{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261007-advance-20261008-r03-continuity-0016",
  "pilot_number": "R0005-03341",
  "number": 3341,
  "family_id": "qf-continuity-affine-value",
  "title": {
    "zh-Hant": "第 3341 題：連續仿射模型的點值",
    "en": "Question 3341: Point Value of a Continuous Affine Model"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261007-advance-20261008-r03-continuity-0016",
    "batch_id": "batch-20261007-advance-20261008-r03-continuity-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-continuity"
    ],
    "title_zh": "連續仿射模型的點值",
    "stem_zh": "全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-16x+(3)，求 f(4)。",
    "answer": {
      "kind": "short_text",
      "value": "-61",
      "explanation_zh": "點值=-61。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "連續仿射模型的點值"
      ]
    },
    "variant": {
      "family_id": "qf-continuity-affine-value",
      "seed": 202610083016,
      "parameters": {
        "m": -16,
        "b": 3,
        "a": 4,
        "operation": "continuous_affine_value",
        "domain": "reals",
        "semantic_template": "qf-continuity-affine-value/{\"inputs\":[\"-16\",\"3\",\"4\"],\"operation\":\"continuous_affine_value\"}"
      }
    },
    "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-r03-continuity-0016",
    "batch_id": "batch-20261007-advance-20261008-r03-continuity-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "24b795f1a61832bdb3f60585aa2a39d2480f3b428e7babe86d8b3236b74e6a39",
      "family_id": "qf-continuity-affine-value",
      "seed": 202610083016,
      "semantic_template": "qf-continuity-affine-value/{\"inputs\":[\"-16\",\"3\",\"4\"],\"operation\":\"continuous_affine_value\"}"
    },
    "fields": {
      "title": "Point Value of a Continuous Affine Model",
      "stem": "On the whole real domain, f(x)=(-16)x+(3). Find the defined point value f(4).",
      "answer": {
        "kind": "short_text",
        "value": "-61",
        "explanation": "Exact substitution gives m*a+b=-61. This is the stated total affine model's point value, not a silently filled value of a punctured function."
      },
      "skills": [
        "Point Value of a Continuous 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。連續仿射函數 f(x)=-16x+(3)，求 f(4)。",
        "en": "On the whole real domain, f(x)=(-16)x+(3). Find the defined point value f(4)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "declared real model;center a=4",
      "after": "distinguish punctured limits,point values and a new extension",
      "relation": "implies",
      "rule_id": "continuity_model_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只使用明示實數公式；點值、去心極限及另建延拓的值不是同一欄位。",
        "en": "Use the declared real formulas;point values,punctured limits and values of a newly defined extension are different data."
      },
      "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 slope times center := mul(-16, 4)",
      "after": "affine slope times center = -64",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "將中心a代入該仿射公式的乘法部分。",
        "en": "Substitute the center a into this affine formula's product term."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 affine slope times center，不以小數近似替代。",
          "en": "Recompute affine slope times center with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-16",
          "4"
        ],
        "output": "-64",
        "label": "affine slope times center"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "affine center value := sum(-64, 3)",
      "after": "affine center value = -61",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "再加本分支截距，不混用另一側的常數。",
        "en": "Then add this branch's intercept,not the other branch's constant."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 affine center value，不以小數近似替代。",
          "en": "Recompute affine center value with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-64",
          "3"
        ],
        "output": "-61",
        "label": "affine center value"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "f(x)=-16x+3",
      "after": "f(4)=-61",
      "relation": "implies",
      "rule_id": "affine_point_evaluation_only",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本題只求已宣告仿射模型的點值；單一讀值不是任意函數連續性的證明。",
        "en": "This task evaluates the declared affine model at one point;a single reading does not prove continuity of an arbitrary 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
    }
  ],
  "math_model": {
    "result": "-61",
    "claim_scope": "declared_affine_point_value"
  },
  "conclusion": {
    "canonical_value": "-61",
    "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-r03-continuity-foundations",
      "batch_path": "public/data/questions/batches/batch-20261007-advance-20261008-r03-continuity-foundations/questions.jsonl",
      "batch_sha256": "1efeddd307a49cfd385a7e27892fe281bb5880419652b78ce889fdc4b0106df2",
      "original_line": 16,
      "original_line_sha256": "2d6f5f1febd0e18a5e97015b38f3765d8b2a06bcce0cd5e81de38c5e38516f0f",
      "question_compact_sha256": "24b795f1a61832bdb3f60585aa2a39d2480f3b428e7babe86d8b3236b74e6a39",
      "english_row_compact_sha256": "4afd2661faa3168ea24d0cf69288b6dc5314a5e91a83a553e1a222271e8767d0",
      "english_manifest_path": "public/data/i18n/editions/batch-20261007-advance-20261008-r03-continuity-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261007-advance-20261008-r03-continuity-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-continuity": {
        "sha256": "500bf8bf13b82d10311338ec1e1ec96d1b7b1d3fcff6113697be491180bdb9e6",
        "english_sha256": "3d9b3ecf4edf7bc99e0a106ce8d24abe7e3fe8a8423ef9ab92a33510611f8d61",
        "original_path": "public/data/mko/continuity.json",
        "english_path": "public/data/i18n/editions/mko-continuity.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "66b95c054a23815e6aa9999f9605667abcb96e0c5a97b71cd67b67041065878a",
    "original_candidate_sha256": "191d2c11a1cc9e2c2208debfce7245ec8510e4689185cd230a09f2ed51a2dbd3",
    "original_candidate_line_sha256": "191d2c11a1cc9e2c2208debfce7245ec8510e4689185cd230a09f2ed51a2dbd3"
  },
  "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-p6",
    "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": "5d74de11610ebc6037a4fc9946d77154d4ed18389f8f0feeb823148b6320c4c2",
      "question_first_witness_sha256": "1fba4ab0f13c2cfcc4d9fdebe492c442d43dd45700394a443daa28f333355ed9"
    },
    "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": "7ab5c03e29f5a844c3051f4cecdc3aac3ee5be81d8429793fa9c90755b5e0bf7",
      "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."
  }
}