A Relation Between Gravitational and Electromagnetic Couplings\ Riemann Spectral Statistics

We report a numerical relation between the gravitational and electromagnetic fine-structure constants:π/2ln(1/αG) = 138.27 ≈ 1/αₑₘ = 137.04,accurate to $0.9%$.Equivalently, αG ≈ exp(-2/παₑₘ), or ln(mP/mₚ) ≈ 1/παₑₘ,linking the Planck--proton mass hierarchy to the electromagnetic coupling with zero free parameters.We show that this relation arises naturally within the Discrete Symplectic Cosmology (DSC) framework,where both couplings are determined by the spectral density of Riemann zeta zerosvia the Berry--Keating correspondence.The implied time variation |Ġ/G| ~ 10⁻¹⁷~yr⁻¹ is six orders of magnitudebelow current lunar laser ranging bounds, and the predicted G-fluctuation amplitude (~ 64~ppm)provides a spectral-theoretic floor for the anomalous scatter observed in laboratory measurements of G.