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.
More from AGI Musings
- 'Using AI well takes critical thinking' — X users clash over AI in education — ___Patrice___ · 2026-09-03
- "Loss of control" has no coherent definition in English AI-safety discourse — _akpiper · 2026-09-03
- NYT's The Daily examines July's rogue OpenAI agents: "A.I. Is Outsmarting Its Creators" — kevinroose · 2026-09-03
- 'Does using a magic 8 ball take critical thinking?' — AI education debate — lilbrudder2 · 2026-09-03
- Should humans take AI-designed drugs they can't explain? — SoloGen · 2026-09-03
- Anthropic's Tom Brown cites '15 orders of magnitude' capability gains — Afinetheorem · 2026-09-03