Vogan's strong-stability basis conjecture

Let $F$ be a local field, let $G$ be a quasi-split connected reductive linear algebraic group over $F$, let $\lambda\in\Lambda({}^LG)$ be an infinitesimal parameter, and let $H_\lambda$ act on $V_\lambda$. For an $H_\lambda$-orbit $C\subseteq V_\lambda$, let $\eta^{\operatorname{Evs}}_C$ be the virtual representation defined by the microlocal construction, and call a virtual representation strongly stable if it is strongly stable in Vogan's sense. Vogan's strong-stability basis conjecture. Each $\eta^{\operatorname{Evs}}_C$ is strongly stable, and the collection $\{\eta^{\operatorname{Evs}}_C\mid C\subseteq V_\lambda\text{ an }H_\lambda\text{-orbit}\}$ is a basis for the Grothendieck group of strongly stable virtual representations with infinitesimal character $\lambda$. The paper identifies this with an adaptation of Vogan's conjecture; the supplied text does not state that it is proved.