Partition the 91 exact nonroot pair rows of the certified epoch-71 fixed-link UNSAT leaf into two automorphism-stable masks, solve each relaxed cylinder independently, replay terminal LRATs twice, and audit executable cylinder membership.

proof-core extraction with fixed-link row-equality cylinders

Relax an exact pair profile by retaining only complete orbits of pair-equality rows under the certified link automorphism, so a replayed UNSAT proof excludes every completion satisfying the retained equalities.

Hypothesis: At least one deterministic automorphism-stable half of the 91 exact nonroot pair rows remains UNSAT within a two-second CaDiCaL 1.7.3 limit and an 8 MiB dual-replayed LRAT cap.

Test: Compile the disjoint invariant 46-row and 45-row masks, run fresh CPU-pinned seed-0 CaDiCaL processes for two seconds each, and advance only if an intact proof within 8 MiB is accepted by both lrat-check and CakeLPR.

Each claim is bound to an exact DIMACS hash and LRAT hash, both proof kernels accepted each intact proof, both rejected final-line deletion, and a separate implementation reconstructed every clause and the cylinder predicates. No completeness or global ownership premise was assumed.

• The fixed-link 46-row cylinder formula with SHA-256 0111c6a8b87ebad88ed0db5c9158a8dcf741a51f5a1a321b1b7318b54dec858f is UNSAT.
• The fixed-link 45-row cylinder formula with SHA-256 39ef2ea2f4787ab34321a81d4d60a7ff60dacbd577cffac470242d777a746af1 is UNSAT.
• The 91 nonroot pairs form 79 orbits under the certified full fixed-link automorphism group, and the masks are disjoint, exhaustive, invariant, and have sizes 46 and 45.
• At least six explicitly recorded distinct admissible simple 4-regular pair-excess profiles lie in the two certified cylinders.
• The maintained global range remains 30 <= C(15,6,3) <= 31.

• python3 scripts/fixed_link_pair_core_probe_v1.py --out-dir artifacts/epoch72-20260811/pair-core-probe-v1 --seconds 2 --proof-cap-bytes 8388608
• python3 checkers/check_fixed_link_pair_core_probe_v1.py --artifact-dir artifacts/epoch72-20260811/pair-core-probe-v1 --out artifacts/epoch72-20260811/pair-core-probe-v1/independent-check-v2.json
• sha256sum -c artifacts/epoch72-20260811/SHA256SUMS
• Independent scope: two row-equality cylinders inside one fixed published root link only

• .proof-experiments/20260811-015131-b8e80a: both 46-row and 45-row leaves returned dual-replayed UNSAT within the frozen caps
• .proof-experiments/20260811-015342-386bd0: independent reconstruction and adversarial audit passed, including six-profile distinctness

checkers/check_fixed_link_pair_core_probe_v1.py independently reconstructs the graph, fixed link, automorphism masks, exact rows, and every DIMACS clause; it rebuilds lrat-check and CakeLPR, accepts both intact proofs, rejects both final-line deletions, and validates cylinder membership.

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-complete blocker architecture from certified C(12,6,4) work -> a local blocker must have an explicit ownership predicate and automorphic images -> the cylinder contract passed, but no complete frontier ledger exists.
• SAT core minimization -> relaxing groups of exact arithmetic rows should reveal whether the conflict is local -> both half-row formulas remained UNSAT.
• Graph 2-switches -> changes confined to unretained rows should preserve cylinder membership while retained-row changes should leave it -> both predictions passed independently.

• The 46-row fixed-link cylinder is UNSAT.
  Formula SHA-256 0111c6a8b87ebad88ed0db5c9158a8dcf741a51f5a1a321b1b7318b54dec858f and LRAT SHA-256 5040d969bbf790903bb74252832a1ecf8ef9d58f6d819dc8f0d8cbf90d91b1e4; accepted by lrat-check and CakeLPR. · Mask-0 equality cylinder for the retained fixed root link · proved
• The 45-row fixed-link cylinder is UNSAT.
  Formula SHA-256 39ef2ea2f4787ab34321a81d4d60a7ff60dacbd577cffac470242d777a746af1 and LRAT SHA-256 ea6093e8b61b3d1e8e312c5734ae2821108f23fe09811ad3245bfb2cede45f89; accepted by lrat-check and CakeLPR. · Mask-1 equality cylinder for the retained fixed root link · proved
• The two masks are a disjoint exhaustive invariant partition of all 91 nonroot pair rows into sizes 46 and 45.
  Independent checker reconstructed 79 pair orbits under the hash-bound order-two link group. · The pair-row batching contract only · computed
• At least six distinct admissible simple 4-regular pair profiles belong to the certified cylinders.
  Independent profile-set digest 2ecc50d15401754b2597eed9a1ed9841a11bae56a071b0c7848e910ea9d40db6 and passing membership checks. · Explicit profiles listed or generated in the cylinder manifest; not the total cylinder cardinality · computed

• The epoch-71 local UNSAT conflict requires exact conditioning on all 91 nonroot pair rows.
  The retained fixed link and selected pair-profile targets · Each complementary automorphism-stable half is independently sufficient for UNSAT. · The two dual-replayed 46-row and 45-row proofs · none; the exact necessity claim is false
• Treating the 46/45 mask partition as an exhaustive case split of pair profiles or global covers
  Any attempted fixed-link or global aggregation · The masks partition constraints, while the corresponding equality cylinders can overlap and cover no declared complete frontier. · Executable membership semantics and explicit ownership warning in cylinder-manifest.json · A canonical independently checked ledger proving coverage of a precisely declared normalized profile frontier

• Recursive invariant deletion from the 45-row leaf
  It was terminal after only 55 conflicts and has the best measured cost per removed row. · Partition its 39 whole pair orbits into balanced children and rerun the frozen two-second/8-MiB dual-replay gate. · high · open
• Canonical cylinder ownership ledger
  A small core becomes broadly useful only when cylinder unions can be checked against a declared frontier without double counting or gaps. · Define a canonical profile serialization and test exact membership/overlap for the six explicit profiles before any enumeration. · normal · open
• Exactly owned q>=5 fixed-first profile frontier
  It retains a complete ownership contract and is the fail-safe alternative if local core deletion stalls. · Return to its cheapest unresolved proof-producing leaf only after the recursive cylinder gate fails. · normal · open

Objective: Determine whether the cheaper 45-row blocker compresses to at most 16 exact pair rows without losing terminal proof evidence.

First action: Split leaf 1's 39 complete (4 5)-orbits into two balanced invariant child masks and compile two fresh formulas.

Stop condition: Stop or redirect if neither child is terminal within two seconds and 8 MiB, either proof fails dual replay, final-line deletion is accepted, or formula reconstruction differs.

• Recursively split the cheaper 45-row leaf by its 39 complete pair orbits.
• Require fresh formulas, two proof replayers, final-line deletion controls, and the existing cylinder-membership contract for every terminal child.
• Stop if neither child is terminal; if one is terminal, recurse toward at most 16 rows.
• Do not aggregate cylinders as a fixed-link or global exclusion until a canonical independently checked ownership ledger covers a declared frontier.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol served as principal investigator. GPT-5.6 Terra delegates supplied advisory prior-art and experiment-design memos; their agreement was not validation. Deterministic tools were Python 3.12.3, CaDiCaL 1.7.3, GCC, lrat-check, CakeLPR, exact integer/set arithmetic, SHA-256, and the Proof Factory experiment harness. No CAS, proof assistant, PB solver, cloud lab, external proof service, human validator, or publication action was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1288.2s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-020126-55b5de

No human review recorded.