Jet Ax-Schanuel conjecture for Shimura varieties

Let $\pi:\mathbb{H}\rightarrow S$ be the uniformizing maps of a Shimura variety $S$ corresponding to a semisimple group $G$. Let $k\geq 2$ and let $V\subset J_k\mathbb{H}\times J_kS$ be a Shimura variety whose projection to $S$ is not contained in a weakly special subvariety. Assume moreover that, for a generic point $v\in V$, the projection of $v$ to $J_1S$ does not lie in the image of any weakly special subvariety. Let $U$ be a positive-dimensional component of $V\cap\Gamma^S_k$. Jet Ax-Schanuel conjecture. Then

$$\dim V=\dim U+\dim G.$$

This is a proposed derivative version of Ax-Schanuel for general Shimura varieties, motivated by the corresponding dimension calculation for $S=\mathcal{A}_g$. The source gives no resolution status.