Poisson boundary conjecture for totally strongly irreducible random walks

Let $E$ be a Euclidean space of dimension $d\geq 3$, and let $\nu$ be a totally strongly irreducible probability distribution supported on a discrete subgroup of $\mathrm{SL}(E)$. Assume that $\nu$ has finite entropy. Poisson boundary conjecture. The Poisson boundary of $\nu$ is isomorphic to $\mathrm{Fl}_{\Theta(\nu)}(E)$ endowed with the $\nu$-stationary probability distribution $F^\infty_*\nu^{\otimes\mathbb{N}}$. This would identify the Poisson boundary for the random walk with the stationary flag-space model under finite entropy and the stated irreducibility and discreteness assumptions; the source presents this as a statement to be proved, so its resolution remains open here.