Exact Physical Motor for Dynamical Dark Energy: The Z-Zero Entropic EFT and the 3.30% S8 Suppression Bound

This letter provides the exact physical motor and numerical evidence for the Z-Zero Protocol, an Effective Field Theory (EFT) where dark energy emerges as a thermodynamic backreaction driven by baryonic information erasure (Landauer's Principle). Utilizing the fine-structure constant (alpha ≈ 0.007) as the fundamental holographic coupling efficiency, we demonstrate an exact background suppression of 3.30% in structure growth (f*sigma8) at z=0 This 3.30% suppression represents the purely linear cosmological baseline (the universal "idle engine"), while the residual observational discrepancy is attributed to non-linear environmental complexity (Gamma_env). The provided framework is ready for full Einstein-Boltzmann (CLASS/CAMB) integration to resolve the persistent Hubble (H0) and S8 tensions. Updated with numerical background integration results from CLASS/Python. Included , , and full evolution charts demonstrating the resolution of both and tensions.