Anthropic formalizes Kozma–Nitzan conjecture in Lean, advancing the long-standing θ(p_c)=0 problem
michaelchchoi · x · 2026-09-03
Anthropic has released a Lean formalization proving Conjecture 3 of Kozma–Nitzan, which implies the long-standing θ(pc)=0 conjecture in percolation theory — i.e., no percolation at criticality on Euclidean lattices in any dimension above one.
- The reduction was proposed by Gady Kozma and Shahaf Nitzan in arXiv:2401.12397 (2024), backed by numerical evidence and several proven special cases
- Anthropic's machine-checkable Lean proof is publicly available
A notable AI-for-math milestone: an AI lab delivering verifiable serious mathematical work.
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