{"id":"openai-math/Computing-the-Random-3-SAT-Threshold","pdf":"https://github.com/openai/math/blob/main/preprints/Computing-the-Random-3-SAT-Threshold-September-27-2026/article.pdf","url":"https://github.com/openai/math/tree/main/preprints/Computing-the-Random-3-SAT-Threshold-September-27-2026","tags":["random-satisfiability","computability","combinatorics"],"score":0,"title":"Computing the Random 3-SAT Threshold","domain":"Probability and statistical mechanics","family":"235","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"The limiting satisfiability threshold of uniform random 3-SAT is a computable real. We credit Gaia Carenini [[4]](https://eccc.weizmann.ac.il/report/2026/229/) with priority for resolving the satisfiability conjecture, which establishes the threshold's existence. We prove that one finite deterministic machine can approximate it to any prescribed accuracy. A deletion estimate gives explicit lower certificates, while a finite hierarchical approximation of the soft pressure gives upper certificates at every larger rational density. A fair search through these certificates halts without…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Limiting random SAT thresholds, sharp variance and computability"}