The open-parameter conjecture for generic ABV-packets

Let $G$ be any quasi-split reductive group over a $p$-adic field $F$, and let $\phi$ be a local Langlands parameter of $G$. An open parameter is a parameter whose orbit is open in the relevant Vogan variety. Open-parameter conjecture for ABV-packets.

$$\Pi^{\mathrm{ABV}}_\phi(G) \text{ contains a generic representation if and only if } \phi \text{ is open}.$$

This generalizes the Gross–Prasad–Rallis and enhanced Shahidi conjectures to ABV-packets without assuming that the parameter is of Arthur type; the paper presents it as conjectural.