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Research / Aug 28, 2026

Vanishing percolation probability at criticality in every dimension

Is there almost surely no infinite cluster at the critical parameter for nearest-neighbour bond percolation on the integer lattice in every dimension at least two?

Model / AI: Anthropic Claude

machine-checked (formal gluing conjecture)self-reported (formal gluing conjecture)
Aug 28, 2026

Claude-generated Lean development

Model / AI: Anthropic Claude

machine-checked (formal gluing conjecture)self-reported (formal gluing conjecture)

Anthropic's formal-math artifact reports a Lean proof of Kozma and Nitzan's Conjecture 3 via conditioned covariance inequalities, closing the previously open dimensions 3 through 10 if the formal statement and cited implication match the prose claims.

Source read 2026-09-08. Read the pinned artifact and audit record identified by the source registry. The artifact was not rebuilt, and its removal from the main branch is retained as a caveat.