Basmajian–Hakobyan–Pandazis–Šarić strong Kahn–Marković conjecture

Let $X(\{\ell_n\},\{t_n\})$ be a flute surface whose cuff lengths form a non-decreasing sequence $\{\ell_n\}$, and let each twist parameter satisfy $t_n\in\{0,1/2\}$. Strong Kahn–Marković conjecture. For every non-decreasing sequence of lengths $\{\ell_n\}$, there is a choice of twists $t_n\in\{0,1/2\}$ such that $X(\{\ell_n\},\{t_n\})$ is parabolic. Since parabolicity is equivalent here to ergodicity of the geodesic flow on the unit tangent bundle, this is a stronger version of the Kahn–Marković conjecture; the supplied text gives no resolution.