The conformal embedding convergence conjecture for random planar maps

For each $n\in{\bf N}$, let $M_n$ be a random planar map sampled as in the planar-map model above, and embed it into $\mathbbm S^2$ or a subset of $\mathbbm C$ by a discrete conformal embedding. The embedding induces an area measure and a metric on the target surface. Conformal embedding convergence conjecture. The induced area measure and metric converge in the scaling limit to the area measure and metric, respectively, associated with $\gamma$-LQG. This is a conjectural continuum-limit statement for conformally embedded random planar maps. The supplied context does not indicate a general proof, and convergence of metric properties is described as particularly poorly understood.