  We relate the Riemann curvature of a holographic spacetime to an entanglement
property of the dual CFT state: the Berry curvature of its modular
Hamiltonians. The modular Berry connection encodes the relative bases of nearby
CFT subregions while its bulk dual, restricted to the code subspace, relates
the edge-mode frames of the corresponding entanglement wedges. At leading order
in 1/N and for sufficiently smooth HRRT surfaces, the modular Berry connection
simply sews together the orthonormal coordinate systems covering neighborhoods
of HRRT surfaces. This geometric perspective on entanglement is a promising new
tool for connecting the dynamics of entanglement and gravitation.
