Pink–Zilber conjecture for curves in semiabelian schemes

Let $\mathcal{S}$ be a semiabelian scheme over a variety $\mathcal{Y}$ defined over $\mathbb{C}$, and let $V\subset \mathcal{S}$ be a curve which is not contained in any proper algebraic subgroup of $\mathcal{S}$. Define

$$\mathcal{S}^{[2]}:=\bigcup_{y\in\mathcal{Y}}B_y,$$

where $B_y$ is the union of all algebraic subgroups of the fibre $\mathcal{S}_y$ of codimension at least $2$.

Pink–Zilber conjecture. The intersection $V\cap\mathcal{S}^{[2]}$ is finite.

This is a special case of the Pink–Zilber unlikely-intersections conjecture, extending Manin–Mumford-type statements to families of algebraic subgroups in semiabelian varieties. Its status is not specified in the source.