{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261014-advance-20261110-r02-mean-value-theorem-0041",
  "pilot_number": "R0043-22291",
  "number": 22291,
  "family_id": "qf-mod41-mvt-secant-slope",
  "title": {
    "zh-Hant": "第 22291 題：微分中值定理",
    "en": "Question 22291: The Secant Uses Exact Endpoint Values and a Nonzero Denominator"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261014-advance-20261110-r02-mean-value-theorem-0041",
    "batch_id": "batch-20261014-advance-20261110-r02-mean-value-theorem-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-mean-value-theorem"
    ],
    "title_zh": "微分中值定理",
    "stem_zh": "f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={\"A\":1,\"B\":5,\"C\":226,\"a\":-17,\"b\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(430, 640, 35, 6, exact_endpoint_secant_slope)",
      "explanation_zh": "Wave6第四層核對=(430, 640, 35, 6, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "微分中值定理"
      ]
    },
    "variant": {
      "family_id": "qf-mod41-mvt-secant-slope",
      "seed": 202611102041,
      "parameters": {
        "A": 1,
        "B": 5,
        "C": 226,
        "a": -17,
        "b": 18,
        "domain": "Exact_polynomial_mean_value_theorem",
        "operation": "mvt-secant-slope",
        "semantic_template": "qf-mod41-mvt-secant-slope/{\"A\":1,\"B\":5,\"C\":226,\"a\":-17,\"b\":18}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_or_symbolic_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-14",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261014-advance-20261110-r02-mean-value-theorem-0041",
    "batch_id": "batch-20261014-advance-20261110-r02-mean-value-theorem-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "5717f32a50230043fd8e5d8e8f81212fc8cbb13120b58c708a892682e6b4ea41",
      "family_id": "qf-mod41-mvt-secant-slope",
      "seed": 202611102041,
      "semantic_template": "qf-mod41-mvt-secant-slope/{\"A\":1,\"B\":5,\"C\":226,\"a\":-17,\"b\":18}"
    },
    "fields": {
      "title": "The Secant Uses Exact Endpoint Values and a Nonzero Denominator",
      "stem": "Use the whole real polynomial f(t)=A*t^2+B*t+C with A=1, B=5, C=226, a=-17, b=18 and a<b. Coefficients are quadratic, linear and constant in that order. This declared polynomial is continuous on [a,b] and differentiable on (a,b); finite samples do not certify those hypotheses for an arbitrary function. Give (value_at_a, value_at_b, interval_length, secant_slope, certificate).",
      "answer": {
        "kind": "expression",
        "value": "(430, 640, 35, 6, exact_endpoint_secant_slope)",
        "explanation": "Compute f(a), f(b), b−a and (f(b)−f(a))/(b−a) exactly. This is an average slope, not an asserted endpoint derivative or finite-sampling differentiability proof. The exact result, retaining the requested order, is (430, 640, 35, 6, exact_endpoint_secant_slope)."
      },
      "skills": [
        "The Secant Uses Exact Endpoint Values and a Nonzero Denominator"
      ],
      "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": "f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={\"A\":1,\"B\":5,\"C\":226,\"a\":-17,\"b\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Use the whole real polynomial f(t)=A*t^2+B*t+C with A=1, B=5, C=226, a=-17, b=18 and a<b. Coefficients are quadratic, linear and constant in that order. This declared polynomial is continuous on [a,b] and differentiable on (a,b); finite samples do not certify those hypotheses for an arbitrary function. Give (value_at_a, value_at_b, interval_length, secant_slope, certificate)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source operation=mvt-secant-slope;original snapshot and mathematics retained",
      "after": "explicit ordered source output fields=[value_at_a, value_at_b, interval_length, secant_slope, certificate]",
      "relation": "implies",
      "rule_id": "source_ordered_interface_explicit_without_javascript",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原題歷史介面標記保留，直接列來源有序欄位，不需JavaScript；MVT由原mode選欄序，不補空欄或看答案形狀猜。tag與固定No保原聲稱範圍。",
        "en": "Retain the historical interface marker and list ordered source fields without JavaScript.MVT fields come from the original mode,without padding or answer-shape inference.Tags and fixed No markers retain their claim scope."
      },
      "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": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "ORIGINAL WHOLE f(t)=(1)t^2+(5)t+(226);a=-17<b=18;all endpoint[Ax,Axx,Bx,Axx+Bx,Axx+Bx+C] rows=[[-17, 289, -85, 204, 430], [18, 324, 90, 414, 640]]",
      "after": "English source ALL endpoint intermediate SAFE guards passed;polynomial continuous on CLOSED[a,b] and differentiable on OPEN(a,b),not inferred from finite samples",
      "relation": "implies",
      "rule_id": "mvt_whole_polynomial_hypotheses_and_SAFE_source_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "有限和／乘積保連續與可微，導數是2At+B；這是完整公式的性質，不是用端點樣本猜中間。SAFE只是來源數字投影資格，不等於數學上多項式只能取這些值。",
        "en": "Finite sums/products preserve continuity and differentiability,with derivative2At+B.These are properties of the whole formula,not an inference from endpoint samples.SAFE guards qualify source numeric projection,not the mathematical domain of polynomials."
      },
      "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": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "MVT endpointa ORIGINAL A times x := mul(1, -17)",
      "after": "MVT endpointa ORIGINAL A times x = -17",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointa ORIGINAL A times x，不以小數近似替代。",
          "en": "Recompute MVT endpointa ORIGINAL A times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "-17"
        ],
        "output": "-17",
        "label": "MVT endpointa ORIGINAL A times x"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "MVT endpointa A*x times x := mul(-17, -17)",
      "after": "MVT endpointa A*x times x = 289",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointa A*x times x，不以小數近似替代。",
          "en": "Recompute MVT endpointa A*x times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-17",
          "-17"
        ],
        "output": "289",
        "label": "MVT endpointa A*x times x"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "MVT endpointa ORIGINAL B times x := mul(5, -17)",
      "after": "MVT endpointa ORIGINAL B times x = -85",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointa ORIGINAL B times x，不以小數近似替代。",
          "en": "Recompute MVT endpointa ORIGINAL B times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "5",
          "-17"
        ],
        "output": "-85",
        "label": "MVT endpointa ORIGINAL B times x"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "MVT endpointa quadratic plus linear := sum(289, -85)",
      "after": "MVT endpointa quadratic plus linear = 204",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointa quadratic plus linear，不以小數近似替代。",
          "en": "Recompute MVT endpointa quadratic plus linear with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "289",
          "-85"
        ],
        "output": "204",
        "label": "MVT endpointa quadratic plus linear"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "MVT endpointa plus ORIGINAL constant := sum(204, 226)",
      "after": "MVT endpointa plus ORIGINAL constant = 430",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointa plus ORIGINAL constant，不以小數近似替代。",
          "en": "Recompute MVT endpointa plus ORIGINAL constant with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "204",
          "226"
        ],
        "output": "430",
        "label": "MVT endpointa plus ORIGINAL constant"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "MVT endpointb ORIGINAL A times x := mul(1, 18)",
      "after": "MVT endpointb ORIGINAL A times x = 18",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointb ORIGINAL A times x，不以小數近似替代。",
          "en": "Recompute MVT endpointb ORIGINAL A times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "18"
        ],
        "output": "18",
        "label": "MVT endpointb ORIGINAL A times x"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "MVT endpointb A*x times x := mul(18, 18)",
      "after": "MVT endpointb A*x times x = 324",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointb A*x times x，不以小數近似替代。",
          "en": "Recompute MVT endpointb A*x times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "18",
          "18"
        ],
        "output": "324",
        "label": "MVT endpointb A*x times x"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "MVT endpointb ORIGINAL B times x := mul(5, 18)",
      "after": "MVT endpointb ORIGINAL B times x = 90",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointb ORIGINAL B times x，不以小數近似替代。",
          "en": "Recompute MVT endpointb ORIGINAL B times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "5",
          "18"
        ],
        "output": "90",
        "label": "MVT endpointb ORIGINAL B times x"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "MVT endpointb quadratic plus linear := sum(324, 90)",
      "after": "MVT endpointb quadratic plus linear = 414",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointb quadratic plus linear，不以小數近似替代。",
          "en": "Recompute MVT endpointb quadratic plus linear with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "324",
          "90"
        ],
        "output": "414",
        "label": "MVT endpointb quadratic plus linear"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "MVT endpointb plus ORIGINAL constant := sum(414, 226)",
      "after": "MVT endpointb plus ORIGINAL constant = 640",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT endpointb plus ORIGINAL constant，不以小數近似替代。",
          "en": "Recompute MVT endpointb plus ORIGINAL constant with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "414",
          "226"
        ],
        "output": "640",
        "label": "MVT endpointb plus ORIGINAL constant"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "MVT ORIGINAL endpoint f(b) minus f(a) := sub(640, 430)",
      "after": "MVT ORIGINAL endpoint f(b) minus f(a) = 210",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT ORIGINAL endpoint f(b) minus f(a)，不以小數近似替代。",
          "en": "Recompute MVT ORIGINAL endpoint f(b) minus f(a) with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "640",
          "430"
        ],
        "output": "210",
        "label": "MVT ORIGINAL endpoint f(b) minus f(a)"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "MVT ORIGINAL ordered interval length := sub(18, -17)",
      "after": "MVT ORIGINAL ordered interval length = 35",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT ORIGINAL ordered interval length，不以小數近似替代。",
          "en": "Recompute MVT ORIGINAL ordered interval length with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "18",
          "-17"
        ],
        "output": "35",
        "label": "MVT ORIGINAL ordered interval length"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "MVT exact secant slope := div(210, 35)",
      "after": "MVT exact secant slope = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。",
        "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 MVT exact secant slope，不以小數近似替代。",
          "en": "Recompute MVT exact secant slope with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "210",
          "35"
        ],
        "output": "6",
        "label": "MVT exact secant slope"
      }
    }
  ],
  "math_model": {
    "result": [
      430,
      640,
      35,
      "6",
      "exact_endpoint_secant_slope"
    ]
  },
  "conclusion": {
    "canonical_value": "(430, 640, 35, 6, exact_endpoint_secant_slope)",
    "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-20261014-advance-20261110-r02-mean-value-theorem-foundations",
      "batch_path": "public/data/questions/batches/batch-20261014-advance-20261110-r02-mean-value-theorem-foundations/questions.jsonl",
      "batch_sha256": "8ba45e49fc1080aa7ff54d64afad99686fb70f44ad68b49ff9bf82c95b3f3256",
      "original_line": 41,
      "original_line_sha256": "861043e22a74c22d3469392df7a6afe80e93d663e31374d4cc05b07cb0c44d9d",
      "question_compact_sha256": "5717f32a50230043fd8e5d8e8f81212fc8cbb13120b58c708a892682e6b4ea41",
      "english_row_compact_sha256": "778ad3434410c25adfd12377b59996e0f0422473bc2ec664b47320699ed72690",
      "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261110-r02-mean-value-theorem-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261110-r02-mean-value-theorem-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-mean-value-theorem": {
        "sha256": "b56d8d37a21b32c9fbbbb984216cdf4275d9e8a0935e41ffa69680e727899f0b",
        "english_sha256": "5567acf26533764eb5f0ebe7fe5993adffea616c5b5dead898553ab35d8c201e",
        "original_path": "public/data/mko/mean-value-theorem.json",
        "english_path": "public/data/i18n/editions/mko-mean-value-theorem.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "747b98e75085a6b55251b2d7e04bbf7c60cb5500e5047439b2798fb5f45538fa",
    "original_candidate_sha256": "a9ed435f8ba4bc1e033aed815d8c957f888ae27d2de5b990428000c2fff07e48",
    "original_candidate_line_sha256": "a9ed435f8ba4bc1e033aed815d8c957f888ae27d2de5b990428000c2fff07e48"
  },
  "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-20261026-009-p44",
    "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": "49cf6ec60211c92d1c0c302663af4d44479635dc8181fb61a20c3374288e21c5",
      "question_first_witness_sha256": "10fd25b4643e5ff12753daceaa61f9f2499bf381f65ef96e9d21185c7c0d0c5e"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 15,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "f6d580ae4f59f08be338d75bfa9df3f7632fce1f1e7c1f4b3de8246b90d057e6",
      "arithmetic_steps": 13
    },
    "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."
  }
}