Benjamini–Schramm Conjecture 8 on critical site percolation in planar graphs

Let $G$ be a planar graph, and consider i.i.d. Bernoulli site percolation at parameter $p=\tfrac{1}{2}$. Benjamini–Schramm Conjecture 8. If percolation occurs almost surely, meaning that there exists an infinite open cluster almost surely, then almost surely there are infinitely many infinite open clusters. This conjecture addresses the possible multiplicity of infinite clusters at the critical parameter on general planar graphs; the source describes the issue as subtle and largely open.