The hypergraph generalization conjecture for cycle-flow entropy vectors

Let a nesting balanced network be a directed network satisfying the nesting and balance conditions used in the cycle-flow prescription, and let its entropy vector be defined by the maximum cycle flow associated with each subsystem. Hypergraphs similarly define entropy vectors through their hypergraph entropy prescription.

Hypergraph generalization conjecture. Every entropy vector representable by a hypergraph can be represented using the cycle-flow prescription on a nesting balanced network.

The authors exhibit examples showing that the cycle-flow model reproduces hypergraph entropy vectors and state that proving the general claim remains open. This would establish that the hypergraph entropy cone is contained in the cone defined by cycle flows.