---
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  "path": "/open-problems/matter/electron-solution",
  "title": "OP-MAT-001 · 稳定有限能量电子解",
  "title_en": "OP-MAT-001 · Stable Finite-Energy Electron Solution",
  "category": "物质与拓扑",
  "summary": "ASD 用最小负电荷扇区中的闭合取向结构描述电子。第四章已给出取向场、有限能量边界、拓扑流和电荷匹配；第五章给出一参数尺度能量的唯一正驻点及径向二阶检查。尺度稳定机制已有解析结果，研究任务由此进入完整三维电子构型。",
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  "evidence_status": "UNTESTED",
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      "label": "局域化",
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      "en": "Topology"
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    {
      "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"
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    {
      "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"
    },
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      "label": "现象学要求",
      "en": "Requirements"
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  "canonical_scope": "正式研究框架；粒子理论尚未闭合",
  "source_chapter": "第四、五章",
  "source_reference": "第四章 §2 式（4.17）—（4.29）；第五章 §6 式（5.6.21）—（5.6.30）",
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    "/open-problems/matter/mass-generation",
    "/open-problems/matter/spin-statistics",
    "/open-problems/matter/proton-structure",
    "/open-problems/matter/mass-spectrum",
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  "equations": [
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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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  ],
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  "translation_path": "/en/open-problems/matter/electron-solution",
  "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-boundary",
  "problem": {
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      "Numerical analysis",
      "Stability theory"
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    "difficulty": "Open research",
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    "deliverable": "先交付一份可复算的电子扇区求解：方程残差、边界与网格收敛、背景扣除能量、拓扑积分及扰动谱。由同一核心—周围场系统继续计算电荷、质量和旋转响应，逐项标明标定参数。",
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    "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": [
      "径向尺度极小值不代替完整三维解和全部扰动稳定性；2π 内部相位标记不单独决定三维映射度。"
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}
---
## 已经得到的结果

ASD 用最小负电荷扇区中的闭合取向结构描述电子。第四章已给出取向场、有限能量边界、拓扑流和电荷匹配；第五章给出一参数尺度能量的唯一正驻点及径向二阶检查。尺度稳定机制已有解析结果，研究任务由此进入完整三维电子构型。

<Equation name="mat-boundary" />

<Equation name="sd-derrick" />

## 仍需完成的研究

固定共同作用量、目标空间、系数来源和边界，求最小电荷扇区的有限能量解；计算非径向扰动、平移和旋转零模，检查分裂与辐射。若保留有序幅度，需检查过零解缠；若核心周期运动，则采用周期背景的 Floquet 检查。

## 下一份可复核成果

先交付一份可复算的电子扇区求解：方程残差、边界与网格收敛、背景扣除能量、拓扑积分及扰动谱。由同一核心—周围场系统继续计算电荷、质量和旋转响应，逐项标明标定参数。

## 适用范围与研究入口

径向尺度极小值不代替完整三维解和全部扰动稳定性；2π 内部相位标记不单独决定三维映射度。

[stability](/theory/matter/stability) · [electron](/theory/matter/electron) · [localization](/theory/matter/localization) · [master equation](/theory/space-dynamics/master-equation) · [matter](/theory/matter)

<CanonicalSource />