{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261010-r06-variance-0022",
  "pilot_number": "R0008-04522",
  "number": 4522,
  "family_id": "qf-density10-variance-contributions",
  "title": {
    "zh-Hant": "第 4522 題：逐點的中心平方貢獻",
    "en": "Question 4522: Every Centered Variance Contribution"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261010-r06-variance-0022",
    "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-variance"
    ],
    "title_zh": "逐點的中心平方貢獻",
    "stem_zh": "有限歸一化模型；S={0,…,2}，F=𝒫(S)，質量=[22, 2, 1]、D=25，權重為質量/D；X值=[-21, 2, 22]。先取μ=E[X]，按索引0起列 w_i(X_i−μ)²，不省零項。",
    "answer": {
      "kind": "expression",
      "value": "[174262/15625, 472392/15625, 972196/15625]",
      "explanation_zh": "逐點中心平方項=[174262/15625, 472392/15625, 972196/15625]。先求精確均值再平方偏差與加權；零權重異值保留零項，這是概率量，非樣本估計。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 3,
      "skills": [
        "逐點的中心平方貢獻"
      ]
    },
    "variant": {
      "family_id": "qf-density10-variance-contributions",
      "seed": 202610106022,
      "parameters": {
        "masses": [
          22,
          2,
          1
        ],
        "D": 25,
        "values": [
          -21,
          2,
          22
        ],
        "operation": "density10_variance_contributions",
        "domain": "finite_integer_random_variable",
        "semantic_template": "qf-density10-variance-contributions/[[\"0\",\"22/25\"],[\"-23\",\"2/25\"],[\"-43\",\"1/25\"]]"
      }
    },
    "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-0022",
    "batch_id": "batch-20261008-advance-20261010-r06-variance-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "09b3bb312d5287aa493b30a346255471cef1b5913708f6f1defece1a705ae2ff",
      "family_id": "qf-density10-variance-contributions",
      "seed": 202610106022,
      "semantic_template": "qf-density10-variance-contributions/[[\"0\",\"22/25\"],[\"-23\",\"2/25\"],[\"-43\",\"1/25\"]]"
    },
    "fields": {
      "title": "Every Centered Variance Contribution",
      "stem": "S={0,…,2}, F=P(S), masses=[22, 2, 1], D=25, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. X=[-21, 2, 22] in index order. First take μ=E[X]; list w_i(X_i−μ)² in index order, without omitting zeros. Use exact reduced fractions with positive denominators, retaining /1 for integers.",
      "answer": {
        "kind": "expression",
        "value": "[174262/15625, 472392/15625, 972196/15625]",
        "explanation": "Find the exact mean, square each deviation, then weight it; a differing zero-weight value still contributes zero. These are finite probability quantities, not sample-variance estimates. The exact result, retaining the requested order, is [174262/15625, 472392/15625, 972196/15625]."
      },
      "skills": [
        "Every Centered Variance Contribution"
      ],
      "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=[22, 2, 1]、D=25，權重為質量/D；X值=[-21, 2, 22]。先取μ=E[X]，按索引0起列 w_i(X_i−μ)²，不省零項。",
        "en": "S={0,…,2}, F=P(S), masses=[22, 2, 1], D=25, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. X=[-21, 2, 22] in index order. First take μ=E[X]; list w_i(X_i−μ)² in index order, without omitting zeros. Use exact reduced fractions with positive denominators, retaining /1 for integers."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "total mass numerator := sum(22, 2, 1)",
      "after": "total mass numerator = 25",
      "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": [
          "22",
          "2",
          "1"
        ],
        "output": "25",
        "label": "total mass numerator"
      }
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "probability weight0 := div(22, 25)",
      "after": "probability weight0 = 22/25",
      "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": [
          "22",
          "25"
        ],
        "output": "22/25",
        "label": "probability weight0"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "probability weight1 := div(2, 25)",
      "after": "probability weight1 = 2/25",
      "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",
          "25"
        ],
        "output": "2/25",
        "label": "probability weight1"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "probability weight2 := div(1, 25)",
      "after": "probability weight2 = 1/25",
      "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",
          "25"
        ],
        "output": "1/25",
        "label": "probability weight2"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "values=[-21, 2, 22];weights=[22/25, 2/25, 1/25]",
      "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(22/25, -21)",
      "after": "target variable weighted value0 = -462/25",
      "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": [
          "22/25",
          "-21"
        ],
        "output": "-462/25",
        "label": "target variable weighted value0"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "target variable weighted value1 := mul(2/25, 2)",
      "after": "target variable weighted value1 = 4/25",
      "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": [
          "2/25",
          "2"
        ],
        "output": "4/25",
        "label": "target variable weighted value1"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "target variable weighted value2 := mul(1/25, 22)",
      "after": "target variable weighted value2 = 22/25",
      "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": [
          "1/25",
          "22"
        ],
        "output": "22/25",
        "label": "target variable weighted value2"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "target variable mean := sum(-462/25, 4/25, 22/25)",
      "after": "target variable mean = -436/25",
      "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": [
          "-462/25",
          "4/25",
          "22/25"
        ],
        "output": "-436/25",
        "label": "target variable mean"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "centered difference0 := sub(-21, -436/25)",
      "after": "centered difference0 = -89/25",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先減去此變數自己的精確均值。",
        "en": "Subtract this variable's own exact mean."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered difference0，不以小數近似替代。",
          "en": "Recompute centered difference0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-21",
          "-436/25"
        ],
        "output": "-89/25",
        "label": "centered difference0"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "centered square0 := square(-89/25)",
      "after": "centered square0 = 7921/625",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "平方偏差必非負，不把負偏差直接當作變異項。",
        "en": "The squared deviation is nonnegative;do not use a signed deviation itself as a variance term."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered square0，不以小數近似替代。",
          "en": "Recompute centered square0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "-89/25"
        ],
        "output": "7921/625",
        "label": "centered square0"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "centered contribution0 := mul(22/25, 7921/625)",
      "after": "centered contribution0 = 174262/15625",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "乘同索引機率；零權重即使有大偏差仍貢獻0。",
        "en": "Multiply by the aligned probability;a zero weight contributes0 even for a large deviation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered contribution0，不以小數近似替代。",
          "en": "Recompute centered contribution0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "22/25",
          "7921/625"
        ],
        "output": "174262/15625",
        "label": "centered contribution0"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "centered difference1 := sub(2, -436/25)",
      "after": "centered difference1 = 486/25",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先減去此變數自己的精確均值。",
        "en": "Subtract this variable's own exact mean."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered difference1，不以小數近似替代。",
          "en": "Recompute centered difference1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "2",
          "-436/25"
        ],
        "output": "486/25",
        "label": "centered difference1"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "centered square1 := square(486/25)",
      "after": "centered square1 = 236196/625",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "平方偏差必非負，不把負偏差直接當作變異項。",
        "en": "The squared deviation is nonnegative;do not use a signed deviation itself as a variance term."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered square1，不以小數近似替代。",
          "en": "Recompute centered square1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "486/25"
        ],
        "output": "236196/625",
        "label": "centered square1"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "centered contribution1 := mul(2/25, 236196/625)",
      "after": "centered contribution1 = 472392/15625",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "乘同索引機率；零權重即使有大偏差仍貢獻0。",
        "en": "Multiply by the aligned probability;a zero weight contributes0 even for a large deviation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered contribution1，不以小數近似替代。",
          "en": "Recompute centered contribution1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2/25",
          "236196/625"
        ],
        "output": "472392/15625",
        "label": "centered contribution1"
      }
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "centered difference2 := sub(22, -436/25)",
      "after": "centered difference2 = 986/25",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先減去此變數自己的精確均值。",
        "en": "Subtract this variable's own exact mean."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered difference2，不以小數近似替代。",
          "en": "Recompute centered difference2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "22",
          "-436/25"
        ],
        "output": "986/25",
        "label": "centered difference2"
      }
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "centered square2 := square(986/25)",
      "after": "centered square2 = 972196/625",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "平方偏差必非負，不把負偏差直接當作變異項。",
        "en": "The squared deviation is nonnegative;do not use a signed deviation itself as a variance term."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered square2，不以小數近似替代。",
          "en": "Recompute centered square2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "square",
        "inputs": [
          "986/25"
        ],
        "output": "972196/625",
        "label": "centered square2"
      }
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "centered contribution2 := mul(1/25, 972196/625)",
      "after": "centered contribution2 = 972196/15625",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "乘同索引機率；零權重即使有大偏差仍貢獻0。",
        "en": "Multiply by the aligned probability;a zero weight contributes0 even for a large deviation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 centered contribution2，不以小數近似替代。",
          "en": "Recompute centered contribution2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1/25",
          "972196/625"
        ],
        "output": "972196/15625",
        "label": "centered contribution2"
      }
    },
    {
      "id": "S019",
      "uses": [
        "G001",
        "S018"
      ],
      "before": "[174262/15625, 472392/15625, 972196/15625]",
      "after": "all indexed centered-square contributions retained",
      "relation": "implies",
      "rule_id": "complete_centered_variance_terms",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每個基本結果都列出一項且不省零項；這些是完整機率量，不是樣本估計。",
        "en": "Retain one term for every outcome,including zeros.These are quantities of the complete probability law,not sample estimates."
      },
      "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": [
      "174262/15625",
      "472392/15625",
      "972196/15625"
    ],
    "mean": "-436/25"
  },
  "conclusion": {
    "canonical_value": "[174262/15625, 472392/15625, 972196/15625]",
    "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": 22,
      "original_line_sha256": "7e0405b3cdfeecd05f4fb7ac5f89d54f8c2a559f21b7b401adcf9d6f8398bf3d",
      "question_compact_sha256": "09b3bb312d5287aa493b30a346255471cef1b5913708f6f1defece1a705ae2ff",
      "english_row_compact_sha256": "e9090f58a3fd88bb072bfc869d634ca8d8de90a1f503428b89340255cea6ed9d",
      "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": "633306993ab9b91e15df2faeb6f78468bd0aec058f29c523a286fee153613bd0",
    "original_candidate_line_sha256": "633306993ab9b91e15df2faeb6f78468bd0aec058f29c523a286fee153613bd0"
  },
  "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": "87cbae490a3c7af6dd3290877a13d5bb1ec5d74fdb57807a0b5de48d50d257e2",
      "arithmetic_steps": 17
    },
    "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."
  }
}