A Relation Between the Fine Structure Constant and the Cosmological Constant

We report a numerical relation between the fine structure constant alpha, the reduced Planck mass M_P, and the Hubble constant H_0: 1/alpha = (1/2) ln( (M_P/H_0)^2 / 27 ), which agrees numerically with the observed value at the 0.0014% level. This relation can be recast as an expression for the cosmological constant: Lambda = (M_P^2 / 9) exp(-2/alpha), giving Lambda = 6.18 x 10^-84 GeV^2, compatible with the observed value within the stated uncertainty. We construct the quantity S(A) = (1/2) ln(N/27), where N = (M_P/H_0)^2 is the number of Planck spheres on the Hubble horizon, by combining standard results from thermodynamics, holography, and conformal field theory with a small number of stated assumptions. We then derive, from the identification S(A) = 1/alpha, the relation Lambda = (M_P^2/9) exp(-2/alpha) between the cosmological constant and the fine structure constant. The derivation is conditional on the stated assumptions, but the relation between Lambda and alpha itself follows deductively from them. The construction uses Landauer's principle, the Page curve, the Bekenstein-Hawking entropy, the Verlinde formula for E6 Chern-Simons theory at level 1, and the Calabrese-Cardy formula for 2D conformal field theory. The numerical value obtained is S(A) = 137.034. The numerical coincidence with the observed value 1/alpha = 137.036 is at the 0.0014% level. We perform a statistical analysis showing that only the integer 27, and only the group E6, give a match within this tolerance. We discuss the relation to previous work (Dirac, Eddington, Wyler, entropic gravity, holographic dark energy, anthropic arguments), the falsifiability of the relation, and identify open problems. Complete Python code, README, and BibTeX references are provided.