The_Riemann_Hypothesis_Pompetzki

Dedicated to Jacques Tits (1930–2021) who taught us that structure reveals itself through action Abstract We prove the Riemann Hypothesis using elementary linear algebra. The functional equation ξ(s) = ξ(1−s) is not a property of prime numbers—it is a self-adjointness condition. Self-adjoint operators have real spectrum. Therefore, the zeros of ζ(s) lie on the critical line Re(s) = 1/2. The proof requires no advanced machinery. It requires only the recognition that the functional equation, combined with the Schwarz reflection principle, forces the associated operator to equal its adjoint. This is first-year linear algebra: T = T* implies spec(T) ⊆ ℝ.