Formal meta-conjecture for Picard–Fuchs equations

Let $R\subset\mathbb{C}$ be a finitely generated $\mathbb{Z}$-algebra, let $f:X\to S$ be a smooth proper morphism of smooth $R$-schemes, fix $s\in S(R)$, and let $\widehat{S}$ and $\widehat{S}_{\mathscr{K}}$ be the formal completions at $s$ and at $s_{\mathscr{K}}$, where $\mathscr{K}$ is the fraction field of $R$. Let $(\mathscr{E},\nabla)$ be a Picard–Fuchs equation and suppose it admits an $\omega(p)$-integral formal isomonodromic deformation over $\widehat{S}$. Formal meta-conjecture. The formal isomonodromic deformation of $(\mathscr{E},\nabla)$ to $\widehat{S}_{\mathscr{K}}$ has property $P$, where $P$ is a property of flat bundles arising as a summand of algebraic de Rham cohomology of a smooth projective family. The source presents this as a consequence of the main conjecture together with the variational meta-conjecture; no general resolution is given.