{
  "abstract": "自发比数理论:比值的构造理论。数学对象为 n 维正实比值矢量 q∈Λⁿ=(0,∞)ⁿ——取值与维数均不预设。四条公理与一条定义生长出完整结构链:层级谱(一阶 n、二阶 C(n,2)、链式约束后独立自由度 n−1)、形状空间(Weyl 腔 Aₙ₋₁)与结构地图定理(对称=测度零、部分对称类按整数分拆计数、一般位置=完全破缺)、单纯形同构定理(与成分单纯形精确同构,往返误差 4.4e-16,对数比坐标同一)、对数墙定理(形状-标度分离+退化边界的连续势必含对数标度分量——自发动力学的墙项是结构必然而非建模选择)、差型唯一性定理(形状层耦合势由对称性唯一钉死)。特例化:成分数据分析几何=静力学截面特例,椭球形状分析=三维截断特例。学术对照:比的基础化四幕史(欧多克索斯/von Staudt/Cayley–Klein/Buckingham)之上的第五幕;静力学比值结构有先例(Aitchison),对象本体自发动力学无对应。核心测度论内容 Lean 形式化零 sorry。中文主版。 Spontaneous ratio structures: a constructive theory of ratios. The mathematical object is an n-dimensional positive ratio vector q∈Λⁿ=(0,∞)ⁿ, with neither values nor dimension presupposed. Four axioms and one definition grow a complete structural chain: the hierarchy spectrum, the shape space (Weyl chamber Aₙ₋₁) with the structure-map theorem (symmetry = measure zero; general position = complete symmetry breaking), the simplex isomorphism theorem (exact isomorphism with the compositional simplex, round-trip error 4.4e-16), the logarithmic wall theorem (the wall of the spontaneous dynamics is a structural necessity, not a modeling choice), and the difference-type uniqueness theorem. Specialization: compositional data analysis geometry is the static sectional case. Scholarly comparison: the fifth act atop the four-act history of founding the ratio; static ratio structures have precedents (Aitchison), object-ontological spontaneous dynamics has no counterpart. Core measure-theoretic content formalized in Lean with zero sorry. English edition.",
  "abstract_shown": true,
  "affiliations": [
    "Xingyi Juexiao Information Consulting Center"
  ],
  "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/6n9j1dd850js8.bib",
  "cited_by": 9,
  "doi": "10.5281/zenodo.22783548",
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  "id": "6n9j1dd850js8",
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  "landing_url": "https://doi.org/10.5281/zenodo.22783548",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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      "openalex",
      "2608|Mathematics and Applications"
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  "openalex": "W7213423059",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/6n9j1dd850js8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7213423059",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.22783548"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Mathematics and Applications",
      "subfield": "geometry-topology"
    }
  ],
  "title": "自发比数理论:比值空间上的层级与自发动力学 / Spontaneous Ratio Structures: Hierarchy and Spontaneous Dynamics on the Ratio Space",
  "title_text": "自发比数理论:比值空间上的层级与自发动力学 / Spontaneous Ratio Structures: Hierarchy and Spontaneous Dynamics on the Ratio Space",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:21Z",
  "url": "https://research.draconitic.com/paper/6n9j1dd850js8",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}