Regularizing Relativistic Singularities through a C ∞ -Smooth Extension of the d'Alembert Invariance: Implications for the Hubble Tension

We derive a $C^\infty$-smooth extension of classical relativity that regularizes singularities of SRT by replacing the divergent Lorentz factor with a structurally complete boost. Unlike the metric truncation inherent in Special Relativity, our Asymptotic Lorentz Relativity (ALR) framework provides the "missing information" necessary for a non-singular description of the high-energy regime. We demonstrate that the $5\sigma$ Hubble tension is not a statistical anomaly but an analytical residue of this truncation. By restoring d'Alembertian form-invariance, we identify a Hubble Matching Scale (HMS) that reconciles local SH0ES measurements with global Planck constraints without auxiliary parameters. The framework aligns with recent calls for a fundamental update to the cosmological model (Binney et al. 2025) and addresses fundamental divergences in field theory (Leuchs & Sánchez-Soto 2025).