The unoriented percolation incipient infinite cluster scaling conjecture

Let $d>6$. For each $rgeq 2$, let $\vec{t}=(t_1,\ldots,t_{r-1})\in\mathbb{R}^{r-1}$ and $\vec{k}\in\mathbb{R}^{d(r-1)}$. Let $\rho^{(\mathrm{pe})}_{\vec{n}}(\vec{x})$ denote the unoriented percolation incipient infinite cluster $r$-point function, with graph-distance time coordinates defined by shortest occupied paths. The constants $A,V,v$ and $\delta\in(0,1)$ are those occurring in the scaling relation (rhoscal).

Unoriented percolation scaling conjecture. There exist constants $A,V,v$ and $\delta\in(0,1)$ such that the scaling relation (rhoscal) holds for $\rho^{(\mathrm{pe})}$.

This conjectures convergence of the unoriented percolation incipient infinite cluster's moment measures to those of ICSBM above the percolation upper-critical dimension. The preceding text states that the relevant incipient infinite cluster measure exists, but the scaling limit remains unproved.