André's nilpotency conjecture for algebraic connections

Let $U$ be a smooth complex curve, and let $(V,\nabla)$ be an irreducible algebraic connection on $U$. Suppose that there is a spreading-out $({\mathcal U},{\mathcal V},\nabla)$ of $(U,V,\nabla)$ over $S$ such that $({\mathcal V},\nabla)$ is globally nilpotent.

André's nilpotency conjecture. Then $(V,\nabla)$ is motivic.

This is described as a nilpotency conjecture communicated by H. Esnault and attributed in the source to André. The source notes that André's version assumes $U$ is defined over $\bar{\mathbb Q}$ and requires nilpotent $p$-curvature only at a density-one set of primes, so the cited version is stronger than the global-nilpotency formulation here.