An H2 Tracking Vacuum Sector from Causal Coarse Graining

This paper derives an effective dark energy sector from causal coarse graining of a UV system on the closed time path. In the short memory regime, the nonlocal dynamics reduce to an effective local Markov description, yielding a unique lowest order covariant driver for the coarse variable. Infrared renormalization drives the system toward a late time vacuum sector proportional to M_Pl^2 H^2, while controlled H2 tracking selects the Ohmic universality class. The framework is mapped to the EFT of dark energy in a minimally coupled late time baseline with luminal tensor speed and a ghost free scalar sector. The paper examines background closure, stability, Solar System consistency, and linear growth, and compares the model with DESI DR2 BAO, PantheonPlus supernovae, and Planck 2018 CMB data. The analysis reports an improved fit relative to LambdaCDM with one additional parameter and a preferred CPL ridge slope near q about 3. The paper also distinguishes clearly between derived results and phenomenological assumptions. Derived results include driver uniqueness, kernel moment reduction, one shell flow, Ohmic selection, and truncation error bounds. Assumptions include the scale choice mu = chi H, the normalization choice kappa = 3, and anchoring of the overall amplitude to the present dark energy density.