Vogan's strengthened FPP conjecture for Hermitian modules

Let $G$ be a complex simple Lie group, and let $\pi$ be an irreducible, fully supported, Hermitian $(\mathfrak{g},K)$-module with real infinitesimal character $(\Lambda,-\Lambda)$ such that $\Lambda$ is dominant. Say that $\Lambda$ lies inside FPP if

$$\langle \Lambda, \beta_i^{\vee} \rangle \leq 1$$

for all simple roots $\beta_i$.

Vogan's strengthened FPP conjecture. Suppose $\Lambda$ does not lie inside FPP. Then $\pi$ is not unitary up to level $\mathfrak{p}$.

This is presented as a stronger version of the FPP conjecture for complex groups and concerns the reduction of the unitary dual for fully supported Hermitian modules. The supplied text does not state the resolution or scope of the proof for this strengthened formulation.