Verifying spiral minimal product structure through the Takahashi Theorem

TL;DR

This paper confirms the spiral minimal product structure using the Takahashi Theorem, providing detailed computational verification that was previously omitted.

Contribution

It offers a comprehensive computational verification of the spiral minimal product structure via the Takahashi Theorem, filling a gap in prior work.

Findings

Successful verification of the structure

Detailed computational methodology provided

Clarification of the theorem's application

Abstract

We verify the spiral minimal product structure through the Takahashi Theorem with full computational details which were omitted in [LZ].