Note on Asymptotic Lorentz Relativity: Mathematical Truncation of Boost Factors and the Resolution of Einsteinian Singularities

This manuscript provides a critical mathematical deepening of Asymptotic Lorentz Relativity (ALR) by exposing the fundamental presence of the canonical geometric series within foundational kinematics. It demonstrates that classical relativistic singularities at the light limit are not absolute physical laws, but rather algebraic artifacts resulting from a severe truncation of the infinite geometric series. While Newtonian mechanics retains only the first term (S_0) and Einsteinian relativity truncates the series at the first two terms (S_1), ALR utilizes the complete, un-truncated infinite sequence (S_∞) to regularize the boundary without modifying the action with artificial higher-order curvature terms.