Local–Global Generative Structure of L-Functions: RH, Sato–Tate, and Langlands Reinterpreted

Abstract

This paper presents a generative-theoretic reinterpretation of the Riemann Hypothesis, Sato–Tate Conjecture, and Langlands Correspondence, showing that their local, intermediate, and global behaviors arise as stability conditions within a single prime-centered hierarchical structure.