Coxeter's A_d-hypothesis on minimal-density perfect forms

A perfect form is a positive definite quadratic form whose associated Delone subdivision is determined by its minimal vectors; Voronoi's first perfect form is the first form in Voronoi's enumeration in a given dimension. Coxeter's $\mathsf{A}_d$-hypothesis. Voronoi's first perfect form gives the minimal packing density among all perfect forms of a given dimension. The hypothesis concerns the opposite extreme from the difficult search for perfect forms of maximal packing density; the source gives no resolution of the claim.