Canonical integral models conjecture for quasi-parahoric Shimura varieties

Let $({\mathsf{G}}, {\mathsf{X}})$ be a Shimura datum satisfying the condition referred to as Eq. SV5, and let $\mathcal{G}/\mathbb{Z}_p$ be a quasi-parahoric model of $G$. Set

$$K_p=\mathcal{G}(\mathbb{Z}_p).$$

Canonical integral models conjecture. For every such Shimura datum and quasi-parahoric model, there exists a system of canonical integral models $\{\mathscr{S}_K({\mathsf{G}}, {\mathsf{X}})\}_{K^p}$ of $\{\mathbf{Sh}_K({\mathsf{G}}, {\mathsf{X}})\}_{K^p}$.

This extends the conjecture of Pappas and Rapoport from parahoric to quasi-parahoric groups. The source does not state a resolution, so the conjecture is recorded as open.