Voronoi candidate conjecture for modular symbols

Let ${\mathbf v}=[v_1,\dots,v_n]$ be a modular symbol with $\|{\mathbf v}\|>1$. Define

$$b({\mathbf v})=\sum_i v_i v_i^t.$$

For a top-dimensional cone $\sigma$ in the Voronoi decomposition containing $b({\mathbf v})$, let $\operatorname{vert}\sigma$ denote the primitive points corresponding to the face generating $\sigma$, and let $\operatorname{cand}{\mathbf v}$ be the set of nonzero lattice points that can be written as $w=\sum_i q_i v_i$ with $0\leq |q_i|<1$. Voronoi candidate conjecture. If $\sigma$ is a top-dimensional cone containing $b({\mathbf v})$, then

$$\operatorname{cand}{\mathbf v}\cap\operatorname{vert}\sigma\ne\varnothing.$$

This conjecture would provide a geometrically natural way to choose candidates that reduce modular symbols. It is stated as a conjectural technique for implementing the modular symbol algorithm and is asserted to hold in all dimensions; the paper notes that the Voronoi reduction algorithm has unknown complexity and that the Voronoi decomposition is difficult to determine in general.