Relative bicentralizer formula for the continuous core

Let $N \subset M$ be an inclusion of von Neumann algebras with expectation, and let $\varphi \in N_*$ be a faithful normal state. Write $c(N)=N \rtimes_{\sigma^\varphi} \mathbb{R}$ and let $c(M)$ be the corresponding continuous core. Let $\mathord{\mathrm{B}}(N \subset c(M),\varphi)$ be the relative bicentralizer, and let $(\varphi^{\mathrm{i}t})_{t\in\mathbb{R}}$ be the one-parameter group of unitaries in $c(N)$ implementing $\sigma^\varphi$. Relative bicentralizer conjecture.

$$\mathord{\mathrm{B}}(N \subset c(M),\varphi)=\{\varphi^{\mathrm{i}t}\mid t\in\mathbb{R}\}”\vee(N'\cap c(M)).$$

The formula is proposed for arbitrary inclusions with expectation and is intended to compute the relative bicentralizer through the relative flow of weights; the supplied text does not state that it has been proved in full.