Flatness conjecture for pseudo-maximal spin local models

Let $F$ be a discretely valued field with ring of integers $\CO$, let $k$ be its residue field, and let $n\geq 1$. For a non-empty subset $I\subset[0,n]$, let $\Lambda_I$ be the associated standard self-dual lattice chain and let $\RM_I^\pm=\RM^\pm_{\Lambda_I}$ be its spin local model. Flatness conjecture. For any non-empty subset $I\subset[0,n]$, the spin local model $\RM_I^\pm$ is flat over $\CO$. This is the standard-chain formulation of the flatness problem, and it is equivalent to the corresponding assertion for arbitrary self-dual lattice chains after conjugacy. The supplied text gives no resolution of the conjecture.