Dickenstein–Nill rational codegree conjecture for lattice polytopes

Let $P$ be an $n$-dimensional lattice polytope, and let $\mu(P)$ denote its $\mathbb Q$-codegree. A Cayley sum is a polytope obtained by assembling lattice polytopes along the vertices of a simplex.

Dickenstein–Nill rational codegree conjecture. If

$$\mu(P)>\frac{n+1}{2},$$

then $P$ decomposes as a Cayley sum of lattice polytopes of dimension at most

$$\left\lfloor 2\bigl(n+1-\mu(P)\bigr)\right\rfloor.$$

This reformulation extends the integral codegree conjecture to the rational setting. The source presents it as open, while noting results in several special cases.