The intersection-cohomology ordinariness conjecture

Let $X$ be a projective variety over a number field $F$, let $n$ be an integer, and let $F^s$ be a separable closure of $F$. For every prime number $\ell$, consider the Newton polygon $\operatorname{NP}(\operatorname{Frob}_{\mathfrak{p}}|_{IH^n(X\otimes_FF^s,\mathbb{Q}_{\ell})})$ and the Hodge–Tate polygon $\operatorname{HTP}(IH^n(X\otimes_FF^s,\mathbb{Q}_{\ell}))$.

Intersection-cohomology ordinariness conjecture. For every prime number $\ell$, there exists an infinite set of maximal ideals $\mathfrak{p}$ of $\mathscr{O}_F$ with residue characteristic different from $\ell$ such that

$$\operatorname{NP}(\operatorname{Frob}_{\mathfrak{p}}|_{IH^n(X\otimes_FF^s,\mathbb{Q}_{\ell})})=\operatorname{HTP}(IH^n(X\otimes_FF^s,\mathbb{Q}_{\ell})).$$

This is presented as the analogue of the ordinariness conjecture for intersection cohomology. The source provides partial verification in special motivic settings but no general resolution.