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arXiv · 2506.01359

The random $k$-SAT Gibbs uniqueness threshold revisited

Arnab Chatterjee·Amin Coja-Oghlan·Catherine Greenhill·Vincent Pfenninger·Maurice Rolvien·Pavel Zakharov·Kostas Zampetakis
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Abstract

We prove that for any $k\geq3$ for clause/variable ratios up to the Gibbs uniqueness threshold of the corresponding Galton-Watson tree, the number of satisfying assignments of random $k$-SAT formulas is given by the `replica symmetric solution' predicted by physics methods [Monasson, Zecchina: Phys. Rev. Lett. (1996)]. Furthermore, while the Gibbs uniqueness threshold is still not known precisely for any $k\geq3$, we derive new lower bounds on this threshold that improve over prior work [Montanari and Shah: SODA (2007)].The improvement is significant particularly for small $k$.

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Arnab Chatterjee, Amin Coja-Oghlan, Catherine Greenhill, Vincent Pfenninger, Maurice Rolvien, Pavel Zakharov, Kostas Zampetakis. 2025-06-02. The random $k$-SAT Gibbs uniqueness threshold revisited. https://arxiv.org/abs/2506.01359

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