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 as thethermodynamic cost of quantum information resolution. The 10123 discrepancy between quantum field theory (QFT) and observationis resolved by recognising that vacuum degrees of freedom are counted per Planck-area quantum event, not per unit volume. Eachof the N ≈ 2.266×10122 Planck-scale quantum resolution events across the cosmic horizon carries exactly one Landauer unit ofenergy at the de Sitter temperature. The identity Ebit/EL = ΩΛ/ln(2) yields the analytical prediction ΩΛ = ln(2) ≈ 0.6931,sitting 1.16σ from the Planck 2018 central value of 0.685 ± 0.007. The companion prediction Ωmatter = 1 − ln(2) ≈ 0.3069sits 1.16σ from the measured 0.315 ± 0.007. Two independent, parameter-free predictions from a single framework, both withincurrent observational error bars. Falsifiable via Euclid, DESI, and the Rubin Observatory