{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260922-angle-supplement-measure-0011",
  "pilot_number": "R0001-01261",
  "number": 1261,
  "family_id": "qf-angle-supplement-measure",
  "title": {
    "zh-Hant": "第 1261 題：互補角量值",
    "en": "Question 1261: Supplementary Angle Measure"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260922-angle-supplement-measure-0011",
    "batch_id": "batch-20260922-angle-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-angle"
    ],
    "title_zh": "互補角量值",
    "stem_zh": "角 θ 的量值明示為 68°。求一個與 θ 互補的角量值（整數度數）；不要求兩角相鄰，也不由圖猜測。",
    "answer": {
      "kind": "short_text",
      "value": "112°",
      "explanation_zh": "互補的明示量值和為 180°；180−68=112，故答案為 112°。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "互補",
        "整數度數相加"
      ]
    },
    "variant": {
      "family_id": "qf-angle-supplement-measure",
      "seed": 20261133,
      "parameters": {
        "theta": 68,
        "unit": "degree",
        "range": "0<theta<180",
        "operation": "supplement",
        "target_sum": 180,
        "semantic_template": "qf-angle-supplement-measure/{\"operation\":\"supplement\",\"range\":\"0<theta<180\",\"target_sum\":180,\"theta\":68,\"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-supplement-measure-0011",
    "batch_id": "batch-20260922-angle-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "6c0f3dea8714c7b6209198e342abc3bcbc5d731484442569b9a852c12954feec",
      "family_id": "qf-angle-supplement-measure",
      "seed": 20261133,
      "semantic_template": "qf-angle-supplement-measure/{\"operation\":\"supplement\",\"range\":\"0<theta<180\",\"target_sum\":180,\"theta\":68,\"unit\":\"degree\"}"
    },
    "fields": {
      "title": "Supplementary Angle Measure",
      "stem": "Angle θ has the explicitly stated measure 68°. Find an integer-degree measure supplementary to θ; adjacency is not required and no value is inferred from a diagram.",
      "answer": {
        "kind": "short_text",
        "value": "112°",
        "explanation": "Supplementary measures sum to 180°; 180−68=112, so the answer is 112°."
      },
      "skills": [
        "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": "角 θ 的量值明示為 68°。求一個與 θ 互補的角量值（整數度數）；不要求兩角相鄰，也不由圖猜測。",
        "en": "Angle θ has the explicitly stated measure 68°. Find an integer-degree measure supplementary to θ; adjacency is not required and no value is inferred from a diagram."
      }
    }
  ],
  "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": "θ=68°; required sum=180°",
      "after": "θ+φ=180°",
      "relation": "implies",
      "rule_id": "angle_sum_equation",
      "conditions": [],
      "explanation": {
        "zh-Hant": "把互餘或互補定義先寫成等式。",
        "en": "Express the complementary or supplementary definition as an equation first."
      },
      "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": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "φ := sub(180, 68)",
      "after": "φ = 112",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩邊同減原角度，求出另一角。",
        "en": "Subtract the original angle from the target sum."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 φ，不以小數近似替代。",
          "en": "Recompute φ with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "180",
          "68"
        ],
        "output": "112",
        "label": "φ"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "θ+φ := sum(68, 112)",
      "after": "θ+φ = 180",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "乘回／加回核對指定總角度。",
        "en": "Add back to verify the required total measure."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 θ+φ，不以小數近似替代。",
          "en": "Recompute θ+φ with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "68",
          "112"
        ],
        "output": "180",
        "label": "θ+φ"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "0<68<180",
      "after": "0<112<180; answer=112°",
      "relation": "implies",
      "rule_id": "positive_degree_result",
      "conditions": [],
      "explanation": {
        "zh-Hant": "結果是正角度並保留度數單位；不增加相鄰或共線假設。",
        "en": "The result is positive and retains degree units; no adjacency or collinearity assumption is added."
      },
      "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": {
    "theta": 68,
    "target": 180,
    "result": "112"
  },
  "conclusion": {
    "canonical_value": "112°",
    "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": 61,
      "original_line_sha256": "33d2b15a1bbc317215cef3423b0f3b32488c35a56bee53c7a55814408ec8c4b8",
      "question_compact_sha256": "6c0f3dea8714c7b6209198e342abc3bcbc5d731484442569b9a852c12954feec",
      "english_row_compact_sha256": "6fcc43ed71e253f697a39f46f6226981f18cdcab7ed7e9f901df5bd0382425f7",
      "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": "00bc5d26e87e4bbb4d5f1cd98ffdf5d4d7944a41db5a4990585fc40b2f176e9c",
    "original_candidate_line_sha256": "00bc5d26e87e4bbb4d5f1cd98ffdf5d4d7944a41db5a4990585fc40b2f176e9c"
  },
  "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": 5,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "7d095100a488d99cf1ab1066598a1586f31e36d5410dcc4cce6a73f5b1616c0f",
      "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."
  }
}