Conjecture that the display-to-local-Shimura comparison morphism is an isomorphism

Assume that the Bültel–Pappas moduli functor is representable, and let $(\mathcal{M}^{\operatorname{BP}})_\eta$ be its generic fibre over $\operatorname{Spa}(\breve{E})$. Restrict this sheaf and the local Shimura variety $\operatorname{Sh}_K$ to the category of smooth complete affinoid adic spaces over $\operatorname{Spa}(\breve{E})$. The comparison morphism of sheaves

$$\Upsilon^{\mathrm{sm}}\colon (\mathcal{M}^{\operatorname{BP}})_\eta\!\mid_{\operatorname{SmAffd}_{\operatorname{Spa}(\breve{E})}}\rightarrow \operatorname{Sh}_K\!\mid_{\operatorname{SmAffd}_{\operatorname{Spa}(\breve{E})}}$$

Comparison-isomorphism conjecture. The morphism $\Upsilon^{\mathrm{sm}}$ is an isomorphism.

This predicts that the generic fibre of the Bültel–Pappas display moduli problem agrees with the associated local Shimura variety on smooth affinoid adic spaces. The source supplies no resolution status, so it is recorded as open.