Classical Zilber–Pink conjecture for mixed Shimura varieties

Let $X \stackrel{\iota}{\hookrightarrow} {\mathcal S}$ be a closed irreducible algebraic subvariety of a mixed Shimura variety ${\mathcal S}$. Let $\mathrm{HL}(X,\iota)_{\mathrm{atyp}}$ denote the atypical Hodge locus associated with the inclusion $\iota$. Zilber–Pink conjecture. The atypical Hodge locus

$$\mathrm{HL}(X,\iota)_{\mathrm{atyp}}$$

is not Zariski-dense in $X$. This is the classical mixed-Shimura formulation, and the source explains that the conjecture for variations of mixed Hodge structures of mixed Shimura type reduces to it. Its resolution status is not established by the supplied text.