α^(3/2) Suppression of Holographic Information Dissipation: Predicting EPOCH's Cosmological Timescale from Quantum Impedance Matching

We identify a phenomenological connection between the fine-structure constant (α ≈ 1/137) and cosmological information dissipation rates that predicts the dark energy decay timescale observed in the EPOCH framework. Kim (2025) empirically determined τ_eff = 21 ± 1.2 Gyr through fitting Type Ia supernova, baryon acoustic oscillation, and CMB data, but the physical origin of this value remained unexplained. We propose that dissipation is suppressed by quantum impedance mismatch at the holographic boundary. Information stored on the 2D cosmological horizon (coupling ∼ α) must transfer to 3D bulk thermalization (coupling ∼ α²). Impedance matching theory predicts the effective coupling is their geometric mean: χ = α^(3/2) ≈ 6.2 × 10^(-4). This yields a parameter-free prediction: τ_eff = 1/(α^(3/2) H_0) ≈ 22 Gyr, matching Kim's empirical value within 6%. Additionally, the √α factor (8.54%) matches the Hubble tension (9% discrepancy between early and late measurements) to within measurement uncertainties, suggesting a unified framework for multiple cosmological anomalies.