Absence of critical Bernoulli site percolation on $\mathbb Z^d$ for $d \ge 3$

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Absence of critical Bernoulli site percolation on $\mathbb Z^d$ for $d \ge 3$ parent of this event

Claims $\theta(p_c)=0$ for nearest-neighbour Bernoulli site percolation on $\mathbb Z^d$ for every $d\ge3$ (theorem KNAll.Site.site_no_percolation_at_critical), by proving the Kozma-Nitzan gluing inequality for independent hyperedges, representing site percolation by incidence hyperedges, and running the lattice exploration of the bond proof. The intermediate dimensions were open. The planar case is classical and outside the formal statement. The same repository proves Kozma-Nitzan Conjectures 1 to 4 and 6, answers Questions 5, 7 and 9, and refutes one reading of Question 8. OpenAI's release (24 September 2026) later gave critical site nonpercolation on $\mathbb Z^3$ only, crediting this work; its quasi-transitive theorem is bond only, so the site form of Benjamini-Schramm Conjecture 4 beyond $\mathbb Z^d$ stays open. parent of this event

VibeMathed record: Absence of critical Bernoulli site percolation on $\mathbb Z^d$ for $d \ge 3$ evidence for this event

Absence of critical Bernoulli site percolation on $\mathbb Z^d$ for $d \ge 3$ evidence for this event

Lean repository: percolation-after-anthropic (Bou-Rabee and Leder) evidence for this event

Comparator challenge: the headline statement in plain Mathlib evidence for this event

Kozma-Nitzan connection inequalities, companion manuscript (5 September 2026) evidence for this event

Kozma and Nitzan, A reduction of the theta(p_c)=0 problem to a conjectured inequality (arXiv:2401.12397) evidence for this event

Bond percolation on Z^d, the result this extends evidence for this event

Companion: Critical bond and site percolation on the cubic lattice evidence for this event

Quanta Magazine coverage evidence for this event

This event attributed to ChatGPT 5.6 (per the exposition page; the author's other documents also name Claude and GLM models)

This event attributed to Ahmed Bou-Rabee

This event attributed to Justin Leder