Correction to "$C_1$ in [2] is zero"

TL;DR

This paper corrects a previous result by showing that a certain constant $C_1$ is non-zero, clarifying the resolution of an inequality issue in a prior monograph, and acknowledging a mistake in the original proof.

Contribution

It provides a correction to a previous claim, demonstrating that $C_1$ is non-zero and confirming the validity of the referenced resolution.

Findings

$C_1$ is non-zero after correction.

The correction confirms the resolution of the inequality issue.

The original mistake has been acknowledged and rectified.

Abstract

John Morgan and G,Tian pointed out a mistake in the concluding argument for our paper entitled "$C_1$ in [2] is zero", which was recently published in arXiv:1512.02098. We hereby acknowledge this mistake and correct the computation, leading to the conclusion that $C_1$ is non-zero and that their reference [2] does indeed fully address and resolve the issue raised by the counter-example which we provided in [3] to the inequality (19.10) in their monograph [1].