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

TL;DR

This paper critiques the analytical derivation of random close packing volume fractions in two and three dimensions presented in a recent Physical Review Letters article, questioning its validity and the adequacy of the subsequent Erratum.

Contribution

It provides a critical commentary highlighting issues with the derivation and clarifications of the original analytical results on random close packing.

Findings

The derivation in the original paper is problematic and unjustified.

The Erratum does not address the concerns raised.

The critique questions the validity of the analytical solutions.

Abstract

In this short commentary we provide our comment on the article "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$" and its subsequent Erratum that are recently published in Physical Review Letters. In that Letter, the author presented an explicit analytical derivation of the volume fractions $\phi_{\rm RCP}$ for random close packings (RCP) in both $d=2$ and $d=3$. Here we first briefly show the key parts of the derivation in Ref.~\cite{Za22}, and then provide arguments on why we think the derivation of the analytical results is problematic and unjustified, and why the Erratum does not address or clarify the concerns raised previously by us.