  Beginning from the Ashtekar formulation of canonical general relativity, we
derive a physical Hamiltonian written in terms of (classical) loop gravity
variables. This is done by gauge-fixing the gravitational fields within a
complex of three-dimensional cells such that curvature and torsion vanish
within each cell. The resulting theory is holographic, with the bulk dynamics
being captured completely by degrees of freedom living on cell boundaries.
Quantization is readily obtainable by existing methods.
