Vector-bundle-injection conjecture for the infinitesimal period map

Let $(f:V\to U,\mathcal{L})\in\mathcal{M}_h(U)$ be the polarized family referred to in Theorem, and let $S$ and $T$ be the loci appearing there. Vector-bundle-injection conjecture. The map

$$(\rho^{n-1,1}\otimes\iota)\circ\tau^{n,0}$$

is a vector bundle injection at every point of $U\setminus(S+T)$.

This assertion concerns the infinitesimal period-map data associated with a polarized family. The source supplies no further context establishing whether the claim is proved or remains open.