---
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  "path": "/open-problems/space-dynamics/continuum-microscopic",
  "title": "OP-SD-004 · 连续与微观的对应",
  "title_en": "OP-SD-004 · Continuum-to-Microscopic Correspondence",
  "category": "空间动力学",
  "summary": "等连接 FCC 标量模型已有全波数余弦色散、二阶矩与长波展开。连续时间格点、完整多分量场及反馈后的纵横速度是不同检查层次。本次核对发现式（5.1.11）与随后半角式、四阶展开的系数不能全部按现有写法恒等成立，具体差异在 FCC 专题就地列出。",
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  "locale": "zh",
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      "label": "自由度",
      "en": "Degrees of freedom"
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      "label": "纵向场",
      "en": "Longitudinal field"
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      "path": "/theory/space-dynamics/transverse-field",
      "label": "横向场",
      "en": "Transverse field"
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    {
      "path": "/theory/space-dynamics/wave-propagation",
      "label": "波传播",
      "en": "Wave propagation"
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    {
      "path": "/theory/space-dynamics/longitudinal-waves",
      "label": "自由纵波",
      "en": "Longitudinal waves"
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    {
      "path": "/theory/space-dynamics/longitudinal-transverse-coupling",
      "label": "纵横耦合",
      "en": "L–T coupling"
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      "label": "连续动力学",
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      "label": "FCC 候选",
      "en": "FCC-like model"
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      "label": "母方程前沿",
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      "label": "实验矩阵",
      "en": "Tests"
    }
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  "canonical_scope": "连续场基础；按具体结论标注状态",
  "source_chapter": "第五章",
  "source_reference": "第五章 §1.1—§1.2 式（5.1.1）—（5.1.13）；§6.3 式（5.6.12）—（5.6.13）",
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  "source_manifest_url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json",
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    "/open-problems/space-dynamics/unified-dynamics",
    "/open-problems/space-dynamics/equal-speed",
    "/open-problems/space-dynamics/stable-topology",
    "/open-problems/space-dynamics/longitudinal-wave-detection",
    "/open-problems/space-dynamics/source-coupling"
  ],
  "equations": [
    "sd-fcc-moment",
    "sd-fcc-dispersion"
  ],
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    "已经得到的结果",
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  ],
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  "translation_path": "/en/open-problems/space-dynamics/continuum-microscopic",
  "mathematical_review": "INCOMPLETE",
  "evidence_note": "约束、一致性和提案分别记录；本轮未新增实验拟合。",
  "equation": "sd-fcc-moment",
  "problem": {
    "expertise": [
      "Lattice dynamics",
      "Homogenization"
    ],
    "difficulty": "Open research",
    "missing_result": "先逐个近邻求和、展开并固定系数约定，保留原稿式号并提交差异，不静默替换。再从完整连接律求全部分支、粗粒化权重及误差阶，检验非均匀背景的投影混合和微观刷新前沿。",
    "deliverable": "交付可复算近邻表、动力学矩阵、式间系数核对与作者可审查的更正选项；其后才给出依赖该系数的色散图、适用范围和方向实验响应。",
    "current_state": "等连接 FCC 标量模型已有全波数余弦色散、二阶矩与长波展开。连续时间格点、完整多分量场及反馈后的纵横速度是不同检查层次。本次核对发现式（5.1.11）与随后半角式、四阶展开的系数不能全部按现有写法恒等成立，具体差异在 FCC 专题就地列出。"
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      "p2244",
      "p2303"
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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": [
      "高对称性不替代连接动力学，二阶各向同性不证明全部波数各向同性，连续时间有限邻接不自动给出严格零响应光锥。"
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    "source_reference": "Ch. 4 §4.1; Ch. 5 §§4, 6",
    "source_version": "SD-51779505a476",
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---
## 已经得到的结果

等连接 FCC 标量模型已有全波数余弦色散、二阶矩与长波展开。连续时间格点、完整多分量场及反馈后的纵横速度是不同检查层次。本次核对发现式（5.1.11）与随后半角式、四阶展开的系数不能全部按现有写法恒等成立，具体差异在 FCC 专题就地列出。

<Equation name="sd-fcc-moment" />

<Equation name="sd-fcc-dispersion" />

## 仍需完成的研究

先逐个近邻求和、展开并固定系数约定，保留原稿式号并提交差异，不静默替换。再从完整连接律求全部分支、粗粒化权重及误差阶，检验非均匀背景的投影混合和微观刷新前沿。

## 下一份可复核成果

交付可复算近邻表、动力学矩阵、式间系数核对与作者可审查的更正选项；其后才给出依赖该系数的色散图、适用范围和方向实验响应。

## 适用范围与研究入口

高对称性不替代连接动力学，二阶各向同性不证明全部波数各向同性，连续时间有限邻接不自动给出严格零响应光锥。

[fcc model](/theory/space-dynamics/fcc-model) · [wave propagation](/theory/space-dynamics/wave-propagation) · [continuum dynamics](/theory/space-dynamics/continuum-dynamics) · [space dynamics](/theory/space-dynamics)

<CanonicalSource />
