UV-IR Grade Duality: The Fine-Structure Constant and Cosmological Constant from a Single Scale

We show that the fine-structure constant \(\alpha\) (an ultraviolet observable, measured at \(M_Z \approx 91\) GeV) and the cosmological constant \(\Lambda\) (an infrared observable, measured at \(H_0 \approx 10^{-33}\) eV) are both determined by a single parameter: the SUSY mass multiplier \(f \approx 2.12\) in the Latent grade hierarchy. The \(\alpha\) constraint determines \(f\) through transcendental renormalization group equations (\(f_\alpha = 2.120735\)); the \(\Lambda\) constraint determines \(f\) through an algebraic power-law seesaw (\(f_\Lambda = 2.117859\)). These two independent determinations agree to 0.14% — despite \(\Lambda\) being 2062 times more sensitive to \(f\) than \(\alpha\). We call this the UV-IR grade duality: UV and IR observables are different grade projections of the same analyticity radius. The self-consistent scale \(f_{\text{SC}} = 2.11786\) (\(M_{\text{eff}} = 5604\) GeV) simultaneously gives \(1/\alpha = 137.035\) (0.0005% deviation) and \(\rho_\Lambda = 2.524 \times 10^{-47}\) GeV\(^4\) (0.11% deviation). The duality makes a quantitative prediction: two-loop corrections must close the 0.14% gap, and any measurement of the SUSY spectrum will test both constraints simultaneously.