Resolution of the Hubble Tension from an Exact Theorem Connecting the Cosmological Constant, de Sitter Entropy and a Discrete Algebraic Structure

The 5σ discrepancy between Planck CMB (H₀ = 67. 36 ± 0. 54 km/s/Mpc) and Type Ia supernova distance ladder (H₀ = 73. 04 ± 1. 04 km/s/Mpc) measurements of the Hubble constant remains one of the most significant open problems in cosmology. We present a derivation of H₀ from a discrete algebraic structure with zero adjustable parameters. The cosmological constant Λ and the de Sitter horizon entropy SdS satisfy the exact theorem Λ · SdS · αGUT · 7 = 1, where αGUT = 1/42 is a structural coupling derived from a 14-element exceptional Lie algebra. Given the observed value of Λ, this theorem fixes H₀ = 70. 38 km/s/Mpc. The prediction agrees to within 0. 01 km/s/Mpc with the recent JWST measurement of H₀ = 70. 39 ± 1. 22 (stat) ± 1. 33 (sys) km/s/Mpc by Freedman et al. (2024) using the Tip of the Red Giant Branch method, and sits between the two original conflicting measurements. The result is falsifiable: if future independent measurements settle outside the range 70. 38 ± 0. 5 km/s/Mpc, the underlying theorem fails. The framework also predicts an exact dark energy equation of state w = −1, providing an independent observational test.