Reversal Dual Calculus: Harmonic Regularization in Gravitational Potential and Zeta Function Duality

Gravitational singularities in General Relativity and divergent series in Analytic Number Theory represent fundamental challenges in standard mathematical analysis. This paper introduces an application of Reversal Dual Calculus (RDC), a framework built upon the harmonic branch of non-Newtonian calculus, to integrate standard linear addition with parallel (reciprocal) addition. We demonstrate that RDC provides a formal mechanism for pole-zero reversal. By applying the parallel mode of RDC to the gravitational potential, we propose a modified Schwarzschild metric that regularizes the singularity at into a smooth core, necessitating an effective energy-momentum tensor analogous to modern regular black hole theories. Furthermore, we present a duality that maps the non-trivial zeros of the Riemann zeta function to poles of a parallel zeta function strictly along the axis.