A Geometric Resolution of the Hubble Tension via G2-Metric Scaling and the 3/14 Coupling Constant

The 5-sigma discrepancy between early-universe (Planck CMB) and local (SH0ES) measurements of the Hubble constant (H0) represents a critical challenge to the Lambda-CDM model. This paper proposes a scale-invariant metric theory, the G-Theorem, which identifies the Hubble tension as a geometric projection effect. By defining a topological coupling constant kappa = 3/14, derived from the dimensional ratio of the Lie algebras su(2) and g2 (the automorphism group of the octonions), we establish a transformation between the global background flow and the local matter-influenced metric. We show that the local Hubble constant follows the relation H_local = H_global * sqrt(1 + kappa). Applying the Planck value of H_global approx. 67.4 km/s/Mpc, the model predicts H0 approx. 74.21 km/s/Mpc, showing exceptional agreement with current local observations.