Theta-packet induction irreducibility conjecture

Let $\psi$ be a local $A$-parameter with non-bounded Weil-group image that is a localization of a global elliptic $A$-parameter. Write

$$\psi=(\psi_{\tau_1}|\cdot|^{s_1}+\cdots+\psi_{\tau_r}|\cdot|^{s_r})+\psi_0+\left((\psi_{\tau_1}|\cdot|^{s_1}+\cdots+\psi_{\tau_r}|\cdot|^{s_r})^c\right)^\vee,$$

with $s_1\geq\cdots\geq s_r>0$, and let $\psi_0$ be a local $A$-parameter for $G_0$. For $\pi_0\in\Pi_{\psi_0}^\theta(G_0)$, define

$$I(\pi_0)=\operatorname{Ind}_P^G\left(\tau_1|\det|^{s_1}\boxtimes\cdots\boxtimes\tau_r|\det|^{s_r}\boxtimes\pi_0\right).$$

Theta-packet induction conjecture. The representation $I(\pi_0)$ is irreducible for every $\pi_0\in\Pi_{\psi_0}^\theta(G_0)$. Moreover, if $I(\pi_0)\simeq I(\pi'_0)$ for $\pi_0,\pi'_0\in\Pi_{\psi_0}^\theta(G_0)$, then $\pi_0\simeq\pi'_0$. This conjecture predicts irreducibility and injectivity of the indicated parabolic induction, extending the packet construction beyond bounded local parameters; no resolution is given in the source.