  We show that the smooth geometry of a hyperbolic 3-manifold emerges from a
classical spin system defined on a 2d discrete lattice, and moreover show that
the process of this "dimensional oxidation" is equivalent with the dimensional
reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we
propose an equality between (1) the 4d superconformal index of a 4d N=1
superconformal quiver gauge theory described by a bipartite graph on T^2 and
the partition function of a classical integrable spin chain on T^2. The 2d spin
system is lifted to a hyperbolic 3-manifold after the dimensional reduction and
the Higgsing of the 4d gauge theory.
