Oort's Hecke orbit conjecture for principally polarized abelian varieties

Let $p>0$, let $g$ be a positive integer, and let $x=\left[\left(A_x,\lambda_x\right)\right]$ be a $\overline{\mathbb{F}}_p$-point of the moduli space $\mathcal{A}_g$ of $g$-dimensional principally polarized abelian varieties in characteristic $p$. Denote by $\mathcal{H}(x)$ the Hecke orbit of $x$, and by the Newton polygon stratum containing $x$ the corresponding locally closed subvariety of $\mathcal{A}_g$. Oort's Hecke orbit conjecture. The Hecke orbit $\mathcal{H}(x)$ is Zariski dense in the Newton polygon stratum of $\mathcal{A}_g$ which contains $x$. This is the original formulation of the Hecke orbit conjecture, predicting that Hecke symmetries characterize the central foliation. The statement has been proved in various settings by a series of papers.