Exhaustive type-4 endpoint pair-excess skeleton/link interface census with explicit stabilizer inverse lifts and direct positive witnesses.

endpoint skeleton-link interface census

Enumerate both normalized-pair endpoints' weight-two excess-neighbour multisets, quotient the 8,281 ordered headers under the fixed type-4 stabilizer, and construct degree-18 families covering every endpoint-containing triple.

Hypothesis: At least one of the 8,281 labelled type-4 endpoint pair-excess headers is incompatible with exact degree 18 and coverage of all triples containing either endpoint of the normalized multiplicity-five pair.

Test: Construct an explicit inverse lift for every stabilizer orbit and a directly checkable positive partial-cover witness for every canonical header; universal survival falsifies the pruning hypothesis.

Explicit witnesses prove survival for every canonical orbit, and the checked inverse lifts transfer that survival to every labelled header. Because internal triples and internal pair multiplicities were deliberately omitted, these witnesses cannot establish global covers or rule out 54-block covers.

• The 8,281 ordered type-4 endpoint excess headers form exactly 104 orbits under the 10,368-element fixed-family stabilizer.
• Every one of those 8,281 headers admits a 54-block degree-18 family covering all 169 triples containing endpoint 0 or 1.
• Among the 104 particular deterministic witnesses saved in this packet, the minimum full-coverage defect is 67, attained at canonical indices 36 and 88; this is not a lower bound over all witnesses for those headers.
• No maintained covering-number bound changes.

• sha256sum -c artifacts/type4-endpoint-skeleton-link-interface-20260811/manifest.sha256: PASS
• Producer result SHA-256 b50054e5cafa48be071656cc5ae06141b875b6b24e6b479925314322090ff16f
• Independent checker reconstructed 91 one-endpoint headers, 8,281 raw headers, 104 orbits, and a 10,368-element stabilizer.
• Byte-identical producer regeneration passed.
• Seven lift/header/block/degree mutations were rejected.

• .proof-experiments/20260811-040315-e2e224: final deterministic producer completed in 24.720 seconds and retained all 8,281 headers.
• .proof-experiments/20260811-040424-253f82: regeneration completed with result SHA-256 b50054e5cafa48be071656cc5ae06141b875b6b24e6b479925314322090ff16f.
• .proof-experiments/20260811-040842-b8003e: independent lift, witness, and global-defect audit passed.
• .proof-experiments/20260811-040918-ce53e1: byte-identity check and seven fail-closed mutations passed.

checkers/check_type4_endpoint_skeleton_link_interface_v1.py independently derives the group from root-incidence fibres, reconstructs all orbits and lifts, and directly verifies block domains, distinctness, degree 18, endpoint pair excesses, endpoint-free capacities, all endpoint triples, and full defects.

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

• Orbit-stabilizer classification -> retain explicit inverse lifts before quotienting -> produced a complete 8,281-to-104 map with independently checked coverage.
• Bipartite degree-sequence switching -> preserve exact point degrees while repairing coverage -> constructed every tested endpoint-link and endpoint-free capacity witness.
• Certificate-first covering computations -> require replayable negative evidence -> no construction failure was promoted as an exclusion.

• The type-4 endpoint header universe has 8,281 labelled members and 104 fixed-family stabilizer orbits.
  Independent reconstruction in artifacts/type4-endpoint-skeleton-link-interface-20260811/independent-check.json. · Ordered weight-two excess-neighbour multisets at endpoints 0 and 1 of the canonical type-4 family. · computed
• Every header has a degree-18 witness covering all triples containing endpoint 0 or 1.
  Direct representative checks plus complete raw inverse lifts. · The exact endpoint necessary relaxation only. · computed
• The residual endpoint-free degree identity is 8+r_z-s_0z-s_1z.
  Subtracting the two endpoint residual pair counts and fixed-family degree r_z from total degree 18. · Canonical type-4 fixed roots and any allowed endpoint header. · proved
• The 104 saved deterministic witnesses contain no 54-cover and have minimum defect 67.
  Exact full-coverage histogram in the independent check. · Only the saved witnesses, not all witnesses compatible with each header. · computed

• Use endpoint pair-excess placement plus complete endpoint-link coverage and degree capacity to eliminate a type-4 header.
  All 8,281 labelled headers represented by 104 checked orbits. · Every orbit has a directly checked positive witness. · artifacts/type4-endpoint-skeleton-link-interface-20260811/independent-check.json · Add a proved internal-pair or internal-triple constraint absent from this relaxation.
• Use the deterministic v1 interface constructor as a competitive direct cover search.
  Its 104 saved canonical witnesses. · Their best full defect is 67, versus the campaign's existing independently checked defect-10 seed. · Exact defect histogram in the independent check. · A materially changed objective or completion mechanism that first beats defect 10 in a bounded matched pilot.
• Repeat the completed fixed-pair link relaxation.
  The saved 431-cell, 754-target audit. · It was already completed and all targets survived. · artifacts/type4-complete-pair-link-gate-20260809/independent-check.json · Genuinely new labelled information beyond link marginals.

• Proof-capable matched encoding pilot for a globally complete pair-normalized branch.
  A replayed UNSAT result or checked SAT model is terminal, while a 20% decision reduction is a measurable prerequisite for scale-up. · After owner approval, freeze one encoding delta, branch, seed, and conflict cap; independently reconstruct the CNF and compare decisions. · high · open
• Materially different exact-degree constructive repair from the defect-10 seed.
  A 54-cover remains directly checkable, and endpoint-interface witnesses are not competitive seeds. · After owner approval, specify a bounded multi-step or meet-in-the-middle repair mechanism and require independently checked defect below 10. · high · open
• Compressed internal-Z pair-skeleton/triple-coverage interface.
  This targets exactly the information omitted by the closed endpoint relaxation. · First derive an exact capacity identity and count the canonical frontier; stop before solving if it approaches the rejected 65,765,700-header scale. · normal · open

Objective: Select one exact successor scope with the best expected validated uncertainty reduction, subject to owner approval.

First action: Present the proof-capable matched encoding pilot and materially different defect-below-10 constructive pilot as the two approval choices, including immutable protocols and stop gates.

Stop condition: Do not dispatch without approval; redirect immediately on encoding disagreement, failed proof replay, no 20% decision reduction, or no constructive defect below 10.

• Do not repeat or enlarge the endpoint-only skeleton-link relaxation.
• Obtain human approval for the exact next experiment scope before dispatch.
• If the constructive route is approved, require a materially different exact-degree repair mechanism and an independently checked defect below 10.
• If the negative route is approved, use a proof-capable matched encoding pilot and require at least 20% fewer decisions before scale-up.
• Retain complete DRAT/LRAT replay and exhaustive partition requirements for any global exclusion.

• 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/2607.23766 ↗

GPT-5.6 Sol served as principal investigator. GPT-5.6 Terra delegates supplied advisory reconnaissance only and were not validators. Accepted evidence used Python 3.12.3 exact enumeration, deterministic degree-preserving switching, SHA-256, coreutils integrity checks, and the computational-researcher experiment harness. Preliminary Z3 4.13.0, SciPy 1.11.4/HiGHS, and CaDiCaL 1.7.3 timing formulations were stopped as inefficient and support no claim. No CAS, proof assistant, lab job, package installation, external write, publication, or Git operation was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

2049.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-041435-31cbdd

No human review recorded.