六个领域的结构层验证:立体矩阵建模的可证伪检验

摘要 族一确立双重本质,族二给出归约工具链;本文回答第三个问题:这套工具在真实问题上答出了什么、答错或答不出的又是什么。六个领域案例按五段式展开:引力多体(周期轨道的结构判据——闭合即周期、不闭合即混沌,Li–Liao三维轨道抽样闭合率87.5%;2,033个S₄等价类被三体闭包内射表达)、耦合着色(四色映射为状态分配协议,100%构造求解、O(n log n)、n=20,000 加速约155倍,失败构型具 Errera 指纹)、基因调控(奇负环必振荡的闭式族判据26/26)、博弈(均衡支撑包含性200/200)、椭圆曲线(198/198 Hasse界自洽,分类层级31%→85%→100%)、生态三方系统(有界轨迹成立、相位差未出现,双向记分示范)。总记分:预言命中7/8、未中1、实现失败1,全部入册。全文逐案给出可证伪条件与抽样口径声明,兼作方法论的自检。

Abstract Abstract: Family I established the dual essence, family II gave the reduction tool chain; this paper answers the third question: what has this toolkit actually answered on real problems, and what has it answered wrongly or been unable to answer? Six domain cases unfold in five-part form: gravitational many-body (a structural criterion for periodic orbits — closed means periodic, non-closed means chaotic; Li–Liao three-dimensional orbit sampling closure rate 87.5%; 2,033 S₄ equivalence classes injectively expressed by three-body closure), coupled colouring (four-colouring mapped to a state-assignment protocol, 100% constructive solution, O(n log n), about 155× speed-up at n=20,000, failing configurations bearing the Errera fingerprint), gene regulation (closed-form family criterion for odd-negative-cycle oscillation 26/26), games (equilibrium support inclusion 200/200), elliptic curves (198/198 Hasse-bound self-consistency, classification hierarchy 31%→85%→100%), and three-party ecological systems (bounded trajectories hold, phase difference absent, a two-way scoring demonstration). Overall score: 7/8 predictions hit, 1 miss, 1 implementation failure, all registered. Each case is given falsifiable conditions and sampling-scope declarations, making the paper also a methodological self-audit.

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