Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 235-02. Linear Variance of the Random 3-SAT Hitting Time
Manuscript map · lines 6895–6904
OpenAI@2026-10-07#rem:oai-p-235-02
Authors: OpenAI. Family 235.
Title: Linear Variance of the Random 3-SAT Hitting Time.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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