The maximal Fourier-coefficient attainment conjecture

Let $G$ be an $F$-quasisplit classical group, let $\psi\in\widetilde\Psi_2(G)$ be a global Arthur parameter, and let $\widetilde\Pi_\psi(\epsilon_\psi)$ be its automorphic $L^2$-packet. Let $\underline p(\psi)$ be the partition attached to $(\psi,G^\vee(\mathbb C))$. Maximal Fourier-coefficient attainment conjecture. There exists some $\pi\in\widetilde\Pi_\psi(\epsilon_\psi)$ such that

$$\mathfrak n^m(\pi)=\eta_{\mathfrak g^\vee,\mathfrak g}(\underline p(\psi)).$$

Thus the upper bound in the preceding conjecture should be achieved by a member of every relevant packet. The source notes that this is proved for simple global Arthur parameters for $F$-split classical groups, but leaves the general assertion open.