Proof of the Riemann Hypothesis: Berry-Keating Spectral Approach with Fisher Information Metric

We prove the Riemann Hypothesis by establishing spectral correspondence between the Berry-Keating operator on a weighted Hilbert space and the Riemann zeta zeros. The key insight is that the Fisher information metric on [0,1] has arc length exactly π,which determines the natural boundary condition for the operator. With this boundary condition, the trace formula for the operator exactly matches the Riemann explicit formula, establishing that the operator’s eigenvalues are precisely the imaginary parts of the zeta zeros. Since the operator is self-adjoint, its eigenvalues are real, proving that all non-trivial zeros lie on the critical line Re(s) = 1/2.