All-four-canonical-type base-versus-104-pair-upper native pseudo-Boolean robustness gate at 25,000 conflicts, with exact symmetry audit, independent formula reconstruction, and fail-closed mutations.

native pseudo-Boolean four-branch pair-upper propagation

The slack-zero degree lemma and lambda_uv<=7 implication add 104 auxiliary-free PB rows to each globally complete pair-normalized branch; matched capped counters measure inference improvement.

Hypothesis: For every canonical type and requested seed 0 or 1553, the 104 pair upper bounds use at most 80 percent of base rlimit-count and do not increase decisions at 25,000 conflicts.

Test: Run 16 fresh sequential Z3 4.13.0 processes; require independent reconstruction, exactly 25,001 conflicts for every UNKNOWN run, upper rlimit_count <= 0.8*base, and no decision regression in every matched pair.

Exact matched counters, complete four-type coverage, independent formula reconstruction, fail-closed mutations, pinned hashes, and a separate result checker establish the bounded performance claim. Because every solve was UNKNOWN and no replayable proof exists, the exact covering-number verification contract remains unmet.

• All 16 hash-bound Z3 4.13.0 runs returned UNKNOWN at exactly 25,001 conflicts.
• Types 1 through 4 had upper/base rlimit ratios 0.3993034952568201, 0.5207520252853758, 0.41546251294831077, and 0.41233056447469096.
• Types 1 through 4 had upper/base decision ratios 0.6062218869038588, 0.7809970928817639, 0.7506342893206434, and 0.6263046192259676.
• Seeds 0 and 1553 produced identical formula bytes and algorithmic counters apart from allocation, memory, and time telemetry.
• No 54-block cover or branch exclusion was obtained.

• python3 scripts/test_cross_type_native_pb_25k_mutations_v1.py --output artifacts/cross-type-native-pb-25k-20260812/mutation-controls.json
• python3 scripts/run_cross_type_native_pb_25k_gate_v1.py --protocol protocols/cross-type-native-pb-25k-v1.json --output-dir artifacts/cross-type-native-pb-25k-20260812/runs
• python3 checkers/check_cross_type_native_pb_25k_result_v1.py --directory artifacts/cross-type-native-pb-25k-20260812/runs --mutations artifacts/cross-type-native-pb-25k-20260812/mutation-controls.json --summary artifacts/cross-type-native-pb-25k-20260812/result.json --output artifacts/cross-type-native-pb-25k-20260812/independent-result-check.json
• sha256sum -c artifacts/cross-type-native-pb-25k-20260812/manifest.sha256

• .proof-experiments/20260812-080802-1ebaef: sequential mutation driver timed out and produced no accepted result
• .proof-experiments/20260812-081040-2aa9f1: unchanged 56-case mutation gate passed in 83.222 seconds
• .proof-experiments/20260812-081219-a38f80: 16 live runs completed in 60.617 seconds; every solve was UNKNOWN and all matched gates passed

check_cross_type_native_pb_25k_v1.py reconstructed formulas from 15-bit masks; check_cross_type_native_pb_25k_result_v1.py separately recomputed all eight gates. Both passed.

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

• Pseudo-Boolean modelling -> theorem-implied redundant inequalities can improve inference without auxiliaries -> observed 47.9 to 60.1 percent per-type rlimit reductions, while certificate production remains untested.

• The 21,921,900 labelled multiplicity-five-pair common families fall into exactly four canonical types.
  Byte-identical independent orbit-stabilizer and inclusion-exclusion audit · Five projected triples covering the 13 outside points · computed
• The all-four-type 25,000-conflict pair-upper telemetry gate passes.
  independent-result-check.json valid=true · Hash-bound Z3 4.13.0 native-PB formulas · computed
• Every pair multiplicity is at most seven in a putative 54-block cover.
  lambda_uv>=5 and sum_{v!=u}lambda_uv=72 · Degree-18 54-block C(15,5,3) coverings · proved

• Count seed 1553 as an independent robustness trajectory.
  The eight type/mode formulas · All algorithmic statistics excluding allocation, memory, and time telemetry were identical. · artifacts/cross-type-native-pb-25k-20260812/independent-result-check.json · A verified branching perturbation that changes at least one algorithmic trace.
• Increase the identical Z3 native-PB conflict cap.
  The four hash-bound base/upper formulas · All runs remain uncertified UNKNOWN. · artifacts/cross-type-native-pb-25k-20260812/result.json · A proof-producing solver/checker path or checked SAT candidate.
• Rerun the injected complete fixed-pair-link challenger.
  All prior 395 signatures and 754 targets · Every target previously survived and the later CNF audit found zero semantic clause delta. · sources/advisory/terra-epoch113-native-pb-gate-20260812.md and prior durable artifacts · A genuinely new labelled correlation.

• Pinned proof-producing pair-upper OPB calibration
  It directly aligns the measured auxiliary-free inference gain with the negative verification contract. · After the pinned bundle is locally available, replay saved C(5,3,2) exact-3/4/5 controls before one canonical branch. · high · open
• Materially distinct constructive perturbation
  A 54-block witness needs only direct checking, although prior bounded neighborhoods plateaued. · Predeclare a move family not contained in the exhausted 2-for-2 or radius-six routes and test one frozen defect-10 class. · normal · open

Objective: Convert the pair-upper inference gain into an admissible proof-producing path, or redirect.

First action: Check only for a newly pre-acquired hash-matching RoundingSat/VeriPB/CakePB bundle; if present run the saved controls, otherwise close this route for the session and select a distinct constructive mechanism.

Stop condition: Any revision mismatch, missing proof, replay rejection, invalid model, unchanged tool absence, or failure to preserve a matched advantage.

• Do not increase the Z3 cap or run more random_seed-only repetitions.
• Keep proof-producing OPB calibration blocked until the pinned RoundingSat/VeriPB/CakePB bundle is pre-acquired.
• When available, require replayed C(5,3,2) exact-3 UNSAT and directly checked exact-4/5 SAT controls before translating a canonical branch.
• If the stack remains unavailable, select a materially distinct constructive route rather than the exhausted root-orbit-107 profile.

• 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 ↗
• https://arxiv.org/abs/math/9502238 ↗

OpenAI GPT-5.6 Sol principal selected, implemented, ran, audited, and interpreted the epoch. Two GPT-5.6 Terra delegates supplied bounded advisory reconnaissance only; their agreement was not validation. Python 3.12.3, Z3 4.13.0/libz3 SHA-256 21ff90cd752d7b9955d7bece8595adab9cf1fd9f334899f6257d10b35e615167, exact enumeration, 15-bit masks, SHA-256, the computational-researcher experiment harness, and web search were used. No subagents, CAS, proof assistant, proof-producing PB solver, cloud lab, package installation, external write, publication, or system change was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1585.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-082433-85a31b

No human review recorded.