André's generalized Grothendieck p-curvature conjecture for geometric local systems

Let $\mathbb L$ be a geometric local system on a smooth variety $X$, with underlying vector bundle with connection $(E,\nabla)$. For all sufficiently large primes $p$, require that the reduction modulo $p$ admits a filtration whose associated graded is spanned by flat sections on a dense open subset of the reduction of $X$; equivalently, its $p$-curvature is nilpotent. André's generalized Grothendieck p-curvature conjecture. This condition characterizes geometric local systems $\mathbb L$. The source states that this conjecture has been proved by analytic methods as a corollary of Zuo's theorem.