Description: This preprint presents a formal and definitive solution to the Collatz Conjecture (3n+1 problem) by introducing the framework of Sexagesimal Harmony Mathematics (SHM). Departing from traditional decimal and binary perspectives, this work demonstrates that the apparent chaos of the Collatz sequences is an artifact of the radix system used for observation. By mapping the dynamical system onto a Sexagesimal Harmonic Manifold (M₆0), the author reveals that the number 60, as a superior highly composite number, acts as a "modular sink" that dissipates the arithmetic energy of the 3n+1 operation. The core of the proof lies in the López Convergence Lemma, which establishes a Sexagesimal Harmonic Norm (|M) that functions as a Lyapunov stability function. Under this metric, the Collatz mapping is proven to be a global contraction toward the unit attractor 1, mathematically prohibiting the existence of infinite loops or divergent trajectories. The paper details the Algoritmo de Armonía Sexagesimal (AAS), a computational and logical framework that has verified this convergence with unprecedented efficiency. This discovery not only resolves a century-old enigma in number theory but also opens new avenues in post-quantum cryptography, high-precision signal processing, and the study of transcendental stability. Key Contributions: Formal definition of the Sexagesimal Harmonic Manifold (M₆0). Establishment of the López Convergence Lemma and the Harmonic Metric. Proof of the "Modular Sink" effect in base-60 radices. Introduction of the Sexagesimal Harmony Algorithm (AAS) for deterministic numerical verification. About the Author: Ing. Alexander López is an independent researcher from Coto Brus, Costa Rica, specializing in harmonic analysis and the structural properties of highly composite numbers.
Jorge Alexander Lopez Miranda (Wed,) studied this question.