The quantum-state realization conjecture for hypergraph entropy rays

Let $G_K$ be a hypergraph defining a $K$-party state construction, and let $\Ket{G_K}$ denote the resulting $K$-party quantum state. The construction uses AME tensors at bulk vertices, GHZ tensors on hyperedges, and contractions of tensor indices, with the local basis choices in the AME tensors to be fixed by a refinement of the bulk-vertex rule. Quantum-state realization conjecture. There exists an appropriate refinement of the bulk-vertex rule such that the entropies of all subsystems of $\Ket{G_K}$ agree precisely with the entropies obtained from the min-cut prescription applied to $G_K$, up to a common scaling factor. The conjecture would establish a direct quantum-state realization of the entropy rays produced by hypergraphs; the paper reports this only for examples and leaves the universal refinement open.