Acyclic system conjecture for mixed subdivisions

Let $[n]=\{1,\ldots,n\}$ and $[d]=\{1,\ldots,d\}$. A system of permutations records the permutations obtained from the boundary data of a mixed subdivision of $n\Delta_{d-1}$, and it is acyclic when it contains no forbidden cyclic pattern. Acyclic system conjecture. A system of permutations comes from a mixed subdivision of $n\Delta_{d-1}$ if and only if it is acyclic. This extends the stated two-dimensional acyclic-system theorem to arbitrary $d$; the supplied text gives no resolution status.