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

Hyperstaticity and loops in frictional granular packings