立体矩阵的翻转图动力学与归约收敛

摘要 立体矩阵(SM)的分解不是静态对象:每个张量的全部分解经翻转(flip)移动连成一张图——翻转图——SM对象由此自带动力学。本文系统建立SM的内蕴动力学理论,整合前期结构研究的闭链复形研究、前期 SMM 研究的翻转图普查与商空间地貌研究。内蕴篇给出四组结果:其一,移动集公理与守恒量——flip/plus/reduce 的恒等式基础,张量本身为严格守恒量(数万步游走精确门控零失败);其二,闭链的链复形理论——体的八元组结构引理(一般 n 完整证明)、体数公式 b(n)=12n³(n−1)、4:1闭链律 b=4β₃(不等式方向已证,等号为带精确阻塞点描述的猜想)、原生闭链消失律 G'(n)=0(n≥5);其三,重力场定理——秩函数在翻转图上诱导源-汇分层,朴素分解类是不可返回的源点,plus 是唯一逆流通道;其四,纹理定律——闭链谱以2-闭链为主导(跨容器占比稳定于15–17%)、新类发现的爆发式节律(间隔变异系数 CV≈5–7)、成本率拐点作为空间已被认知完毕的可计算停机信号。表征篇讨论外在动力学:PDE 演化可编码为冻结过渡态上的影子(纲领级命题)。本文如实标注能力分级:已证的是表征能力,计算效率优势无任何证据。

Abstract Abstract: The decompositions of a stereo matrix (SM) are not a static object: all decompositions of each tensor are linked by flip moves into a graph — the flip graph — so an SM object carries its own dynamics. This paper systematically establishes the intrinsic dynamics of SM, integrating the earlier chain-complex study, the flip-graph census and the quotient-space landscape study. The intrinsic part gives four groups of results: first, the move-set axioms and conserved quantities — the identity basis of flip/plus/reduce, with the tensor itself a strict conserved quantity (tens of thousands of walk steps, exact gating, zero failures); second, the chain-complex theory of closed chains — the octet structure lemma for cells (complete proof for general n), the cell-count formula b(n)=12n³(n−1), the 4:1 closed-chain law b=4β₃ (inequality direction proved, equality a conjecture with an explicit obstruction description), and the native closed-chain vanishing law G′(n)=0 (n≥5); third, the gravity-field theorem — the rank function induces source–sink stratification on the flip graph, the naive decomposition class is an irrevocable source, and plus is the unique upstream channel; fourth, the texture law — the closed-chain spectrum is dominated by 2-chains (cross-container share stable at 15–17%), new-class discovery exhibits a bursty rhythm (interval coefficient of variation CV≈5–7), and the cost-rate knee is a computable stopping signal that the space has been fully cognized. The representational part discusses extrinsic dynamics: PDE evolution can be encoded as a shadow on frozen transition states (programme-level proposition). Capability grading is stated honestly: what is proved is representational capacity; no evidence whatsoever supports a computational-efficiency advantage.

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