Simplicity conjecture for multiplicity modules of graded double affine Hecke algebras

For a simple perverse sheaf $\mathcal{S}$ in the block $\mathcal{D}_{G_{\underline0}}(\mathfrak{g}^{nil}_{\underline\eta})_{\xi}$, define

[\mathbb{I}_{\xi}:\mathcal{S}]=\bigoplus_{[\mathfrak{p}_{*}]\in\underline\mathfrak{P}^{\xi}}[{}^{p}\operatorname{H}\mathbf{I}_{[\mathfrak{p}_{*}]}:\mathcal{S}].

By the preceding corollary, this is a module for $\mathbb{H}_{c,\eta/m}(W_{\mathrm{aff}}^{\xi})$. Simplicity conjecture. In the notation above, $[\mathbb{I}_{\xi}:\mathcal{S}]$ is a simple $\mathbb{H}_{c,\eta/m}(W_{\mathrm{aff}}^{\xi})\otimes_{\mathbb{Q}}\overline{\mathbb{Q}}_{\ell}$-module. This predicts that the multiplicity modules arising from simple perverse sheaves give simple modules for the graded double affine Hecke algebra; the supplied text does not state whether the conjecture is proved or remains open.