  The hyperstatic nature of granular packings of perfectly rigid disks is
analyzed algebraically and through numerical simulation. The elementary loops
of grains emerge as a fundamental element in addressing hyperstaticity. Loops
consisting of an odd number of grains behave differently than those with an
even number. For odd loops, the latent stresses are exterior and are
characterized by the sum of frictional forces around each loop. For even loops,
the latent stresses are interior and are characterized by the alternating sum
of frictional forces around each loop. The statistics of these two types of
loop sums are found to be Gibbsian with a "temperature" that is linear with the
friction coefficient mu when mu<1.
