Lytchak's boundary-open-set conjecture for CAT(0) spaces

Let $X$ be a locally compact CAT(0) space with a geometric group action. Write $\partial_T X$ for its Tits boundary. Lytchak's conjecture. Then $\partial_T X$ contains a relatively compact open subset. This conjecture is presented as a generalization of the preceding theorem, which establishes such an open subset under the additional presence of a periodic flat. Its general validity remains open.