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