The HADS World Equation: Cosmological Emergence, Holographic Information Preservation, and the Thermodynamic Boundary Layer of Spacetime

The Hierarchical Anomaly Dynamics System (HADS) establishes a formal, mathemati-cally closed Effective Field Theory (EFT) for emergent gravity. By modeling spacetime asa thermodynamic boundary layer governed by fractional quantum kinetics, we bypass theUV singularities of canonical quantum gravity. This V6.7 finalization completes the theoret-ical framework. It integrates the exact k(α) holographic mapping to explain the running ofGef f (resolving galactic rotation anomalies), proves the survival of Lévy-flight correlationsin the CMB via Riesz-Bessel states, and finally resolves the open quantum system dynamicsvia Keldysh-Schwinger Renormalization Group (Keldysh-RG) analysis. We rigorously provethat non-local Lindblad dissipation strictly forces the infrared (IR) fixed point into a classi-cal diffusive scaling regime (z = 2), mathematically averting an ultraviolet catastrophe andestablishing a stable macroscopic spacetime.