Non-trivial percolation transition conjecture for supercritical random planar maps

Fix $Q\in(0,2)$ and consider site percolation on $\mathcal M_k$ with open boundary condition: boundary vertices are open, while each interior vertex is independently open with probability $p$ and closed with probability $1-p$. An open cluster is a connected component of the open vertices. Critical percolation probability conjecture. There exists $p_c=p_c(Q)\in(0,1)$ such that, for every $p<p_c$ and every $k\in\mathbb N$, almost surely there are no infinite open clusters, whereas for $p>p_c$ and every $k\in\mathbb N$, the open cluster containing $\partial\mathcal M_k$ is infinite with positive probability. This asserts a non-trivial phase transition, while the behavior at $p=p_c$ is addressed separately.