{
  "analytic": "superposition-geometry",
  "kind": "declared_analytical_or_constructed_example",
  "experimental_model_result": false,
  "panels": [
    {
      "kind": "vectors",
      "vectors": [
        [
          1.0,
          0.0
        ],
        [
          -0.4999999999999998,
          0.8660254037844387
        ],
        [
          -0.5000000000000004,
          -0.8660254037844385
        ]
      ],
      "xlabel": "Dimension1",
      "ylabel": "Dimension2"
    },
    {
      "kind": "heat",
      "matrix": [
        [
          1.0,
          -0.4999999999999998,
          -0.5000000000000004
        ],
        [
          -0.4999999999999998,
          0.9999999999999999,
          -0.4999999999999998
        ],
        [
          -0.5000000000000004,
          -0.4999999999999998,
          1.0000000000000002
        ]
      ],
      "xlabel": "Feature index",
      "ylabel": "Feature index",
      "unit": "Inner product"
    }
  ],
  "title": "Three feature directions cannot be pairwise orthogonal in 2D",
  "assumptions": "Three unit vectors at0,120,240 degrees; no trained network or discovered feature.",
  "worked": "三个方向两两内积均−0.5，说明该构造存在交叉读取。真实模型是否使用此结构及其语义，仍需独立输入、干预和行为验证。",
  "source_ids": [
    "arxiv-2209.10652",
    "arxiv-1902.10186",
    "attention"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "固定任务与内部记录",
    "候选方向及特征命名",
    "独立相关性检验",
    "消融 / 补丁 / 随机对照",
    "必要性与充分性",
    "新输入上的机制预测"
  ]
}