Random SAT benchmark and transition calibration

Edition 9 October 2026 v2. Bounded benchmark evidence module; low commercial confidence.

Research finding

Four source manuscripts distinguish fixed-k limiting thresholds, the older variance bound, the newer linear 3-SAT companion and computability without efficiency. Proper whole clauses repeat. Carenini retains threshold-existence priority; selected formal scope does not include the newer linear companion.

Problem and buyer

SAT solver researchers and verification-tool teams need reproducible stress suites whose clause law, transition regime and timeout handling are explicit. A suite can otherwise confuse solver timeouts with unsatisfiability or compare runs across different random distributions.

What the finding could enable

A runnable proper-clause stream audit preserves duplicate clauses, exact tiny first-failure witnesses, explicit caps and independent versus solver-claimed bounds. Exact coupon controls expose wrong-law and censoring errors. No new SAT solver or practical threshold-digit service is established.

Technical and commercial limits

Asymptotic centering does not certify finite-size bias. Exact mode is limited to sixteen variables and bounded work. Supplied law declarations and seeded pseudorandom fixtures do not prove iid randomness. CP-SAT UNSAT statuses remain unverified without a checked proof. Source algorithms and full proofs were not executed.

Minimal architecture

Canonical proper-clause rank generator -> saved ordered original clauses -> bounded exact reference or existing CP-SAT adapter -> independent SAT witness checks -> distinct UNSAT evidence/bounds and right-censoring -> retained JSON report and coupon calibration.

Existing alternatives and differentiation

PySAT already wraps established SAT engines and supports incremental calls; its bounded calls can return unknown when a budget is exhausted. The proposed addition is distribution and transition calibration with disciplined evidence, rather than another solver wrapper. Carenini’s primary report confirms an independent threshold-existence proof and should be credited when describing novelty. PySAT solver API, ECCC TR26-229.

Monetization hypothesis

Hypothesis: AUD 3,000–10,000 for benchmark integration, then AUD 300–1,000 monthly for recurring regression analysis. At an illustrative AUD 5,000 integration fee, 25 engineering hours costed at AUD 150/hour leave AUD 1,250 before compute, support and overhead. A solver vendor may already maintain equivalent suites for less.

Validation experiment

679 passing controls, 60 exact streams at n=6/10/16, nine CP-SAT comparisons with matching exact first failures, six larger solver-only cases and a real tiny-budget UNKNOWN. Independent assignment enumeration and inclusion-exclusion validate finite controls, not limiting source claims or customer usefulness.

Conditions to reject or defer

Reject if random suites fail to predict regressions on the buyer’s workloads, if open tooling already satisfies the workflow, or if solver compute dominates a realistic fee. Defer threshold-digit generation until the source algorithm’s practical cost is understood.

Next concrete action

Keep the integration low confidence. Before a standalone service, validate a permissioned structured regression corpus, a checked UNSAT-proof path and a recurring costly evidence gap beyond current libraries. Facility Plan Auditor remains the first commercial experiment.

Detailed evidence

Source scope, computability costs, exact coupon control and preserved conventional comparisons.