  A method has been found to analyze Edwards' granular contact force
probability functional for a special case. As a result, the granular contact
force probability density functions are obtained from first principles for this
case. The results are in excellent agreement with the experimental and
simulation data. The derivation assumes Edwards' flat measure -- a density of
states that is uniform within the metastable regions of phase space. The
enabling assumption, supported by physical arguments and empirical evidence, is
that correlating information is not significantly recursive through loops in
the packing. Maximizing a state-counting entropy results in a transport
equation that can be solved numerically. For the present this has been done
using the "mean structure approximation," projecting the density of states
across all angular coordinates to more clearly identify its predominant
non-uniformities. These features are: (1) the grain factor (Psi) related to
grain stability and strong correlation between the contact forces on the same
grain, and (2) the structure factor (Upsilon) related to Newton's third law and
strong correlation between neighboring grains.
