Griffiths' conjecture on simultaneous normalization of periods

Let $f:\mathfrak{X}\to S$ be an algebraic family of polarized algebraic manifolds over a quasi-projective manifold $S$, with period map $\Phi:S\to\Gamma\backslash D$ and lifted period map $\widetilde{\Phi}:\widetilde{S}\to D$ on the universal cover $\widetilde{S}$ of $S$. For each $s\in S$, let $\Phi(X_s)$ denote the period of the fiber $X_s=f^{-1}(s)$. Griffiths' conjecture. There exists a simultaneous normalization of all the periods $\Phi(X_s)$ for $s\in S$; more precisely, the image $\widetilde{\Phi}(\widetilde{S})$ lies in a bounded domain in a complex Euclidean space. This conjecture concerns the simultaneous normalization of period maps arising from geometry. The cited context presents it as Griffiths' Conjecture 10.1; the supplied text does not state whether it has been resolved.