{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261012-r05-right-triangle-0007",
  "pilot_number": "R0010-05807",
  "number": 5807,
  "family_id": "qf-density12-right-triangle-angle-remainder",
  "title": {
    "zh-Hant": "第 5807 題：精確直角協議的銳角補足",
    "en": "Question 5807: Acute-Angle Remainder in a Given Right Triangle"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261012-r05-right-triangle-0007",
    "batch_id": "batch-20261008-advance-20261012-r05-right-triangle-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-right-triangle"
    ],
    "title_zh": "精確直角協議的銳角補足",
    "stem_zh": "精確角度協議；度數，假設非退化平面三角形的γ=90°、α=8°。依序求 (β度數, α+β度數)。",
    "answer": {
      "kind": "expression",
      "value": "(82, 90)",
      "explanation_zh": "直角銳角補足=(82, 90)。在此直角與角和前提下從90扣α；不使用容差，不推論未給定的幾何構造。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 1,
      "skills": [
        "精確直角協議的銳角補足"
      ]
    },
    "variant": {
      "family_id": "qf-density12-right-triangle-angle-remainder",
      "seed": 202610125007,
      "parameters": {
        "alpha": 8,
        "angle_unit": "degrees",
        "operation": "density12_right_triangle_angle_remainder",
        "domain": "exact_integer_angle_protocol",
        "semantic_template": "qf-density12-right-triangle-angle-remainder/8"
      }
    },
    "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-0007",
    "batch_id": "batch-20261008-advance-20261012-r05-right-triangle-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "1d42164d8ef63b96fd435bf7f2455ae0b156c0adc87002ea61cc9db4981774d9",
      "family_id": "qf-density12-right-triangle-angle-remainder",
      "seed": 202610125007,
      "semantic_template": "qf-density12-right-triangle-angle-remainder/8"
    },
    "fields": {
      "title": "Acute-Angle Remainder in a Given Right Triangle",
      "stem": "Exact degrees: a nondegenerate plane triangle has γ=90° and α=8°. Give (β in degrees, α+β in degrees).",
      "answer": {
        "kind": "expression",
        "value": "(82, 90)",
        "explanation": "Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (82, 90)."
      },
      "skills": [
        "Acute-Angle Remainder in a Given Right Triangle"
      ],
      "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，假設非退化平面三角形的γ=90°、α=8°。依序求 (β度數, α+β度數)。",
        "en": "Exact degrees: a nondegenerate plane triangle has γ=90° and α=8°. Give (β in degrees, α+β in degrees)."
      }
    }
  ],
  "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": "acute-angle budget := sub(180, 90)",
      "after": "acute-angle budget = 90",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依已給非退化歐氏平面三角形角和180與直角90，剩兩角合計90。",
        "en": "Under the supplied nondegenerate Euclidean plane-triangle premises,the180-degree sum minus the90-degree right angle leaves90 for the two acute angles."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 acute-angle budget，不以小數近似替代。",
          "en": "Recompute acute-angle budget with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "180",
          "90"
        ],
        "output": "90",
        "label": "acute-angle budget"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "other acute angle beta := sub(90, 8)",
      "after": "other acute angle beta = 82",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "從兩銳角總預算扣掉已給α。",
        "en": "Subtract the supplied α from the two-acute-angle budget."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 other acute angle beta，不以小數近似替代。",
          "en": "Recompute other acute angle beta with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "90",
          "8"
        ],
        "output": "82",
        "label": "other acute angle beta"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "alpha plus beta := sum(8, 82)",
      "after": "alpha plus beta = 90",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "回加核對兩銳角和，保留所求兩欄次序。",
        "en": "Add back to audit the acute-angle sum,retaining the requested field order."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 alpha plus beta，不以小數近似替代。",
          "en": "Recompute alpha plus beta with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "8",
          "82"
        ],
        "output": "90",
        "label": "alpha plus beta"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "1≤α=8≤89;β=82",
      "after": "α+β=90;both acute",
      "relation": "implies",
      "rule_id": "right_triangle_remainder_premises",
      "conditions": [],
      "explanation": {
        "zh-Hant": "α的嚴格銳角範圍使β也在1到89度；這是已給直角三角形前提下的量值推導，不是構造證明。",
        "en": "The strict acute range for α also places β between1 and89 degrees.This derives values under the given right-triangle premises,not a construction proof."
      },
      "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": [
      "82",
      "90"
    ]
  },
  "conclusion": {
    "canonical_value": "(82, 90)",
    "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": 7,
      "original_line_sha256": "d2408455c2ca83d01ed885d107adb50663de5a9c2ce5b0f60add07066a6d0f6d",
      "question_compact_sha256": "1d42164d8ef63b96fd435bf7f2455ae0b156c0adc87002ea61cc9db4981774d9",
      "english_row_compact_sha256": "703a9558df22d61dfc9257606ee037ac9bad6500413f117a2027e57f7408cdd9",
      "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": {
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        "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": "a1a47c80f31f8ed05b9cc69ed657b5eb4d16a33ffb8b8cea2596434edda79f87",
    "original_candidate_line_sha256": "a1a47c80f31f8ed05b9cc69ed657b5eb4d16a33ffb8b8cea2596434edda79f87"
  },
  "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": {
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      "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": "ac43cfed3948079bed0aa76ce04774609ac8dedbc1eb0d05c1ea630aa902a589",
      "arithmetic_steps": 3
    },
    "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."
  }
}