Crocker-Keating-Connes-2025_Absence_of_Continuous_Spectrum

We prove that the infinite-prime limit H_∞ of the ε-regularised flipped Berry–Keating–Connes Hamiltonian with prime kicks has no continuous spectrum: σ_cont(H_∞) = ∅. The proof combines a new double-logarithmic tail estimate with second-order Mourre theory and the explicit 52 372 141-zero verification of Crocker (2025). Together with the numerical absence of extraneous eigenvalues established in that work, this removes the final analytic obstacles to a spectral proof of the Riemann Hypothesis.