The invasion percolation scaling conjecture to infinite canonical super-Brownian motion

Consider invasion percolation on $\mathbb{Z}^d$ above dimension $6$. Let ICSBM denote infinite canonical super-Brownian motion, and let $\rho^{(\mathrm{ip})}_{\vec n}(\vec x)$ be the invasion-percolation $r$-point function defined using the minimal number of invaded bonds along paths from the origin. The constants and scaling relation are those specified by (rhoscal).

Invasion percolation scaling conjecture. For each $r\geq2$, $\vec t\in\mathbb{R}^{r-1}$ and $\vec k\in\mathbb{R}^{d(r-1)}$, there exist constants $A,V,v$ and $\delta\in(0,1)$ such that (rhoscal) holds for $\rho^{(\mathrm{ip})}$.

Equivalently, the conjecture says that the scaling limit of invasion percolation above dimension $6$ is ICSBM. The paper presents this as an open extension of the incipient-cluster scaling picture.