The tempered L-packet conjecture for unitary groups

Let $F$ be a local field and let ${\rm U}_N(F)$ be a unitary group. A Langlands parameter is a homomorphism

$$\phi:\mathcal{W}_F'\longrightarrow{}^L{\rm U}_N.$$

A parameter is tempered when its image in ${\rm GL}_N(\mathbb{C})$ is bounded, and let $\Pi_\phi$ denote the associated finite multi-set of representations. Tempered L-packet conjecture. If an $L$-packet contains a tempered element, then all of its elements are tempered. Moreover, every tempered $L$-packet $\Pi_\phi$ of ${\rm U}_N(F)$ contains a representation $\pi_0$ that is generic. The conjecture is used to reduce the study of local gamma-, $L$-, and epsilon-factors to generic representations; the surrounding discussion says that it is known in characteristic zero and is part of work addressing the positive-characteristic case.