A Theory of Global Mass Duality for Subluminal‒ Superluminal Motion Based on the Paradigm of Analytic Continuation

AbstractThe mass‒velocity relation in classical special relativity is defined only for subluminal motion. Itdiverges at the speed of light and yields no real physical definition in the superluminal regime,which artificially splits the physical system of velocity into a one-sided valid domain. By analogywith the analytic continuation of the Riemann zeta function in complex analysis: an originalmathematical expression is convergent only on one side of the domain; cross-pole continuationcan construct a globally self-consistent functional structure and establish cross-singularityduality relations. Following the same paradigm, this paper takes the speed of light as a firstorder pole and extends the relativistic mass function from the subluminal interval to the fullpositive real velocity domain including superluminal velocities. Through induction of theessential rules governing variable motion, we derive the core cross-light-cone singularity dualityrelation . It is demonstrated that subluminal and superluminal objects paired by theproduct equal to possess identical relativistic mass, establishing a unified global mass‒velocity framework covering both subluminal and superluminal regimes. This work fills atheoretical gap in conventional physics, which only investigates one-sided motion and lackssummarization of cross-singularity multiplicative duality.cv1 v2 = c2c2Keywords: analytic continuation; mass‒velocity relation; superluminal motion; dualitysymmetry; singularity; kinematic law