{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261007-advance-20261008-r04-derivative-0053",
  "pilot_number": "R0016-08528",
  "number": 8528,
  "family_id": "qf-derivative-finite-quotient",
  "title": {
    "zh-Hant": "第 8528 題：指定非零步長的有限差商",
    "en": "Question 8528: Finite Difference Quotient at a Specified Nonzero Step"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261007-advance-20261008-r04-derivative-0053",
    "batch_id": "batch-20261007-advance-20261008-r04-derivative-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-derivative"
    ],
    "title_zh": "指定非零步長的有限差商",
    "stem_zh": "全實數論域，以下函數／點均以明示實數模型解讀。f(x)=2x²+(-10)x+(4)，x=0、整數步長 h=3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。",
    "answer": {
      "kind": "expression",
      "value": "-4/1",
      "explanation_zh": "指定步差商=-4/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 1,
      "skills": [
        "指定非零步長的有限差商"
      ]
    },
    "variant": {
      "family_id": "qf-derivative-finite-quotient",
      "seed": 202610084053,
      "parameters": {
        "a2": 2,
        "a1": -10,
        "a0": 4,
        "x": 0,
        "h": 3,
        "operation": "finite_quadratic_quotient",
        "domain": "reals",
        "semantic_template": "qf-derivative-finite-quotient/{\"inputs\":[\"2\",\"-10\",\"0\",\"3\"],\"operation\":\"finite_quadratic_quotient\"}"
      }
    },
    "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": "2026-10-07",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261007-advance-20261008-r04-derivative-0053",
    "batch_id": "batch-20261007-advance-20261008-r04-derivative-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "d3e4a0c94f167482ba4f845ff4c7a602f84e0d6e776dde499392ddcc7e8a5a77",
      "family_id": "qf-derivative-finite-quotient",
      "seed": 202610084053,
      "semantic_template": "qf-derivative-finite-quotient/{\"inputs\":[\"2\",\"-10\",\"0\",\"3\"],\"operation\":\"finite_quadratic_quotient\"}"
    },
    "fields": {
      "title": "Finite Difference Quotient at a Specified Nonzero Step",
      "stem": "On all R, f(t)=(2)t²+(-10)t+(4), allowing a2=0. At x=0 and nonzero finite h=3, compute (f(x+h)−f(x))/h. Give a reduced fraction with positive denominator, retaining /1 for integers.",
      "answer": {
        "kind": "expression",
        "value": "-4/1",
        "explanation": "The specified finite quotient is -4/1, equal in this model to 2a2*x+a1+a2*h. It is a finite difference quotient, not a claim that every finite-step value is the derivative, even when a special case agrees."
      },
      "skills": [
        "Finite Difference Quotient at a Specified Nonzero Step"
      ],
      "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": "全實數論域，以下函數／點均以明示實數模型解讀。f(x)=2x²+(-10)x+(4)，x=0、整數步長 h=3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。",
        "en": "On all R, f(t)=(2)t²+(-10)t+(4), allowing a2=0. At x=0 and nonzero finite h=3, compute (f(x+h)−f(x))/h. Give a reduced fraction with positive denominator, retaining /1 for integers."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "declared real formula on all R;derivative means the two-sided h->0 quotient limit",
      "after": "finite-step evaluation and derivative existence are separate",
      "relation": "implies",
      "rule_id": "derivative_limit_definition_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "導數由[f(x+h)−f(x)]/h在h→0、h≠0的雙側極限定義；有限一次代值不是任意函數可微的證據。",
        "en": "A derivative is the two-sided limit of[f(x+h)−f(x)]/h as h→0 with h≠0.One finite evaluation is not evidence that an arbitrary function is differentiable."
      },
      "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": "at original x a*x := mul(2, 0)",
      "after": "at original x a*x = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at original x a*x，不以小數近似替代。",
          "en": "Recompute at original x a*x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "0"
        ],
        "output": "0",
        "label": "at original x a*x"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "at original x a*x+b := sum(0, -10)",
      "after": "at original x a*x+b = -10",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at original x a*x+b，不以小數近似替代。",
          "en": "Recompute at original x a*x+b with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "-10"
        ],
        "output": "-10",
        "label": "at original x a*x+b"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "at original x (a*x+b)*x := mul(-10, 0)",
      "after": "at original x (a*x+b)*x = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at original x (a*x+b)*x，不以小數近似替代。",
          "en": "Recompute at original x (a*x+b)*x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-10",
          "0"
        ],
        "output": "0",
        "label": "at original x (a*x+b)*x"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "at original x f(x) := sum(0, 4)",
      "after": "at original x f(x) = 4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at original x f(x)，不以小數近似替代。",
          "en": "Recompute at original x f(x) with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "4"
        ],
        "output": "4",
        "label": "at original x f(x)"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "f(t)=(2)*t^2+(-10)*t+(4);x=0;f(x)=4;h!=0",
      "after": "f(x+h)-f(x)=h*(2*(2)*(0)+(-10)+(2)*h)",
      "relation": "implies",
      "rule_id": "quadratic_increment_factorization",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用(x+h)²=x²+2xh+h²展開，常數項與原x項相消，再提出h。a2=0時仍是合法的低次模型，不另要求首項非零。",
        "en": "Expand(x+h)²=x²+2xh+h²,cancel the original terms,and factor out h.The a2=0 lower-degree case is valid;no nonzero-leading-coefficient assumption is added."
      },
      "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": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "twice quadratic coefficient := mul(2, 2)",
      "after": "twice quadratic coefficient = 4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 twice quadratic coefficient，不以小數近似替代。",
          "en": "Recompute twice quadratic coefficient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "2"
        ],
        "output": "4",
        "label": "twice quadratic coefficient"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "twice a times x := mul(4, 0)",
      "after": "twice a times x = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 twice a times x，不以小數近似替代。",
          "en": "Recompute twice a times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "4",
          "0"
        ],
        "output": "0",
        "label": "twice a times x"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "linear part of quotient := sum(0, -10)",
      "after": "linear part of quotient = -10",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 linear part of quotient，不以小數近似替代。",
          "en": "Recompute linear part of quotient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "-10"
        ],
        "output": "-10",
        "label": "linear part of quotient"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "shifted input x+h := sum(0, 3)",
      "after": "shifted input x+h = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 shifted input x+h，不以小數近似替代。",
          "en": "Recompute shifted input x+h with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "3"
        ],
        "output": "3",
        "label": "shifted input x+h"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "at shifted x a*x := mul(2, 3)",
      "after": "at shifted x a*x = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at shifted x a*x，不以小數近似替代。",
          "en": "Recompute at shifted x a*x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "3"
        ],
        "output": "6",
        "label": "at shifted x a*x"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "at shifted x a*x+b := sum(6, -10)",
      "after": "at shifted x a*x+b = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at shifted x a*x+b，不以小數近似替代。",
          "en": "Recompute at shifted x a*x+b with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "6",
          "-10"
        ],
        "output": "-4",
        "label": "at shifted x a*x+b"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "at shifted x (a*x+b)*x := mul(-4, 3)",
      "after": "at shifted x (a*x+b)*x = -12",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at shifted x (a*x+b)*x，不以小數近似替代。",
          "en": "Recompute at shifted x (a*x+b)*x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-4",
          "3"
        ],
        "output": "-12",
        "label": "at shifted x (a*x+b)*x"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "at shifted x f(x) := sum(-12, 4)",
      "after": "at shifted x f(x) = -8",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 at shifted x f(x)，不以小數近似替代。",
          "en": "Recompute at shifted x f(x) with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-12",
          "4"
        ],
        "output": "-8",
        "label": "at shifted x f(x)"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "finite increment f(x+h)-f(x) := sub(-8, 4)",
      "after": "finite increment f(x+h)-f(x) = -12",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite increment f(x+h)-f(x)，不以小數近似替代。",
          "en": "Recompute finite increment f(x+h)-f(x) with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-8",
          "4"
        ],
        "output": "-12",
        "label": "finite increment f(x+h)-f(x)"
      }
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "specified finite quotient := div(-12, 3)",
      "after": "specified finite quotient = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 specified finite quotient，不以小數近似替代。",
          "en": "Recompute specified finite quotient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "-12",
          "3"
        ],
        "output": "-4",
        "label": "specified finite quotient"
      }
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "finite-step quadratic correction := mul(2, 3)",
      "after": "finite-step quadratic correction = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite-step quadratic correction，不以小數近似替代。",
          "en": "Recompute finite-step quadratic correction with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "3"
        ],
        "output": "6",
        "label": "finite-step quadratic correction"
      }
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "expanded finite quotient := sum(-10, 6)",
      "after": "expanded finite quotient = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 expanded finite quotient，不以小數近似替代。",
          "en": "Recompute expanded finite quotient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-10",
          "6"
        ],
        "output": "-4",
        "label": "expanded finite quotient"
      }
    },
    {
      "id": "S019",
      "uses": [
        "G001",
        "S018"
      ],
      "before": "finite quotient minus derivative := sub(-4, -10)",
      "after": "finite quotient minus derivative = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步的原始操作數與運算順序精確計算；除法前須先核分母非零。",
        "en": "Evaluate exactly with this step's source operands and operation order.Check a denominator is nonzero before division."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite quotient minus derivative，不以小數近似替代。",
          "en": "Recompute finite quotient minus derivative with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-4",
          "-10"
        ],
        "output": "6",
        "label": "finite quotient minus derivative"
      }
    },
    {
      "id": "S020",
      "uses": [
        "G001",
        "S019"
      ],
      "before": "h=3;finite quotient=-4/1;derivative value=-10",
      "after": "difference=6;a2*h=6",
      "relation": "implies",
      "rule_id": "finite_difference_not_derivative_limit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這裡保留原題指定非零h，答案是有限差商，與導數的差為a2*h。仿射等特殊情形數值可相同，但不能倒推一般有限差商就是導數或證明可微。",
        "en": "Keep the specified nonzero h:the answer is a finite quotient and differs from the derivative by a2*h.Special cases such as an affine model can agree numerically,but this does not identify a general finite quotient with a derivative or prove differentiability."
      },
      "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": "-4"
  },
  "conclusion": {
    "canonical_value": "-4/1",
    "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-20261007-advance-20261008-r04-derivative-foundations",
      "batch_path": "public/data/questions/batches/batch-20261007-advance-20261008-r04-derivative-foundations/questions.jsonl",
      "batch_sha256": "12c2ea336c3fcf77c87dbf06558fe211c51f3f7dd951145c5f88c200dae55752",
      "original_line": 53,
      "original_line_sha256": "64cf065507365c5dc7ea3535e4af4a2fc457132d2977bc93d37115bd48bf9263",
      "question_compact_sha256": "d3e4a0c94f167482ba4f845ff4c7a602f84e0d6e776dde499392ddcc7e8a5a77",
      "english_row_compact_sha256": "181a31ea034ccf683f3885155a5514a2e01d9f695f35c953bec6d56f29bf295a",
      "english_manifest_path": "public/data/i18n/editions/batch-20261007-advance-20261008-r04-derivative-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261007-advance-20261008-r04-derivative-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-derivative": {
        "sha256": "b523a35b9e5c20d66a7346f84ac5bece2c4167b17d46208fdb9b40115deeaf64",
        "english_sha256": "5b384deb770b949487d4788df980511f8844bd2e59d136696e0681c2ee60db1c",
        "original_path": "public/data/mko/derivative.json",
        "english_path": "public/data/i18n/editions/mko-derivative.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "8e8954cf690c44da1ec1efa08994a485c73ca8706b7865d854e3f2cdfd4ca89f",
    "original_candidate_sha256": "b258cae454cf35284d7ba9947e3aa8ad51df8ade41d9bf2f4f2344f67b7c8969",
    "original_candidate_line_sha256": "b258cae454cf35284d7ba9947e3aa8ad51df8ade41d9bf2f4f2344f67b7c8969"
  },
  "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-20261026-005-p17",
    "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": "00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2",
      "question_first_witness_sha256": "198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 20,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "d73bebc8fbed5f674d9d3cf13d5874e6046870b5a5c236453a829694ce53cf50",
      "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."
  }
}