Mixed hybrid conjecture for universal abelian schemes

Let $A$ be an abelian variety over ${\mathbb C}$, and let $P\in A({\mathbb C})$. Let $H_{\Gamma}(A,P)$ be as in the definition referenced in the source, and let $\Sigma\subseteq H_{\Gamma}(A,P)$ be a subset. Let $V\subseteq \overline{\Sigma}^{\operatorname{Zar}}$ be an irreducible component, and let $S\subseteq {\mathbb A}_\Gamma$ be the image of $V$.

Mixed hybrid conjecture. (1) The subvariety $S\subseteq {\mathbb A}_\Gamma$ is weakly special. (2) If, for some $s\in S$, one has $V\cap (A_s)_{\operatorname{tors}}\neq\varnothing$, then there exist $d\in {\mathbb Z}_{\geq 1}$ and an abelian subscheme $\mathcal{B}\leq \mathcal{A}_\Gamma|_S$ such that

$$d\cdot V=\mathcal{B}.$$

Equivalently, $V$ is an irreducible component of

$$\mathcal{B}+\mathcal{A}_\Gamma|_S[d].$$

(3) In general, if $\eta\in S$ is the generic point of $S$ and $V_\eta\subseteq \mathcal{A}_\eta$ is the fibre of $V\subseteq \mathcal{A}_\Gamma$ over $\eta$, then there exist $d\in {\mathbb Z}_{\geq 1}$, a morphism $\phi:A\to \mathcal{A}_\eta$, and an abelian subvariety $B\leq A_\eta$ such that

$$d\cdot V_\eta=\phi(P)+B\subseteq \mathcal{A}_\eta.$$

The first part is established by the cited theorem on the hybrid conjecture for ${\mathbb A}_\Gamma$; the torsion and general fibre assertions describe the remaining mixed hybrid conjecture. The supplied context does not establish their resolution.