{"id":"openai-math/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size","pdf":"https://github.com/openai/math/blob/main/preprints/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026/article.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026","tags":["random-sat","combinatorics","probability"],"score":0,"title":"A Limiting Satisfiability Threshold for Every Fixed Clause Size","domain":"Probability and statistical mechanics","family":"235","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For every fixed integer k ≥ 3, random k -SAT with independent uniformly signed clauses on distinct variables, sampled with replacement, has a finite positive limiting satisfiability threshold. We credit Gaia Carenini [[5]](https://eccc.weizmann.ac.il/report/2026/229/) with priority for resolving the satisfiability conjecture. This paper gives an alternative proof, using concentration of a capped last satisfiable index and a comparison between different system sizes.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Limiting random SAT thresholds, sharp variance and computability"}