IIC hitting conjecture for p-capacity

Let $A\subseteq\mathbb Z^d$ be finite, let $\mathcal C_\infty(z)$ denote the Incipient Infinite Cluster rooted at $z$, and write

$$\tau_\infty(z)=\mathbb P(z\in\mathcal C_\infty(0)).$$

IIC hitting conjecture.

$$\lim_{\|z\|\to\infty}\frac{\mathbb P(\mathcal C_\infty(z)\cap A\neq\varnothing)}{\tau_\infty(z)}=\operatorname{pCap}(A).$$

The preceding theorem gives two-sided bounds of the same order, while the conjecture asks for the exact limiting constant. An analogous statement is known for critical branching random walks, but the percolation limit remains unproved in the supplied text.