The uniform spanning tree scaling conjecture to infinite canonical super-Brownian motion

Let $d>4$. For each $r\geq2$, let $\rho^{(\mathrm{st})}_{\vec n}(\vec x)$ denote the uniform spanning tree $r$-point function, with time coordinates given by distances in the tree from the origin. The constants $A,V,v$ and $\delta\in(0,1)$ are those in (rhoscal).

Uniform spanning tree scaling conjecture. There exist constants $A,V,v$ and $\delta\in(0,1)$ such that (rhoscal) holds for $\rho^{(\mathrm{st})}$.

This conjectures that the uniform spanning tree has ICSBM as its scaling limit above dimension $4$. The motivation is Wilson's construction and the diffusive scaling of loop-erased random walk in dimensions greater than $4$, but the required multi-point convergence is left open.