  We study 3D pure Einstein quantum gravity with negative cosmological
constant, in the regime where the AdS radius $l$ is of the order of the Planck
scale. Specifically, when the Brown-Henneaux central charge $c=3l/2G_N$ ($G_N$
is the 3D Newton constant) equals $c=1/2$, we establish duality between 3D
gravity and 2D Ising conformal field theory by matching gravity and conformal
field theory partition functions for AdS spacetimes with general asymptotic
boundaries. This duality was suggested by a genus-one calculation of Castro et
al. [Phys. Rev. D {\bf 85}, 024032 (2012)]. Extension beyond genus-one requires
new mathematical results based on 3D Topological Quantum Field Theory; these
turn out to uniquely select the $c=1/2$ theory among all those with $c<1$,
extending the previous results of Castro et al..
  Previous work suggests the reduction of the calculation of the gravity
partition function to a problem of summation over the orbits of the mapping
class group action on a "vacuum seed". But whether or not the summation is
well-defined for the general case was unknown before this work. Amongst all
theories with Brown-Henneaux central charge $c<1$, the sum is finite and unique
{\it only} when $c=1/2$, corresponding to a dual Ising conformal field theory
on the asymptotic boundary.
