{"ID":2873891,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05567","arxiv_id":"2509.05567","title":"Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems","abstract":"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.","short_abstract":"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 $\\to$ modul...","url_abs":"https://arxiv.org/abs/2509.05567","url_pdf":"https://arxiv.org/pdf/2509.05567v2","authors":"[\"Hui Li\",\"Yanxin Li\"]","published":"2025-09-06T02:49:21Z","proceeding":"physics.soc-ph","tasks":"[\"physics.soc-ph\",\"cs.SI\",\"nlin.AO\",\"physics.data-an\"]","methods":"[]","has_code":false}