Sail formulation of Oppenheim's conjecture

Let $n\geqslant 3$, let $\Lambda\subset\mathbb{R}^n$ be an $n$-dimensional lattice, and let $\Pi$ be a sail generated by $\Lambda$. A sail's facets and edge stars are its facets and the edge stars of its vertices; they have uniformly bounded determinants when these determinants are bounded by a constant independent of the facet or edge star. Sail formulation of Oppenheim's conjecture. If all facets and edge stars of vertices of $\Pi$ have uniformly bounded determinants, then $\Lambda$ is algebraic.

The paper derives this formulation from its theorem equating positive norm minimum with uniform determinant bounds. It is therefore equivalent to Oppenheim's conjecture and remains open.