The lattice-point maximality conjecture for the Sylvester reflexive simplex

Let $d\geq 4$, and let $S_{Q'_d}$ be the reflexive simplex defined from the Sylvester-sequence weight system in the source. A $d$-dimensional lattice polytope is assumed to have exactly one interior lattice point. Lattice-point maximality conjecture. The reflexive simplex $S_{Q'_d}$ has solely the largest number of lattice points among all such $d$-dimensional lattice polytopes. The conjecture had been checked by computer classification for four-dimensional reflexive polytopes, but the source gives no resolution in general.