Lytchak's Regular Point Conjecture for CAT(0) spaces

Let $X$ be a locally compact CAT(0) space with a geometric group action. A point in a metric space is regular if it has a neighborhood homeomorphic to an open set in a Euclidean space.

Lytchak's Regular Point Conjecture. The Tits boundary $\partial_T X$ contains a regular point.

The source describes this conjecture as completely open and identifies it as a general conjecture underlying the paper's main results. The conjecture asks for Euclidean local structure somewhere in the Tits boundary of every locally compact CAT(0) space with a geometric group action.