The hypergraph–QLR cone equality conjecture

For each $n$, let the $n$-party hypergraph cone be the cone of entropy vectors obtained from $n$-party hypergraphs, and let the $n$-party QLR cone be the cone defined by the quantum linear rank inequalities. Hypergraph–QLR cone conjecture. The $n$-party hypergraph and QLR cones coincide for all $n$. The cones are known to coincide through four parties, and the paper gives contraction-map evidence for five parties; equality in general would identify the hypergraph cone with a cone of quantum-compatible entropy vectors.