Comment on "Explicit Analytical Solution for Random Close Packing in $d = 2$ and $d = 3$"

TL;DR

This paper critiques a recent analytical approach to calculating random close packing densities in 2D and 3D, highlighting its limitations and the lack of generalizability to higher dimensions.

Contribution

It provides a critical analysis of a proposed explicit solution for RCP density, emphasizing its failure to extend to higher dimensions and questioning its validity.

Findings

The proposed solution does not match known high-dimensional behavior.

The low-dimensional agreement appears to be coincidental.

The critique suggests the need for more comprehensive models.

Abstract

A recent letter titled "Explicit Analytical Solution for Random Close Packing in d=2 and d=3" published in Physical Review Letters proposes a first-principle computation of the random close packing (RCP) density in spatial dimensions d=2 and d=3. This problem has a long history of such proposals, but none capture the full picture. This paper, in particular, once generalized to all d fails to describe the known behavior of jammed systems in d>4, thus suggesting that the low-dimensional agreement is largely fortuitous.