{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261010-r06-variance-0076",
  "pilot_number": "R0008-04551",
  "number": 4551,
  "family_id": "qf-density10-variance-first-support-mismatch",
  "title": {
    "zh-Hant": "第 4551 題：正支持相對起點的首個失配",
    "en": "Question 4551: First Mismatch on Positive Probability Support"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261010-r06-variance-0076",
    "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-variance"
    ],
    "title_zh": "正支持相對起點的首個失配",
    "stem_zh": "有限歸一化模型；S={0,…,7}，F=𝒫(S)，質量=[0, 2, 0, 1, 0, 0, 0, 0]、D=3，權重為質量/D；X值=[99, 4, -99, 4, 9, 8, 7, 6]。索引從0；以第一個正質量點的X值為基準，列第一個正質量且X值不同的索引，若無則答無。",
    "answer": {
      "kind": "short_text",
      "value": "無",
      "explanation_zh": "正支持首個失配索引=無。只比較正質量支持，零權重異值不列失配；全部正支持相同給無，非樣本估計。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 1,
      "skills": [
        "正支持相對起點的首個失配"
      ]
    },
    "variant": {
      "family_id": "qf-density10-variance-first-support-mismatch",
      "seed": 202610106076,
      "parameters": {
        "masses": [
          0,
          2,
          0,
          1,
          0,
          0,
          0,
          0
        ],
        "D": 3,
        "values": [
          99,
          4,
          -99,
          4,
          9,
          8,
          7,
          6
        ],
        "operation": "density10_variance_first_support_mismatch",
        "domain": "finite_integer_random_variable",
        "semantic_template": "qf-density10-variance-first-support-mismatch/[\"constant_positive_support\"]"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_integer_rational_arithmetic",
        "producer_finite_enumeration",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-08",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261008-advance-20261010-r06-variance-0076",
    "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "783c3b2ea50650657b2cee5e83e83dc8f742504fb71742d301d43edce4003fac",
      "family_id": "qf-density10-variance-first-support-mismatch",
      "seed": 202610106076,
      "semantic_template": "qf-density10-variance-first-support-mismatch/[\"constant_positive_support\"]"
    },
    "fields": {
      "title": "First Mismatch on Positive Probability Support",
      "stem": "S={0,…,7}, F=P(S), masses=[0, 2, 0, 1, 0, 0, 0, 0], D=3, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. X=[99, 4, -99, 4, 9, 8, 7, 6] in index order. Use the X value at the first positive-mass index as reference. Return the first positive-mass index with a different X value, or none; indices start at 0.",
      "answer": {
        "kind": "short_text",
        "value": "none",
        "explanation": "Ignore differing zero-weight values when checking constancy on positive support. These are finite probability quantities, not sample-variance estimates. The exact result, retaining the requested order, is none."
      },
      "skills": [
        "First Mismatch on Positive Probability Support"
      ],
      "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "有限歸一化模型；S={0,…,7}，F=𝒫(S)，質量=[0, 2, 0, 1, 0, 0, 0, 0]、D=3，權重為質量/D；X值=[99, 4, -99, 4, 9, 8, 7, 6]。索引從0；以第一個正質量點的X值為基準，列第一個正質量且X值不同的索引，若無則答無。",
        "en": "S={0,…,7}, F=P(S), masses=[0, 2, 0, 1, 0, 0, 0, 0], D=3, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. X=[99, 4, -99, 4, 9, 8, 7, 6] in index order. Use the X value at the first positive-mass index as reference. Return the first positive-mass index with a different X value, or none; indices start at 0."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "total mass numerator := sum(0, 2, 0, 1, 0, 0, 0, 0)",
      "after": "total mass numerator = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "所有非負質量必須和D相同，才給總機率1。",
        "en": "Nonnegative masses must sum to D to give total probability1."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 total mass numerator，不以小數近似替代。",
          "en": "Recompute total mass numerator with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "2",
          "0",
          "1",
          "0",
          "0",
          "0",
          "0"
        ],
        "output": "3",
        "label": "total mass numerator"
      }
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "probability weight0 := div(0, 3)",
      "after": "probability weight0 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight0，不以小數近似替代。",
          "en": "Recompute probability weight0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "3"
        ],
        "output": "0",
        "label": "probability weight0"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "probability weight1 := div(2, 3)",
      "after": "probability weight1 = 2/3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight1，不以小數近似替代。",
          "en": "Recompute probability weight1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "2",
          "3"
        ],
        "output": "2/3",
        "label": "probability weight1"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "probability weight2 := div(0, 3)",
      "after": "probability weight2 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight2，不以小數近似替代。",
          "en": "Recompute probability weight2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "3"
        ],
        "output": "0",
        "label": "probability weight2"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "probability weight3 := div(1, 3)",
      "after": "probability weight3 = 1/3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight3，不以小數近似替代。",
          "en": "Recompute probability weight3 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "1",
          "3"
        ],
        "output": "1/3",
        "label": "probability weight3"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "probability weight4 := div(0, 3)",
      "after": "probability weight4 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight4，不以小數近似替代。",
          "en": "Recompute probability weight4 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "3"
        ],
        "output": "0",
        "label": "probability weight4"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "probability weight5 := div(0, 3)",
      "after": "probability weight5 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight5，不以小數近似替代。",
          "en": "Recompute probability weight5 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "3"
        ],
        "output": "0",
        "label": "probability weight5"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "probability weight6 := div(0, 3)",
      "after": "probability weight6 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight6，不以小數近似替代。",
          "en": "Recompute probability weight6 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "3"
        ],
        "output": "0",
        "label": "probability weight6"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "probability weight7 := div(0, 3)",
      "after": "probability weight7 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引將質量除以共同正分母D。",
        "en": "Divide the indexed mass by the common positive denominator D."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 probability weight7，不以小數近似替代。",
          "en": "Recompute probability weight7 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "3"
        ],
        "output": "0",
        "label": "probability weight7"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "values=[99, 4, -99, 4, 9, 8, 7, 6];weights=[0/1, 2/3, 0/1, 1/3, 0/1, 0/1, 0/1, 0/1]",
      "after": "known finite probability law,not a sampled estimate",
      "relation": "implies",
      "rule_id": "probability_variance_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這是完整歸一化機率模型，變異數用其機率權重；不是n−1樣本估計，零質量結果仍保留原索引。",
        "en": "This is the complete normalized probability law,so variance uses its probability weights,not an n−1 sample estimate.Retain original indices of zero-mass outcomes."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "index=0;mass=0;X=99;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "index=1;mass=2;X=4;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "index=2;mass=0;X=-99;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "index=3;mass=1;X=4;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "index=4;mass=0;X=9;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "index=5;mass=0;X=8;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "index=6;mass=0;X=7;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "index=7;mass=0;X=6;anchor X=4",
      "after": "positive-mass mismatch=否",
      "relation": "implies",
      "rule_id": "positive_support_mismatch_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只有正質量且值不同才算失配；零權重上的任意異值不能改變變異數的正支持判定。",
        "en": "A mismatch requires both positive mass and a different value.Arbitrary values at zero-weight outcomes do not change this positive-support test."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S019",
      "uses": [
        "G001",
        "S018"
      ],
      "before": "first positive index=1;all eligible mismatch indices=[]",
      "after": "無",
      "relation": "implies",
      "rule_id": "first_positive_support_mismatch",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按0起算原索引取第一個失配，不取最小X值；若無失配則X在全部正支持上恆定。",
        "en": "Choose the first original0-based mismatch index,not the smallest X-value.No mismatch means X is constant on its positive support."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": "無",
    "anchor_index": 1,
    "mismatch_indices": []
  },
  "conclusion": {
    "canonical_value": "無",
    "explanation": {
      "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261010-r06-variance-foundations/questions.jsonl",
      "batch_sha256": "bf948e230130604866f5ba9ddcbea4e4f81a5774ae5561cad9cde1e0740c4d48",
      "original_line": 76,
      "original_line_sha256": "b1e002323152b52dca32a49bb5bcdf839f2533f890b88f90dc0c6a9eaadc7703",
      "question_compact_sha256": "783c3b2ea50650657b2cee5e83e83dc8f742504fb71742d301d43edce4003fac",
      "english_row_compact_sha256": "bdbba46921e24ad40b5af87f40d68c6cf484b4508e85b683561540c7a8149dde",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261010-r06-variance-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261010-r06-variance-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-variance": {
        "sha256": "282681c1ed2d55f1c853c9759022470c991dd46c2b150626fa4bf654642032bc",
        "english_sha256": "a07a03bffcd0bef45c5514c2b4ba2db48202bf94f336f0d8589082871649306d",
        "original_path": "public/data/mko/variance.json",
        "english_path": "public/data/i18n/editions/mko-variance.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "6dc34e24b0f43c50e49365ca1a1153175f8661d5290c9236df5527bb047157eb",
    "original_candidate_sha256": "087bb26ab5b7c6b4eef48aaeb0f2c024232cdb981e6e7fa15e9f8bcc0d52b118",
    "original_candidate_line_sha256": "087bb26ab5b7c6b4eef48aaeb0f2c024232cdb981e6e7fa15e9f8bcc0d52b118"
  },
  "historical_source_state": {
    "review_state": {
      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-004-p9",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289",
      "question_first_witness_sha256": "caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 19,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "ec0c236c6258c241c981fc9adf777324e2f0d9609e2ee317d3bfabba8b5c7968",
      "arithmetic_steps": 9
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}