Built all nine forced multiplicity-four pair-star incidence leaves and compared one-round preprocessing dimensions against the fixed-first incidence control.

forced pair-star incidence preprocessing

Combine the audited nine-template pair-star quotient with the existing incidence-matrix core, force four common root-pair blocks, exclude later root-pair occurrences, lex-sort the remaining columns, and measure preprocessing before solver search.

Hypothesis: Every one of the nine complete pair-star prefix leaves preprocesses to at most half the remaining variables and clauses of the fixed-first incidence control.

Test: Run pinned CaDiCaL 1.7.3 only as -P1 -c 0 on the control and nine independently reconstructable leaves; require every control/leaf variable and clause ratio, and both geometric means, to be at least 2.0.

The raw logs, simplified DIMACS files, and independent recount agree exactly. Since the declared prerequisite failed for every leaf and geometrically, solver scaling would repeat an encoding whose measured reduction is insufficient.

• The nine epoch-47 CNFs form a complete conditional search cover after choosing and ordering a multiplicity-four pair, without quotienting the root swap.
• Pinned one-round preprocessing leaves 15,281–15,498 variables and 84,108–85,245 clauses across the nine leaves.
• All four 2x continuation gates fail.
• No covering-number bound changed.

• python3 scripts/pair_star_preprocess_discriminator_v1.py --out-dir artifacts/epoch47-20260810/pair-star-preprocess-v1 --baseline artifacts/epoch7-20260808/incidence-matrix-pilot-v1/incidence-matrix.cnf --catalogue artifacts/epoch22-20260809/edge_star_prefix_structural_v1.json --cadical /usr/bin/cadical --root .
• python3 checkers/check_pair_star_preprocess_discriminator_v1.py --manifest artifacts/epoch47-20260810/pair-star-preprocess-v1/preprocess-manifest.json --receipt artifacts/epoch47-20260810/pair-star-preprocess-check-v1.json
• sha256sum -c artifacts/epoch47-20260810/SHA256SUMS

• .proof-experiments/20260810-080100-06b849: generated and preprocessed the control and nine leaves in 15.324 seconds; every 2x gate failed.
• .proof-experiments/20260810-080136-bbf647: independent checker passed in 7.961 seconds and reproduced the stop decision.

checkers/check_pair_star_preprocess_discriminator_v1.py independently reconstructs templates in reverse label order, parses every original and simplified CNF, verifies exact clauses and ownership, recounts used variables, reparses logs, recomputes gates, and rejects two mutations.

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

• Local symmetry quotient -> predicted at least 2x full-CNF compression -> observed only about 1.3x because the shared global core dominates.

• For every point x in a hypothetical 30-cover, sum_{y!=x}(lambda_xy-4)=4, hence a multiplicity-four pair exists.
  Exact degree 12 and pair coverage lower bound lambda_xy>=4. · Every hypothetical 30-block C(15,6,3) cover. · proved
• There are nine audited support types for the four common blocks of a fixed ordered multiplicity-four pair.
  Two epoch-22 enumerators, orbit-stabilizer mass 61,311,250, and independent inclusion-exclusion. · Conditional four-block pair-star prefixes. · computed
• The nine epoch-47 leaves retain 15,281–15,498 variables and 84,108–85,245 clauses after the pinned preprocessing protocol.
  Raw CaDiCaL logs and independently parsed simplified DIMACS files. · The exact hash-bound epoch-47 formulas and CaDiCaL 1.7.3 -P1 -c 0. · computed

• Scale the unchanged pair-star plus current incidence-core CNFs into SAT/LRAT search on the strength of formula-size reduction.
  Exactly the nine epoch-47 formulas and pinned one-round preprocessing protocol. · Every strict 2x variable and clause gate failed; measured gains were only about 1.3x. · artifacts/epoch47-20260810/pair-star-preprocess-check-v1.json · A materially different core, stronger sound preprocessing, proof-valid shared-prefix mechanism, or terminal solver evidence.

• Proof-producing global incidence/PB calibration
  It targets terminal independently replayable evidence and remains materially distinct from the failed prefix-conditioning compression. · Compile the smallest six-representative exact-degree-12 cube and replay one terminal proof with both checkers. · high · open
• Canonical root-link catalogue
  Fixing a complete 12-block root link changes the completion universe rather than only conditioning four columns. · Enumerate canonical links with a 10,000-orbit or 30-minute frontier cap and independently audit ownership. · normal · open

Objective: Test whether a proof-producing global incidence/PB decomposition can generate independently replayable terminal evidence.

First action: Run sha256sum on /usr/bin/cadical, tools/drat-trim/lrat-check.c, tools/cake_lpr/cake_lpr.S, and tools/cake_lpr/basis_ffi.c; verify their provenance, then compile the smallest six-representative exact-degree-12 calibration cube.

Stop condition: Stop or redirect on hash drift, proof-format replay failure, nonterminal output, ownership gaps, or projected certificate size beyond the declared budget.

• Hash-audit the pinned LRAT emitter and both proof replayers.
• Compile the smallest six-representative global incidence/PB calibration cube with exact degree-12 constraints.
• Require one terminal proof replayed by both lrat-check and CakeLPR before any scale-up.
• Retain the canonical root-link catalogue as the immediate structural alternative.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol was principal investigator. Two pre-completed GPT-5.6 Terra delegates supplied advisory route and verification memos; Sol independently audited adopted points, and delegate agreement was not evidence. Deterministic work used CPython 3.12.3, CaDiCaL 1.7.3 in preprocess-only mode, exact integer/set operations, DIMACS parsers, SHA-256, and the Proof Factory experiment harness. No SAT search, CAS, proof assistant, cloud lab, external proof service, or human validator was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1030.3s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260810-080921-0afaf7

No human review recorded.