{"id":"openai-math/Linear-Variance-of-the-Random-3-SAT-Hitting-Time","pdf":"https://github.com/openai/math/blob/main/preprints/Linear-Variance-of-the-Random-3-SAT-Hitting-Time-October-5-2026/linear-variance-of-the-random-3-sat-hitting-time.pdf","url":"https://github.com/openai/math/tree/main/preprints/Linear-Variance-of-the-Random-3-SAT-Hitting-Time-October-5-2026","tags":["random-sat","probability","combinatorics","satisfiability"],"score":0,"title":"Linear Variance of the Random 3-SAT Hitting Time","domain":"Probability and statistical mechanics","family":"235","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For random 3-SAT on n Boolean variables, with independent uniformly signed clauses on three distinct variables sampled with replacement, we prove that the first unsatisfiable prefix has variance $`\\Theta(n)`$. The upper bound removes the logarithmic loss in the earlier variance estimate; the matching lower bound follows from Wilson's transition-width theorem.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Limiting random SAT thresholds, sharp variance and computability"}