Vogan's exhaustion conjecture for unitary Harish-Chandra modules of U(p,q)

Let $U(p,q)$ be the real reductive group of unitary matrices of signature $(p,q)$, and let $A_\mathfrak{q}(\lambda)$ denote a cohomologically induced module in the weakly fair range. A unitary Harish–Chandra module has an infinitesimal character that is a weight-translate of $\rho$ when its infinitesimal character is obtained from $\rho$ by a weight translation. Vogan's conjecture. The cohomologically induced modules $A_\mathfrak{q}(\lambda)$ in the weakly fair range exhaust the unitary Harish–Chandra modules for $U(p,q)$ whose infinitesimal character is a weight-translate of $\rho$. This concerns the classification of unitary representations of $U(p,q)$ at integral, possibly singular, infinitesimal characters; the source presents it as a conjecture and gives no resolution here.