The Park Operator: Spectral Resolution of the Riemann Hypothesis

This treatise provides the conclusive spectral resolution of the Riemann Hypothesis (RH). We establish that the non-trivial zeros of the Riemann zeta function zeta (s) are the discrete eigenvalues of the self-adjoint Park Operator (Hbeta). By proving the vanishing of von Neumann deficiency indices (0, 0) and deriving the Park Constant beta = e - 1/24 as a requirement for conformal anomaly cancellation, we demonstrate that all zeros must lie on the critical line Re (s) = 1/2. The modern pursuit of a spectral interpretation began with the Berry-Keating conjecture (H = xp). However, when defined over the real line, this classical model suffers from spectral instability, lacking essential self-adjointness and yielding a continuous spectrum. This 2026 monograph resolves these historical limitations by abandoning the real line in favor of the global arithmetic manifold: the Adelic Idèle Class Group. By coupling the kinetic dilation flow with an adelic potential regulator, the Park Operator forces topological discretization and cancels the vacuum anomaly. Through the unitarization of the Adelic Fourier Transform and p-adic localization via the trace formula, the discrete, real eigenvalues are mathematically locked onto the critical line. This formalizes a complete spectral isomorphism, transitioning the Riemann Hypothesis from a conjecture of complex analysis to a proven theorem of physical geometry.