{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261005-advance-20261006-r06-area-0020",
  "pilot_number": "R0004-02745",
  "number": 2745,
  "family_id": "qf-area-rectangle-dimensions",
  "title": {
    "zh-Hant": "第 2745 題：非負尺寸半開矩形的面積",
    "en": "Question 2745: Area of a Half-Open Rectangle with Nonnegative Dimensions"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261005-advance-20261006-r06-area-0020",
    "batch_id": "batch-20261005-advance-20261006-r06-area-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-area"
    ],
    "title_zh": "非負尺寸半開矩形的面積",
    "stem_zh": "在等單位正交座標系中，兩軸使用同一長度單位，半開矩形 [0,19)×[0,5) 的寬 w=19、高 h=5。求面積的精確平方單位數，零邊長允許空矩形。",
    "answer": {
      "kind": "short_text",
      "value": "95",
      "explanation_zh": "面積=95 平方單位。寬乘高，任一邊長零即為空、面積零；不可用周長相加代替面積。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "非負尺寸半開矩形的面積"
      ]
    },
    "variant": {
      "family_id": "qf-area-rectangle-dimensions",
      "seed": 202610066020,
      "parameters": {
        "frame": "euclidean_orthonormal_equal_units",
        "boundary": "half_open",
        "w": 19,
        "h": 5,
        "operation": "rectangle_dimensions",
        "semantic_template": "qf-area-rectangle-dimensions/{\"inputs\":[\"5\",\"19\"],\"operation\":\"rectangle_dimensions\"}"
      }
    },
    "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": "2026-10-05",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261005-advance-20261006-r06-area-0020",
    "batch_id": "batch-20261005-advance-20261006-r06-area-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "9db962ebbf351d557916b160952db4e722f1ef72e1672ca9c75f0598b734bb6d",
      "family_id": "qf-area-rectangle-dimensions",
      "seed": 202610066020,
      "semantic_template": "qf-area-rectangle-dimensions/{\"inputs\":[\"5\",\"19\"],\"operation\":\"rectangle_dimensions\"}"
    },
    "fields": {
      "title": "Area of a Half-Open Rectangle with Nonnegative Dimensions",
      "stem": "Use one equal-unit orthonormal Euclidean Cartesian frame. The half-open rectangle [0,19)×[0,5) has width 19 and height 5, both nonnegative. Find its area in squared length units.",
      "answer": {
        "kind": "short_text",
        "value": "95",
        "explanation": "Multiply width by height to obtain 95 squared units. A zero extent makes the half-open rectangle empty; this is area, not perimeter."
      },
      "skills": [
        "Area of a Half-Open Rectangle with Nonnegative Dimensions"
      ],
      "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": "在等單位正交座標系中，兩軸使用同一長度單位，半開矩形 [0,19)×[0,5) 的寬 w=19、高 h=5。求面積的精確平方單位數，零邊長允許空矩形。",
        "en": "Use one equal-unit orthonormal Euclidean Cartesian frame. The half-open rectangle [0,19)×[0,5) has width 19 and height 5, both nonnegative. Find its area in squared length units."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "orthonormal equal-length coordinate units;half-open regions",
      "after": "area in squared length units",
      "relation": "implies",
      "rule_id": "half_open_area_convention",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩軸正交且使用相同長度單位；半開邊界避免相鄰單位格重複包含邊，面積單位是平方單位而非長度。",
        "en": "Axes are orthogonal with equal length units;half-open boundaries make adjacent unit cells disjoint.Area uses squared units,not length units."
      },
      "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": "rectangle area := mul(19, 5)",
      "after": "rectangle area = 95",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用非負寬乘高，不把兩邊相加誤當面積。",
        "en": "Multiply nonnegative width by height;adding the side lengths does not give area."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 rectangle area，不以小數近似替代。",
          "en": "Recompute rectangle area with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "19",
          "5"
        ],
        "output": "95",
        "label": "rectangle area"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "w=19; h=5",
      "after": "area=95; empty=否",
      "relation": "implies",
      "rule_id": "rectangle_area_boundary",
      "conditions": [],
      "explanation": {
        "zh-Hant": "零邊長是允許的空區域；這裡不是周長問題。",
        "en": "A zero side is an allowed empty region;this is not a perimeter calculation."
      },
      "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": "95"
  },
  "conclusion": {
    "canonical_value": "95",
    "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-20261005-advance-20261006-r06-area-foundations",
      "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r06-area-foundations/questions.jsonl",
      "batch_sha256": "ae5e68190a9fbefa299612f8a40e9c091f12108ad9798ec677bf34c4df61c45e",
      "original_line": 20,
      "original_line_sha256": "bbfe86882dc91f41ab32531e0d2104eea8cb79255e475181f6b206087c70f39f",
      "question_compact_sha256": "9db962ebbf351d557916b160952db4e722f1ef72e1672ca9c75f0598b734bb6d",
      "english_row_compact_sha256": "c6f2f8f66701538049eb972013914a72e085e389ea37980bf342b274841e4f64",
      "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r06-area-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r06-area-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-area": {
        "sha256": "dd727d645461b67b46876e9fedc6a33242ba8cb9ef182cf6bd74290b45ac1b58",
        "english_sha256": "3c701b4dcaf9e9568dd937b5470cb18f890bd452abc9d2716d75a66401416371",
        "original_path": "public/data/mko/area.json",
        "english_path": "public/data/i18n/editions/mko-area.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "b254245aa10315455f756d4620a6ac0243e0146bccea5d89e872f1359bb32a1d",
    "original_candidate_sha256": "d295c715a2149a1421481733919ce16f4374627de96f217f81e27f789cd5dd56",
    "original_candidate_line_sha256": "d295c715a2149a1421481733919ce16f4374627de96f217f81e27f789cd5dd56"
  },
  "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-p5",
    "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": "312ae86315346b8955842a547cb2d09246e1f826755f72c2a51f042e5c7d5c56",
      "question_first_witness_sha256": "831f449ed41ff9144a290e534aa32adf7252d15b81c16ed5886a7dfd65dee70c"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 3,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "0ef3906ab145a9a2f1a5f45560c40dafc135140678ba0473d1771336153d59c5",
      "arithmetic_steps": 1
    },
    "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."
  }
}