复杂系统的双重本质:多体耦合与归约

摘要 复杂系统研究长期处于现象相似而理论割裂的状态:微分方程给出数值演化、网络科学给出静态结构、统计物理给出系综规律,涌现、自组织、混沌、相变各造理论。本文提出并实证一个双重本体论主张:复杂系统的本质是多体耦合关系及其归约结构。耦合具有先验的高维拓扑结构——3元耦合对应四面体(648体、162腔),4元耦合对应六面体,N元耦合对应N维单形;任意N元耦合可归约为三元耦合的组合,任意等价类沿规约路径收敛于标准形态(全谱143,930类平均6.98步、最坏7步抵达标准等价类 S*)。据此,立体矩阵(SM)成为复杂系统的书写语言:微分方程给出数值预测,SM给出结构预测。本文给出统一建模协议(耦合矩阵→格化→对称群商化→等价类→序列指纹),并在六个领域实证其跨域有效性:引力多体(周期轨道闭合率87.5%,混沌不闭合)、耦合着色(100%构造求解)、基因调控(26/26闭式族)、博弈(200/200)、椭圆曲线(198/198)、生态三方系统。涌现、自组织、混沌与相变由此获得统一解释:分别为等价类吸引子、规约路径、等价类不闭合、结构分岔。

Abstract Complex-system research has long remained in a state of phenomenological similarity and theoretical fragmentation: differential equations give numerical evolution, network science gives static structure, statistical physics gives ensemble laws, and emergence, self-organization, chaos and phase transition each build their own theory. This paper proposes and substantiates a dual-ontology thesis: the essence of complex systems is multi-body coupling relations and their reduction structure. Coupling possesses an a priori high-dimensional topological structure — 3-way coupling corresponds to a tetrahedron (648 cells, 162 chambers), 4-way coupling to a hexahedron, and N-way coupling to an N-dimensional simplex; any N-way coupling reduces to a combination of 3-way couplings, and any equivalence class converges along the reduction path to the standard form (all 143,930 classes in the spectrum reach the standard equivalence class S* in an average of 6.98 steps and at worst 7). On this basis the Stereo Matrix (SM) becomes the writing language of complex systems: differential equations give numerical predictions, SM gives structural predictions. We give a unified modelling protocol (coupling matrix → latticeization → symmetry-group quotient → equivalence class → sequence fingerprint) and substantiate its cross-domain validity in six fields: gravitational many-body (periodic-orbit closure rate 87.5%, chaos not closing), coupled colouring (100% constructive solution), gene regulation (26/26 closed-form family), games (200/200), elliptic curves (198/198), and three-party ecological systems. Emergence, self-organization, chaos and phase transition thereby receive a unified explanation: respectively as equivalence-class attractor, reduction path, non-closure of equivalence classes, and structural bifurcation.

本记录含中文版与英文版两个文件(Bilingual: Chinese + English DOCX)。