The Langlands-Abhary Correspondence: Non-Abelian Class Field Theory and Automorphic Forms in Predictive Metallogeny

Abstract: The stochastic modeling of metallogenic systems in orogenic belts has historically been constrained by the fundamental limitations of Euclidean geometry and linear geostatistics. This paper establishes a radical theoretical framework, the Langlands-Abhary Correspondence, which posits a rigorous isomorphism between the arithmetic of Langlands dual groups and the thermodynamics of ore genesis. By conceptualizing the "Mineralized Crustal Continuum" as a global number field 𝐹 and mineralizing fluids as automorphic representations over the adele ring 𝔸 𝐹, we apply the full machinery of non-abelian class field theory to exploration geology. We derive the Abhary-Langlands Conjecture, demonstrating that the 𝐿-functions associated with high-grade ore deposits coincide with the Artin 𝐿-functions of the underlying Galois representations of the tectonic manifold. Utilizing the Arthur-Selberg trace formula, we provide a deterministic bound on mineral endowment, proving that giant ore deposits are spectral invariants of the moduli space.

کلیدواژه ها:

Langlands Program ، Automorphic Representations ، Adelic Rings ، Arthur-Selberg Trace Formula ، Galois Representations ، Predictive Metallogeny