Cohomological smoothness conjecture for the non-very-special locus

Let $\mathscr{M}_{b,[\mu]}^\tau$ be the fixed-determinant fiber of the moduli diamond, and let $\mathscr{M}_{b,[\mu]}^{\tau,\mathrm{vsp}}$ be the very special locus, consisting of points whose intersection of the fibers of the Hodge–Tate and Hodge period maps is not isolated. Denote its open complement by

$$\mathscr{M}_{b,[\mu]}^{\tau,\mathrm{non\text{-}vsp}}.$$

Cohomological smoothness conjecture. The structure morphism

$$\mathscr{M}_{b,[\mu]}^{\tau,\mathrm{non\text{-}vsp}}\longrightarrow\operatorname{Spd}\mathbb{C}_p$$

is cohomologically smooth. This is the precise conjecture formulated for the non-very-special locus; the source’s abstract says that it is proved for EL infinite-level Rapoport–Zink spaces, whereas its general status is not resolved by the supplied excerpt.