Margulis' bounded diagonal orbit conjecture

Let $X_d=\mathrm{SL}_d(\mathbb{R})/\mathrm{SL}_d(\mathbb{Z})$ and let $A$ be the connected diagonal subgroup

$$A=\{\operatorname{diag}(e^{t_1},\ldots,e^{t_d}):t_1,\ldots,t_d\in\mathbb{R},\ \sum_{i=1}^d t_i=0\}.$$

An $A$-orbit is bounded if its image in $X_d$ is bounded. Margulis' conjecture. Every bounded $A$-orbit in $X_d$ is compact. This is the classical conjecture motivating the paper's refined statements about bounded cone orbits; the source does not state a resolution.