The Atiyah Conjecture with rational coefficients

Let $G$ be a torsion-free group, let $m,n$ be positive integers, and let $A\in M_{m,n}(\mathbb{Q}G)$. Write $r_A\colon \mathcal{N}(G)^m\to\mathcal{N}(G)^n$ for right multiplication by $A$, and let $\dim_{\mathcal{N}(G)}$ denote von Neumann dimension. Atiyah Conjecture. The group $G$ satisfies the Atiyah Conjecture with rational coefficients if, for every such matrix $A$,

$$\dim_{\mathcal{N}(G)}\bigl(\ker(r_A\colon \mathcal{N}(G)^m\to\mathcal{N}(G)^n)\bigr)\in\mathbb{Z}.$$

This is the integrality assertion needed in the construction of the $L^2$-torsion polytope. The supplied text gives the definition but no resolution status for the conjectural condition itself.