The spanning-tree and GFF scaling-limit conjecture for random triangulations

Let $(M,T,\phi_1,\phi_2)\in\mathcal M_n^\bullet$ be sampled from~, where $M$ is a triangulation, $T$ is a uniform spanning tree with wired boundary conditions, and $\phi_1,\phi_2$ are independent discrete zero-boundary Gaussian free fields on $M$. Let $P$ be the path traversing $T$ in contour (depth-first) order, starting and ending at a marked boundary vertex.

The spanning-tree and GFF scaling-limit conjecture. Under an appropriate scaling as $n\to\infty$, the 4-tuple $(M,P,\phi_1,\phi_2)$ converges in law to a unit boundary length $\sqrt{8/3}$-LQG disk together with an $\operatorname{SLE}_8$ curve starting and ending at the same marked boundary point and two independent zero-boundary GFFs.

This conjecture is motivated by the convergence of the triangulation to the free area Brownian disk, the discrete GFF to the continuum GFF, and the Peano curve of a uniform spanning tree to $\operatorname{SLE}_8$. The source does not state a resolution.