Orbit-Method description of the unitary dual for real reductive groups

Let $G_{\mathbb{R}}$ be a real reductive group. Let $\Pi_u(G_{\mathbb{R}})$ be the set of equivalence classes of irreducible unitary $G_{\mathbb{R}}$-representations, and let $\Pi_0(G_{\mathbb{R}})$ be the corresponding set of birationally rigid unipotent representations. For every Levi subgroup $L_{\mathbb{R}}$ of $G_{\mathbb{R}}$, let $I(\Pi_0(L_{\mathbb{R}}))$ denote the representations obtained from these representations by the stated sequence of real parabolic induction, unitarity-preserving cohomological induction, generalized complementary-series constructions, and extraction of direct summands. Orbit-Method conjecture. There is an equality

$$\Pi_u(G_{\mathbb{R}})=\bigcup_{L_{\mathbb{R}}\subset G_{\mathbb{R}}}I(\Pi_0(L_{\mathbb{R}})),$$

where the union runs over all $G_{\mathbb{R}}$-conjugacy classes of Levi subgroups of $G_{\mathbb{R}}$. This conjecturally describes the entire unitary dual by starting with birationally rigid unipotent representations of Levi subgroups and applying the three unitary-preserving procedures. The source leaves the generalized complementary-series construction imprecise and presents the equality as conjectural; no resolution is given.