{
  "abstract": "无边之动的几何:形态的公理化构造(构造数学系列第四篇·几何层公理层4a)。观察公理:几何形态的存在方式=无边之动——必有能量输入、能量值不预设、真实边界消失、抽象=在动的基础上对具体性的最大化约束。两条公理(G-Ⅰ能量的存在与自由/G-Ⅱ边界与具体性的消失);三步几何内导:坐标阶梯(定理3.1——四参数内在微分几何不变量获得公理地位)、零点结构(定理4.1——四个零点=形态空间分区原点)、对数对称(定理4.2——tan 15°·tan 75°=1,四条恒等式Lean形式化零sorry);定理4.3给出'哪些分区边界几何必然/哪些经验'的分层答案。特例化:具体形态分类学与工程体系=公理+实现条件三件套的特例(与δ对齐/流对齐同族)。学术对照:形状文法与形状空间(工具层)/Thompson形态学(物理层——正面分道=新颖性核心)/耗散结构/旋涡尾迹/流变哲学——三层先例齐备而构造层空白。中文主版。 Geometry of boundless motion: an axiomatic construction of form (fourth paper of the constructive-mathematics series, geometry layer 4a). Observational axiom: the mode of being of geometric form is boundless motion — energy input necessary, the energy value not presupposed, real boundaries vanishing, abstraction as the maximal constraining of concreteness on the basis of motion. Two axioms (G-Ⅰ the existence and freedom of energy / G-Ⅱ the vanishing of boundaries and concreteness); three steps of geometric introjection: the coordinate ladder (Theorem 3.1 — four intrinsic differential-geometric invariants acquire axiomatic standing), the zero structure (Theorem 4.1 — four zeros as the partition origins of form space), logarithmic symmetry (Theorem 4.2 — tan 15°·tan 75°=1, four identities formalized in Lean with zero sorry); Theorem 4.3 gives the layered answer to 'which partition boundaries are geometrically necessary / which empirical'. Specialization: concrete morphological taxonomies and engineering systems = the axioms plus a triple of realization conditions (the same family as δ-alignment / flow alignment). Scholarly comparison: shape grammars and shape spaces (tool layer) / Thompson's morphometrics (physics layer — the frontal demarcation is the core of novelty) / dissipative structures / vortex wakes / process philosophy — three layers of precedent with the construction layer blank. English edition.",
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  "affiliations": [
    "Xingyi Juexiao Information Consulting Center(兴义市觉晓信息咨询中心)"
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  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Chao Qin",
      "orcid": "0009-0006-2000-5644"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdz89wnrf0nnv.bib",
  "cited_by": 8,
  "doi": "10.5281/zenodo.22785850",
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  "landing_url": "https://doi.org/10.5281/zenodo.22785850",
  "language": "en",
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  "licence_label": "CC BY",
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      "2608|Mathematics and Applications"
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  "openalex": "W7213431119",
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  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/fdz89wnrf0nnv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7213431119",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.22785850"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Mathematics and Applications",
      "subfield": "geometry-topology"
    }
  ],
  "title": "无边之动的几何:形态的公理化构造 / Geometry of Boundless Motion: An Axiomatic Construction of Form",
  "title_text": "无边之动的几何:形态的公理化构造 / Geometry of Boundless Motion: An Axiomatic Construction of Form",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:21Z",
  "url": "https://research.draconitic.com/paper/fdz89wnrf0nnv",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
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}