  Thermal fluctuations are not large enough to lead to state changes in
granular materials. However, such materials do achieve reproducible bulk
properties, suggesting that they are controlled by an underlying statistical
mechanics analogous to thermodynamics. We make this connection concrete by
providing a first principles derivation of the multiplicity and thus the
entropy of the force networks of such granular packings. We directly measure
the multiplicity of force networks using a newly proposed protocol based on the
phase space volume of allowed force configurations. Analogous to Planck's
constant, we find a scale factor, $h_f$, that discretizes this phase space
volume into a multiplicity. To determine this constant, we measure angoricity
over a wide range of pressures using the method of overlapping histograms. By
combining these measurements, we concretely link thermodynamic approaches of
angoricity with the microscopic multiplicity of the Force Network Ensemble.
