Agrarian analogue of the virtually free-by-cyclic theorem

Let $\mathbb F$ be a skew-field. The groups and invariants in the paper include the agrarian cohomological dimension $\operatorname{cd}_{\mathbb F}$ and the agrarian Betti numbers $b_i^{\mathcal D_{\mathbb F H}}$. Agrarian generalisation conjecture. The main result remains valid after replacing every occurrence of $\operatorname{cd}_{\mathbb Q}$ by $\operatorname{cd}_{\mathbb F}$ and every $L^2$-Betti number $b_i^{(2)}$ by the agrarian Betti number $b_i^{\mathcal D_{\mathbb F H}}$. This would extend the paper's virtually free-by-cyclic conclusions from rational and $L^2$-invariants to agrarian invariants over arbitrary skew-fields. The source states this as the paper's concluding conjecture; no resolution is given.