Is Dark Energy the Cost of Time? An Analytical Derivation of Ω_Λ = ln(2) from Information-Theoretic Constraints

We propose a parameter-free derivation of the dark energy density ΩΛ by identifying observed vacuum energy asthe thermodynamic work required for cosmic information processing. By reconciling the 10123 discrepancy between quantumfield theory (QFT) and observation through a holographic counting of degrees of freedom, we demonstrate that each holographicbit on the cosmic horizon carries exactly one Landauer unit of energy at the de Sitter temperature. We predict an analyticalvalue of ΩΛ = ln(2) ≈ 0.6931, sitting 1.16σ from the Planck 2018 central value of 0.685 ± 0.007. We further predictΩmatter = 1 − ln(2) ≈ 0.3069, compared to the measured 0.315 ± 0.007 (1.16σ). Two independent, parameter-free predictionsfrom a single framework, both within current observational error bars. Falsifiable via Euclid, DESI, and the Rubin Observatory