Self-Organization from Constrained Geometric Radiation

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Computer Science > Machine Learning arXiv:2610.10621 (cs) [Submitted on 7 Oct 2026] Title: Self-Organization from Constrained Geometric Radiation Authors: Ming Lei.

计算机科学 > 机器学习 arXiv:2610.10621 (cs) [提交于 2026 年 10 月 7 日] 标题：受限几何辐射下的自组织作者：Ming Lei。

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.

摘要：在没有外部驱动的封闭系统中，动态秩序是如何自发产生的？现有的范式都需要外部能量流、温度淬火或缓慢驱动。在此，我们报告了耦合度量演化系统中通过几何辐射诱导的约束自组织。

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.

模拟揭示了一个普遍的四阶段循环：应力积累、超指数辐射、混沌坍缩以及向分形极限环的收敛；这是一种我们称之为“楔形吸引子”的新型吸引子拓扑结构，具有五个量子化曲率状态和分形微涨落。

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.

我们确定了四个共同充分条件：不可逆的几何视界、来自量子相干性的持续应力注入、不相容曲率之间的内源性几何张力，以及有效涨落。它们的协同作用在视界边界触发了临界雪崩。

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.

我们证明了三个定理：几何视界定理、几何能量耗散定理（暗示封闭系统中的波状熵演化）以及作为相变通道的辐射定理。我们进一步建立了约束诱导自组织定理：这些条件以概率一保证了完整循环的发生。

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.

系统扫描揭示了临界噪声阈值和辐射起始的幂律标度。我们验证了跨越 12 种配置、多种噪声类型和三种几何流的普适性。这项工作为封闭系统自组织建立了一个新范式，在经典非线性约束与引力视界之间构建了精确的数学对偶。