Conjecture on the intersection of Jiang and dual Arthur packets

Let $G_n$ be the group considered in the paper, let $\psi$ be a local Arthur parameter, let $\widetilde\Pi^J_\psi$ be the Jiang packet, let $\widehat\Pi_{\phi_{\widehat\psi}}$ be the dual of the local $L$-packet attached to the dual parameter, and let $\widetilde\Pi_\psi$ be the ambient packet. Packet-intersection conjecture. The sets $\widetilde\Pi^J_\psi$ and $\widehat\Pi_{\phi_{\widehat\psi}}$ have nonempty intersection. Moreover, if $\pi\in\widetilde\Pi_\psi$ is the unique representation such that $\widehat\pi\in\Pi_{\phi_{\widehat\psi}}$ corresponds to the trivial character of the component group of $\phi_{\widehat\psi}$, then $\pi\in\widetilde\Pi^J_\psi$. The conjecture relates Jiang packets to dual local $L$-packets and predicts a distinguished common representation. No resolution is given in the source.