Width-one conjecture for odd-dimensional thin simplices

A thin simplex is a lattice simplex of lattice width at most one, and its lattice width is the minimum width over all nonzero integral linear functionals. Width-one conjecture. In odd dimensions all thin simplices have width $1$.

This conjecture is motivated by computations showing no thin simplices of width at least two in the odd dimensions examined. Its general validity remains open.