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 55.3 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 the 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. Note to Version 2.0: This revised edition integrates the exact derivation of the walking parameter (ε ≈ 0.0318) based on F‑Theory flux quantization (K = 3), replacing previous effective estimates. The gravitational‑wave spectrum has been recalculated assuming a fast holographic transition (β/H* ≈ 100), shifting the signal peak to 1.05 Hz in the DECIGO band. Furthermore, the “Resonant Protection” mechanism is introduced to robustify baryogenesis against plasma friction, and the scalar dark‑matter mass is uniquely fixed at the parameter‑free prediction mη ≈ 13.1 GeV.