Ogus' principle for Hodge-type Shimura varieties

Consider a Hodge-type Shimura variety $S_K$ over a field of characteristic $p$ with universal family of abelian schemes $Y/S_K$, and let $H^g_{{\rm dR}}(Y/S_K)=\wedge^gH^1_{{\rm dR}}(Y/S_K)$ be its Calabi–Yau-type $F$-Zip. Let $k$ be an algebraically closed field containing the residue field, let $\mu$ be the associated cocharacter, and write $\operatorname{ord}_x$ for the vanishing order at $x$ and $\mathsf{clp}_x$ for the corresponding co-length of the Hodge filtration.

Ogus' principle. Assume that the conjugacy class of $\mu$ is defined over $\mathbf{F}_p$. For every $x\in S_K(k)$,

$$\operatorname{ord}_x \mathrm{Ha}(H^g_{{\rm dR}}(Y/S_K))=\mathsf{clp}_x H^g_{{\rm dR}}(Y/S_K).$$

This proposes that the vanishing order of the classical Hasse invariant at every point equals the co-length of the Hodge filtration. It extends the expected relationship between Hasse invariants and Frobenius–Hodge-filtration geometry to Hodge-type Shimura varieties; the supplied context does not state whether the principle has been proved or remains open.