Single-bubble conjecture for Clifford-Euclidean orders

Let $\mathcal{O}$ be an order in the relevant Clifford algebra, and suppose that it is Clifford-Euclidean, meaning that it admits the Clifford-Euclidean division property used to construct its fundamental domain. A boundary bubble is one of the boundary spheres or bubbles occurring in that fundamental-domain construction. Single-bubble conjecture. If $\mathcal{O}$ is Clifford-Euclidean, then every boundary bubble has radius $1$, and there exists a fundamental domain requiring only a single bubble. The claim is based on experimental observations; the source gives no proof or resolution.