Pappas–Rapoport flatness conjecture for orthogonal spin local models

Let $F$ be a complete discretely valued field with ring of integers $\mathcal{O}$, uniformizer $\pi$, and residue field $k$ of characteristic $p>2$. Let $V=F^{2n}$ with a split non-degenerate symmetric bilinear form, let $G=\operatorname{GO}(V,\psi)$, and let $\mathcal{L}$ be a self-dual periodic lattice chain. The naive local model $\mathcal{M}^{\mathrm{naive}}_{\mathcal{L}}$ has generic fiber the orthogonal Grassmannian $\operatorname{OGr}(n,2n)_F$, and the spin local model $\mathcal{M}^{\pm}_{\mathcal{L}}$ is the closed subscheme defined by the spin $\pm$-condition. Pappas–Rapoport's conjecture. The spin local model $\mathcal{M}^{\pm}_{\mathcal{L}}$ is flat over $\mathcal{O}$. This conjecture proposes that the spin condition corrects the non-flatness of the naive local model for split even orthogonal similitude groups at arbitrary parahoric level. The source does not state whether the conjecture is resolved.