Dwork's conjecture on globally nilpotent rank-two bundles

Let $\overline{C}$ be a smooth projective curve of genus $0$ defined over a number field, and let $({\mathcal E}, \nabla)$ be a flat vector bundle of rank $2$ which is globally nilpotent. Dwork's conjecture. Either the monodromy group of ${\mathcal E}$ is commensurable to a triangle group or ${\mathcal E}$ has an algebraic solution. The paper states that its Teichmüller-curve constructions provide counterexamples to Dwork's conjecture, so the asserted dichotomy does not hold in general.