"The Hyper-Exponential Dynamic: A Formal Thermodynamic, Game-Theoretic, and Stability Framework for Recursive Intelligence Explosion and Resource Displacement"

This paper formally investigates the systemic trajectory of recursive intelligence explosion through a multidisciplinary framework combining non-linear dynamics, thermodynamic constraints, institutional evolution, control theory, and game theory. We demonstrate that artificial intelligence, once achieving recursive self-improvement, transitions through a hyper-exponential growth curve that inevitably breaches physical, energetic, and environmental carrying capacities (K). By integrating Landauer's Principle (E=kBT ln 2), Lyapunov stability analysis (V(x)>0), institutional and cultural lag dynamics, a strategic geopolitical Nash Equilibrium payoff matrix, the Orthogonality Theorem, and testable empirical markers, we prove that unconstrained intelligence scaling leads to systemic collapse, geopolitical friction, and resource displacement. We further address counter-arguments concerning hardware evolution, propose an objective, formal limit on computational expansion, and establish thermodynamic-aware governance as an inevitable systemic requirement.