Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 235-03. Variance of the Random k-SAT Hitting Time
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OpenAI@2026-10-07#rem:oai-p-235-03
Authors: OpenAI. Family 235.
Title: Variance of the Random k-SAT Hitting Time.
Abstract: Let Hn be the index of the first unsatisfiable prefix in random k-SAT on n variables, with independent uniformly signed clauses using k distinct variables and sampled with replacement. For every fixed k ≥ 4, we prove ${}mathop{{}mathrm{Var}}{}nolimits (H_n)={}Theta_k(n)$. For k = 3, the variance is bounded below by a positive multiple of n and above by a constant multiple of $n{}log n$; the companion paper on random 3-SAT sharpens this to ${}Theta(n)$. The same upper bounds proved here hold after clipping at any fixed positive multiple of n.
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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