Rank-removal conjecture for adelic and arithmetic cohomology

Let $k$ be a number field, let $\mathbf{G}$ be a connected and simply connected almost simple $k$-algebraic group, and let $V$ be a unitary $\mathbf{G}(k)$-representation. Theorem~ gives its conclusion under the hypothesis $\operatorname{rank}_k\mathbf{G}\geq 2$. Rank-removal conjecture. The assumption

$$\operatorname{rank}_k\mathbf{G}\geq 2$$

can be removed from that theorem. This would extend the theorem's decomposition and cohomology-vanishing conclusions to all such groups; the source says that later results provide evidence but does not state a proof of the full removal.