The arbitrary-boundary network decomposition conjecture

Let $\Sigma$ be a network with $n\geq2$ boundary vertices. An extremal-ray realization is a subnetwork whose entropy vector realizes an extremal ray of the $n$-boundary-region holographic entropy cone. The arbitrary-boundary network decomposition conjecture. A network with $n\geq2$ boundary vertices decomposes into subnetworks, each of which is an extremal-ray realization of the $n$-boundary-region holographic entropy cone. This generalizes the proposed four-partite network decomposition; the source reports numerical evidence for the four-boundary case, while no general proof is given.