The $2\pi$-circle splitting conjecture for CAT(0) boundaries

Let $G$ be a one-ended group acting geometrically on a CAT(0) space $X$, and let $\partial X$ denote its boundary. Assume that $\partial X$ has no finite cut and that a circle of Tits length $2\pi$ separates $\partial X$. $2\pi$-circle splitting conjecture. Either $G$ is virtually $\pi_1S\times\mathbb{Z}$, where $S$ is a closed surface, or $G$ splits over a group virtually isomorphic to $\mathbb{Z}^2$. This conjecture seeks to detect algebraic splittings from separating Tits circles in CAT(0) boundaries; its status is not resolved in the supplied source.