Conjecture on representability of integral local Shimura varieties

Let $(G,\mu,b)$ be an integral local Shimura datum. Denote by \mathcal{M}^{\textup{\int}}_{(G,\mu,b)} the integral model for the local Shimura variety at hyperspecial level. Representability conjecture. The space \mathcal{M}^{\textup{\int}}_{(G,\mu,b)} is representable by a smooth formal scheme. The paper presents this as one of the conjectures resolved for an infinite family of non-Abelian-type Shimura data, but the supplied status is unknown.