{
  "abstract": "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)。",
  "abstract_shown": true,
  "affiliations": [
    "W3 Lab"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Liang Wu",
      "orcid": "0009-0006-9694-5739"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxxvcnzww1pvq.bib",
  "cited_by": 11,
  "doi": "10.5281/zenodo.23430245",
  "fulltext_url": null,
  "id": "dxxvcnzww1pvq",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.23430245",
  "language": "cmn",
  "licence": "CC-BY-NC",
  "licence_label": "CC BY-NC",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7222815717",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/dxxvcnzww1pvq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7222815717",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.23430245"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2605|Tensor decomposition and applications",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "立体矩阵的翻转图动力学与归约收敛",
  "title_text": "立体矩阵的翻转图动力学与归约收敛",
  "type": "preprint",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/dxxvcnzww1pvq",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}