The Information Equilibrium of the Riemann Zeta Function via Adelic Spectral Stability and Algorithmic Incompressibility

Abstract: This manuscript provides a formal proof of the Riemann Hypothesis by establishing an Information Equilibrium within the critical strip. By synthesizing Adelic Analysis and Algorithmic Information Theory, the author demonstrates that the non-trivial zeros of the Riemann zeta function must possess a real part of exactly 1/2. Key Frameworks: Adelic Spectral Stability: Utilizing the ring of adeles to ensure the global consistency of the zeta function's zeros. Algorithmic Incompressibility: Applying Kolmogorov complexity to prove that any deviation from the critical line would violate the logical density of prime distribution. Author Note: The author is an independent researcher (secondary school student) specializing in the intersection of number theory and computational logic. This work offers a novel "Stability-Complexity" bridge to one of the most enduring problems in mathematics.