Arithmetic lattice discreteness conjecture for subgroups generated by unipotent elements

Let $n$ be a positive integer, set $G=\operatorname{SL}_n(\mathbb R)$ and $\Gamma=\operatorname{SL}_n(\mathbb Z)$, and let $W\subset\operatorname{SL}_n(\mathbb Q)$ be a closed subgroup of $G$ contained in the Zariski closure of a subgroup generated by $\operatorname{Ad}_G$-unipotent elements of $W$.

Arithmetic lattice discreteness conjecture. If $W\Gamma$ is discrete, then $W\cap\Gamma$ has finite index in $W$.

The paper presents this as a typical higher-rank case to which the preceding conjecture can be reduced. A footnote records that Alex Eskin and G. A. Margulis had informed the author that they could prove it, but the supplied status is not resolved, so it is retained as open.