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.

Machine Learning (cs.LG)

F.2.2; G.1.0; I.2.6

arXiv:2610.10621 [cs.LG]

(or arXiv:2610.10621v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.10621 Focus to learn more arXiv-issued DOI via DataCite

Supplementary_Information.pdf

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