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

This paper establishes the minimal mathematical skeleton for the HADS World Equation, a formal effective field theory (EFT) of emergent gravity. Moving beyond kinematic formulations, we address the dynamic emergence of transversal, massless spin-2 gravitons by utilizing dissipative ghost suppression to satisfy unitarity constraints. Furthermore, we present a microscopic holographic framework, demonstrating that integrating anyonic quantum dimensions via the Verlinde formula converges to the exact Bekenstein-Hawking entropy (S = A/4G_eff). Finally, we implement fractional Callan-Harvey anomaly cancellation on a long-range lattice, establishing a strictly falsifiable architecture with orthogonal non-Gaussian signatures (f_NL^orth) for upcoming precision cosmology.