Absence of critical Bernoulli bond percolation on $\mathbb Z^d$ in every dimension $d \ge 2$

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Absence of critical Bernoulli bond percolation on $\mathbb Z^d$ in every dimension $d \ge 2$ parent of this event

Claims $\theta(p_c) = 0$ for every $d \ge 2$, by proving Kozma-Nitzan Conjecture 3 and its reduction to critical percolation. The previously open dimensions $3 \le d \le 10$ are included. The formal statement concerns vanishing at $p_c$; continuity of $\theta$ on the whole interval is a classical consequence rather than the formal target. No claim is intended concerning site percolation or other lattices. A stronger claim, no infinite cluster at p_c for bond percolation on every infinite connected locally finite quasi-transitive graph with p_c < 1 (which includes Z^d for every d >= 2), appeared in OpenAI's math release on 24 September 2026 with a Lean challenge; see benjamini-schramm-criticality-bond. parent of this event

VibeMathed record: Absence of critical Bernoulli bond percolation on $\mathbb Z^d$ in every dimension $d \ge 2$ evidence for this event

Absence of critical Bernoulli bond percolation on $\mathbb Z^d$ in every dimension $d \ge 2$ evidence for this event

Challenge.lean: the trusted statement, in plain Mathlib evidence for this event

AUDIT.md: their build, axiom and comparator record evidence for this event

Gil Kalai's report, with his caveats evidence for this event

summary.pdf: the repository's own guide to the proof evidence for this event

formalization.yaml: provenance, cost and disclosed divergences evidence for this event

No percolation at criticality, from the same 1996 Benjamini-Schramm paper evidence for this event

Earlier site result on Z^d, d >= 3, cited by the manuscripts (Bou-Rabee) evidence for this event

This event attributed to Anthropic Claude models (specific version undisclosed)

This event attributed to Justin Leder