The cyclicity conjecture for optimal covering maps

Let $\mathcal{M}$ be a geminal orbit closure, and let the optimal covering map associated with $\mathcal{M}$ be the covering map of minimal degree arising in the classification of such orbit closures. Cyclicity conjecture. The optimal covering map is a cyclic cover. The paper presents this as an open problem at its conclusion; the conjecture concerns the structure of optimal covering maps for geminal orbit closures.