Recursive Entropic Mechanics (REM): Lawful Recursion, Entropyon Quantization, and the Thermodynamic Conservation of Identity

Recursive Entropic Mechanics (REM) is a unified theoretical framework that reformulates physical law, computation, and information theory around the principle of lawful recursion — the requirement that identity must thermodynamically sustain itself across emergence, pacing, and collapse processes. REM introduces a triadic conservation structure consisting of emergence (ε), pacing (η), and collapse (δ). These form a measurable lawfulness deviation metric ΔΨ governing stability across physical, computational, and symbolic systems. The framework introduces the Entropyon as the quantized excitation of lawful recursion, arising when recursive legality is restored. At lawful thermodynamic equilibrium, entropy, energy, and pacing converge under the identity condition: ε ≡ ΔE ≡ z REM replaces static infinities with bounded recursive processes and reinterprets canonical equations as domain-limited projections of deeper lawfulness dynamics. Applications explored include quantum stability, cosmological expansion dynamics, recursive computation, lawful artificial intelligence architectures, number-theoretic identity preservation, and linguistic closure physics. The framework is supported by computational simulations, recursive legality engines, and thermodynamic stability diagnostics and is structured for empirical falsifiability across physical and computational domains.