Uniform exponential decay below one-half for circle packings

Let $E_{\mathcal{S},p}(s_0,r)$ be the event that $s_0$ is connected to distance $r$ by open disks in site percolation with parameter $p$. Uniform exponential decay conjecture. There exists a function $f:(0,1/2)\to(0,\infty)$ such that, for every $0<p<1/2$, every circle packing $\mathcal{S}$, and every $s_0\in\mathcal{S}$ with

$$D:=\sup_{s\in\mathcal{S}}\operatorname{diam}(s)<\infty,$$

for every $r>0$,

$$\mathbb{P}(E_{\mathcal{S},p}(s_0,r))\leq \exp\left(-f(p)\frac{r}{D}\right).$$

This is conjectured as the subcritical counterpart to the critical one-half conjecture and would provide decay uniform over circle packings with bounded disk diameters. The source does not state a resolution.