Dying percolation conjecture solved in all dimensions, with AI in the loop
Singularitarian · x · 2026-09-03
Gil Kalai reports that the dying percolation conjecture — that at the critical probability, θ(pc) = 0 and there is no infinite cluster almost surely — has been solved in all dimensions.
Key points:
- In 2024, Gady Kozma and Shahaf Nitzan showed the conjecture follows from a much more general conjecture about percolation on general graphs, one many expected to be refuted.
- The result was previously known only for planar and high-dimensional percolation.
- Kalai describes the proof as solved "by AI", building on the Kozma–Nitzan conjecture.
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