Chudnovsky–Chudnovsky conjecture on globally nilpotent indigenous bundles

Let $\overline{C}$ be a smooth projective curve defined over a number field. Let $({\mathcal E}, \nabla)$ be an indigenous bundle on $\overline{C}$, and let $\Gamma\subset \operatorname{PSL}_2(\mathbb{R})$ be the monodromy group of ${\mathcal E}$. Suppose that ${\mathcal E}$ is globally nilpotent. Chudnovsky–Chudnovsky conjecture. Then $\Gamma$ is either arithmetic or commensurable to a triangle group. The paper presents Teichmüller-curve examples whose associated bundles are globally nilpotent while their monodromy groups are neither arithmetic nor commensurable to triangle groups, explicitly producing counterexamples to this conjecture.