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 S_dS satisfy the exact theorem Λ · S_dS · α_GUT · 7 = 1, where α_GUT = 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.