We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10(4) frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky-Stillinger and force-biased algorithms are distributed in a narrow density range from φ = 0.634-0.636 to φ≈ 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to φ≈ 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret φ≈ 0.64 as the random-close packing (RCP) limit and φ≈ 0.65 as a lower bound of the glass close packing (GCP) limit, whereas φ = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density φLT. The three characteristic densities φLT, φRCP, and φGCP are determined for polydisperse packings with log-normal sphere radii distributions.

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Different approaches are applied and compared, which are universally applicable to quantify pore coordination, pore and pore-throat connectivity, and geometric tortuosity.

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