This research provides a formal proof of Beal’s Conjecture (Aˣ + Bʸ = Cᶻ) by generalizing the Law of Parity Divergence. Building on the author’s earlier work regarding uniform-exponent Diophantine mappings, this paper introduces the Generalized Lama Reduction to analyze equations with asymmetric curvature. Key Findings Asymmetric Manifold Mapping: Demonstrates how higher-degree asymmetric powers can be projected onto a 2-dimensional Euclidean plane to analyze integer simultaneity. Infinite Descent of Bases: Proves that a coprime state ( (A, B, C) = 1) for x, y, z > 2 forces a recursive "Square Trap, " leading to a mathematically impossible infinite descent of integer bases. The Harmonic Bridge: Establishes that a common prime factor is a structural requirement—a dimensional anchor—necessary to reconcile different power curvatures within a singular geometric manifold. This paper bridges the gap between algebraic number theory and topology, providing both a theoretical framework and numerical verification for the necessity of common prime factors in power-sum equations. Related Works This publication is a continuation of the research established in: Lama, T. D. (2026). A Metric for Parity Divergence in n-Degree Diophantine Mappings.
Tsering Dawa Lama (Fri,) studied this question.