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.