{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261005-advance-20261006-r05-circle-0068",
  "pilot_number": "R0004-02943",
  "number": 2943,
  "family_id": "qf-circle-diameter",
  "title": {
    "zh-Hant": "第 2943 題：非負半徑的直徑長",
    "en": "Question 2943: Diameter Length for a Nonnegative Radius"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261005-advance-20261006-r05-circle-0068",
    "batch_id": "batch-20261005-advance-20261006-r05-circle-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-circle"
    ],
    "title_zh": "非負半徑的直徑長",
    "stem_zh": "在等單位正交座標系中，兩軸使用同一長度單位，圓的非負半徑 r=17。求直徑長，使用同一長度單位。",
    "answer": {
      "kind": "short_text",
      "value": "34",
      "explanation_zh": "直徑=34。直徑長是半徑的兩倍，不依無關的圓心位置變化，也不是面積或周長。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "非負半徑的直徑長"
      ]
    },
    "variant": {
      "family_id": "qf-circle-diameter",
      "seed": 202610065068,
      "parameters": {
        "r": 17,
        "frame": "euclidean_orthonormal_equal_units",
        "operation": "circle_diameter",
        "semantic_template": "qf-circle-diameter/{\"inputs\":[\"17\"],\"operation\":\"circle_diameter\"}"
      }
    },
    "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-r05-circle-0068",
    "batch_id": "batch-20261005-advance-20261006-r05-circle-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "bf9de287183981ac66191a906add555b4587256b783b76c5fdea1459fa6d16b8",
      "family_id": "qf-circle-diameter",
      "seed": 202610065068,
      "semantic_template": "qf-circle-diameter/{\"inputs\":[\"17\"],\"operation\":\"circle_diameter\"}"
    },
    "fields": {
      "title": "Diameter Length for a Nonnegative Radius",
      "stem": "Use one equal-unit orthonormal Euclidean Cartesian frame. The circle radius is r=17≥0. Find its diameter length.",
      "answer": {
        "kind": "short_text",
        "value": "34",
        "explanation": "The diameter length is 2r=34 in the same length unit, including zero at radius zero."
      },
      "skills": [
        "Diameter Length for a Nonnegative Radius"
      ],
      "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，圓的非負半徑 r=17。求直徑長，使用同一長度單位。",
        "en": "Use one equal-unit orthonormal Euclidean Cartesian frame. The circle radius is r=17≥0. Find its diameter length."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "orthonormal equal-length units;r=17≥0",
      "after": "C={P:distance(P,O)=r} is a boundary,not a filled disk",
      "relation": "implies",
      "rule_id": "circle_boundary_convention",
      "conditions": [],
      "explanation": {
        "zh-Hant": "圓指到圓心距離恰為r的邊界；內部不是圓上的同義詞。半徑0採退化點集{O}，沒有圓內點，直徑長0。",
        "en": "The circle is the boundary at distance exactly r from the center,not the filled disk.For r=0 use the degenerate singleton{O},with no inside points and diameter length0."
      },
      "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": "diameter length := sum(17, 17)",
      "after": "diameter length = 34",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "相反兩方向各一個半徑相加得2r；結果是長度，不是周長或面積。",
        "en": "Add two opposite radial lengths to obtain2r;this is a length,not circumference or area."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 diameter length，不以小數近似替代。",
          "en": "Recompute diameter length with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "17",
          "17"
        ],
        "output": "34",
        "label": "diameter length"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "radius=17",
      "after": "diameter=34",
      "relation": "implies",
      "rule_id": "diameter_twice_radius",
      "conditions": [],
      "explanation": {
        "zh-Hant": "圓心位置不影響長度；r=0時直接得到0，不除以r。",
        "en": "The center location does not affect this length;for r=0 the result is0 without division by r."
      },
      "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": "34"
  },
  "conclusion": {
    "canonical_value": "34",
    "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-r05-circle-foundations",
      "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r05-circle-foundations/questions.jsonl",
      "batch_sha256": "f91314751461a37c852b683b0c62ae64ee964eaf2877eb78901259982b7dbe02",
      "original_line": 68,
      "original_line_sha256": "46bfa4164419f851fd5c1365abe04c89d34fd2725fd9f3c40ce4fbfebd509a16",
      "question_compact_sha256": "bf9de287183981ac66191a906add555b4587256b783b76c5fdea1459fa6d16b8",
      "english_row_compact_sha256": "19e7e51a05d33142536d45ad76e53f78c21a785481a2b63a1a21751e8ff32ae6",
      "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r05-circle-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r05-circle-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-circle": {
        "sha256": "f5666d01288a4c7140be59abad5dbf093293c9136d7d60dc752a79a497d99d2e",
        "english_sha256": "e3c801529b17bbcfc6b73fef34a12a234a6dedbbaf8f1e283d3371fd2c7290d0",
        "original_path": "public/data/mko/circle.json",
        "english_path": "public/data/i18n/editions/mko-circle.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "b254245aa10315455f756d4620a6ac0243e0146bccea5d89e872f1359bb32a1d",
    "original_candidate_sha256": "a679944f9f7e01589e542615fd185d4dad20e0535d5982132c1ce0e844588ad2",
    "original_candidate_line_sha256": "a679944f9f7e01589e542615fd185d4dad20e0535d5982132c1ce0e844588ad2"
  },
  "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": "0d582075d1ec2b5a366e934f6585b37e024a3763113d58bb8a897a70eec98847",
      "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."
  }
}