Verification and Closure of Derivations in Complete 5D Solitonic Theory: Fundamental Derivation of k0 = 0.1 and Resolution of Black Hole Singularities

This document provides a systematic verification and rigorous completion of all mathematical derivations presented in Complete 5D Solitonic Theory: Fundamental Derivation of k0 = 0.1 and Resolution of Black Hole Singularities by A. Copinet and N. Copinet (HAL Id: hal-05132691, 2025; corrected version: Zenodo DOI: 10.5281/zenodo.17350608). Through five successive passes of mathematical scrutiny, 22 corrections were identified and resolved, ranging from sign conventions and algebraic identities to coefficient inconsistencies and logical gaps in proof structures. Crucially, none of these corrections modifies any physical result or observable prediction of the original theory. The fundamental constant k0 = 0.1, the number of topological sectors N = 10, the solitonic field profiles, the singularity resolution mechanism, and all experimental predictions (gravitational wave echoes, Hawking temperature corrections, black hole shadow modifications) remain exactly as stated in the original publication. The present work strengthens the theoretical foundation by replacing heuristic arguments with rigorous proofs, correcting intermediate algebraic steps, and ensuring full consistency between the main text and its supporting appendices.