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