The O_2 Rokhlin-dimension conjecture for compact Lie group actions

Let $G$ be a compact Lie group, and let $\alpha\colon G\to\operatorname{Aut}(\mathcal{O}_2)$ be an action with finite Rokhlin dimension with commuting towers. The Rokhlin property is the stronger equivariant regularity property referred to in the source.

The $\mathcal{O}_2$ Rokhlin-dimension conjecture. The action $\alpha$ has the Rokhlin property.

The claim would identify finite Rokhlin dimension with commuting towers and the Rokhlin property for actions on $\mathcal{O}_2$. The supplied text presents it as suggested by results in the cited literature and gives no resolution, so its status remains open.