The scaling-limit conjecture for critical Fortuin–Kasteleyn planar maps

Let $q\text{-FK}$ planar maps denote the critical Fortuin–Kasteleyn planar maps with parameter $q$, and let $\gamma$ be a parameter in $[\sqrt 2,2)$ satisfying

$$q=2+2\cos\left(\frac{\gamma^2\pi}{2}\right).$$

Scaling-limit conjecture. When $0\leq q\leq4$, the $q$-FK planar map converges in the scaling limit to a $\gamma$-Liouville quantum gravity surface. When $q>4$, it converges in the scaling limit to the continuum random tree.