math_cms/public/data/tree.json

{
  "id": "M00",
  "label": "初中数学知识体系",
  "children": [
    {
      "id": "M01",
      "label": "数与代数",
      "children": [
        {
          "id": "S01",
          "label": "数的认识与运算",
          "children": [
            {
              "id": "R01",
              "label": "整数与自然数",
              "skills": ["整数概念", "自然数概念", "数轴位置"],
              "direct_score": [1,2],
              "related_score": [1,2],
              "children": []
            },
            {
              "id": "R02",
              "label": "有理数分类",
              "skills": ["正数负数", "零", "分数小数互化"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "R03",
              "label": "有理数加减法",
              "skills": ["同号相加", "异号相减", "数轴表示运算"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "R04",
              "label": "有理数乘除法",
              "skills": ["符号法则", "倒数", "乘方意义"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "R05",
              "label": "幂与指数",
              "skills": ["指数意义", "幂的运算性质"],
              "direct_score": [1,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "R06",
              "label": "科学记数法",
              "skills": ["有效数字", "数量级"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "R07",
              "label": "平方与平方根",
              "skills": ["平方意义", "算术平方根"],
              "direct_score": [2,4],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "R08",
              "label": "立方与立方根",
              "skills": ["立方运算", "立方根概念"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "R09",
              "label": "实数",
              "skills": ["无理数", "实数分类", "数轴连续性"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            }
          ]
        },

        {
          "id": "S02",
          "label": "代数式与整式运算",
          "children": [
            {
              "id": "A01",
              "label": "代数式基本概念",
              "skills": ["字母表示数", "代入求值", "代数式结构"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "A02",
              "label": "整式的概念",
              "skills": ["单项式", "多项式", "次数"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "A03",
              "label": "同类项合并",
              "skills": ["合并规则", "规范化表达"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "A04",
              "label": "去括号与加减法",
              "skills": ["符号处理", "括号运算"],
              "direct_score": [2,4],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "A05",
              "label": "整式乘法",
              "skills": ["分配律", "单项式乘多项式", "多项式乘多项式"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "A06",
              "label": "特殊乘法公式",
              "skills": ["平方差公式", "完全平方公式"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },

            {
              "id": "A07",
              "label": "因式分解（基础）",
              "skills": ["提公因式法", "公式法"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "A08",
              "label": "因式分解（进阶）",
              "skills": [
                "分组分解",
                "十字相乘",
                "AC分解法",
                "拆项构造分解"
              ],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            },

            {
              "id": "A09",
              "label": "因式分解综合应用",
              "skills": [
                "识别分解形式",
                "构造分解",
                "复杂代数式化简"
              ],
              "direct_score": [5,7],
              "related_score": [7,12],
              "children": []
            }
          ]
        },

        {
          "id": "S03",
          "label": "分式与分式运算",
          "children": [
            {
              "id": "F01",
              "label": "分式概念",
              "skills": ["整式做分子分母", "分式值域"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "F02",
              "label": "分式约分",
              "skills": ["因式约分", "整体法"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "F03",
              "label": "分式通分",
              "skills": ["最小公倍式", "整体通分"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "F04",
              "label": "分式加减法",
              "skills": ["通分", "同分母加减"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "F05",
              "label": "分式乘除法",
              "skills": ["倒数乘法", "因式消去"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "F06",
              "label": "分式综合化简",
              "skills": ["整体代数化简", "复杂表达式处理"],
              "direct_score": [3,6],
              "related_score": [5,8],
              "children": []
            }
          ]
        },

        {
          "id": "S04",
          "label": "实数与根式运算",
          "children": [
            {
              "id": "RS01",
              "label": "平方根",
              "skills": ["平方根意义", "正负根"],
              "direct_score": [1,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "RS02",
              "label": "立方根",
              "skills": ["立方根意义", "实数范围讨论"],
              "direct_score": [1,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "RS03",
              "label": "根式的基本性质",
              "skills": ["根式拆分", "根式乘除"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "RS04",
              "label": "根式化简",
              "skills": ["二次根式化简", "最简根式"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "RS05",
              "label": "根式混合运算",
              "skills": ["同类项合并", "整体化简"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            }
          ]
        },

        {
          "id": "S05",
          "label": "代数建模基础",
          "children": [
            {
              "id": "M01A",
              "label": "代数式表示现实问题",
              "skills": ["变量表示数量", "式子表示关系"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "M01B",
              "label": "数量关系建模",
              "skills": ["数形结合", "方程建模"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "M01C",
              "label": "复杂代数式结构分析",
              "skills": ["拆项分析", "整体处理"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            }
          ]
        }
      ]
    },
    {
      "id": "M02",
      "label": "方程与不等式",
      "children": [
        {
          "id": "E01",
          "label": "一元一次方程",
          "children": [
            {
              "id": "E01A",
              "label": "方程基本概念",
              "skills": ["未知数", "等式性质", "等式变形"],
              "direct_score": [1,2],
              "related_score": [2,3],
              "children": []
            },
            {
              "id": "E01B",
              "label": "移项与合并同类项",
              "skills": ["移项规则", "符号处理"],
              "direct_score": [2,3],
              "related_score": [3,4],
              "children": []
            },
            {
              "id": "E01C",
              "label": "方程解的检验",
              "skills": ["代入检验", "增根分析"],
              "direct_score": [1,2],
              "related_score": [2,3],
              "children": []
            }
          ]
        },

        {
          "id": "E02",
          "label": "一元一次方程组",
          "children": [
            {
              "id": "E02A",
              "label": "代入法",
              "skills": ["代入变量", "化简求解"],
              "direct_score": [2,4],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "E02B",
              "label": "加减法",
              "skills": ["同系数构造", "消元"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "E02C",
              "label": "方程组应用建模",
              "skills": ["数量关系分析", "二元问题建模"],
              "direct_score": [3,5],
              "related_score": [5,7],
              "children": []
            }
          ]
        },

        {
          "id": "E03",
          "label": "不等式与不等式组",
          "children": [
            {
              "id": "E03A",
              "label": "不等式性质",
              "skills": ["基本性质", "不等式方向判断"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "E03B",
              "label": "一元一次不等式",
              "skills": ["移项变形", "解集表示"],
              "direct_score": [2,4],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "E03C",
              "label": "数轴表示解集",
              "skills": ["区间表示法", "开闭区间理解"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "E03D",
              "label": "不等式组",
              "skills": ["两个不等式共同解集", "区间交集"],
              "direct_score": [3,4],
              "related_score": [4,6],
              "children": []
            }
          ]
        },

        {
          "id": "E04",
          "label": "分式方程",
          "children": [
            {
              "id": "E04A",
              "label": "分式方程概念",
              "skills": ["整式作分母", "方程定义域"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "E04B",
              "label": "方程去分母",
              "skills": ["最小公倍式", "消分母技巧"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "E04C",
              "label": "增根分析",
              "skills": ["定义域限制", "代入检验"],
              "direct_score": [2,3],
              "related_score": [4,6],
              "children": []
            }
          ]
        },

        {
          "id": "E05",
          "label": "一元二次方程",
          "children": [
            {
              "id": "E05A",
              "label": "配方法",
              "skills": ["完全平方构造", "顶点式连接"],
              "direct_score": [3,4],
              "related_score": [5,7],
              "children": []
            },
            {
              "id": "E05B",
              "label": "求根公式",
              "skills": ["判别式", "根的表达"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "E05C",
              "label": "因式分解解法",
              "skills": ["二次三项式识别", "零乘积定律"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "E05D",
              "label": "根与系数关系",
              "skills": ["韦达定理", "求参数"],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "E05E",
              "label": "方程根的分布",
              "skills": ["根的符号判断", "根的位置"],
              "direct_score": [4,6],
              "related_score": [7,10],
              "children": []
            }
          ]
        },

        {
          "id": "E06",
          "label": "方程思想与实际应用",
          "children": [
            {
              "id": "APP_E1",
              "label": "行程问题方程建模",
              "skills": ["路程速度时间关系", "方程建模"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "APP_E2",
              "label": "工程问题方程建模",
              "skills": ["工作效率", "整体工作量划分"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "APP_E3",
              "label": "溶液浓度建模",
              "skills": ["百分比", "方程求解"],
              "direct_score": [3,4],
              "related_score": [5,7],
              "children": []
            },
            {
              "id": "APP_E4",
              "label": "几何方程建模",
              "skills": ["几何量关系", "代数化处理"],
              "direct_score": [4,6],
              "related_score": [6,9],
              "children": []
            }
          ]
        }
      ]
    },
    {
      "id": "M03",
      "label": "几何图形与性质",
      "children": [
        {
          "id": "G01",
          "label": "基本几何知识",
          "children": [
            {
              "id": "G01A",
              "label": "点线面基本关系",
              "skills": ["点线面概念", "线段长度", "射线"],
              "direct_score": [1,2],
              "related_score": [1,3],
              "children": []
            },
            {
              "id": "G01B",
              "label": "角的概念与分类",
              "skills": ["锐角钝角直角", "平角周角"],
              "direct_score": [1,2],
              "related_score": [2,3],
              "children": []
            },
            {
              "id": "G01C",
              "label": "角的度量",
              "skills": ["量角器使用", "角度换算"],
              "direct_score": [1,2],
              "related_score": [2,3],
              "children": []
            },
            {
              "id": "G01D",
              "label": "对顶角与邻补角",
              "skills": ["对顶角相等", "补角性质"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            }
          ]
        },

        {
          "id": "G02",
          "label": "平行线与角",
          "children": [
            {
              "id": "G02A",
              "label": "平行线判定",
              "skills": ["同位角相等", "内错角相等", "同旁内角互补"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "G02B",
              "label": "平行线性质",
              "skills": ["对应角相等", "内错角相等"],
              "direct_score": [2,3],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "G02C",
              "label": "平移与图形性质",
              "skills": ["平移定义", "图形保持性"],
              "direct_score": [1,3],
              "related_score": [3,5],
              "children": []
            }
          ]
        },

        {
          "id": "G03",
          "label": "三角形",
          "children": [
            {
              "id": "G03A",
              "label": "三角形分类",
              "skills": ["按角分类", "按边分类"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "G03B",
              "label": "三角形基本性质",
              "skills": ["三角形内角和", "外角定理"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "G03C",
              "label": "三角形稳定性",
              "skills": ["边构成条件", "三角形不等式"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "G03D",
              "label": "角平分线性质",
              "skills": ["等距性质", "分线比例"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "G03E",
              "label": "中线与垂心",
              "skills": ["中线定义", "三角形重心"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "G03F",
              "label": "三角形全等（核心）",
              "skills": ["SSS", "SAS", "AAS"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "G03G",
              "label": "全等三角形判定综合应用",
              "skills": ["构造辅助线", "转化为全等"],
              "direct_score": [4,6],
              "related_score": [6,9],
              "children": []
            }
          ]
        },

        {
          "id": "G04",
          "label": "四边形与平行四边形",
          "children": [
            {
              "id": "G04A",
              "label": "四边形分类",
              "skills": ["一般四边形性质", "特殊四边形识别"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "G04B",
              "label": "平行四边形判定",
              "skills": ["对边平行", "对角线平分"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "G04C",
              "label": "平行四边形性质",
              "skills": ["对边相等", "对角相等"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "G04D",
              "label": "特殊四边形：矩形",
              "skills": ["判定", "对角线相等"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "G04E",
              "label": "特殊四边形：菱形",
              "skills": ["对角线垂直", "对角线平分角"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "G04F",
              "label": "特殊四边形：正方形",
              "skills": ["综合性质", "全能图形应用"],
              "direct_score": [1,3],
              "related_score": [4,8],
              "children": []
            }
          ]
        },

        {
          "id": "G05",
          "label": "圆与相关性质",
          "children": [
            {
              "id": "G05A",
              "label": "圆的基本性质",
              "skills": ["半径直径", "同心圆"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "G05B",
              "label": "弦与圆心距",
              "skills": ["弦长变化", "圆心距关系"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "G05C",
              "label": "切线性质",
              "skills": ["切线垂直半径", "切割线定理"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "G05D",
              "label": "圆周角定理（核心）",
              "skills": ["圆周角等于同弧所对圆心角的一半"],
              "direct_score": [3,5],
              "related_score": [6,9],
              "children": []
            },
            {
              "id": "G05E",
              "label": "弧长与扇形面积",
              "skills": ["弧长公式", "扇形面积公式"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            }
          ]
        },

        {
          "id": "G06",
          "label": "几何综合与辅助线",
          "children": [
            {
              "id": "G06A",
              "label": "常用辅助线方法",
              "skills": ["延长线", "平移", "作垂线", "作角平分线"],
              "direct_score": [3,5],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "G06B",
              "label": "数形结合思想",
              "skills": ["代数化几何", "几何量化"],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "G06C",
              "label": "几何证明基础",
              "skills": ["已知与求证", "推理链", "结构化证明"],
              "direct_score": [4,6],
              "related_score": [7,12],
              "children": []
            }
          ]
        }
      ]
    },
    {
      "id": "M04",
      "label": "图形度量",
      "children": [
        {
          "id": "M04A",
          "label": "基础度量概念",
          "children": [
            {
              "id": "M04A1",
              "label": "长度与单位换算",
              "skills": ["毫米厘米米换算", "比例应用"],
              "direct_score": [1,2],
              "related_score": [2,3],
              "children": []
            },
            {
              "id": "M04A2",
              "label": "面积单位与换算",
              "skills": ["平方厘米", "平方米", "单位换算"],
              "direct_score": [1,2],
              "related_score": [2,3],
              "children": []
            },
            {
              "id": "M04A3",
              "label": "体积单位与换算",
              "skills": ["立方厘米", "立方分米", "升"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            }
          ]
        },

        {
          "id": "M04B",
          "label": "周长计算",
          "children": [
            {
              "id": "M04B1",
              "label": "三角形周长",
              "skills": ["三边相加", "条件关系转换"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "M04B2",
              "label": "四边形周长",
              "skills": ["平行四边形", "矩形", "菱形"],
              "direct_score": [1,3],
              "related_score": [2,5],
              "children": []
            },
            {
              "id": "M04B3",
              "label": "圆的周长",
              "skills": ["周长公式", "π的应用"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            }
          ]
        },

        {
          "id": "M04C",
          "label": "面积计算",
          "children": [
            {
              "id": "M04C1",
              "label": "三角形面积",
              "skills": ["底×高÷2", "高的作法"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "M04C2",
              "label": "四边形面积",
              "skills": ["平行四边形", "梯形面积"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "M04C3",
              "label": "圆与扇形面积",
              "skills": ["扇形面积公式", "弧长关系"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "M04C4",
              "label": "组合图形面积",
              "skills": ["拆分法", "补形法"],
              "direct_score": [3,5],
              "related_score": [5,9],
              "children": []
            }
          ]
        },

        {
          "id": "M04D",
          "label": "立体几何度量（表面积与体积）",
          "children": [
            {
              "id": "M04D1",
              "label": "长方体与正方体",
              "skills": ["表面积公式", "体积公式", "几何特征"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            },
            {
              "id": "M04D2",
              "label": "棱柱与棱锥初步",
              "skills": ["底面积×高", "侧面积结构"],
              "direct_score": [3,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "M04D3",
              "label": "圆柱体积与表面积",
              "skills": ["圆柱体积公式", "侧面积公式"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "M04D4",
              "label": "立体几何展开图",
              "skills": ["展开图识别", "面与面的关系"],
              "direct_score": [2,4],
              "related_score": [4,6],
              "children": []
            }
          ]
        },

        {
          "id": "M04E",
          "label": "图形变换与度量保持",
          "children": [
            {
              "id": "M04E1",
              "label": "平移",
              "skills": ["方向与距离", "度量保持"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "M04E2",
              "label": "旋转",
              "skills": ["旋转中心", "旋转角度"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "M04E3",
              "label": "轴对称",
              "skills": ["对称轴", "对应点性质"],
              "direct_score": [2,4],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "M04E4",
              "label": "图形变换综合",
              "skills": ["三大变换组合", "不变量分析"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            }
          ]
        },

        {
          "id": "M04F",
          "label": "图形度量综合应用",
          "children": [
            {
              "id": "M04F1",
              "label": "几何量与代数结合",
              "skills": ["代数化几何", "未知数建模"],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "M04F2",
              "label": "中考图形计算综合题",
              "skills": ["面积体积混合", "多步骤推理"],
              "direct_score": [4,7],
              "related_score": [7,12],
              "children": []
            }
          ]
        }
      ]
    },
    {
      "id": "M05",
      "label": "相似与勾股",
      "children": [
        {
          "id": "SIM01",
          "label": "相似三角形判定",
          "children": [
            {
              "id": "SIM01A",
              "label": "相似三角形概念",
              "skills": ["对应角相等", "对应边成比例"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "SIM01B",
              "label": "AA 相似判定",
              "skills": ["两角对应相等", "角角相似"],
              "direct_score": [3,5],
              "related_score": [5,7],
              "children": []
            },
            {
              "id": "SIM01C",
              "label": "SAS 比例判定",
              "skills": ["两边成比例", "夹角相等"],
              "direct_score": [3,5],
              "related_score": [5,7],
              "children": []
            },
            {
              "id": "SIM01D",
              "label": "SS 比例判定",
              "skills": ["三组成比例", "比例验证"],
              "direct_score": [3,5],
              "related_score": [5,7],
              "children": []
            },
            {
              "id": "SIM01E",
              "label": "相似三角形判定综合应用",
              "skills": ["构造相似", "比例线段构造"],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            }
          ]
        },

        {
          "id": "SIM02",
          "label": "相似三角形性质",
          "children": [
            {
              "id": "SIM02A",
              "label": "对应边成比例",
              "skills": ["比例关系建立", "比例计算"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "SIM02B",
              "label": "面积比",
              "skills": ["面积比 = 边比平方", "相似比关系"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "SIM02C",
              "label": "体积比基础",
              "skills": ["三维图形相似的体积比", "边比立方"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "SIM02D",
              "label": "线段比例分割（平行线）",
              "skills": ["平行线分线段比例", "三线段比例定理"],
              "direct_score": [3,5],
              "related_score": [5,9],
              "children": []
            },
            {
              "id": "SIM02E",
              "label": "相似性质综合应用",
              "skills": ["构造辅助线", "代数几何结合"],
              "direct_score": [4,7],
              "related_score": [7,12],
              "children": []
            }
          ]
        },

        {
          "id": "PY01",
          "label": "勾股定理与直角三角形",
          "children": [
            {
              "id": "PY01A",
              "label": "勾股定理",
              "skills": ["a² + b² = c²", "几何意义"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "PY01B",
              "label": "勾股逆定理",
              "skills": ["判定是否为直角三角形"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            },
            {
              "id": "PY01C",
              "label": "勾股数",
              "skills": ["常见勾股数", "比例放缩"],
              "direct_score": [2,3],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "PY01D",
              "label": "直角三角形性质",
              "skills": ["锐角三角函数雏形", "特殊直角三角形"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            }
          ]
        },

        {
          "id": "PY02",
          "label": "勾股定理应用",
          "children": [
            {
              "id": "PY02A",
              "label": "平面距离计算",
              "skills": ["坐标系距离", "几何点距"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            },
            {
              "id": "PY02B",
              "label": "最短路径问题",
              "skills": ["反射法", "路径构造"],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "PY02C",
              "label": "复杂图形中的直角关系",
              "skills": ["几何结构分析", "辅助线构造"],
              "direct_score": [4,7],
              "related_score": [7,12],
              "children": []
            },
            {
              "id": "PY02D",
              "label": "勾股+相似综合（中考核心）",
              "skills": ["相似构造", "比例 + 勾股联合"],
              "direct_score": [4,7],
              "related_score": [8,14],
              "children": []
            }
          ]
        },

        {
          "id": "SIM03",
          "label": "相似与勾股在压轴题中的整合",
          "children": [
            {
              "id": "SIM03A",
              "label": "辅助线构造策略",
              "skills": ["平移法", "延长线法", "旋转法"],
              "direct_score": [5,7],
              "related_score": [7,12],
              "children": []
            },
            {
              "id": "SIM03B",
              "label": "比例关系链",
              "skills": ["多组比例建立", "代数化比例"],
              "direct_score": [5,7],
              "related_score": [8,14],
              "children": []
            },
            {
              "id": "SIM03C",
              "label": "直角结构构造",
              "skills": ["构造垂线", "反射构造直角"],
              "direct_score": [4,6],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "SIM03D",
              "label": "几何综合（压轴结构）",
              "skills": ["相似 + 勾股 + 面积 + 角度", "多步骤推理"],
              "direct_score": [6,9],
              "related_score": [10,18],
              "children": []
            }
          ]
        }
      ]
    },
    {
      "id": "M06",
      "label": "统计与概率",
      "children": [
        {
          "id": "ST01",
          "label": "数据收集与整理",
          "children": [
            {
              "id": "ST01A",
              "label": "数据的获取与抽样",
              "skills": ["总体与样本", "简单随机抽样"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "ST01B",
              "label": "数据分类整理",
              "skills": ["分组整理", "列表与频数"],
              "direct_score": [1,3],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "ST01C",
              "label": "频数与频率",
              "skills": ["频数", "频率", "累计频率"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            }
          ]
        },

        {
          "id": "ST02",
          "label": "数据的统计量（集中趋势）",
          "children": [
            {
              "id": "ST02A",
              "label": "平均数（均值）",
              "skills": ["计算平均数", "加权平均"],
              "direct_score": [2,3],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "ST02B",
              "label": "中位数",
              "skills": ["排序", "奇偶位置处理"],
              "direct_score": [1,3],
              "related_score": [2,5],
              "children": []
            },
            {
              "id": "ST02C",
              "label": "众数",
              "skills": ["数据出现频率最高", "分类众数"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            }
          ]
        },

        {
          "id": "ST03",
          "label": "数据的离散程度（新课标 2022）",
          "children": [
            {
              "id": "ST03A",
              "label": "极差",
              "skills": ["最大-最小", "数据波动"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "ST03B",
              "label": "方差概念（初步）",
              "skills": ["偏差平方和", "离散程度理解"],
              "direct_score": [2,3],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "ST03C",
              "label": "标准差（认识）",
              "skills": ["方差开根号", "稳定性判断"],
              "direct_score": [2,3],
              "related_score": [4,7],
              "children": []
            }
          ]
        },

        {
          "id": "ST04",
          "label": "统计图表示与分析",
          "children": [
            {
              "id": "ST04A",
              "label": "条形图",
              "skills": ["分类比较", "趋势识别"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "ST04B",
              "label": "折线图",
              "skills": ["变化趋势", "最大最小值判断"],
              "direct_score": [1,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "ST04C",
              "label": "扇形图",
              "skills": ["角度表示频率", "组成比例分析"],
              "direct_score": [2,3],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "ST04D",
              "label": "统计图综合解读",
              "skills": ["关系推理", "数据变化分析"],
              "direct_score": [3,5],
              "related_score": [5,8],
              "children": []
            }
          ]
        },

        {
          "id": "ST05",
          "label": "概率初步",
          "children": [
            {
              "id": "ST05A",
              "label": "随机事件",
              "skills": ["必然事件", "不可能事件", "随机事件理解"],
              "direct_score": [1,2],
              "related_score": [2,4],
              "children": []
            },
            {
              "id": "ST05B",
              "label": "古典概率（等可能模型）",
              "skills": ["概率 =  favorable / total", "等可能事件"],
              "direct_score": [2,3],
              "related_score": [3,5],
              "children": []
            },
            {
              "id": "ST05C",
              "label": "实验概率",
              "skills": ["频率逼近概率", "大量试验规律"],
              "direct_score": [2,3],
              "related_score": [3,6],
              "children": []
            },
            {
              "id": "ST05D",
              "label": "简单树状图与列表法",
              "skills": ["列举所有可能", "概率空间构建"],
              "direct_score": [2,4],
              "related_score": [4,7],
              "children": []
            }
          ]
        },

        {
          "id": "ST06",
          "label": "统计与概率综合应用（中考核心）",
          "children": [
            {
              "id": "ST06A",
              "label": "统计综合题",
              "skills": ["多图表综合分析", "数据趋势推断"],
              "direct_score": [3,5],
              "related_score": [5,9],
              "children": []
            },
            {
              "id": "ST06B",
              "label": "概率综合题",
              "skills": ["树状图+表格法", "多阶段概率"],
              "direct_score": [3,5],
              "related_score": [6,10],
              "children": []
            },
            {
              "id": "ST06C",
              "label": "统计与概率融合应用",
              "skills": ["现实问题建模", "基于数据的概率推断"],
              "direct_score": [4,6],
              "related_score": [7,12],
              "children": []
            }
          ]
        }
      ]
    }
  ]
}