# 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](https://pysathq.github.io/docs/html/api/solvers.html), [ECCC TR26-229](https://eccc.weizmann.ac.il/report/2026/229/).

## 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](../../prototypes/random-sat-stream-2026-10-09-v1/report.md).