  We introduce a novel model of multipartite entanglement based on topological
links, generalizing the graph/hypergraph entropy cone program. We demonstrate
that there exist link representations of entropy vectors which provably cannot
be represented by graphs or hypergraphs. Furthermore, we show that the
contraction map proof method generalizes to the topological setting, though now
requiring oracular solutions to well-known but difficult problems in knot
theory.
