Volume determination conjecture for stable scissors congruence classes

Let $M$ be a hyperbolic manifold, and let its stable scissors congruence class mean its scissors congruence class after adjoining a common hyperbolic polyhedron. Let $\operatorname{vol}(M)$ denote its hyperbolic volume. Volume determination conjecture. The stable scissors congruence class of $M$ is determined by $\operatorname{vol}(M)$. The source states that this would follow from another conjecture and places it in the context of the Borel regulator characterization of stable scissors congruence. No resolution is given.