{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261012-r05-right-triangle-0083",
  "pilot_number": "R0010-05858",
  "number": 5858,
  "family_id": "qf-density12-right-triangle-pi-multiple",
  "title": {
    "zh-Hant": "第 5858 題：未取週期的π倍角資格",
    "en": "Question 5858: Exact π-Multiple Candidate without Periodic Wrapping"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261012-r05-right-triangle-0083",
    "batch_id": "batch-20261008-advance-20261012-r05-right-triangle-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-right-triangle"
    ],
    "title_zh": "未取週期的π倍角資格",
    "stem_zh": "精確角度協議；π倍數弧度候選θ=(4/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。",
    "answer": {
      "kind": "expression",
      "value": "(720/7, 否)",
      "explanation_zh": "π倍角度數與直角資格=(720/7, 否)。以180乘π係數並精確約分，再核是否90；450不當90，不使用容差或浮點π。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 1,
      "skills": [
        "未取週期的π倍角資格"
      ]
    },
    "variant": {
      "family_id": "qf-density12-right-triangle-pi-multiple",
      "seed": 202610125083,
      "parameters": {
        "pi_n": 4,
        "pi_d": 7,
        "angle_unit": "pi_radians",
        "operation": "density12_right_triangle_pi_multiple",
        "domain": "exact_pi_multiple_candidate",
        "semantic_template": "qf-density12-right-triangle-pi-multiple/\"4/7\""
      }
    },
    "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": "2026-10-08",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261008-advance-20261012-r05-right-triangle-0083",
    "batch_id": "batch-20261008-advance-20261012-r05-right-triangle-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "3176593801b3a719d44a247e5693e8a8169b489d4981df128c10448715e14794",
      "family_id": "qf-density12-right-triangle-pi-multiple",
      "seed": 202610125083,
      "semantic_template": "qf-density12-right-triangle-pi-multiple/\"4/7\""
    },
    "fields": {
      "title": "Exact π-Multiple Candidate without Periodic Wrapping",
      "stem": "Candidate θ=(4/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.",
      "answer": {
        "kind": "expression",
        "value": "(720/7, No)",
        "explanation": "Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (720/7, No)."
      },
      "skills": [
        "Exact π-Multiple Candidate without Periodic Wrapping"
      ],
      "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": "精確角度協議；π倍數弧度候選θ=(4/7)π。依序求 (θ的精確度數, 是否恰等90°)，不取模或包回週期。",
        "en": "Candidate θ=(4/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "angle unit=pi_radians;exact declared protocol",
      "after": "check qualifications before geometric conclusions;no tolerance",
      "relation": "implies",
      "rule_id": "exact_right_angle_protocol",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只使用明示精確角度協議，不由示意圖讀數或使用浮點容差；候選角度資料尚不代表已構造三角形。",
        "en": "Use the declared exact angle protocol,not a sketch or floating tolerance.Candidate angle data do not by themselves construct a triangle."
      },
      "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": "exact pi coefficient := div(4, 7)",
      "after": "exact pi coefficient = 4/7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "θ=(n/d)π先求精確有理係數，分母正且非零。",
        "en": "For θ=(n/d)π,first compute its exact rational coefficient with a positive nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 exact pi coefficient，不以小數近似替代。",
          "en": "Recompute exact pi coefficient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "4",
          "7"
        ],
        "output": "4/7",
        "label": "exact pi coefficient"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "unwrapped degree value := mul(180, 4/7)",
      "after": "unwrapped degree value = 720/7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用π弧度等於180度換算，不代浮點π。",
        "en": "Convert using π radians=180 degrees,without a floating value for π."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 unwrapped degree value，不以小數近似替代。",
          "en": "Recompute unwrapped degree value with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "180",
          "4/7"
        ],
        "output": "720/7",
        "label": "unwrapped degree value"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "θ=4/7π;degrees=720/7",
      "after": "exactly90°=否",
      "relation": "implies",
      "rule_id": "unwrapped_pi_right_angle_test",
      "conditions": [],
      "explanation": {
        "zh-Hant": "判準是原角度恰等90，不把450度或負角取模包回90。",
        "en": "Test whether the original angle is exactly90 degrees;do not reduce450 degrees or a negative angle modulo a full turn."
      },
      "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": [
      "720/7",
      false
    ],
    "pi_coefficient": "4/7"
  },
  "conclusion": {
    "canonical_value": "(720/7, 否)",
    "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-20261008-advance-20261012-r05-right-triangle-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261012-r05-right-triangle-foundations/questions.jsonl",
      "batch_sha256": "a82cbe73c6672ee21e31a91afdddabf23460352695856d7b376cdfe7b3811de2",
      "original_line": 83,
      "original_line_sha256": "80b12cd151f5e09aed54a43fde994f74c43ea1ac7538e18065097eb6126f9fa4",
      "question_compact_sha256": "3176593801b3a719d44a247e5693e8a8169b489d4981df128c10448715e14794",
      "english_row_compact_sha256": "1254a37e172c1c847bbea18506145bdd0128af6680306043f8a65f20c37b6f74",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261012-r05-right-triangle-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261012-r05-right-triangle-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-right-triangle": {
        "sha256": "189cad28fbc4231852d6848d7f5209ff5d91a3b2dabd6380708fc678de0a758e",
        "english_sha256": "d07ac2fbb2083e7157e6f68c93440219d29942ce16690399e7ac0757ed7df20d",
        "original_path": "public/data/mko/right-triangle.json",
        "english_path": "public/data/i18n/editions/mko-right-triangle.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "aeab777a3897ae2c01315b86b5e9b9a43ffb59b075efae44fd95d447123d32f1",
    "original_candidate_sha256": "44a0646cb7a3a8e33026590c4b8ec8459b47faca895c935198e8179e65512307",
    "original_candidate_line_sha256": "44a0646cb7a3a8e33026590c4b8ec8459b47faca895c935198e8179e65512307"
  },
  "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-p11",
    "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": "0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06f",
      "question_first_witness_sha256": "0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fc"
    },
    "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": "a4a5fb0f5210884da9ee250dcbf8509caeef9cb5f68c3f999a70fc362a6463e6",
      "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."
  }
}