Weak Complex Ax conjecture, optimal components formulation

Let $X=Y(1)^n$ with uniformising map $\pi:\mathbb{H}^n\to X(\mathbb{C})$. For a subvariety $V\subseteq X$, a component is an irreducible component of $W\cap\pi^{-1}(V)$ for an algebraic subvariety $W\subseteq\mathbb{H}^n$. Its defect is

$$\delta(A)=\dim\operatorname{Zcl}(A)-\dim A.$$

A component is optimal for $V$ if no strictly larger component has defect at most $\delta(A)$; it is geodesic if it is a component arising from a weakly special $W=\operatorname{Zcl}(A)$. Weak Complex Ax conjecture. Every optimal component with respect to $V$ is geodesic. The source states that this formulation is formally equivalent to the preceding geometric formulation and records the analogous result for semi-abelian varieties, but does not establish the modular assertion.