Cassels–Swinnerton-Dyer–Margulis conjecture on bounded diagonal orbits

Let $D$ be the diagonal group of $\operatorname{SL}_n(\mathbb{R})$ where $n\ge 3$. A $D$-orbit in $\operatorname{SL}_n(\mathbb{R})/\operatorname{SL}_n(\mathbb{Z})$ is relatively compact when its closure is compact. Cassels–Swinnerton-Dyer–Margulis conjecture. Any relatively compact $D$-orbit in $\operatorname{SL}_n(\mathbb{R})/\operatorname{SL}_n(\mathbb{Z})$ is closed.

This conjecture concerns topological rigidity of diagonal actions on homogeneous spaces and was posed by Cassels and Swinnerton-Dyer for $n=3$ and by Margulis in general. Its status is not specified in the supplied text.