Noise sensitivity of Voronoi percolation

Let $V$ be a Voronoi tiling of $\mathbb{R}^2$ generated by a Poisson point process, and colour its cells independently blue with probability $1/2$. Let $f_N^V$ encode the blue crossing event for the rectangle $R_N$, using the cells that intersect $R_N$.

Voronoi noise-sensitivity conjecture. Voronoi percolation is noise sensitive at criticality.

The conjecture complements the question of whether the tiling itself reveals information about crossings when the colouring is unknown. The paper also expects the analogous result when both the Poisson point process and the colouring are resampled; the stated conjecture concerns resampling the colouring for an almost every Poisson tiling.