FUSF connectedness threshold conjecture for supercritical random planar maps

Let $\mathcal M_k$ be the supercritical random planar map, and let its free uniform spanning forest (FUSF) be the forest obtained from the free boundary condition. FUSF connectedness threshold conjecture. If $Q>\sqrt{5/2}$, equivalently ${\mathbf{c}}>16$, then almost surely the FUSF on $\mathcal M_k$ is connected and consists of a single tree. If $Q<\sqrt{5/2}$, equivalently ${\mathbf{c}}<16$, then on the event that $\mathcal M_k$ has infinitely many vertices, the FUSF almost surely has infinitely many connected components. The threshold is motivated by the Euclidean Hausdorff dimension $5/4$ of SLE$_2$ and the expected scaling of loop-erased random walk; the critical value is not addressed.