Critical exponent for glassy packing of rigid spheres and disks

A simple conjecture on the behavior of the canonical ensemble partition function for a system of rigid spheres and disks, as random close packing is approached, is supported in a suggestive manner by definite trends that emerge from ``derivative-logarithm'' analyses of the low-density virial series with the presently known coefficients. The conjecture predicts that the inverse pressure at random close packing should become zero with infinite slope, whereas it very probably does so with finite slope as the ordered closest-packing limit is approached.