Gromov's quadratic Dehn function conjecture for higher-rank arithmetic groups

Let $\mathbf{G}$ be the algebraic group over the global field $K$ and let $S$ be the specified finite set of places, with ring of $S$-integers $\mathcal{O}_S$. Write

$$k(\mathbf{G},S)=\sum_{v\in S}\operatorname{rank}_{K_v}(\mathbf{G})$$

for the geometric rank, and let the Dehn function measure the minimum filling area of null-homotopic words in $\mathbf{G}(\mathcal{O}_S)$. Gromov's conjecture. If $k(\mathbf{G},S)\geq 3$, then the Dehn function of $\mathbf{G}(\mathcal{O}_S)$ is quadratic. This conjecture extends a conjecture of Gromov and concerns the isoperimetric behavior of higher-rank arithmetic groups. The source presents it as a conjecture; no resolution is supplied here.