{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261012-r05-right-triangle-0074",
  "pilot_number": "R0010-05849",
  "number": 5849,
  "family_id": "qf-density12-right-triangle-marked-vertices",
  "title": {
    "zh-Hant": "第 5849 題：標記直角索引與對邊端點",
    "en": "Question 5849: Labeled Right Vertex and Opposite Side"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261012-r05-right-triangle-0074",
    "batch_id": "batch-20261008-advance-20261012-r05-right-triangle-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-right-triangle"
    ],
    "title_zh": "標記直角索引與對邊端點",
    "stem_zh": "精確角度協議；度數，頂點索引1、2、3依序有angles=[24, 66, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。",
    "answer": {
      "kind": "expression",
      "value": "(3, [1, 2], [24, 66])",
      "explanation_zh": "直角索引與對邊端點=(3, [1, 2], [24, 66])。按標記順序找90，對邊端點是其餘兩索引，不排序角度換標記；不使用容差，不宣稱構造證明。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "標記直角索引與對邊端點"
      ]
    },
    "variant": {
      "family_id": "qf-density12-right-triangle-marked-vertices",
      "seed": 202610125074,
      "parameters": {
        "angles": [
          24,
          66,
          90
        ],
        "angle_unit": "degrees",
        "operation": "density12_right_triangle_marked_vertices",
        "domain": "exact_integer_angle_protocol",
        "semantic_template": "qf-density12-right-triangle-marked-vertices/[24,66,90]"
      }
    },
    "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-0074",
    "batch_id": "batch-20261008-advance-20261012-r05-right-triangle-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "8fc14ca5072eb94cda61d23b7256000da825b0b30e2721f911b8362d192bcdfa",
      "family_id": "qf-density12-right-triangle-marked-vertices",
      "seed": 202610125074,
      "semantic_template": "qf-density12-right-triangle-marked-vertices/[24,66,90]"
    },
    "fields": {
      "title": "Labeled Right Vertex and Opposite Side",
      "stem": "Exact degrees: vertex indices 1,2,3 have ordered angles=[24, 66, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).",
      "answer": {
        "kind": "expression",
        "value": "(3, [1, 2], [24, 66])",
        "explanation": "Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [24, 66])."
      },
      "skills": [
        "Labeled Right Vertex and Opposite Side"
      ],
      "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；度數，頂點索引1、2、3依序有angles=[24, 66, 90]，已要求正角、和180且唯一90。依序列 (直角頂點索引, 對邊兩端點索引列表, 其他頂點的有序銳角值)。",
        "en": "Exact degrees: vertex indices 1,2,3 have ordered angles=[24, 66, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "angle unit=degrees;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": "three candidate angle sum := sum(24, 66, 90)",
      "after": "three candidate angle sum = 180",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先完整相加三個有序角值；負值或0仍作待核資料，不先當合法三角形。",
        "en": "Add the three ordered candidate angles completely;negative or zero values remain data to audit,not assumed valid triangle angles."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 three candidate angle sum，不以小數近似替代。",
          "en": "Recompute three candidate angle sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "24",
          "66",
          "90"
        ],
        "output": "180",
        "label": "three candidate angle sum"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "angle sum minus180 := sub(180, 180)",
      "after": "angle sum minus180 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "角和缺陷方向是總和減180。",
        "en": "The signed angle-sum defect is total minus180."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 angle sum minus180，不以小數近似替代。",
          "en": "Recompute angle sum minus180 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "180",
          "180"
        ],
        "output": "0",
        "label": "angle sum minus180"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "positive flags=[是, 是, 是];sum=180;defect=0",
      "after": "positive180-degree qualification=是",
      "relation": "implies",
      "rule_id": "positive_triangle_angle_qualification",
      "conditions": [],
      "explanation": {
        "zh-Hant": "三角形角度協議要全部正且精確和180；和缺陷0不能抵消零角或負角的非法性。",
        "en": "The triangle-angle protocol requires all angles positive and sum exactly180;zero sum defect does not excuse a zero or negative angle."
      },
      "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": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "original labeled angles=[24, 66, 90];right vertex=3",
      "after": "(3, [1, 2], [24, 66])",
      "relation": "implies",
      "rule_id": "marked_right_vertex_opposite_endpoints",
      "conditions": [],
      "explanation": {
        "zh-Hant": "直角頂點用1起算索引，對邊端點是其餘兩頂點；不先排序角度再更換原標記。",
        "en": "Use the original1-based right-vertex index;the opposite-side endpoints are the other two vertices.Do not sort angles and thereby relabel vertices."
      },
      "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": [
      3,
      [
        1,
        2
      ],
      [
        24,
        66
      ]
    ],
    "sum_degrees": "180"
  },
  "conclusion": {
    "canonical_value": "(3, [1, 2], [24, 66])",
    "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": 74,
      "original_line_sha256": "5488058feae5087f297620791e41bed18e7cc9c913a288f2f2a756d277a02821",
      "question_compact_sha256": "8fc14ca5072eb94cda61d23b7256000da825b0b30e2721f911b8362d192bcdfa",
      "english_row_compact_sha256": "24ba26ffe4fc1d1aae73ac705355190439d6b98f0b5717c2c9f822723c730f4d",
      "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": "8090c79c28c6ef128b568b21d9d8cacd5f454eb18b8975bdab61e97a56970c95",
    "original_candidate_line_sha256": "8090c79c28c6ef128b568b21d9d8cacd5f454eb18b8975bdab61e97a56970c95"
  },
  "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": 5,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "133ba247883c73457482a435355fbbe1618695ec90f3389fcc92a7de467db6cd",
      "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."
  }
}