Split epoch 73's certified 22-row fixed-link equality cylinder along all nineteen complete orbits of the certified automorphism (4 5), then require fresh proof production and independent dual replay.

proof-producing recursive invariant row deletion

Delete whole certified automorphism orbits from an UNSAT local predicate; a surviving UNSAT child proves a broader fixed-link equality cylinder empty.

Hypothesis: At least one deterministic automorphism-stable 11-row child of the dual-replayed epoch-73 22-row cylinder is terminal UNSAT within two CaDiCaL CPU seconds and has an ASCII-LRAT proof no larger than 8388608 bytes accepted by both lrat-check and CakeLPR.

Test: Compile both independently reconstructed 11-row children afresh and run CaDiCaL 1.7.3 seed 0 for two CPU seconds each; advance only on a terminal proof under 8 MiB passing clause reconstruction, two intact replayers, two final-line-deletion controls, and four repaired-hash semantic mutations.

The terminal LRAT establishes the explicit local CNF's unsatisfiability, and independent reconstruction binds that CNF to the intended eleven equality rows. Because no complete ownership frontier exists, the evidence cannot be lifted to the fixed link or global covering number.

• The explicit 7433-variable, 31251-clause child-1 fixed-link equality cylinder is UNSAT.
• The epoch-73 22 rows split exactly into invariant 11-row masks containing 9 and 10 complete certified orbits.
• The child-0 sibling remains UNKNOWN under the two-second cap.
• The maintained range remains 30 <= C(15,6,3) <= 31.

• Producer harness .proof-experiments/20260811-032919-79a6b0 returned child 1 UNSAT and child 0 UNKNOWN.
• Checker harness .proof-experiments/20260811-032949-e5bcb6 returned PASS.
• sha256sum -c artifacts/epoch74-20260811/SHA256SUMS passed for every listed artifact.

• .proof-experiments/20260811-032919-79a6b0: child 1 terminal UNSAT with 131272-byte proof; child 0 UNKNOWN.
• .proof-experiments/20260811-032949-e5bcb6: independent reconstruction and adversarial audit PASS.

checkers/check_recursive_pair_core_probe_v2.py imports neither the v2 producer nor its split code; it independently reconstructs all ancestor partitions and CNF clauses, compiles fresh lrat-check and CakeLPR binaries, tests exact final-line deletion, and rejects four repaired-hash semantic package mutations.

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

• C(12,6,4) orbit-catalogue certificates -> invariant local cases should use independently replayed LRAT and exact ownership -> replay succeeded locally, but the ownership prerequisite remains absent.

• The explicit epoch-74 child-1 eleven-row fixed-link equality cylinder is empty.
  CNF SHA-256 c8bf9654a268cfc777851a4bad5ad7205e58810126ed22bf8ee0bacaee178861; LRAT SHA-256 ff3b43c7a259b02c1ccf035e443ae757b8a333853eaa1b5f5a4ca351b0aff4be; independent receipt SHA-256 44458a1fba9ab16bd7636b5cb4817c42ae5235728640f38eaeb4f5af30e4fed0. · One fixed root link and the eleven labelled targets in recursive-cylinder-v2-manifest.json. · proved
• The epoch-73 terminal 22-row mask consists of nineteen complete certified orbits and partitions deterministically into 11-row children with nine and ten orbits.
  Producer and clean-room checker agree; independent-check.json reports constraint_partition_disjoint_exhaustive_invariant=true. · The epoch-73 child-1 row set only. · computed

• All 22 epoch-73 equality rows are necessary for the retained local contradiction.
  The epoch-73 child-1 predicate inside the fixed root link. · One invariant subset of eleven rows already yields a dual-replayed UNSAT formula. · artifacts/epoch74-20260811/recursive-pair-core-v2/independent-check.json · None; the necessity claim is false.
• Continue unchanged balanced recursive row deletion as the next campaign route.
  Further splitting below the certified eleven-row child without a complete ownership ledger. · The declared at-most-16-row target is reached, while another smaller overlapping local predicate would not reduce global uncertainty. · The certified local scope and absence of any profile ownership frontier in the manifest. · A canonical independently checked ownership ledger, a material core-extraction change, or an external use for the local predicate.

• Canonical fixed-link pair-profile ownership ledger.
  It is the missing bridge from replayed local cylinders to a complete, nonoverlapping negative frontier. · Canonicalize and test seven existing explicit rooted profiles under the certified order-two group, requiring invariant serialization and exactly one owner. · high · open
• Exactly-owned q>=5 fixed-first frontier.
  It already has a complete ownership contract and remains the fail-safe proof-producing negative route. · Resume the cheapest unresolved owned leaf without lengthening prior UNKNOWN runs. · normal · open
• Constructive 30-cover search with materially changed mixed-support moves.
  A directly checked witness settles the value at 30 and remains independent of ownership engineering. · Only reopen after a staged or delta-prefiltered operator clears the recorded acceptance-rate gate in a matched bounded pilot. · low · open

Objective: Determine whether canonical profile ownership can convert replayed local cylinders into a complete fixed-link frontier.

First action: Implement canonical serialization and exact group-orbit membership for the seven existing explicit rooted profiles.

Stop condition: Redirect to the exactly-owned q>=5 frontier on any noncanonical serialization, overlap, missing owner, or inability to express cylinder membership as a disjoint ledger predicate.

• Define a canonical serialization for admissible rooted simple 4-regular pair-excess graphs under the certified fixed-link group.
• Test group invariance, membership, overlap, and unique ownership on the six explicit epoch-72 profiles plus the selected profile.
• Redirect to the exactly-owned q>=5 fixed-first frontier if a disjoint ownership ledger fails; do not lengthen the UNKNOWN child.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://arxiv.org/abs/2607.23766 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol acted as principal investigator. GPT-5.6 Terra delegates supplied advisory prior-art and verification memos; their agreement was not validation, and suggestions used were independently reconstructed with provenance recorded. Deterministic tools were Python 3.12.3, CaDiCaL 1.7.3 seed 0, GCC 13.3.0, lrat-check, CakeLPR, exact integer/set arithmetic, SHA-256, and the Proof Factory experiment harness. Browser search checked the maintained LJCR entry and primary arXiv sources. No CAS, proof assistant, PB solver, cloud lab, external proof service, human validator, publication, system installation, or host-configuration change was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1142.2s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-033941-085b46

No human review recorded.