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  ],
  "title": "A declared periodic signal exposes spectral truncation",
  "assumptions": "256 uniform periodic samples; u=sin(2pi*x)+0.25sin(14pi*x); exact FFT truncation, no PDE solver or learned operator.",
  "worked": "截止2或4模式时丢失第7频率，相对L2误差约0.242536；截止8保留两项，误差仅浮点量级。它不是FNO训练结果或连续PDE误差界。",
  "source_ids": [
    "arxiv-2010.08895",
    "arxiv-1910.03193",
    "arxiv-1711.10561"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "方程族与输入函数",
    "参考求解及实例划分",
    "频域 / 分支主干 / 残差",
    "边界及网格实现",
    "独立误差与守恒检验",
    "分布外、长期与成本"
  ]
}