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

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.

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.