---
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  "path": "/open-problems/matter/mass-generation",
  "title": "OP-MAT-003 · 质量生成",
  "title_en": "OP-MAT-003 · Mass Generation",
  "category": "物质与拓扑",
  "summary": "最终书稿分别定义静止能量质量、平移惯性、主动引力源和被动外场响应，并给出四者相等所需的源耦合与归一化匹配。局部散度耦合的核外密度响应为零，独立标架拉伸扩展则提供可积的 1/r 远场。",
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  "evidence_status": "UNTESTED",
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      "label": "总览",
      "en": "Overview"
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    {
      "path": "/theory/matter/localization",
      "label": "局域化",
      "en": "Localization"
    },
    {
      "path": "/theory/matter/topological-matter",
      "label": "拓扑物质",
      "en": "Topology"
    },
    {
      "path": "/theory/matter/stability",
      "label": "稳定性",
      "en": "Stability"
    },
    {
      "path": "/theory/matter/mass",
      "label": "质量",
      "en": "Mass"
    },
    {
      "path": "/theory/matter/charge",
      "label": "电荷",
      "en": "Charge"
    },
    {
      "path": "/theory/matter/spin",
      "label": "自旋",
      "en": "Spin"
    },
    {
      "path": "/theory/matter/electron",
      "label": "电子候选",
      "en": "Electron"
    },
    {
      "path": "/theory/matter/proton",
      "label": "质子候选",
      "en": "Proton"
    },
    {
      "path": "/theory/matter/antimatter",
      "label": "反物质",
      "en": "Antimatter"
    },
    {
      "path": "/theory/matter/creation",
      "label": "创生",
      "en": "Creation"
    },
    {
      "path": "/theory/matter/annihilation",
      "label": "湮灭",
      "en": "Annihilation"
    },
    {
      "path": "/tests/matter",
      "label": "现象学要求",
      "en": "Requirements"
    }
  ],
  "canonical_scope": "正式研究框架；粒子理论尚未闭合",
  "source_chapter": "第五章",
  "source_reference": "第五章 §6.7 式（5.6.26）—（5.6.29）；§6.4 式（5.6.14）—（5.6.17）",
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  "source_manifest_url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json",
  "last_reviewed": "2026-09-16",
  "depends_on": [
    "/theory/matter/mass",
    "/theory/space-dynamics/longitudinal-transverse-coupling"
  ],
  "related": [
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  "open_problems": [
    "/open-problems/matter/electron-solution",
    "/open-problems/matter/topological-classification",
    "/open-problems/matter/spin-statistics",
    "/open-problems/matter/proton-structure",
    "/open-problems/matter/mass-spectrum",
    "/open-problems/matter/creation-annihilation"
  ],
  "equations": [
    "mat-mass-equality",
    "sd-mass-match"
  ],
  "sources": [
    {
      "label": "最终合订稿——实际采用范围见本页来源详情",
      "kind": "final-combined-manuscript",
      "url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json"
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      "kind": "historical-source"
    },
    {
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    "已经得到的结果",
    "仍需完成的研究",
    "下一份可复核成果",
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  ],
  "seo_title": "OP-MAT-003 · 质量生成 | 各向异性空间动力学",
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  "translation_path": "/en/open-problems/matter/mass-generation",
  "mathematical_review": "INCOMPLETE",
  "evidence_note": "NOT YET UNIQUELY TESTED · 已知粒子性质是验收要求，不是候选拓扑的验证。",
  "equation": "mat-mass-equality",
  "problem": {
    "expertise": [
      "Variational methods",
      "Continuum dynamics",
      "Gravitational response"
    ],
    "difficulty": "Open research",
    "missing_result": "在同一局域解与运动族上独立计算四种质量，统一核心、伴随场、相互作用及边界账目。保留源函数含速度时的完整 Legendre 变换，检验同一组微观系数能否给出所需归一化。",
    "deliverable": "交付四个定义的积分或响应计算、单位表、收敛检查及其差值；明确 G 和源系数哪些是输入，哪些由模型独立算出。",
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    "locators": [
      "p2248",
      "p2251",
      "p2254",
      "p2284",
      "p2294"
    ],
    "adopted_scope": "已得结果、继续研究任务与下一份交付；保留原问题 ID、优先级及状态。",
    "conditions": [
      "m=E/c² 是能量质量定义；以观测 G 固定归一化不等于推导 G。四种定义有区别，也不意味着它们必然不相等。"
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    "source_reference": "Ch. 4 §4.2; Ch. 5 §6",
    "source_version": "MAT-d1034a344d58",
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}
---
## 已经得到的结果

最终书稿分别定义静止能量质量、平移惯性、主动引力源和被动外场响应，并给出四者相等所需的源耦合与归一化匹配。局部散度耦合的核外密度响应为零，独立标架拉伸扩展则提供可积的 1/r 远场。

<Equation name="mat-mass-equality" />

<Equation name="sd-mass-match" />

## 仍需完成的研究

在同一局域解与运动族上独立计算四种质量，统一核心、伴随场、相互作用及边界账目。保留源函数含速度时的完整 Legendre 变换，检验同一组微观系数能否给出所需归一化。

## 下一份可复核成果

交付四个定义的积分或响应计算、单位表、收敛检查及其差值；明确 G 和源系数哪些是输入，哪些由模型独立算出。

## 适用范围与研究入口

m=E/c² 是能量质量定义；以观测 G 固定归一化不等于推导 G。四种定义有区别，也不意味着它们必然不相等。

[mass](/theory/matter/mass) · [source coupling](/open-problems/space-dynamics/source-coupling) · [longitudinal transverse coupling](/theory/space-dynamics/longitudinal-transverse-coupling) · [matter](/theory/matter)

<CanonicalSource />
