Igusa-stack conjecture for Shimura varieties

Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum satisfying $\operatorname{rank}_{\mathbb Q}(\mathsf{Z}^\circ)=\operatorname{rank}_{\mathbb R}(\mathsf{Z}^\circ)$, let $\Xi$ denote the relevant Igusa datum, and let $\mathscr{S}_{K_p}(\mathsf{G},\mathsf{X})^\diamond$ be the infinite-level diamond associated with the integral models. Let $\mathrm{Sht}_{\mathcal{G},\mu,\delta=1}$ and $\mathrm{Bun}_{G,\mu^{-1}}$ be the indicated shtuka and bundle substacks. Igusa-stack conjecture. There is a small v-sheaf $\mathrm{Igs}_{\Xi}(\mathsf{G},\mathsf{X})$ over $\operatorname{Spd}\mathbb F_p$, equipped with an action of $\mathsf{G}(\mathbb A_f^p)$ and an invariant map $\overline{\pi}_{\mathrm{HT}}:\mathrm{Igs}_{\Xi}(\mathsf{G},\mathsf{X})\to\mathrm{Bun}_{G,\mu^{-1}}$. For every quasi-parahoric model $\mathcal{G}$ of $G$ with $K_p=\mathcal{G}(\mathbb Z_p)$, there is an equivariant map $q_{\mathrm{Igs}}:\mathscr{S}_{K_p}(\mathsf{G},\mathsf{X})^\diamond\to\mathrm{Igs}_{\Xi}(\mathsf{G},\mathsf{X})$ making the displayed square with $\pi_{\mathrm{crys}}$ and $\mathrm{BL}^{\circ}$ $2$-commutative and $2$-Cartesian; the construction is functorial in morphisms of Shimura data and compatible with the diagram. The conjecture is presented as the good-reduction version of Zhang's conjecture, with the additional SV5 assumption and quasi-parahoric models; its general status is not resolved in the source.