Moduli spaces of level structures on mixed characteristic local shtukas

We consider the flat moduli space of parahoric level structures on a local shtuka and show that it is representable over a smooth p-adic formal scheme by establishing the dilatation theory of v-sheaves. We apply this result to the canonical integral model of a Shimura variety at hyperspecial level and identify the flat moduli space of parahoric level structures with the canonical integral model at the corresponding parahoric level. We prove a similar result for integral models of local Shimura varieties.