The maximal and minimal Arthur-parameter conjecture

Let $G$ be a reductive group and let $\pi$ be an irreducible admissible representation of $G$. Define $\Psi(\pi)=\\{\psi\in\Psi^+(G)\mid \pi\in\Pi_\psi\\}$, let $\phi_\psi$ be the associated $L$-parameter, and let $\lambda_{\phi_\psi}$ be its infinitesimal parameter. The maximal and minimal Arthur-parameter conjecture. For any $\psi_1,\psi_2\in\Psi(\pi)$, one has $\lambda_{\phi_{\psi_1}}=\lambda_{\phi_{\psi_2}}$. Moreover, there are $\psi^{\max}(\pi),\psi^{\min}(\pi)\in\Psi(\pi)$ such that

$$\psi^{\max}(\pi)\geq_C\psi\geq_C\psi^{\min}(\pi)$$

for every $\psi\in\Psi(\pi)$.