Vogan's orbit method conjecture for real reductive groups

Let $G_{\mathbb R}$ be the real points of a connected reductive algebraic group, and let $\mathsf{Cov}^{i\mathbb R}(G_{\mathbb R})$ denote the real co-adjoint covers of $G_{\mathbb R}$. Let $\Pi_u(G_{\mathbb R})$ be the irreducible unitary representations of $G_{\mathbb R}$. For a real co-adjoint cover $\widetilde{\mathcal O}\in\mathsf{Cov}^{i\mathbb R}(G_{\mathbb R})$ satisfying a suitable integrality condition, Vogan's orbit method conjecture. There is an associated finite set of irreducible unitary representations

$$\Pi^{\mathsf{Kir}}_{\widetilde{\mathcal O}}(G_{\mathbb R})\subset\Pi_u(G_{\mathbb R}),$$

and

$$\bigcup_{\widetilde{\mathcal O}}\Pi^{\mathsf{Kir}}_{\widetilde{\mathcal O}}(G_{\mathbb R})$$

should exhaust most of $\Pi_u(G_{\mathbb R})$. This is a formulation of the orbit-method philosophy for unitary representation theory; the qualification “most” leaves the precise scope of the exhaustion assertion unresolved.