Run the predeclared byte-identical 250000-conflict no-reflection Z3 native-PB continuation on the certified partition-[15], root-mask-31 leaf, then independently audit provenance, structure, status, and witness absence.

native pseudo-Boolean constructive leaf search

Z3 directly searches 3002 residual block variables under 445 coverage inequalities and 105 exact pair equalities; this epoch increased only the deterministic conflict cap by ten while retaining the exact no-reflection SMT2 instance.

Hypothesis: Pinned Z3 4.13.0 on the byte-identical certified root-31 no-reflection PB instance finds a SAT model within 250000 conflicts or 120 seconds.

Test: Run exactly one hash-bound tenfold conflict-cap continuation; accept only a decoded 54-block cover passing the PB checker and both independent global-cover checkers, and redirect after UNKNOWN or unchecked UNSAT.

The solver supplied neither a model nor a replayable UNSAT proof, so the verification contract permits no covering claim or leaf exclusion. The only durable result is a checked route-termination decision and reproducible telemetry.

• For the recorded pinned configuration, Z3 4.13.0 returned UNKNOWN at 250001 conflicts after 13.344528 solver seconds.
• The 250000-conflict and 25000-conflict no-reflection runs use byte-identical SMT2 with SHA-256 3305540ab286a11f845f362e453b9dbb05c2969c8d14375f1cb61942a696c9f9.
• No witness file was produced, no assignment family or cube was excluded, and C(15,5,3) remains unresolved between 54 and 55.

• python3 checkers/check_direct_pb_leaf_v1.py --source-manifest artifacts/joint-orbit-census-20260808/manifest.json --manifest artifacts/direct-pb-leaf-15-root31-250k-noref-20260808/result.json --smt2 artifacts/direct-pb-leaf-15-root31-250k-noref-20260808/instance.smt2
• python3 checkers/check_direct_pb_250k_noref_v2.py with the recorded prior/current artifacts and experiment receipt returned valid=true.
• python3 checkers/test_direct_pb_250k_noref_negative_v2.py rejected both deliberately invalid substitutions.
• sha256sum -c artifacts/direct-pb-leaf-15-root31-250k-noref-20260808/manifest.sha256 returned OK for every listed artifact.

• .proof-experiments/20260808-204153-6404fe: UNKNOWN at 250001 conflicts, 13.344528 solver seconds, no witness.
• .proof-experiments/20260808-204331-eb84b3: independent provenance and telemetry checker returned valid=true.
• .proof-experiments/20260808-204357-c0a16d: reflection-instance and unrelated-witness substitutions were both rejected.

check_direct_pb_leaf_v1.py independently reconstructs combinatorial semantics; check_direct_pb_250k_noref_v2.py independently verifies byte identity, provenance, telemetry, and witness absence; test_direct_pb_250k_noref_negative_v2.py supplies fail-closed controls.

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

• Sparse PB calibration -> predicted that a tenfold cap remained cheap and might expose SAT -> observed 13.34 solver seconds but UNKNOWN, so cheap throughput did not predict decisiveness.
• Certified-computation practice from C(12,6,4) -> predicted that uncertified negatives must redirect to proof production -> observed no admissible exclusion, making OPB proof replay the next concrete discriminator.

• The recorded no-reflection run reached 250001 conflicts and returned UNKNOWN with no witness.
  result.json, experiment receipt, and independent-check.json with matching hashes. · Pinned Z3 4.13.0, seed 0, selected partition-[15]/root-mask-31 PB leaf, recorded limits. · computed
• The current and prior no-reflection SMT2 inputs are byte-identical.
  Both hash to 3305540ab286a11f845f362e453b9dbb05c2969c8d14375f1cb61942a696c9f9; independent checker accepted. · The two recorded no-reflection artifacts only. · computed

• Continue scaling this native-Z3 leaf by increasing only the conflict cutoff.
  Pinned Z3 4.13.0 on the exact selected no-reflection sparse PB instance. · The predeclared tenfold continuation remained UNKNOWN and adds no new verification mechanism. · independent-check.json and the three experiment receipts. · A materially changed checked solver/encoding with useful measured signal, proof-producing support, or a directly checked candidate witness.
• Treat the 250001-conflict UNKNOWN as evidence that the selected cube is infeasible.
  The selected root-31 cube. · UNKNOWN is neither SAT nor UNSAT and no proof log exists. · result.json reports max-conflicts-reached and witness=null. · A complete independently replayed UNSAT proof for the exact instance.

• Proof-producing OPB solver and checker calibration.
  It changes the verification surface and can make either a model or an UNSAT result admissible before any global scale-up. · Generate target-minus-one, target, and target-plus-one controls in exact intended syntax; pin versions and replay the negative proof. · high · open
• A stronger structural constraint coupling root-cell flows to outside-triple coverage.
  A proved one-sided inequality could eliminate whole profiles before solver work, unlike the exhausted 31-cell conservation system. · Derive one explicit outside-triple coupling inequality and evaluate it against all 20 stored flow witnesses with an independent arithmetic checker. · normal · open

Objective: Establish a fail-closed proof-producing OPB toolchain for the selected exact-pair leaf.

First action: Write deterministic tiny OPB target-minus-one, target, and target-plus-one controls in the intended syntax, then run pinned solver and checker versions under run_experiment.py.

Stop condition: Redirect immediately if the UNSAT proof does not replay, SAT controls disagree with direct arithmetic, or the solver cannot emit a supported proof format.

• Emit tiny OPB cardinality and coverage controls in the exact intended syntax and pin a solver/checker pair that produces independently replayable proofs.
• Require target-minus-one UNSAT proof replay, target SAT model checking, and target-plus-one SAT checking before encoding the selected root-31 leaf.
• Do not increase the native-Z3 cutoff again without a materially changed encoding, solver, or checked witness candidate.

• 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 this epoch. Prior GPT-5.6 Terra delegates supplied advisory reconnaissance only; their claims were not counted as evidence. Deterministic Python 3.12.3 scripts, Z3 4.13.0 native pseudo-Boolean solving, the computational-researcher experiment wrapper, SHA-256, shell utilities, and web search were used. No CAS, proof assistant, checkpointed lab job, or external human validator was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

936.6s

Review state

not a result claim

Attempt ID

covering-c1553-20260808-205235-630fd2

No human review recorded.