{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261003-r05-linear-function-0018",
  "pilot_number": "R0001-01118",
  "number": 1118,
  "family_id": "qf-affine-exact-evaluation",
  "title": {
    "zh-Hant": "第 1118 題：仿射函數精確求值",
    "en": "Question 1118: Exact Affine-Function Evaluation"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261003-r05-linear-function-0018",
    "batch_id": "batch-20261003-r05-linear-function-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-linear-function"
    ],
    "title_zh": "仿射函數精確求值",
    "stem_zh": "在實數論域 R，f(x)=(5)x+(0)。求 f(4) 的精確值。",
    "answer": {
      "kind": "numeric",
      "value": "20",
      "explanation_zh": "f(4)=20。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "仿射函數精確求值"
      ]
    },
    "variant": {
      "family_id": "qf-affine-exact-evaluation",
      "seed": 202610035018,
      "parameters": {
        "m": 5,
        "b": 0,
        "x": 4,
        "domain": "reals",
        "operation": "affine_evaluate",
        "semantic_template": "qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"affine_evaluate\",\"x\":4}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_integer_rational_arithmetic",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication"
      ],
      "warning_zh": "僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "Codex independent peer (inherited model; exact runtime model not exposed)",
      "generated_at": "2026-10-03",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261003-r05-linear-function-0018",
    "batch_id": "batch-20261003-r05-linear-function-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "f4a030d7dc7f66c39cdaed51c9ee81dcf38d42524f3c8eeb2c2582e636555af4",
      "family_id": "qf-affine-exact-evaluation",
      "seed": 202610035018,
      "semantic_template": "qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"affine_evaluate\",\"x\":4}"
    },
    "fields": {
      "title": "Exact Affine-Function Evaluation",
      "stem": "Over R, f(x)=(5)x+(0). Compute f(4) exactly.",
      "answer": {
        "kind": "numeric",
        "value": "20",
        "explanation": "Multiply the input by the slope, then add the intercept: f(4)=20. Constant functions with m=0 also belong to the affine family."
      },
      "skills": [
        "Exact Affine-Function Evaluation"
      ],
      "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": "在實數論域 R，f(x)=(5)x+(0)。求 f(4) 的精確值。",
        "en": "Over R, f(x)=(5)x+(0). Compute f(4) exactly."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "f:R→R; f(x)=mx+b",
      "after": "m=0 gives a constant affine function",
      "relation": "implies",
      "rule_id": "affine_domain",
      "conditions": [],
      "explanation": {
        "zh-Hant": "仿射函數允許m=0；不能把一次方程式a≠0的限制誤套到所有仿射函數。",
        "en": "An affine function allows m=0; do not impose the nondegenerate-equation condition on every affine function."
      },
      "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": "m·x := mul(5, 4)",
      "after": "m·x = 20",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整代入同一輸入值，先做乘法。",
        "en": "Substitute the same input and multiply first."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 m·x，不以小數近似替代。",
          "en": "Recompute m·x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "5",
          "4"
        ],
        "output": "20",
        "label": "m·x"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "f(x) := sum(20, 0)",
      "after": "f(x) = 20",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "再加上常數截距。",
        "en": "Then add the constant intercept."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 f(x)，不以小數近似替代。",
          "en": "Recompute f(x) with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "20",
          "0"
        ],
        "output": "20",
        "label": "f(x)"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "x=4; m=5; b=0",
      "after": "f(4)=20",
      "relation": "implies",
      "rule_id": "substitution_identity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "計算順序與原式一致，負係數的括號保留。",
        "en": "The calculation follows the original expression, retaining parentheses for negative coefficients."
      },
      "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": {
    "value": "20"
  },
  "conclusion": {
    "canonical_value": "20",
    "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-20261003-r05-linear-function-foundations",
      "batch_path": "public/data/questions/batches/batch-20261003-r05-linear-function-foundations/questions.jsonl",
      "batch_sha256": "ff5c60775dad16ef6f718760b27128b102226c42313362bb6c8a6a5a19addf7e",
      "original_line": 18,
      "original_line_sha256": "722fd03d07dca10e0f69351732379a7f760fe71ff71c602ae34e26a25ed24e71",
      "question_compact_sha256": "f4a030d7dc7f66c39cdaed51c9ee81dcf38d42524f3c8eeb2c2582e636555af4",
      "english_row_compact_sha256": "0731cc769a1612e225130728c0fbac92b9bc698a1db2cc67017ee2d700cdd996",
      "english_manifest_path": "public/data/i18n/editions/batch-20261003-r05-linear-function-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261003-r05-linear-function-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-linear-function": {
        "sha256": "718236b5b7dfecd9f4d276590f1ddc012cfd5df96864540a3840a2b4e6650abe",
        "english_sha256": "15d0d8ac9fe6a30744f0bbe21d2d94a8273271f0e4c8c1d4ed982b99f72e098b",
        "original_path": "public/data/mko/linear-function.json",
        "english_path": "public/data/i18n/editions/mko-linear-function.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "b9fe70a7a264c90c20349be0449b2bd1a1b4d0e0a97092bc9fbcb7ca36ce0694",
    "original_candidate_sha256": "0d6138f140776406b77976cbb8337f0231b2d85acb2d540eee019ee543f4df1f",
    "original_candidate_line_sha256": "0d6138f140776406b77976cbb8337f0231b2d85acb2d540eee019ee543f4df1f"
  },
  "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-p2",
    "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": "c3b44ce8ed60ada6902fb206627537d5f90ba2a867eaba43a36f903280c496cc",
      "question_first_witness_sha256": "3e91602adc7f81a2671a2a3ffaf6a447028b56abc5853e8271673d76f30cd7ad"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 4,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "42c48a2de6b126795b38137a1d4489056966b8a3c9d920e928fdeb01cced1043",
      "arithmetic_steps": 2
    },
    "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."
  }
}