Self-Organization from Constrained Geometric Radiation

Abstract

How does dynamic order emerge spontaneously in closed systems without external driving? Existing paradigms all require external energy flows, temperature quenching, or slow driving. Here we report constraint-induced self-organization via geometric radiation in coupled metric evolution systems. Simulations reveal a universal four-stage cycle: stress accumulation, super-exponential radiation, chaotic collapse, and convergence to a fractal limit cycle, a novel attractor topology we term the wedge-shaped attractor, with five quantized curvature states and fractal micro-fluctuations. We identify four jointly sufficient conditions: an irreversible geometric horizon, persistent stress injection from quantum coherence, endogenous geometric tension between incompatible curvatures, and effective fluctuations. Their synergy triggers a critical avalanche at the horizon boundary. We prove three theorems: the Geometric Horizon Theorem, the Geometric Energy Dissipation Theorem (implying wave-like entropy evolution in closed systems), and the Radiation as Phase Transition Channel Theorem. We further establish the Constraint-Induced Self-Organization Theorem: these conditions guarantee the complete cycle with probability one. Systematic scans reveal a critical noise threshold and power-law scaling of radiation onset. We verify universality across 12 configurations, multiple noise types, and three geometric flows. This work establishes a new paradigm for closed-system self-organization, forging an exact mathematical duality between classical nonlinear constraints and gravitational horizons.