The weak Spread Out Simplices Conjecture

Let $n\Delta_{d-1}$ be the $(d-1)$-simplex dilated by $n$. A collection of $n$ unit simplices in it is spread out if every subsimplex of size $k$ contains at most $k$ of them. An acyclic system of permutations is a system whose associated directed graph is acyclic for every pair of labels.

Weak Spread Out Simplices Conjecture. Any $n$ spread out simplices in $n\Delta_{d-1}$ can be achieved as the simplices of an acyclic system of permutations.

This is presented as the converse of the theorem asserting that the simplices arising from an acyclic system are spread out. The supplied status evidence identifies it as a counterexample to the Acyclic System Conjecture, so it is refuted.