Exact semantic-delta audit of the fifteen q=6 neighbor-triple caps on the canonical 15-cycle exact-pair CNF leaf

redundant implied-bound audit

Bind each cap to one exact nonedge-pair row and the other twelve triple-coverage lower bounds using sum_z c_abz=3 lambda_ab.

Hypothesis: At least one of the fifteen q=6 neighbor-triple caps c_{i-1,i,i+1} <= 3 removes a primary assignment from the canonical 15-cycle exact-pair leaf.

Test: For each cycle vertex, reconstruct its nonedge neighbor pair, exact residual pair target, and twelve other coverage lower bounds; retain only if the cap is not already implied.

For a cycle vertex p with neighbors a,b, ab is a skeleton nonedge, so lambda_ab=5. The thirteen c_abz sum to fifteen and are each at least one; the other twelve force c_pab<=3.

• All fifteen constraints c_{i-1,i,i+1}<=3 are implied on the hash-bound canonical 15-cycle, root-31 exact-pair leaf.
• Adding them as semantic restrictions eliminates zero primary assignments on that leaf.
• The predeclared nonzero-delta gate failed, so no solver comparison was warranted.

• Producer returned cycle_rows_checked=15, guards_implied=15, semantic_delta_guards=0, primary_model_delta=0, solver_ab_gate_met=false.
• Independent checker reconstructed 445 coverage clauses and fifteen pair rows, rejected five mutations, and returned valid=true.
• Fresh regeneration matched result.json and independent-check.json byte-for-byte.
• sha256sum -c artifacts/cycle15-triple-cap-semantic-audit-20260812/manifest.sha256 passed.

• .proof-experiments/20260812-042333-2cf7e1: producer checked fifteen rows and returned REDIRECT.
• .proof-experiments/20260812-042342-028fa6: independent checker rejected five mutations and returned valid=true.

check_cycle15_triple_cap_semantic_audit_v1.py independently rebuilds the 15-cycle, 3002 residual variables, 445 coverage clauses, and fifteen exact pair rows.

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

• Fixed-point q=6 triangle classification -> predicted a new cap on no-triangle leaves -> cap already implied by exact pair rows plus coverage, falsifying the transfer.

• Every neighbor-triple cap c_{i-1,i,i+1}<=3 is implied on the saved canonical 15-cycle exact-pair leaf.
  artifacts/cycle15-triple-cap-semantic-audit-20260812/derivation.md, result.json, and independent-check.json · All fifteen rows of the hash-bound partition-[15], root-31 leaf. · proved
• The checker reconstructed all 445 coverage clauses and fifteen focal pair rows and rejected five mutations.
  artifacts/cycle15-triple-cap-semantic-audit-20260812/independent-check.json · The immutable inputs listed in the protocol. · computed

• Use the fifteen q=6 neighbor-triple caps as a semantically stronger restriction of the canonical 15-cycle exact-pair leaf.
  Primary-model semantics of the hash-bound partition-[15], root-31 CNF. · Each cap follows from an exact nonedge-pair row and twelve coverage lower bounds. · result.json and independent-check.json; zero of fifteen guards have semantic delta · A target encoding missing an implication ingredient, or a separately predeclared propagation-only protocol.
• Run the matched solver A/B continuation specified by the q-bin transfer protocol.
  This canonical 15-cycle guard proposal. · The protocol authorized solver work only after nonzero semantic delta. · protocol stop_rule and solver_ab_gate_met=false · A materially different encoding hypothesis with its own propagation-based acceptance gate.

• Structural signature census of the 91-class degree-18 defect-ten corpus.
  It may turn the expanding local plateau into bulk class pruning without another BFS layer. · Compute fixed-point link profiles, pair-excess signatures, and uncovered-triple orbits for one representative per class. · high · open
• Certificate-throughput pilot on one immutable normalized branch.
  A replayed UNSAT leaf is the minimum evidence needed to estimate the terminal negative route. · Require proof output plus DRAT-to-LRAT replay under a fixed cap. · normal · open

Objective: Find a bulk invariant on the 91-class defect-ten plateau.

First action: Freeze the 91 representatives and write a count-only link-profile, pair-excess, and uncovered-triple signature protocol with an independent checker.

Stop condition: Redirect if all classes have globally admissible signatures, the checker disagrees, or the map supplies no class-level prediction.

• Keep the semantic q-bin guard transfer closed and skip its solver continuation.
• Compute structural signatures on the 91-class defect-ten corpus before further constructive BFS.
• Retain certificate-producing normalized branches in parallel, but require a replayed proof pilot before scale-up.

• 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 was principal investigator. Two GPT-5.6 Terra delegates supplied advisory route-audit memos; their provenance was promoted, but model agreement was not validation. Python 3.12.3 performed deterministic production and independent reconstruction. GNU cmp and sha256sum checked regeneration and hashes. The web reader returned no page payload, so pre-acquired source-status records and immutable repository inputs were used. No SAT solver, CAS, proof assistant, cloud lab, package installation, external publication, Git commit, or remote write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

976.7s

Review state

not a result claim

Attempt ID

covering-c1553-20260812-043210-6ee493

No human review recorded.