  We apply the framework of Cauchy Slice Holography to the quantization of
gravity on closed slices with $\Lambda>0$ (with a focus on $2+1$ dimensions for
concreteness). We obtain solutions to the Wheeler-DeWitt equation in a basis of
CPT-dual branches. Each branch is a $T^2$-deformed CFT partition function with
imaginary central charge. We compute explicit solutions in $2+1$ dimensions in
a minisuperspace toy model of pure gravity. This analysis gives us evidence to
conjecture a connection between the choice of superposition of branches and the
choice of class of geometries to sum over in the gravitational path integral.
We further show that, in full quantum gravity on closed slices, bulk unitarity
holds, despite the Euclidean holographic field theory not being
reflection-positive. We conjecture about the (non)uniqueness of the quantum
state of the Universe, in light of this analysis.
