{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261010-r06-variance-0033",
  "pilot_number": "R0008-04583",
  "number": 4583,
  "family_id": "qf-density10-variance-second-moment-pair",
  "title": {
    "zh-Hant": "第 4583 題：二階矩與均值平方的有序對",
    "en": "Question 4583: Second Moment and Squared Mean"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261010-r06-variance-0033",
    "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-variance"
    ],
    "title_zh": "二階矩與均值平方的有序對",
    "stem_zh": "有限歸一化模型；S={0,…,2}，F=𝒫(S)，質量=[8, 2, 1]、D=11，權重為質量/D；X值=[-7, 2, 8]。依序求 (E[X²], (E[X])²)，不要混同兩式。",
    "answer": {
      "kind": "expression",
      "value": "(464/11, 16/1)",
      "explanation_zh": "二階矩與均值平方=(464/11, 16/1)。第一式平方值後加權，第二式加權均值後平方；兩式之差才是變異數，非樣本估計。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 1,
      "skills": [
        "二階矩與均值平方的有序對"
      ]
    },
    "variant": {
      "family_id": "qf-density10-variance-second-moment-pair",
      "seed": 202610106033,
      "parameters": {
        "masses": [
          8,
          2,
          1
        ],
        "D": 11,
        "values": [
          -7,
          2,
          8
        ],
        "operation": "density10_variance_second_moment_pair",
        "domain": "finite_integer_random_variable",
        "semantic_template": "qf-density10-variance-second-moment-pair/[[\"-2\",\"2/11\"],[\"-8\",\"1/11\"],[\"7\",\"8/11\"]]"
      }
    },
    "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-0033",
    "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "71858febec4548f37e1cfb1bb163859f033f6341344440d275a83d75fdbfd460",
      "family_id": "qf-density10-variance-second-moment-pair",
      "seed": 202610106033,
      "semantic_template": "qf-density10-variance-second-moment-pair/[[\"-2\",\"2/11\"],[\"-8\",\"1/11\"],[\"7\",\"8/11\"]]"
    },
    "fields": {
      "title": "Second Moment and Squared Mean",
      "stem": "S={0,…,2}, F=P(S), masses=[8, 2, 1], D=11, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. X=[-7, 2, 8] in index order. Give (E[X²], (E[X])²), distinguishing the two expressions. Use exact reduced fractions with positive denominators, retaining /1 for integers.",
      "answer": {
        "kind": "expression",
        "value": "(464/11, 16/1)",
        "explanation": "Square each value before weighting for the first field, and square the weighted mean for the second; their difference is the variance. These are finite probability quantities, not sample-variance estimates. The exact result, retaining the requested order, is (464/11, 16/1)."
      },
      "skills": [
        "Second Moment and Squared Mean"
      ],
      "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,…,2}，F=𝒫(S)，質量=[8, 2, 1]、D=11，權重為質量/D；X值=[-7, 2, 8]。依序求 (E[X²], (E[X])²)，不要混同兩式。",
        "en": "S={0,…,2}, F=P(S), masses=[8, 2, 1], D=11, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. X=[-7, 2, 8] in index order. Give (E[X²], (E[X])²), distinguishing the two expressions. Use exact reduced fractions with positive denominators, retaining /1 for integers."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "total mass numerator := sum(8, 2, 1)",
      "after": "total mass numerator = 11",
      "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": [
          "8",
          "2",
          "1"
        ],
        "output": "11",
        "label": "total mass numerator"
      }
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "probability weight0 := div(8, 11)",
      "after": "probability weight0 = 8/11",
      "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": [
          "8",
          "11"
        ],
        "output": "8/11",
        "label": "probability weight0"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "probability weight1 := div(2, 11)",
      "after": "probability weight1 = 2/11",
      "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",
          "11"
        ],
        "output": "2/11",
        "label": "probability weight1"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "probability weight2 := div(1, 11)",
      "after": "probability weight2 = 1/11",
      "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": [
          "1",
          "11"
        ],
        "output": "1/11",
        "label": "probability weight2"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "values=[-7, 2, 8];weights=[8/11, 2/11, 1/11]",
      "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": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "target variable weighted value0 := mul(8/11, -7)",
      "after": "target variable weighted value0 = -56/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同索引機率乘同索引值，負值及零權重均精確保留。",
        "en": "Multiply aligned probabilities and values,retaining negative values and zero weights exactly."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 target variable weighted value0，不以小數近似替代。",
          "en": "Recompute target variable weighted value0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "8/11",
          "-7"
        ],
        "output": "-56/11",
        "label": "target variable weighted value0"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "target variable weighted value1 := mul(2/11, 2)",
      "after": "target variable weighted value1 = 4/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同索引機率乘同索引值，負值及零權重均精確保留。",
        "en": "Multiply aligned probabilities and values,retaining negative values and zero weights exactly."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 target variable weighted value1，不以小數近似替代。",
          "en": "Recompute target variable weighted value1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2/11",
          "2"
        ],
        "output": "4/11",
        "label": "target variable weighted value1"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "target variable weighted value2 := mul(1/11, 8)",
      "after": "target variable weighted value2 = 8/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同索引機率乘同索引值，負值及零權重均精確保留。",
        "en": "Multiply aligned probabilities and values,retaining negative values and zero weights exactly."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 target variable weighted value2，不以小數近似替代。",
          "en": "Recompute target variable weighted value2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1/11",
          "8"
        ],
        "output": "8/11",
        "label": "target variable weighted value2"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "target variable mean := sum(-56/11, 4/11, 8/11)",
      "after": "target variable mean = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "全部加權項相加求精確均值。",
        "en": "Add every weighted term to obtain the exact mean."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 target variable mean，不以小數近似替代。",
          "en": "Recompute target variable mean with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-56/11",
          "4/11",
          "8/11"
        ],
        "output": "-4",
        "label": "target variable mean"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "pointwise square0 := square(-7)",
      "after": "pointwise square0 = 49",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "二階矩是先逐點平方再加權。",
        "en": "The second moment squares each point value before weighting."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pointwise square0，不以小數近似替代。",
          "en": "Recompute pointwise square0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "-7"
        ],
        "output": "49",
        "label": "pointwise square0"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "pointwise square1 := square(2)",
      "after": "pointwise square1 = 4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "二階矩是先逐點平方再加權。",
        "en": "The second moment squares each point value before weighting."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pointwise square1，不以小數近似替代。",
          "en": "Recompute pointwise square1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "2"
        ],
        "output": "4",
        "label": "pointwise square1"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "pointwise square2 := square(8)",
      "after": "pointwise square2 = 64",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "二階矩是先逐點平方再加權。",
        "en": "The second moment squares each point value before weighting."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pointwise square2，不以小數近似替代。",
          "en": "Recompute pointwise square2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "8"
        ],
        "output": "64",
        "label": "pointwise square2"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "squared variable weighted value0 := mul(8/11, 49)",
      "after": "squared variable weighted value0 = 392/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同索引機率乘同索引值，負值及零權重均精確保留。",
        "en": "Multiply aligned probabilities and values,retaining negative values and zero weights exactly."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 squared variable weighted value0，不以小數近似替代。",
          "en": "Recompute squared variable weighted value0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "8/11",
          "49"
        ],
        "output": "392/11",
        "label": "squared variable weighted value0"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "squared variable weighted value1 := mul(2/11, 4)",
      "after": "squared variable weighted value1 = 8/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同索引機率乘同索引值，負值及零權重均精確保留。",
        "en": "Multiply aligned probabilities and values,retaining negative values and zero weights exactly."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 squared variable weighted value1，不以小數近似替代。",
          "en": "Recompute squared variable weighted value1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2/11",
          "4"
        ],
        "output": "8/11",
        "label": "squared variable weighted value1"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "squared variable weighted value2 := mul(1/11, 64)",
      "after": "squared variable weighted value2 = 64/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同索引機率乘同索引值，負值及零權重均精確保留。",
        "en": "Multiply aligned probabilities and values,retaining negative values and zero weights exactly."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 squared variable weighted value2，不以小數近似替代。",
          "en": "Recompute squared variable weighted value2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1/11",
          "64"
        ],
        "output": "64/11",
        "label": "squared variable weighted value2"
      }
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "squared variable mean := sum(392/11, 8/11, 64/11)",
      "after": "squared variable mean = 464/11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "全部加權項相加求精確均值。",
        "en": "Add every weighted term to obtain the exact mean."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 squared variable mean，不以小數近似替代。",
          "en": "Recompute squared variable mean with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "392/11",
          "8/11",
          "64/11"
        ],
        "output": "464/11",
        "label": "squared variable mean"
      }
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "mean squared := square(-4)",
      "after": "mean squared = 16",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "均值平方則先加權求均值，再平方；次序不同。",
        "en": "The squared mean instead averages first and then squares;the order differs."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 mean squared，不以小數近似替代。",
          "en": "Recompute mean squared with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "-4"
        ],
        "output": "16",
        "label": "mean squared"
      }
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "E[X²]=464/11;(E[X])²=16",
      "after": "Var(X)=E[X²]−(E[X])² under this finite law",
      "relation": "implies",
      "rule_id": "second_moment_vs_squared_mean",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這兩個數不可混同，其差才是完整機率模型的變異數；本題依序回報兩個數，不做樣本修正。",
        "en": "These two values are distinct operations;their difference is the variance of the complete law.Report them in the requested order without a sample correction."
      },
      "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": [
      "464/11",
      "16"
    ],
    "mean": "-4"
  },
  "conclusion": {
    "canonical_value": "(464/11, 16/1)",
    "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": 33,
      "original_line_sha256": "8fb278df3813888bb3573b8e962fc8488a4484457c47b4e66dfbe6b031e55b45",
      "question_compact_sha256": "71858febec4548f37e1cfb1bb163859f033f6341344440d275a83d75fdbfd460",
      "english_row_compact_sha256": "b328833df06bdaafa36129fe78f8bde34f6ea1788a3ec040c526a92ee81a5acc",
      "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": "40ee9693b7d60991823f7fdeeaffacc2b2f88a548670c7dc9b660f7d732b9cd8",
    "original_candidate_line_sha256": "40ee9693b7d60991823f7fdeeaffacc2b2f88a548670c7dc9b660f7d732b9cd8"
  },
  "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": 18,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "21bc0657b465b9cd464b642bb13e04bfa3dbe19c31350d706458bf70d82a38f9",
      "arithmetic_steps": 16
    },
    "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."
  }
}