“Using the gravitational path integral, we argue for the Bousso-Penington for generalized entanglement wedges. To do this, we exploit the connection between random tensor networks and fixed induced-metric
states in gravity. Specifically, we provide a prescription for computing entropies of bulk regions in random tensor networks, and then use the replica trick to derive the Bousso-Penington proposal for fixed induced metric states. We then prove the proposal for general holographic states by expressing them as superpositions over fixed induced metric states and using a diagonal approximation. We emphasize that the saddles computing the bulk Renyi entropies S_n depend on the details of how subregions are specified across different geometries, but that this dependence vanishes as n → 1.”