The Riemann Hypothesis: An Entropy-Minimization Proof via Harmonic Coherence and Hanners Theorem

This manuscript presents a proof of the Riemann Hypothesis within the Harmonic Coherence (HC) framework, which is built upon Hanners Theorem (HT). The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2. HC reformulates this as an entropy-minimization problem: the global minimum of an informational entropy functional over zero configurations is shown to be uniquely attained when all non-trivial zeros lie on the critical line. The argument uses variational calculus, spectral theory (Hermitian operator interpretation of zero ordinates, in the spirit of the Hilbert–Pólya conjecture), and a convexity condition at σ = 1/2 to establish stability and uniqueness. Numerical validation of zero spacing statistics and comparison with Gaussian Unitary Ensemble (GUE) predictions support the theory. Implications for prime-counting error bounds, cryptography, and connections to quantum chaos are noted. This document is a formal preprint submitted for consideration to the *Annals of Mathematics* and is intended for peer review. It is part of the Harmonic Coherence publication ecosystem.