立体矩阵建模的统一协议:四领域实例与四色机制
Year: 2026
Type: preprint
Abstract: 摘要 本文将系列之一的建模方法展开为可复算的统一协议与案例集,回答:SM建模在多个相异的领域上是否保持同一骨架、同一结构律?统一协议包括建模五步 M1–M5、分析六步 A1–A6 与判读三规范(外部标尺隔离、能力边界强制声明、双向记分)。四个预注册实例:引力三体混沌系综(150条轨道、81,525样本,闭式核验 f=12×37、b=8×15、β₃=2×15 全部精确,广义密度律 b/β₃=4.0 在各阈值无一例外;预言 G4 未命中入册并直接催生密度定理)、三基因布尔调控网络(13基元×{激活,抑制}=26实例与 Milo 2002 普查一致;三抑制环 S=∅ 当且仅当奇负环必振荡,与 Elowitz–Leibler 判据一致)、三人两策略博弈(200局系综加 McKelvey–McLennan 旗舰例,闭式 f=13|S|、b=8m、β₃=2m 全零失败;纯均衡支撑包含性200/200)、元胞自动机 EC198。四色机制的SM构造:平面三角剖分4-染色100%构造成功、复杂度 O(n log n)、Errera 构型指纹(1,1,1,2)(本文不声称给出四色定理新证明)。跨实例共同点:同一骨架,唯一差异在耦合构造规则;外部对应一致地发生在模式/判据/极值层级而非精细动力学层级。 Abstract This paper expands the modelling method of the first paper into a reproducible unified protocol and case set, asking: does SM modelling preserve the same skeleton and the same structural laws across quite different domains? The unified protocol comprises five modelling steps M1–M5, six analysis steps A1–A6, and three interpretative norms (external-ruler isolation, mandatory capability-boundary declaration, two-way scoring). Four pre-registered cases: a gravitational three-body chaotic ensemble (150 orbits, 81,525 samples; closed-form checks f=12×37, b=8×15, β₃=2×15 all exact, the generalized density law b/β₃=4.0 holding at every threshold without exception; prediction G4 missed, registered, and directly giving rise to the density theorem); a three-gene Boolean regulatory network (13 motifs × {activation, inhibition} = 26 instances consistent with the Milo 2002 census; a three-inhibition cycle S=∅ iff an odd negative cycle necessarily oscillates, consistent with the Elowitz–Leibler criterion); a three-player two-strategy game (a 200-round ensemble plus the McKelvey–McLennan flagship example; closed forms f=13|S|, b=8m, β₃=2m with zero failures; pure-equilibrium support inclusion 200/200); and cellular automaton EC198. SM construction of the four-colour mechanism: planar triangulation 4-colouring succeeds 100%, complexity O(n log n), Errera configuration fingerprint (1,1,1,2) (no new proof of the four-colour theorem is claimed). The common point across instances: one skeleton, the only difference lying in the coupling-construction rule; external correspondence consistently occurs at the level of patterns/criteria/extremes rather than fine-grained dynamics. 本记录含中文版与英文版两个文件(Bilingual: Chinese + English DOCX)。
Author: Wu, Liang
Language: cmn
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222806871