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Computing the Random 3-SAT Threshold

OpenAI

OpenAI Mathopenai-math/Computing-the-Random-3-SAT-ThresholdSep 27, 2026math.PRAI-generatedscore 0

The limiting satisfiability threshold of uniform random 3-SAT is a computable real. We credit Gaia Carenini [[4]](https://eccc.weizmann.ac.il/report/2026/229/) with priority for resolving the satisfiability conjecture, which establishes the threshold's existence. We prove that one finite deterministic machine can approximate it to any prescribed accuracy. A deletion estimate gives explicit lower certificates, while a finite hierarchical approximation of the soft pressure gives upper certificates at every larger rational density. A fair search through these certificates halts without…

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