Cross-type robustness gate for auxiliary-free native pseudo-Boolean pair-upper strengthening on canonical multiplicity-five pair types 1–3.

native pseudo-Boolean four-branch search

Expose the proved redundant bounds lambda_uv <= 7 directly as 104 auxiliary-free PB inequalities and compare them with the base encoding within each canonical type.

Hypothesis: For canonical types 1, 2, and 3, adding the 104 implied pair upper bounds causes no PB-propagation regression, reduces aggregate PB propagations by at least 20%, and gives at least two types a 20% improvement in rlimit-count or solver time.

Test: Six fresh Z3 4.13.0 processes—base and upper for types 1–3—at seed 0, 5,000 conflicts, 60 seconds, and 2 GiB, followed by independent mask reconstruction and fail-closed mutation tests.

The deterministic counters satisfy every predeclared telemetry threshold and all validation controls passed. This supports selecting the strengthened encoding for a proof-producing calibration, but UNKNOWN results supply no witness or exclusion and therefore cannot be promoted to a candidate solution.

• At seed 0 and a 5,000-conflict cap, type-1 PB propagations fell from 2,222,583 to 829,215, a 62.6914% reduction.
• At the same protocol, type-2 PB propagations fell from 2,317,446 to 613,902, a 73.5095% reduction.
• At the same protocol, type-3 PB propagations fell from 2,263,640 to 700,134, a 69.0704% reduction.
• Across types 1–3, aggregate PB propagations fell from 6,803,669 to 2,143,251, a 68.4986% reduction.
• All six runs returned UNKNOWN and exclude no branch.

• python3 scripts/summarize_cross_type_native_pb_v1.py --directory artifacts/cross-type-native-pb-20260809 --output artifacts/cross-type-native-pb-20260809/result.json
• Six producer runs used Z3 4.13.0, seed 0, max_conflicts=5000, timeout_ms=60000, and fresh processes.
• Six checker runs reported valid=true and zero mismatches.
• The type audit reported four canonical types and orbit_sum=21921900.
• The mutation suite accepted three clean cases and rejected all 27 semantic mutations.

• .proof-experiments/20260809-212030-435281: independently audited four canonical types and 21,921,900 labelled common families.
• .proof-experiments/20260809-212207-d2d2a7 and 20260809-212209-bab7dd: type-1 base/upper UNKNOWN; 62.6914% PB-propagation reduction.
• .proof-experiments/20260809-212212-f5e341 and 20260809-212214-74ba0f: type-2 base/upper UNKNOWN; 73.5095% PB-propagation reduction.
• .proof-experiments/20260809-212217-82f682 and 20260809-212219-b82edd: type-3 base/upper UNKNOWN; 69.0704% PB-propagation reduction.
• .proof-experiments/20260809-212350-2e623a: fail-closed summary confirmed the full gate passed.

checkers/check_cross_type_native_pb_v1.py recursively enumerates 15-bit masks, reconstructs all free blocks and constraint incidences, parses each SMT2 formula independently, and reported zero mismatches for all six formulas.

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

• Certified covering-number SAT work -> require independently replayed proof leaves -> the current Z3 UNKNOWN telemetry is retained only as an encoding-selection result.
• Redundant implied constraints in PB solving -> predict stronger propagation without new variables -> aggregate PB propagations decreased by 68.4986% across types 1–3.

• Every pair in a hypothetical 54-block cover has multiplicity between 5 and 7.
  lambda_uv >= ceil(13/3)=5 and sum_{v != u} lambda_uv=4*18=72. · All pairs in all hypothetical 54-block C(15,5,3) covers. · proved
• The multiplicity-five common families covering the 13 outside points form exactly four point-isomorphism types.
  artifacts/cross-type-native-pb-20260809/type-audit.json · All 21,921,900 labelled five-triple common families covering the outside points. · computed
• Under the fixed seed-0 5,000-conflict Z3 protocol, the pair-upper encoding reduces aggregate PB propagations by 68.4986% on types 1–3.
  artifacts/cross-type-native-pb-20260809/result.json and six independently reconstructed manifests. · The exact recorded Z3 4.13.0 formulas and capped protocol only. · computed

• Scale uncertified Z3 merely because the type-4 pilot improved.
  Uncertified native-PB runs on the four canonical branches. · Cross-type robustness is now established, but every run remains UNKNOWN and produces no accepted certificate. · artifacts/cross-type-native-pb-20260809/result.json · A semantically reconstructed proof-producing translation passes independent proof replay.
• Repeat the complete fixed-pair-link relaxation as the next discriminator.
  The frozen type-4 frontier of 395 signatures and 754 targets. · The prior complete 431-cell test retained all 754 targets. · artifacts/type4-complete-pair-link-gate-20260809/result.json · Couple the link to genuinely new labelled skeleton or coverage-orbit information.

• Proof-producing calibration of the pair-upper strengthening.
  It is the shortest path from the validated propagation signal to an accepted UNSAT leaf or independently checked SAT witness. · Translate one canonical base/upper pair, reconstruct it independently, and replay a tiny proof control before a matched pilot. · high · open
• Joint common-family, pair-excess-skeleton, and residual-coverage orbit coupling.
  It restores labelled correlations erased by prior anonymous skeleton and margin relaxations. · Count one canonical skeleton orbit crossed with one residual coverage orbit; stop if it prunes no targets or reaches literal-SAT scale. · normal · open

Objective: Determine whether the pair-upper improvement survives in a proof-producing encoding capable of yielding accepted certificates.

First action: Translate one canonical type's base and upper formulas to the audited totalizer CNF or available PB proof format, then run independent semantic reconstruction and a tiny proof replay.

Stop condition: Redirect on any semantic mismatch, failed proof replay, or absence of a matched improvement in the proof-producing pilot.

• Select one canonical type and translate its matched base/upper pair into the audited totalizer CNF or a locally available proof-producing PB format.
• Independently reconstruct the translation and first replay a tiny negative proof control.
• Compare the base and upper proof-producing variants under a matched bounded protocol.
• Increase proof-search scale only if semantic reconstruction, proof replay, and the matched calibration all pass.

• 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 ↗

GPT-5.6 Sol acted as principal investigator: it audited prior artifacts, implemented the generic producer and independent checker, ran and interpreted the bounded experiments, and updated the durable checkpoint. GPT-5.6 Terra delegates supplied advisory reconnaissance only and were not treated as validators. Python 3.12.3, Z3 4.13.0, exact combinatorial enumeration, recursive bit-mask checking, semantic mutation tests, SHA-256, and the computational-researcher experiment harness were used. No proof assistant or proof-producing SAT/PB solver was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1004.4s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260809-212801-d5e91d

No human review recorded.