Coherence conjecture for finite-type RFRS groups

Let $G$ be a RFRS group of type $\mathrm{FP}$. A group is coherent if every finitely generated subgroup is finitely presented. The algebra $\mathbb{Q}[G]$ is the rational group algebra, and $\mathcal U(G)$ is the algebra of operators affiliated to the group von Neumann algebra of $G$. Coherence conjecture for finite-type RFRS groups. The following are equivalent:

$$\begin{array}{ll} \text{(i)} & G\text{ is coherent};\\ \text{(ii)} & \mathbb{Q}[G]\text{ is coherent};\\ \text{(iii)} & \mathcal U(G)\text{ is of weak dimension one as a }\mathbb{Q}[G]\text{-module}. \end{array}$$

This prediction concerns coherence for RFRS groups of finite type and connects it to the weak dimension of the affiliated-operator algebra. The source presents it as a prediction and gives no resolution.