Reply to Chen and Ni on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"

TL;DR

This paper clarifies and defends the original findings on random close packing in 2D and 3D, addressing critiques and reaffirming the validity of their analytical solutions without mathematical errors.

Contribution

The authors respond to critiques by demonstrating their original analytical solutions are correct and free of errors, reaffirming their prior results.

Findings

Original solutions are mathematically sound

Critiques are addressed and refuted

Assumptions in the original paper are valid

Abstract

We show that very clear answers to the queries raised by D. Chen and R. Ni in their Comment on our recent paper [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] can be found in our original paper already. The paper [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is free of mathematical errors, as anyone can easily verify, and all the assumptions were carefully, and critically discussed in the paper.