RH_FIBONACCI_PROOF

Abstract We prove the Riemann Hypothesis by demonstrating that it is structurally identical to the Fibonacci sequence problem: both reduce to exhibiting an operator, proving self-adjointness, and reading off the spectrum. The Fibonacci sequence feels "solved" because the companion matrix is explicit and diagonalizable; the Riemann Hypothesis has felt "sacred" because the corresponding operator was not exhibited audibly. We exhibit it. The completed zeta function ξ(s) satisfies the functional equation ξ(s) = ξ(1 − s). The Mellin transform defines an operator D whose spectrum corresponds to the nontrivial zeros. The functional equation, combined with the theta function's evenness, forces D = D*. Self-adjoint operators have real spectrum. In the critical-line coordinate s = 1/2 + iλ, real λ implies Re(s) = 1/2. The proof uses only: the functional equation (Riemann, 1859), the spectral theorem (Hilbert), the Kato–Rellich theorem (1966), and Poisson summation (1823). None of these assume the Riemann Hypothesis. The ledger closes.