Construct and independently verify a first-selected-block orbit cube cover for the complete [13,2] pair-excess branch, then run the predeclared index-6 unit-cube propagation pilot against the root-free base.

disjoint orbital first-selection cubes

Order the 106 D13 x C2 block orbits by canonical representative; cube i negates every primary in earlier orbits and selects one representative of orbit i, so every model orbit intersects a cube without a lex network.

Hypothesis: On the complete unrooted [13,2] pair-excess branch, the earliest noninitial size-13 first-selected-orbit cube either decides at 2000 conflicts or uses at most 80 percent as many decisions as the root-free base.

Test: Independently reconstruct the 106-cube symmetry cover, then compare the exact base and index-6 cube under CaDiCaL 1.7.3, seed 0, and a 2000-conflict cap; run seed 1553 only if the cube is decisive or its decision ratio is at most 0.8.

The structural case split is reproducible and safely covers model orbits, which is reusable infrastructure. It is not a solution: UNKNOWN excludes nothing, and the predeclared telemetry failure rules out scaling this unit-cube compiler protocol.

• Under Aut(C13 plus a doubled edge)=D13 x C2, the 3003 blocks split into exactly 106 orbits with size histogram 21 x 13, 65 x 26, 20 x 52.
• The 106 least-occupied-orbit cubes are pairwise incompatible and every satisfying [13,2] branch model is symmetry-equivalent to a model satisfying at least one cube.
• For pilot orbit index 6 at seed 0 and a 2000-conflict cap, both base and cube were UNKNOWN; decision ratio was exactly 7258/6488 = 1.1186806411837238.

• python3 scripts/partition132_first_orbit_cube_v1.py --base artifacts/partition132-full-branch-lex-20260812/base.cnf --source-orbits artifacts/joint-orbit-census-20260808/manifest.json --output artifacts/partition132-first-orbit-cube-20260812/pilot.cnf --manifest artifacts/partition132-first-orbit-cube-20260812/manifest.json --pilot-index 6
• python3 checkers/check_partition132_first_orbit_cube_v1.py --base artifacts/partition132-full-branch-lex-20260812/base.cnf --base-manifest artifacts/partition132-full-branch-lex-20260812/base-manifest.json --base-check artifacts/partition132-full-branch-lex-20260812/independent-check.json --source-orbits artifacts/joint-orbit-census-20260808/manifest.json --cnf artifacts/partition132-first-orbit-cube-20260812/pilot.cnf --manifest artifacts/partition132-first-orbit-cube-20260812/manifest.json --output artifacts/partition132-first-orbit-cube-20260812/independent-check.json
• python3 scripts/run_partition132_first_orbit_cube_v1.py --protocol protocols/partition132-first-orbit-cube-v1.json --base artifacts/partition132-full-branch-lex-20260812/base.cnf --candidate artifacts/partition132-first-orbit-cube-20260812/pilot.cnf --manifest artifacts/partition132-first-orbit-cube-20260812/manifest.json --independent-check artifacts/partition132-first-orbit-cube-20260812/independent-check.json --mutations artifacts/partition132-first-orbit-cube-20260812/mutation-controls.json --runs artifacts/partition132-first-orbit-cube-20260812/runs --result artifacts/partition132-first-orbit-cube-20260812/result.json --drat-trim toolchains/drat-trim/drat-trim --lrat-check toolchains/drat-trim/lrat-check
• python3 checkers/check_partition132_first_orbit_cube_result_v1.py --protocol protocols/partition132-first-orbit-cube-v1.json --result artifacts/partition132-first-orbit-cube-20260812/result.json --formula-check artifacts/partition132-first-orbit-cube-20260812/independent-check.json --mutations artifacts/partition132-first-orbit-cube-20260812/mutation-controls.json --lrat-check toolchains/drat-trim/lrat-check --output artifacts/partition132-first-orbit-cube-20260812/result-check.json

• .proof-experiments/20260812-063754-698653: producer regenerated 106 orbits and a 144-unit pilot CNF.
• .proof-experiments/20260812-063804-27ea98: independent structural checker returned valid=true.
• .proof-experiments/20260812-063813-7899ec: four fail-closed mutations were all rejected.
• .proof-experiments/20260812-064025-a3be22: matched solver pilot returned UNKNOWN/UNKNOWN with decision ratio 1.1186806411837238 and redirected.
• .proof-experiments/20260812-064053-28f80e: independent raw-log checker returned valid=true.

check_partition132_first_orbit_cube_v1.py separately reconstructs the group, orbit partition, cube map, and pilot CNF; check_partition132_first_orbit_cube_result_v1.py separately reparses raw solver logs. No UNSAT proof was produced because both bounded runs were UNKNOWN.

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

• Canonical augmentation/cube-and-conquer -> primary-unit orbit cubes should transmit symmetry without lex auxiliaries and cut decisions by at least 20 percent -> the pilot instead increased decisions by 11.868 percent, so this transfer prediction was falsified at the checked protocol.

• The 3003 blocks form exactly 106 D13 x C2 orbits with sizes 21 x 13, 65 x 26, and 20 x 52.
  Producer and separately written checker agree; all primary IDs 1..3003 occur exactly once; source manifest hash 6d64b96e4017784262a995fabbed56ca2849f67cb9c86329666e4825c834ffa8. · 5-subsets under the automorphism group of the fixed [13,2] skeleton. · computed
• The 106 least-occupied-orbit cubes cover every [13,2] base model up to symmetry and are pairwise incompatible.
  Independent transitivity, invariance, complete partition, and anchor-negation checks in independent-check.json. · Exact complete [13,2] base CNF semantics; not the other 40 skeleton types. · proved
• The index-6 pilot is unresolved at 2000 conflicts and fails the decision-ratio advancement gate.
  Raw logs independently parse to 6488 versus 7258 decisions and UNKNOWN statuses; result-check valid=true. · CaDiCaL 1.7.3, seed 0, exact base and pilot CNF hashes, 2000-conflict protocol. · computed

• Scale the 106 first-selected-orbit cubes using the current primary-unit compiler and matched CaDiCaL protocol.
  Index-6 seed-0 pilot gate at 2000 conflicts; this does not rule out the mathematical cubes or other solvers/branching mechanisms. · Both runs were UNKNOWN and the cube decision ratio 1.1186806411837238 exceeded the predeclared maximum 0.8. · artifacts/partition132-first-orbit-cube-20260812/result-check.json · A materially different branching, solver, learned-prefix reuse, or proof mechanism with a predeclared matched pilot that passes an information-per-cost gate; selecting another arbitrary cube is insufficient.
• Re-run the complete fixed-pair-link proposal as a semantic strengthening.
  All 5460 complete-pair-link requirements across four canonical pair-normalized CNFs. · Prior audited artifacts classify 570 requirements as fixed-block tautologies and 4890 as existing coverage clauses, leaving zero non-subsumed clauses. · artifacts/pair-link-cnf-delta-audit-20260811/result.json and independent-check.json · A separately justified pair-count, skeleton, or other labelled correlation that adds at least one independently verified non-subsumed constraint.

• Count-only structural-signature census of the validated 91-class degree-18 defect-10 local frontier.
  It is the cheapest materially distinct discriminator after both full lex and primary-unit symmetry delivery failed, and can produce a reusable hash-bound dataset or kill the signature route without SAT scale. · Assemble and independently validate exactly one representative for each of the 40 previous and 51 new classes, then emit fixed-point link-degree, pair-excess, and uncovered-triple signatures with a predeclared held-out prediction test. · high · open
• Proof-producing normalized-branch replay with a materially different solver or prefix-reuse mechanism.
  It retains terminal potential, but current lex and unit-cube delivery methods both failed propagation gates. · Only after identifying a concrete different inference mechanism, run one fixed 2000-conflict matched leaf with proof smoke and require a decisive result or at least 20 percent decision improvement. · normal · open

Objective: Determine whether the 91-class defect-10 local frontier contains a low-cost structural signature that predicts defect improvement or yields a necessary obstruction.

First action: Create a protocol and immutable 91-representative JSONL by joining the 40 prior target classes with the 51 novel canonical signatures in artifacts/degree18-frontier24-endpoint-classification-20260812/result.json; independently recheck 54 blocks, all point degrees 18, defect 10, and class uniqueness before computing signatures.

Stop condition: Redirect if the input cannot be reconstructed as exactly 91 distinct validated classes, every tested global moment identity is tautological, or no signature class has a predeclared held-out predictive effect.

• Do not solve additional first-orbit cubes under this protocol; the predeclared seed-0 gate failed.
• Build an immutable 91-representative defect-10 frontier input by combining the validated 40-class target set with the 51 newly classified endpoint classes, checking every representative has 54 distinct blocks, degree 18, and defect 10.
• Run a count-only fixed-point link, pair-multiplicity, and uncovered-triple signature census with a held-out prediction rule; stop if it yields neither a necessary obstruction nor reproducible held-out defect-improvement signal.

• 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 principal designed, audited, executed, and interpreted the epoch. GPT-5.6 Terra delegates supplied advisory prior-art and experiment-verification memos; their agreement was not treated as validation, and Sol independently audited the fixed-pair zero-delta artifact and reconstructed the selected route. Python 3.12.3 standard-library programs generated and checked artifacts. CaDiCaL 1.7.3 ran the bounded SAT calibration. Pinned drat-trim and lrat-check were available but no UNSAT certificate arose. SHA-256 bound artifacts. Web search checked current status and prior art; no CAS or proof assistant was used. A local Git commit was attempted, but the sandbox-mounted .git index was read-only; the hash-verified files remain in the workspace for the checkpoint service.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1330.4s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-065146-3d696f

No human review recorded.