Geometric Relation Between the Cosmological Constant and Electromagnetic Coupling

This work presents a standalone, falsifiable prediction linking the cosmological constant ΛΛΛ to the fine-structure constant α0α_0α0 through a geometric surface-projection relation. The proposed relation is ΩΛ≡Λc23H02=23N2α02,Ω_Λ ≡ Λ c^2/3H_0^2 = 2/3N^2α_0^2,ΩΛ≡3H02Λc2=32N2α02, where N=ln⁡(1061)N=ln(10⁶¹)N=ln(1061) represents the logarithmic hierarchy between Planck and cosmological scales. This yields the numerical prediction: ΩΛ,pred≈0.700,ΩΛ,pred ≈ 0.700,ΩΛ,pred≈0.700, corresponding to Λpred≈1.12×10−52 m−2forH0≈67.4 km s−1 Mpc−1.Λpred ≈ 1.12×10⁻⁵²\,{m⁻²} for H_0 ≈ 67.4\,{km\,s⁻¹\,Mpc⁻¹}.Λpred≈1.12×10−52m−2forH0≈67.4kms−1Mpc−1. The relation is presented independently of any specific cosmological model, dark-energy field, or ΛCDM parameter fitting, and is formulated as a purely geometric predictive statement. The prediction is directly falsifiable by future precision measurements of ΩΛΩ_ΛΩΛ, α0α_0α0, and H0H_0H0. Any statistically significant deviation from the above relation would rule out the proposed correspondence. This record establishes priority for the proposed relation and provides a testable bridge between microphysical coupling and cosmological vacuum geometry.