Analytical Foundations of Holographic Genesis: Thermodynamic, Hydrodynamic, and Spectral Derivations of the Early Universe

This document establishes the mathematical foundations of the Holographic Genesis model. Explicit step-by-step derivations supporting the phenomenology of the confinement phase transition at 50 TeV are presented. The content is structured into five analytical modules: (A) Radion Thermodynamics and vacuum stability via the Goldberger-Wise mechanism; (B) Relativistic hydrodynamics of the domain wall and gravitational wave spectrum; (C) Quantum transport of CP charge and the role of the Chern-Simons term; (D) Group theory for dark matter cogenesis; and (E) Technical appendices on the geometry in the AdS5 bulk.