December 5, 2025Open Access

A Mean Min--Max Lemma for the Equation a+b=c with Absolute Constants and Applications

Key Points

Main finding highlights the significance of absolute constants in the context of Diophantine equations and their proofs.
Key evidence involves establishing the Poincaré identity and the Beal corollary for a+b=c with operational details.
Observational analysis addresses various corollaries and constructs, including the Beal corollary and dyadic stratification.
Significance points to the necessity for reproducible research in exploring complex equations and mathematical theories.

Abstract

Technical supplement to ‘A Mean Min–Max Lemma for a+b=c with Absolute Constants and Applications’. Consolidates full proofs and operational details for the content–height mean principle and the Beal corollary (apᵇq=cr, p, q, r≥3). Appendix A standardizes absolute values, weights, and the product formula; B establishes the exact Poincaré identity on K3 and energy/gap control; C builds the dyadic stratification, block weights, and global gain; D bridges heights and radical with comparison constant αcmp (K) and slack δcmp; E closes the coprime Beal case via finite window and local elimination (congruences, LTE). Includes parameter table, dependency graph, seeds, logs, and reproducibility notes. Keywords: Diophantine equations; content–height; Szpiro/ABC; Beal; Arakelov geometry; spectral methods; LTE; Zsigmondy; reproducible research.

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Cite This Study

Vieira, Paulo (Fri,) studied this question.

synapsesocial.com/papers/694023c82d562116f28fcc4b https://doi.org/https://doi.org/10.5281/zenodo.17833974

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