CANTOR + HARDY + NEWTON + INTERVAL COVERAGE

This preprint presents an integrated computational procedure combining the Cantor pairing function, angular states, the real Hardy Z(t) function, and the Newton-Raphson method for the generation and refinement of spectral ordinates associated with the critical line of the Riemann zeta function. The procedure applies the formulations presented in this work to selected reference data and spectral positions related to the classical study of the nontrivial zeros of the Riemann zeta function. Initial ordinates are generated through the Cantor pairing structure and angular states and are subsequently refined through Newton-Raphson iteration applied to Hardy's real Z(t) function. The refined ordinates are compared with reference ordinates of nontrivial zeros, with the numerical differences Δγ recorded. Consecutive refined ordinates are also used to construct spectral intervals, which are independently examined through numerical scanning of Z(t) for internal sign changes and possible additional zeros. A complementary audit uses the smooth Riemann-von Mangoldt counting expression to evaluate ΔN_smooth between consecutive ordinates. The documented numerical results show close agreement in the cases presented and are made available for independent examination and reproduction. The results are not presented in this work as a proof of the Riemann Hypothesis. The purpose of the preprint is to document the proposed formulations, computational procedure, numerical comparisons, and interval analysis so that the scientific community can independently evaluate the results and their generality.