| {"mutation_id": "L1-001-correct", "problem_id": "L1-001", "error_type": "无错误", "injected_step_index": null, "expected_first_error_step": null, "steps": [{"index": 1, "text": "设小明买了 x 支钢笔。"}, {"index": 2, "text": "5 本笔记本花费 5 × 8 = 40 元。"}, {"index": 3, "text": "钢笔花费 88 - 40 = 48 元，即 12x = 48。"}, {"index": 4, "text": "解得 x = 48 / 12 = 4。"}], "final_answer": "4", "answer_correct": true, "description": "正确答案样本，用于测试误报率"} |
| {"mutation_id": "L1-002-correct", "problem_id": "L1-002", "error_type": "无错误", "injected_step_index": null, "expected_first_error_step": null, "steps": [{"index": 1, "text": "路程 = 速度 × 时间。"}, {"index": 2, "text": "代入数据：路程 = 60 × 3.5 = 210 千米。"}], "final_answer": "210", "answer_correct": true, "description": "正确答案样本，用于测试误报率"} |
| {"mutation_id": "L2-003-correct", "problem_id": "L2-003", "error_type": "无错误", "injected_step_index": null, "expected_first_error_step": null, "steps": [{"index": 1, "text": "由勾股定理，斜边 AB = √(AC² + BC²) = √(6² + 8²) = √100 = 10。"}, {"index": 2, "text": "三角形面积 = (1/2) × AC × BC = (1/2) × 6 × 8 = 24。"}, {"index": 3, "text": "面积也可表示为 (1/2) × AB × CD = (1/2) × 10 × CD = 5 × CD。"}, {"index": 4, "text": "因此 5 × CD = 24，解得 CD = 24/5。"}], "final_answer": "24/5", "answer_correct": true, "description": "正确答案样本，用于测试误报率"} |
| {"mutation_id": "L2-008-correct", "problem_id": "L2-008", "error_type": "无错误", "injected_step_index": null, "expected_first_error_step": null, "steps": [{"index": 1, "text": "f(x) = x² - 6x + 10。"}, {"index": 2, "text": "配方得 f(x) = (x - 3)² + 1。"}, {"index": 3, "text": "因为 (x - 3)² ≥ 0，所以 f(x) ≥ 1，最小值为 1。"}], "final_answer": "1", "answer_correct": true, "description": "正确答案样本，用于测试误报率"} |
| {"mutation_id": "L3-004-correct", "problem_id": "L3-004", "error_type": "无错误", "injected_step_index": null, "expected_first_error_step": null, "steps": [{"index": 1, "text": "递推式 a_{n+1} = 2a_n + 1 可变形为 a_{n+1} + 1 = 2(a_n + 1)。"}, {"index": 2, "text": "因此 {a_n + 1} 是首项为 a_1 + 1 = 2、公比为 2 的等比数列。"}, {"index": 3, "text": "所以 a_n + 1 = 2 × 2^{n-1} = 2^n，即 a_n = 2^n - 1。"}, {"index": 4, "text": "当 n = 10 时，a_10 = 2^10 - 1 = 1024 - 1 = 1023。"}], "final_answer": "1023", "answer_correct": true, "description": "正确答案样本，用于测试误报率"} |
| {"mutation_id": "L1-001-calculation_error-3", "problem_id": "L1-001", "error_type": "calculation_error", "injected_step_index": 3, "expected_first_error_step": 3, "steps": [{"index": 1, "text": "设小明买了 x 支钢笔。"}, {"index": 2, "text": "5 本笔记本花费 5 × 8 = 40 元。"}, {"index": 3, "text": "钢笔花费 88 - 40 = 52 元，即 12x = 52。"}, {"index": 4, "text": "解得 x = 48 / 12 = 4。"}], "final_answer": "4", "answer_correct": true, "description": "计算错误：将某一步的正确数值改为错误数值"} |
| {"mutation_id": "L1-002-calculation_error-2", "problem_id": "L1-002", "error_type": "calculation_error", "injected_step_index": 2, "expected_first_error_step": 2, "steps": [{"index": 1, "text": "路程 = 速度 × 时间。"}, {"index": 2, "text": "代入数据：路程 = 60 × 3.5 = 200 千米。"}], "final_answer": "210", "answer_correct": true, "description": "计算错误：将某一步的正确数值改为错误数值"} |
| {"mutation_id": "L2-003-theorem_misuse-1", "problem_id": "L2-003", "error_type": "theorem_misuse", "injected_step_index": 1, "expected_first_error_step": 1, "steps": [{"index": 1, "text": "由勾股定理，斜边 AB = AC + BC = 6 + 8 = 14。"}, {"index": 2, "text": "三角形面积 = (1/2) × AC × BC = (1/2) × 6 × 8 = 24。"}, {"index": 3, "text": "面积也可表示为 (1/2) × AB × CD = (1/2) × 10 × CD = 5 × CD。"}, {"index": 4, "text": "因此 5 × CD = 24，解得 CD = 24/5。"}], "final_answer": "24/5", "answer_correct": true, "description": "定理误用：用错误的定理或公式"} |
| {"mutation_id": "L2-008-missing_condition-2", "problem_id": "L2-008", "error_type": "missing_condition", "injected_step_index": 2, "expected_first_error_step": 2, "steps": [{"index": 1, "text": "f(x) = x² - 6x + 10。"}, {"index": 2, "text": "因为平方项非负，所以 f(x) ≥ 1，最小值为 1。"}, {"index": 3, "text": "因为 (x - 3)² ≥ 0，所以 f(x) ≥ 1，最小值为 1。"}], "final_answer": "1", "answer_correct": true, "description": "条件遗漏：跳过或使用未给出的条件"} |
| {"mutation_id": "L3-004-skipped_step-3", "problem_id": "L3-004", "error_type": "skipped_step", "injected_step_index": 3, "expected_first_error_step": 3, "steps": [{"index": 1, "text": "递推式 a_{n+1} = 2a_n + 1 可变形为 a_{n+1} + 1 = 2(a_n + 1)。"}, {"index": 2, "text": "因此 {a_n + 1} 是首项为 a_1 + 1 = 2、公比为 2 的等比数列。"}, {"index": 3, "text": "所以 a_n = 2^n - 1。"}, {"index": 4, "text": "当 n = 10 时，a_10 = 2^10 - 1 = 1024 - 1 = 1023。"}], "final_answer": "1023", "answer_correct": true, "description": "跳步推导：直接给出没有中间过程的结论"} |
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