Topological and Thermodynamic Theory of Non-Equilibrium Emergence: A Hierarchical First-Principles Discovery Engine for Autocatalytic Phase Transitions in Open Chemical Networks

While static structure-prediction AIs (e.g., AlphaFold) excel at equilibrium folding, decoding non-equilibrium autocatalytic phase transitions in open chemical networks requires a dynamic, first-principles framework. Here, we present Bio-TMP V5.0, a discovery engine that couples a 20-variable physical master layer (3D CLE-PDEs) with a 5D topological observer layer (Takens embedding, Ollivier-Ricci curvature, and persistent β1 homology). By formalizing phase-space rotational stress as 'Imaginary Dissipation (Im(λ_max))', we derive a closed-form solution for the critical bifurcation boundary. Validated against experimental RNA ribozyme dynamics (Vaidya et al., Nature 2012), Bio-TMP V5.0 precisely pinpoints the critical emergent concentration ([S]_c = 0.57 µM, λ_effective → ≥ 0) where a persistent topological loop (β1 = 1) locks in. This work establishes a foundational physics engine that complements structural AIs, providing an exact thermodynamic criterion and a complete first-principles equation of state for in silico non-equilibrium life emergence screening.