I propose a quantum gravity model in which geometric space emerges from
random bits in a quantum phase transition driven by the combinatorial
Ollivier-Ricci curvature and corresponding to the condensation of short cycles
in random graphs. This quantum critical point defines quantum gravity
non-perturbatively. In the ordered geometric phase at large distances the
action reduces to the standard Einstein-Hilbert term.Comment: Revised version to appear in JHE