{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260912-right-triangle-determination-0003",
  "pilot_number": "R0070-35653",
  "number": 35653,
  "family_id": "qf-right-triangle-determination",
  "title": {
    "zh-Hant": "第 35653 題：直角三角形判定",
    "en": "Question 35653: Identifying a Right Triangle"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260912-right-triangle-determination-0003",
    "batch_id": "batch-20260912-geometry-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-right-triangle"
    ],
    "title_zh": "直角三角形判定",
    "stem_zh": "一個非退化三角形的三內角依序為 20°、90°、70°。它是否為直角三角形？",
    "answer": {
      "kind": "choice",
      "value": "是",
      "choices": [
        "是",
        "否"
      ],
      "explanation_zh": "三角形內角和為 180°，且其中一角是 90°，故為直角三角形。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "內角判定",
        "三角形內角和"
      ]
    },
    "variant": {
      "family_id": "qf-right-triangle-determination",
      "seed": 20260944,
      "parameters": {
        "mode": "angles",
        "angles": [
          20,
          90,
          70
        ]
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-12",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260912-right-triangle-determination-0003",
    "batch_id": "batch-20260912-geometry-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "9878ffa9d095b34a589c67215b218c9ec42eedff086cfe32ed61520f04faec1a",
      "family_id": "qf-right-triangle-determination",
      "seed": 20260944,
      "semantic_template": "qf-right-triangle-determination/20260944"
    },
    "fields": {
      "title": "Identifying a Right Triangle",
      "stem": "A nondegenerate triangle has interior angles 20°, 90°, 70°. Is it a right triangle?",
      "answer": {
        "kind": "choice",
        "value": "Yes",
        "choices": [
          "Yes",
          "No"
        ],
        "explanation": "The angles sum to 180° and one angle is 90°, so the triangle is right."
      },
      "skills": [
        "interior-angle classification",
        "triangle angle sum"
      ],
      "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": "一個非退化三角形的三內角依序為 20°、90°、70°。它是否為直角三角形？",
        "en": "A nondegenerate triangle has interior angles 20°, 90°, 70°. Is it a right triangle?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-right-triangle-determination, [angles, mode]]",
      "after": "derived = [right, null, null]",
      "relation": "implies",
      "rule_id": "R70_SOURCE_bank_specific_interface",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只使用此bank真正明示的欄位、operation/domain與型別；BASE容許保留額外metadata，不把LDL SAFE/集合上限或其他bank的去重規則搬來。",
        "en": "Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。",
          "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "Right triangle ORIGINAL three interior angles sum := sum(20, 90, 70)",
      "after": "Right triangle ORIGINAL three interior angles sum = 180",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Right triangle ORIGINAL three interior angles sum，不以小數近似替代。",
          "en": "Recompute Right triangle ORIGINAL three interior angles sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "20",
          "90",
          "70"
        ],
        "output": "180",
        "label": "Right triangle ORIGINAL three interior angles sum"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "source roles = [[20, 90, 70], 180]",
      "after": "derived = [[否, 是, 否], 是]",
      "relation": "implies",
      "rule_id": "Right_triangle_GIVEN_nondegenerate_angle_sum_then_definition",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這30題均已逐題核三正內角且總和180，符合中英非退化三角形前提；直角三角形定義為其中一內角90。必須先合格三角形，不因非法角資料含90就宣布Yes。",
        "en": "ALL30 actual questions have THREE positive interior angles summing to180,matching the bilingual nondegenerate-triangle premise.A right triangle is defined by ONE angle of90.First qualify the triangle;90 in invalid angle data is not enough."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。",
          "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": "是"
  },
  "conclusion": {
    "canonical_value": "是",
    "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-20260912-geometry-foundations",
      "batch_path": "public/data/questions/batches/batch-20260912-geometry-foundations/questions.jsonl",
      "batch_sha256": "818fc9bd154b15a97199c437c5345260e55307eada85586bf547e52c4ae518dc",
      "original_line": 33,
      "original_line_sha256": "f32c143296a93b784c9ef0e7828ea4fa966e9ae1395f23a4fa7992decd1841cc",
      "question_compact_sha256": "9878ffa9d095b34a589c67215b218c9ec42eedff086cfe32ed61520f04faec1a",
      "english_row_compact_sha256": "fa729cd3c0d2f329f651f0233428ac31a390a6205c1aee0250e0d02ecdd13a3e",
      "english_manifest_path": "public/data/i18n/editions/batch-20260912-geometry-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260912-geometry-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": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff",
    "original_candidate_sha256": "7d862fec3b236efbc9f3316a67184c224336f1c6025e350c6401a7e4036ea724",
    "original_candidate_line_sha256": "7d862fec3b236efbc9f3316a67184c224336f1c6025e350c6401a7e4036ea724"
  },
  "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-20261026-012-p71",
    "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": "9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80",
      "question_first_witness_sha256": "c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab"
    },
    "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": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050",
      "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."
  }
}