Differentiability conjecture for hyperbolic Poisson-Voronoi percolation

Let $p_c(bb)$ denote the critical value for Poisson-Voronoi percolation on the hyperbolic plane as a function of the intensity $bb$. Differentiability conjecture.

$$p_c(bb)$$

is differentiable. The authors deliberately formulate the claim with “differentiable” rather than “smooth” to impose the weaker regularity requirement.