Small-intensity lower bound for hyperbolic Poisson-Voronoi percolation

Let $p_c(bb)$ denote the critical value for Poisson-Voronoi percolation on the hyperbolic plane. Small-intensity lower-bound conjecture. There exists a $bb_0>0$ such that

$$p_c(bb) > (\pi/3)\cdotbb$$

for all $0<bb<bb_0$. The paper notes that the next-order expansion of $p_c(bb)$ could determine this inequality, although a different proof may also settle it.