Pappas–Rapoport spin-condition conjecture for symplectic local models

Let ${\mathcal L}$ be a periodic self-dual lattice chain for the group and cocharacter under consideration. The spin local model $M^{\mathrm{spin}}_{G,\{\mu\},{\mathcal L}}$ is defined by imposing the spin condition on the naive local model.

Pappas–Rapoport spin-condition conjecture. For any periodic self-dual lattice chain ${\mathcal L}$,

$$M^{\mathrm{spin}}_{G,\{\mu\},{\mathcal L}}=M^{\mathrm{loc}}_{G,\{\mu\},{\mathcal L}},$$

that is, $M^{\mathrm{spin}}_{G,\{\mu\},{\mathcal L}}$ is flat over $\operatorname{Spec}{\mathcal O}_F$.

The spin condition is intended to provide a moduli-theoretic description of the flat closure defining the local model. The cited work proposes this equality; the supplied source gives no resolution status.