Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913142556065792 |
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| author | Li, Hui Li, Yanxin |
| author_facet | Li, Hui Li, Yanxin |
| contents | Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\to$ module $\to$ system $\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irreversible progression from structure-dominated to regulation-dominated to intelligence-dominated stages. Empirically, we operationalize functional levels and align life, cosmic, informational, and social systems onto this scale. The resulting trajectories are strictly monotonic and exhibit strong cross-system similarity, with high pairwise cosine similarities and robust stage resonance. We locate current system states and project future transitions. RHN provides a mathematically rigorous, multi-scale framework for reconstructing and predicting system evolution, offering theoretical guidance for designing next-generation intelligent systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems Li, Hui Li, Yanxin Physics and Society Social and Information Networks Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\to$ module $\to$ system $\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irreversible progression from structure-dominated to regulation-dominated to intelligence-dominated stages. Empirically, we operationalize functional levels and align life, cosmic, informational, and social systems onto this scale. The resulting trajectories are strictly monotonic and exhibit strong cross-system similarity, with high pairwise cosine similarities and robust stage resonance. We locate current system states and project future transitions. RHN provides a mathematically rigorous, multi-scale framework for reconstructing and predicting system evolution, offering theoretical guidance for designing next-generation intelligent systems. |
| title | Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems |
| topic | Physics and Society Social and Information Networks Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2509.05567 |