Bicentralizer conjecture for inclusions with expectations

Let $N \subset M$ be an inclusion of von Neumann algebras with expectations. For a strictly semifinite weight $\varphi \in \mathcal{P}(N)$, let $\mathord{\mathrm{B}}(N \subset M,\varphi)$ and $\mathord{\mathrm{b}}(N \subset M,\varphi)$ denote the two bicentralizer algebras defined in the paper. Bicentralizer conjecture.

$$\mathord{\mathrm{B}}(N \subset M,\varphi)=\mathord{\mathrm{b}}(N \subset M,\varphi)$$

for every strictly semifinite weight $\varphi \in \mathcal{P}(N)$. This is the paper's general bicentralizer assertion for inclusions with expectations; the supplied candidate carries no resolution evidence, so its full status remains open.