{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260922-angle-pair-relation-0017",
  "pilot_number": "R0001-01292",
  "number": 1292,
  "family_id": "qf-angle-pair-relation",
  "title": {
    "zh-Hant": "第 1292 題：兩個明示角量值的關係",
    "en": "Question 1292: Relation Between Two Explicit Angle Measures"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260922-angle-pair-relation-0017",
    "batch_id": "batch-20260922-angle-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-angle"
    ],
    "title_zh": "兩個明示角量值的關係",
    "stem_zh": "兩角 α=15°、β=15° 的量值皆明示為整數度數。只由 α+β 判斷，它們是互餘、互補或皆非？",
    "answer": {
      "kind": "short_text",
      "value": "皆非",
      "explanation_zh": "α+β=15+15=30°；和為非 90° 也非 180°，所以皆非。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "互餘",
        "互補",
        "整數度數相加"
      ]
    },
    "variant": {
      "family_id": "qf-angle-pair-relation",
      "seed": 20261239,
      "parameters": {
        "alpha": 15,
        "beta": 15,
        "unit": "degree",
        "range": "0<angle<=180",
        "operation": "pair_relation",
        "semantic_template": "qf-angle-pair-relation/{\"alpha\":15,\"beta\":15,\"operation\":\"pair_relation\",\"range\":\"0<angle<=180\",\"unit\":\"degree\"}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題是 candidate 練習；機械重算僅核對明示條件與指定實例，並非形式證明或人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-22",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260922-angle-pair-relation-0017",
    "batch_id": "batch-20260922-angle-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "690436578917cf1955a7a2d408bf03e57658b3a8aebb63f06c0da8c869be4b28",
      "family_id": "qf-angle-pair-relation",
      "seed": 20261239,
      "semantic_template": "qf-angle-pair-relation/{\"alpha\":15,\"beta\":15,\"operation\":\"pair_relation\",\"range\":\"0<angle<=180\",\"unit\":\"degree\"}"
    },
    "fields": {
      "title": "Relation Between Two Explicit Angle Measures",
      "stem": "Angles α=15° and β=15° have explicitly stated integer measures. Using only α+β, are they complementary, supplementary, or neither?",
      "answer": {
        "kind": "short_text",
        "value": "neither",
        "explanation": "α+β=15+15=30°. Therefore the angles are neither."
      },
      "skills": [
        "complementary angles",
        "supplementary angles",
        "integer-degree addition"
      ],
      "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": "兩角 α=15°、β=15° 的量值皆明示為整數度數。只由 α+β 判斷，它們是互餘、互補或皆非？",
        "en": "Angles α=15° and β=15° have explicitly stated integer measures. Using only α+β, are they complementary, supplementary, or neither?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "angle measurements are explicit integers in degrees",
      "after": "classification uses values, not diagram appearance",
      "relation": "implies",
      "rule_id": "degree_measure_domain",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先保留度數單位與題目宣告範圍，不從圖形外觀估量。",
        "en": "Retain degree units and the declared range rather than estimating from a diagram."
      },
      "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": "α+β := sum(15, 15)",
      "after": "α+β = 30",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "將兩個明示度數相加，順序不影響和。",
        "en": "Add the two explicit degree measures; order does not affect the sum."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 α+β，不以小數近似替代。",
          "en": "Recompute α+β with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "15",
          "15"
        ],
        "output": "30",
        "label": "α+β"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "sum=30°",
      "after": "complementary iff sum90°; supplementary iff sum180°",
      "relation": "implies",
      "rule_id": "angle_pair_definitions",
      "conditions": [],
      "explanation": {
        "zh-Hant": "關係只由和的值決定，本題不要求兩角相鄰。",
        "en": "The relation depends on their sum; adjacency is not required."
      },
      "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": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "α+β=30°",
      "after": "relation=皆非",
      "relation": "implies",
      "rule_id": "angle_pair_verdict",
      "conditions": [],
      "explanation": {
        "zh-Hant": "若和既不是90也不是180，兩個關係都不成立。",
        "en": "If the sum is neither90 nor180, neither relation holds."
      },
      "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": {
    "sum": "30",
    "relation": "皆非"
  },
  "conclusion": {
    "canonical_value": "皆非",
    "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-20260922-angle-foundations",
      "batch_path": "public/data/questions/batches/batch-20260922-angle-foundations/questions.jsonl",
      "batch_sha256": "c555a3fd7d6935bafab101087f804d4fd68cae57c83565d4e9ea920a778b2e56",
      "original_line": 92,
      "original_line_sha256": "c5de96bc358aa571ec5f3e5ee200b1ca793959474ef200a365a557b68af1b991",
      "question_compact_sha256": "690436578917cf1955a7a2d408bf03e57658b3a8aebb63f06c0da8c869be4b28",
      "english_row_compact_sha256": "ce10fe27f28a77e3b7c4826fcd4de86430dab9012e42ae0c649740eed1ed57b4",
      "english_manifest_path": "public/data/i18n/editions/batch-20260922-angle-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260922-angle-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-angle": {
        "sha256": "e77eca47694501f576639c69b49c366d6053b453055167a92e61e9a9b88626da",
        "english_sha256": "c5cbf3ced06829082efdaaf6f2d97bf231e72f882e785bc6b4ecdf390768cc8b",
        "original_path": "public/data/mko/angle.json",
        "english_path": "public/data/i18n/editions/mko-angle.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "b9fe70a7a264c90c20349be0449b2bd1a1b4d0e0a97092bc9fbcb7ca36ce0694",
    "original_candidate_sha256": "cfd3823c9b1b513960fba6e54d4a2ae81e5b2670cc9c72f25d69aba48bd7fad3",
    "original_candidate_line_sha256": "cfd3823c9b1b513960fba6e54d4a2ae81e5b2670cc9c72f25d69aba48bd7fad3"
  },
  "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-p2",
    "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": "c3b44ce8ed60ada6902fb206627537d5f90ba2a867eaba43a36f903280c496cc",
      "question_first_witness_sha256": "3e91602adc7f81a2671a2a3ffaf6a447028b56abc5853e8271673d76f30cd7ad"
    },
    "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": "95898806159ade5ae11f935f5ca2bdb42e8593c4f980c395fa51738163d956c8",
      "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."
  }
}