Toward a robust definition of random close packing

The apparent simplicity of amorphous sphere packings can be misleading. Although jamming hard spheres to random close packing (rcp) has been studied for decades, an unambiguous definition, let alone a first-principle prediction, of rcp remain elusive. Here, we draw inspiration from liquid state theory to identify rcp with the inherent structure of a hard sphere liquid. For a model with a soft interaction potential, inherent states are obtained through an instantaneous energy minimization of an equilibrium liquid configuration, but identifying inherent structures of hard spheres through optimization is a non-trivial problem. Motivated by a recent (meta-)analysis of existing algorithms, we consider the behavior of minimal models of jamming that can be studied using various approaches, notably with tools from stochastic geometry. The resulting insights present a path toward formalizing rcp.