Prasad–Chan same-group Ext conjecture for Arthur type representations

Let $F$ be a non-archimedean local field, let $\Delta\operatorname{SL}_2$ denote the diagonally embedded copy of $\operatorname{SL}_2$ in $\operatorname{SL}_2\times\operatorname{SL}_2$, and let ${\mathcal A}(\pi)$ be the Arthur parameter of an irreducible Arthur type representation $\pi$ of $\operatorname{GL}_n(F)$. Prasad–Chan's conjecture. For irreducible Arthur type representations $\pi_1$ and $\pi_2$ of $\operatorname{GL}_n(F)$,

$$\operatorname{Ext}^*_{\operatorname{GL}_n(F)}(\pi_1,\pi_2)\neq 0$$

if and only if

$${\mathcal A}(\pi_1)|_{W_F\times\Delta\operatorname{SL}_2}\cong {\mathcal A}(\pi_2)|_{W_F\times\Delta\operatorname{SL}_2}.$$

This conjecture characterizes nontrivial extensions between same-group irreducible Arthur type representations by equality of their Arthur parameters after restriction to the Weil group times the diagonal $\operatorname{SL}_2$; the source gives no resolution.