The Rohlin-property characterization conjecture for flows on AFD factors

Let $M$ be an AFD von Neumann algebra and let $\alpha$ be a flow on $M$. A flow has the Rohlin property when it satisfies the Rohlin condition for flows. Its full Connes spectrum and central freeness are the corresponding outerness properties: central freeness means that $\alpha^t$ is centrally free for every nonzero $t\in\mathbf R$. The conjecture also uses a canonical extension

$$\widetilde{\alpha}:\mathbf R\curvearrowright\widetilde{M}$$

of $\alpha$ and its canonical implementation $\pi_{\widetilde{\alpha}}$.

Rohlin-property characterization conjecture. The following three conditions are equivalent:

1. The action $\alpha$ has the Rohlin property.

$$\pi_{\widetilde{\alpha}}(\widetilde{M})'\cap\left(\widetilde{M}\rtimes_{\widetilde{\alpha}}\mathbf R\right)=\pi_{\widetilde{\alpha}}(Z(\widetilde{M})).$$

3. The action $\alpha$ has full Connes spectrum and is centrally free.

This characterization would express the Rohlin property using invariants of flows, an important step toward the complete classification of flows on AFD von Neumann algebras. The source points to the classification work of Masuda and Tomatsu, but does not state a resolution of the conjecture.