Vogan's conjecture on unipotent Harish-Chandra modules

Let $G_{\mathbb{R}}$ be a real reductive group with maximal compact subgroup $K$, complexified Lie algebra $\mathfrak{g}$, and associated decomposition $\mathfrak{g}=\mathfrak{k}\oplus\mathfrak{p}$. Let $X$ be a unipotent Harish-Chandra module, let $\operatorname{AV}(X)\subset(\mathfrak{g}/\mathfrak{k})^*$ be its associated variety, and suppose that $\operatorname{AV}(X)$ contains a single open $K$-orbit $\mathcal{O}\subset\operatorname{AV}(X)$ satisfying

$$\operatorname{codim}(\operatorname{AV}(X)\setminus\mathcal{O},\operatorname{AV}(X))\geq 2.$$

Let $\mathcal{E}\to\mathcal{O}$ be the associated $K$-equivariant vector bundle. Vogan's conjecture. There is an isomorphism

$$X\cong_K\Gamma(\mathcal{O},\mathcal{E})$$

of representations of $K$. Vogan's conjecture asserts that, under these conditions, the equivariant vector bundle determines the unipotent Harish-Chandra module. The source presents this as Vogan's conjecture; its resolution is not specified here.