{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261007-advance-20261008-r04-derivative-0024",
  "pilot_number": "R0016-08524",
  "number": 8524,
  "family_id": "qf-derivative-affine-slope",
  "title": {
    "zh-Hant": "第 8524 題：仿射模型的導數",
    "en": "Question 8524: Derivative of an Affine Model"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261007-advance-20261008-r04-derivative-0024",
    "batch_id": "batch-20261007-advance-20261008-r04-derivative-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-derivative"
    ],
    "title_zh": "仿射模型的導數",
    "stem_zh": "全實數論域，以下函數／點均以明示實數模型解讀。f(x)=11x+(-20)，求 f′(1)。",
    "answer": {
      "kind": "short_text",
      "value": "11",
      "explanation_zh": "導數=11。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 3,
      "skills": [
        "仿射模型的導數"
      ]
    },
    "variant": {
      "family_id": "qf-derivative-affine-slope",
      "seed": 202610084024,
      "parameters": {
        "m": 11,
        "b": -20,
        "x": 1,
        "operation": "affine_derivative",
        "domain": "reals",
        "semantic_template": "qf-derivative-affine-slope/{\"inputs\":[\"11\"],\"operation\":\"affine_derivative\"}"
      }
    },
    "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-0024",
    "batch_id": "batch-20261007-advance-20261008-r04-derivative-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "979f2a1eb9f660d530c9c596cfaae8fdbe4596ddd6d75ebde58ff82da846c2b7",
      "family_id": "qf-derivative-affine-slope",
      "seed": 202610084024,
      "semantic_template": "qf-derivative-affine-slope/{\"inputs\":[\"11\"],\"operation\":\"affine_derivative\"}"
    },
    "fields": {
      "title": "Derivative of an Affine Model",
      "stem": "On all R, f(t)=(11)t+(-20). Find f′(1) in this affine model.",
      "answer": {
        "kind": "short_text",
        "value": "11",
        "explanation": "The nonzero-step quotient is the slope m=11, whose two-sided limit exists. This includes constants; the intercept and center do not change the derivative."
      },
      "skills": [
        "Derivative of an Affine Model"
      ],
      "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)=11x+(-20)，求 f′(1)。",
        "en": "On all R, f(t)=(11)t+(-20). Find f′(1) in this affine model."
      }
    }
  ],
  "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": "affine m*x := mul(11, 1)",
      "after": "affine m*x = 11",
      "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 affine m*x，不以小數近似替代。",
          "en": "Recompute affine m*x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "11",
          "1"
        ],
        "output": "11",
        "label": "affine m*x"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "affine f(x) := sum(11, -20)",
      "after": "affine f(x) = -9",
      "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 affine f(x)，不以小數近似替代。",
          "en": "Recompute affine f(x) with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "11",
          "-20"
        ],
        "output": "-9",
        "label": "affine f(x)"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "f(t)=(11)*t+(-20);x=1;f(x)=-9;h!=0",
      "after": "f(x+h)-f(x)=(11)*h;quotient=11",
      "relation": "implies",
      "rule_id": "affine_increment_cancellation",
      "conditions": [],
      "explanation": {
        "zh-Hant": "展開m(x+h)+b−(mx+b)，常數b與mx抵消，留下mh。只在h≠0時消去h；即使m=0也合法。",
        "en": "Expand m(x+h)+b−(mx+b);the intercept and mx cancel,leaving mh.Cancel h only for h≠0,including the valid m=0 case."
      },
      "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": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "for every h!=0 the quotient is 11",
      "after": "two-sided derivative at 1=11",
      "relation": "implies",
      "rule_id": "constant_quotient_limit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "差商在整個去心鄰域恆為m，因此雙側極限就是m；不是用點值f(x)或截距作導數。",
        "en": "The quotient is identically m throughout a punctured neighborhood,so its two-sided limit is m.The point value or intercept is not the derivative."
      },
      "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": 11
  },
  "conclusion": {
    "canonical_value": "11",
    "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": {
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    "question_binding": {
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      "batch_path": "public/data/questions/batches/batch-20261007-advance-20261008-r04-derivative-foundations/questions.jsonl",
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      "question_compact_sha256": "979f2a1eb9f660d530c9c596cfaae8fdbe4596ddd6d75ebde58ff82da846c2b7",
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      "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"
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        "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": "8f3c68fccd701bd46b9cfaf8e281ba5f4c561562f952a0596a26ce742b4895e5",
    "original_candidate_line_sha256": "8f3c68fccd701bd46b9cfaf8e281ba5f4c561562f952a0596a26ce742b4895e5"
  },
  "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": {
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    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 5,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
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    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
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}