Cayley conjecture for lattice polytopes of large dimension

Let $P\subset\mathbb{R}^d$ be a lattice polytope of dimension $d$ and degree $s$. A Cayley polytope is a lattice polytope expressible as a Cayley sum of lattice polytopes. Cayley conjecture. If $d>2s$, then $P$ is a Cayley polytope of at least $(d+1-2s)$ lattice polytopes.

This conjecture concerns how sufficiently high dimension relative to degree forces a lattice polytope to admit a Cayley decomposition, a structure important in the study of lattice polytopes and their algebro-geometric interpretations. Its status is not resolved by the supplied source context.