The parahoric dependence conjecture for Rapoport–Zink spaces

Let $\mathcal{D}_{\mathbb{Z}_p}$ be an integral Rapoport–Zink datum such that $\mathcal{G}$ is a parahoric group scheme. The associated rigid space is equipped with an action of $J_b(\mathbb{Q}_p)$. Parahoric dependence conjecture. Up to isomorphism, this rigid space with its $J_b(\mathbb{Q}_p)$-action depends on $\mathcal{D}_{\mathbb{Z}_p}$ only through the quadruple $(G,[b],\{\mu\},\mathcal{G})$. This conjecture expresses the expected dependence of Rapoport–Zink spaces on the corresponding local Shimura datum; the source notes that it is known in most EL cases.