Chudnovsky and Chudnovsky's conjecture on globally nilpotent Lamé equations

Consider Lamé equations with parameter $n=-\frac{1}{2}$ defined over $\overline{\mathbb{Q}}$, and the four classes numbered $1,2,3,4$ above. Chudnovsky and Chudnovsky's conjecture. Such Lamé equations are not globally nilpotent, except for the four classes listed as $1,2,3,4$. This conjecture concerns the classification of globally nilpotent Lamé equations and was stated using computer-aided computations; the source gives no resolution status.