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The holographic entropy cone characterizes the relations between entanglemententropies for a spatial partitioning of the boundary spacetime of a holographicCFT in any state describing a classical bulk geometry. We argue that theholographic entropy cone, for an arbitrary number of parties, can bereconstructed from more fundamental data determined solely by subadditivity ofquantum entropy. We formulate certain conjectures about graph models ofholographic entanglement, for which we provide strong evidence, and rigorouslyprove that they all imply that such a reconstruction is possible. Ourconjectures (except only for the weakest) further imply that the necessary datais remarkably simple. In essence, all one needs to know to reconstruct theholographic entropy cone, is a certain subset of the extreme rays of thissimpler "subadditivity cone", namely those which can be realized in holography.This recasting of the bewildering entanglement structure of geometric statesinto primal building blocks paves the way to distilling the essence ofholography for the emergence of a classical bulk spacetime.

The holographic entropy cone from marginal independence