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Linear Variance of the Random 3-SAT Hitting Time

OpenAI

OpenAI Mathopenai-math/Linear-Variance-of-the-Random-3-SAT-Hitting-TimeOct 5, 2026math.PRAI-generatedscore 0

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.

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