# Random SAT benchmark regime calibration

Family 235: Limiting random SAT thresholds, sharp variance and computability. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

SAT solver teams can build reproducible random-instance suites with a correctly documented clause model, limiting threshold and hitting-time variance.

## Applicability and commercial boundary

Computability of the 3-SAT threshold supplies no practical runtime or finite-size convergence rate. The selected formal variance is sharp for k>=4 but retains O(n log n) above a linear lower bound for k=3. The repo credits Gaia Carenini with concurrent threshold-existence priority.

## Initial business decision

Conditional benchmark workflow. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Extract an exact clause generator and finite-size hitting-time experiment using an existing incremental solver, without claiming a new SAT solver.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstract passages and available family scope notes were also inspected; paper-level theorem and algorithm details still require deeper review. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[A Limiting Satisfiability Threshold for Every Fixed Clause Size](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026/article.pdf).