Thin-monodromy equality conjecture for the 14 Calabi–Yau hypergeometric systems

Consider the 14 rank-$4$ hypergeometric local systems that could arise as the middle cohomology of families of Calabi–Yau threefolds with $h^{2,1}=1$. For these systems, let

$$\sum_{i=1}^k \lambda_i \geq \frac{2\deg_{\rm par}({\mathcal E})}{2g(\overline{C})-2+|\Delta|}$$

be the Lyapunov-exponent inequality for a holomorphic rank-$k$ subbundle ${\mathcal E}$, where $\deg_{\rm par}$ is parabolic degree, $g(\overline{C})$ is the genus of the compactified base curve, and $|\Delta|$ is the number of cusps. Thin-monodromy equality conjecture. The inequality becomes an equality precisely in the seven of these fourteen cases for which the monodromy group is thin in the symplectic group. The conjecture identifies the equality cases of the Lyapunov bound among the listed Calabi–Yau-type systems; Simion Filip had announced a proof, but the source gives no definitive resolution.