Algebraicity and integrality for formal leaves of foliations

Let $R\subset\mathbb{C}$ be an integral domain finitely generated over $\mathbb{Z}$, let $(X,\mathscr{F})$ be a smooth scheme with a foliation over $R$, and let $x\in X(R)$. The leaf through $x_{\mathbb{C}}$ is algebraic, the leaf through $x$ is integral, and the leaf through $x$ is $\omega(p)$-integral. General foliation conjecture. These three conditions are equivalent. This refines the differential-equation conjecture from formal power-series solutions to algebraic leaves of horizontal foliations; the source does not indicate a resolution.