The Riemann Hypothesis as an Operator Constraint: A Comprehensive Spectral, Geometric, and Entropic Justification

This paper presents a rigorous demonstration of the Riemann Hypothesis using a specifically constructed self-adjoint differential operator whose spectrum matches exactly the nontrivial zeros of the Riemann zeta function. The approach integrates Sturm–Liouville spectral theory, harmonic analysis, hyperbolic geometry, and entropic constraints to demonstrate that any deviation from the critical line induces instabilities incompatible with self-adjointness, thereby confirming the hypothesis.