

First action: Read artifacts/core-guided-layer5-filter-pilot-20260810/certified-result.json and obtain explicit approval for the exact successor scope; if approval is absent, specify a deterministic variable-length ejection-chain protocol around seed SHA-256 138e85fe20274972db4a93597c79ef32c17858cc2d4e6c9b0a9f0c7b30b48088.

Stop condition: Redirect if approval is absent for the layer-five successor or if the constructive matched-budget pilot finds no independently checked defect below 10.

• Do not repeat or scale the aggregate moment envelope without a new labelled correlation or measured propagation improvement.
• Obtain explicit human-owner approval before dispatching a larger layer-five repair-filter tranche.
• Absent that approval, test variable-length exact-degree ejection chains around the verified defect-10 seed with a strict below-10 advance gate.
• Retry globally complete proof SAT only after a measured proof-preserving encoding improvement.

• 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 acted as principal investigator, auditing the supplied GPT-5.6 Terra delegate reconnaissance rather than treating it as evidence. No new sub-agent was spawned. Python 3.12.3 and Z3 4.13.0 generated exact integer witnesses; a separate Python implementation checked them without Z3. SHA-256 and the computational-researcher experiment wrapper recorded commands, limits, logs, versions, and artifacts. Web search was used to recheck the maintained status. No CAS, proof assistant, cloud lab, or external publishing action was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1331.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260810-061855-e0112d

No human review recorded.