Supercuspidality criterion for unitary-group L-packets

Let $F$ be a local field, let $\phi:\operatorname{WD}_F\to\operatorname{GL}_n(\mathbb{C})$ be an $L$-parameter of the unitary group $\mathrm{U}(V^{\pm})$, and let $\Pi_{\phi}$ be its $L$-packet. A parameter is discrete when it has the discrete nature required for the corresponding packet, and $\operatorname{SL}_2(\mathbb{C})$ denotes the indicated factor of the Weil–Deligne parameter.

Unitary-group supercuspidality conjecture. The packet $\Pi_{\phi}$ consists of supercuspidal representations if and only if $\phi$ is discrete and its restriction to $\operatorname{SL}_2(\mathbb{C})$ is trivial.

The conjecture is motivated by known criteria for symplectic and special orthogonal groups and is proposed here for unitary groups. The source does not state a resolution, so its status remains open.