Algebraicity of the Hodge locus in level at least three

Let ${\mathbb V}$ be a polarizable $\mathbb{Z}$-variation of Hodge structures on a smooth connected complex quasi-projective variety $S$. The level of ${\mathbb V}$ is the number of nontrivial steps in its Hodge filtration.

Algebraicity conjecture in high level. If ${\mathbb V}$ has level at least $3$, then $\operatorname{HL}(S, {\mathbb V}^{\otimes})$ is algebraic.

In the supplied context, this statement is presented as following from the strong Zilber–Pink conjecture together with a theorem excluding typical special subvarieties in level at least three. The candidate itself is marked with unknown status.