Global occurrence conjecture for cohomological representations

Let $G$ be as above, and let $\pi=A_{\mathfrak q}$ be a cohomological representation of $G$ such that

$$\mathfrak l_0\cong\mathfrak l'_0\oplus\mathfrak g_1,$$

where $\mathfrak l'_0$ is a compact Lie algebra and $\mathfrak g_1$ is a non-abelian Lie algebra of the same type as $\mathfrak g_0$. Global occurrence conjecture. There exists a congruence subgroup $\Gamma\subset G$ such that $\pi$ occurs discretely in $L^2(\Gamma\backslash G)$. The immediately preceding theorem proves a more detailed version under additional hypotheses, while the conjectural statement is attributed to the cited results and the automorphic-isolation conjecture; its general status is open.