Batyrev–Juny's reducibility conjecture for high-dimensional Gorenstein polytopes

Let $P$ be a Gorenstein polytope of dimension $d$ and degree $s$. A Gorenstein polytope is reducible with factors $F$ and $G$ if it is a Cayley join of $F$ and $G$ and

$$\operatorname{codeg}(F)+\operatorname{codeg}(G)=\operatorname{codeg}(P),$$

equivalently, if $\deg(F)+\deg(G)=\deg(P)$. Batyrev–Juny's reducibility conjecture. If

$$d>2s,$$

then $P$ is reducible. This strengthens the known Cayley-polytope conclusion for Gorenstein polytopes with $d\ge 2s$. The conjecture is described as a strengthening and is presented without a resolution status in the source.