The satisfiability threshold conjecture: a limiting random k-SAT threshold for every k >= 3

Lineage and corrections

Chvatal and Reed, Mick gets some (the odds are on his side), FOCS 1992 evidence for this event

This event attributed to Unreleased internal OpenAI model

Claims Theorem 1.1: for every fixed $k\ge3$ there is $\alpha_k\in(0,\infty)$ with $\Pr(F_{n,\lfloor cn\rfloor}\in\mathrm{SAT})\to1$ for $c<\alpha_k$ and $\to0$ for $c>\alpha_k$; it says nothing at $c=\alpha_k$ and does not identify $\alpha_k$ for small $k$. Companions claim hitting-time variance $\Theta_k(n)$ for $k\ge4$ and $\Theta(n)$ for $k=3$, and that $\alpha_3$ is a computable real. Priority: the release credits Gaia Carenini's ECCC TR26-229 (made public 5 October 2026) with first resolving the existence conjecture; this is an independent second proof of the same result, not a contradiction. Carenini's paper states that none of its mathematical arguments was generated by a large language model; it proves the existence via a scaling window of width $O(n^{1/2+1/k})$ and the Abbe-Montanari criterion. parent of this event

Companion: Variance of the Random k-SAT Hitting Time evidence for this event

Carenini, ECCC TR26-229 (credited with priority by the release) evidence for this event

Companion: Computing the Random 3-SAT Threshold evidence for this event

The satisfiability threshold conjecture: a limiting random k-SAT threshold for every k >= 3 evidence for this event

Lean Comparator challenge FixedClauseThreshold (not in formalization.yaml) evidence for this event

The satisfiability threshold conjecture: a limiting random k-SAT threshold for every k >= 3 parent of this event

VibeMathed record: The satisfiability threshold conjecture: a limiting random k-SAT threshold for every k >= 3 evidence for this event

Companion: Linear Variance of the Random 3-SAT Hitting Time evidence for this event

Lean solution module OAI/Probability/RandomSAT/Main.lean evidence for this event