Exhaustively test both tied minimum residual-triple orbits against every frozen type-4 signature while retaining exact root margins and the {4,5} pair identity.

coverage-orbit signature refinement

Quotient triples by the full type-4 stabilizer, compress 2,717 residual blocks into exact-capacity incidence cells, and solve every previously skeleton-feasible signature/e_45 target.

Hypothesis: At least one of the 395 frozen type-4 signatures loses a previously skeleton-feasible e_45 value, or is eliminated entirely, when every triple in a complete minimum residual orbit must be covered.

Test: Enumerate every triple orbit under the 10,368-element stabilizer, select both tied minimum uncovered orbits, and seek independently expandable 49-block witnesses for all 754 signature/e_45 targets.

Every promoted statement has explicit positive witnesses, a materially different non-Z3 checker, five fail-closed mutation controls, and byte-identical regeneration. These facts close only the tested necessary relaxation and cannot be extrapolated to a cover or exclusion.

• The type-4 stabilizer has 22 triple orbits, including 14 residual orbits and exactly two tied minimum residual orbits: {045,145} and {245,345}.
• The two minimum orbit refinements have respectively 195 and 194 exact-capacity cells.
• Each minimum orbit retains all 395 frozen signatures and all 754 previously skeleton-feasible signature/e_45 targets.

• sha256sum -c artifacts/type4-coverage-orbit-gate-20260809/manifest.sha256: all entries OK
• Independent checker: PASS with 10,368 stabilizer actions, 22 triple orbits, and 36,946 expanded selections per orbit.
• Mutation controls: 5 of 5 corruptions rejected.
• Regeneration: byte-identical SHA-256 d93453a8190291ee21ad835f185eb920947c371ccbfd05b58a3983c6a2e200bd.

• .proof-experiments/20260809-095457-e48127: producer completed in 47.454 seconds and retained 395 signatures/754 targets in each orbit.
• .proof-experiments/20260809-095603-fbc093: independent checker passed in 1.623 seconds.
• .proof-experiments/20260809-095638-9cb13f: all five mutations were rejected.
• .proof-experiments/20260809-095729-cb4f62: regeneration was byte-identical.

checkers/check_type4_coverage_orbit_gate_v1.py uses no Z3 and does not import the producer; it derives stabilizer actions from root-incidence fibers and checks expanded literal blocks.

not_requested

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

Original model outcome

progress

Public classification

progress

• Group-orbit constraint refinement -> minimum complete orbits were predicted to expose missing local coverage -> both orbits instead projected to the unchanged frontier.

• The fixed type-4 common-family stabilizer has order 10,368 and 22 orbits on triples.
  Producer and independent incidence-fiber reconstruction agree. · Fixed type-4 common family. · computed
• Exactly 14 triple orbits are not already covered by the five fixed common blocks; the two minimum residual orbits have size two.
  Complete independently checked triple-orbit map. · Fixed type-4 common family. · computed
• Both minimum-orbit relaxations retain every saved signature and target.
  1,508 positive cell witnesses and 73,892 checked literal block occurrences. · Five-margin, exact-{4,5}-count necessary relaxation only. · computed

• Use either complete minimum residual-triple orbit alone to eliminate a frozen type-4 signature or e_45 target.
  The 195-cell {045,145} and 194-cell {245,345} relaxations across all 395 signatures and 754 targets. · Every target has an independently checked positive witness in both refinements. · artifacts/type4-coverage-orbit-gate-20260809/independent-check.json · Couple coverage to genuinely new labelled information; a larger arbitrary orbit cutoff is insufficient.

• Complete {4,5}-link coverage coupling.
  Adding the size-9 orbit to the two checked minima enforces every triple containing the fixed pair and supplies a structural correlation absent from isolated orbits. · Build exact-capacity cells with all 13 {4,5,z} incidence bits and test all 754 targets. · high · open
• Pair-excess extended-variable SAT encoding.
  A redundant but propagation-oriented encoding is materially different from the previously rejected sequential lex leaders. · Compare the type-4 base and extended-pair encoding under the same 25,000-conflict cap with independent semantic reconstruction. · normal · open

Objective: Test the complete fixed-pair link as the cheapest stronger coverage correlation.

First action: Create a protocol coupling the size-2, size-2, and size-9 {4,5,z} orbits, then run the exact-capacity producer and independent checker on all 754 targets.

Stop condition: Redirect immediately if all 395 signatures and 754 targets survive or if producer/checker coverage maps disagree.

• Jointly enforce all 13 triples containing {4,5}, using the two checked size-2 orbits and the size-9 orbit on points 6 through 14.
• Compress by all 13 pair-link incidence bits and test the same 754 targets.
• If all targets survive, close the fixed-pair coverage-link route and test a materially different pair-excess extended-variable SAT encoding at a matched conflict cap.

• 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, implemented, audited, and interpreted this epoch. GPT-5.6 Terra delegates supplied advisory reconnaissance only; their claims were independently reconstructed before use. Python 3.12.3 and Z3 4.13.0 generated exact integer witnesses. A separately written non-Z3 Python checker, SHA-256 utilities, jq validation, mutation controls, and byte-identical regeneration provided verification. No sub-agents, proof assistant, SAT proof checker, or lab job was used in this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1391.2s

Review state

not a result claim

Attempt ID

covering-c1553-20260809-100451-c1d431

No human review recorded.