Rapoport's non-emptiness conjecture for Newton strata of Hodge-type Shimura varieties

Let $G$ be unramified over $\mathbb Q_p$, let $K=K_pK^p$ be hyperspecial at $p$, and let $\Theta:\mathscr{S}_K(G,X)(\kappa(\wp))\to B(G)$ be the Newton-point map. Define

$$B(G_{\mathbb Q_p},X):=\left\{\overline{b}\in B(G_{\mathbb Q_p})\mid \kappa_{G_{\mathbb Q_p}}(\overline{b})=\mu^{\natural},\quad \overline{\nu}_{G_{\mathbb Q_p}}(\overline{b})\preceq \overline{\mu}(G,X)\right\}.$$

The Newton strata are the locally closed subvarieties $\mathcal{S}_{\overline{b}}=\Theta^{-1}(\overline{b})$ of $\mathscr{S}_K(G,X)\otimes\overline{\mathbb F}_p$. Rapoport's non-emptiness conjecture. Every element of $B(G_{\mathbb Q_p},X)$ occurs as the Newton point of a geometric point of the special fibre:

$$\operatorname{Im}(\Theta)=B(G_{\mathbb Q_p},X).$$

This asserts that every Newton stratum allowed by the Kottwitz invariant and Newton-point inequality is non-empty. The conjecture is solved: the $\mu$-ordinary case was proved by Wedhorn in the PEL-type setting and by Wortmann for general Hodge-type Shimura varieties, and the cited status evidence identifies the candidate as resolved.