  We characterize the quantum states dual to entanglement wedges in arbitrary
spacetimes, in settings where the matter entropy can be neglected compared to
the geometric entropy. In AdS/CFT, such states obey special entropy
inequalities known as the holographic entropy cone. In particular, the mutual
information of CFT subregions is monogamous (MMI). We extend this result to
arbitrary spacetimes, using a recent proposal for the generalized entanglement
wedge e(a) of a gravitating region a. Given independent input regions a, b, and
c, we prove MMI:
Area[e(a)]+Area[e(b)]+Area[e(c)]-Area[e(ab)]-Area[e(bc)]-Area[e(ca)]+Area[e(abc)]
$\leq$ 0. We expect that the full holographic entropy cone can be extended to
arbitrary spacetimes using similar methods.
