{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260912-pythagorean-missing-side-0003",
  "pilot_number": "R0068-34503",
  "number": 34503,
  "family_id": "qf-pythagorean-missing-side",
  "title": {
    "zh-Hant": "第 34503 題：畢達哥拉斯定理缺邊計算",
    "en": "Question 34503: Missing Side by the Pythagorean Theorem"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260912-pythagorean-missing-side-0003",
    "batch_id": "batch-20260912-geometry-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-euclid-pythagorean-theorem"
    ],
    "title_zh": "畢達哥拉斯定理缺邊計算",
    "stem_zh": "在一個直角三角形中，兩股長分別為 8 與 15。求斜邊長 c。",
    "answer": {
      "kind": "numeric",
      "value": 17,
      "explanation_zh": "c=√(8²+15²)=17。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 4,
      "skills": [
        "畢達哥拉斯定理",
        "平方根"
      ]
    },
    "variant": {
      "family_id": "qf-pythagorean-missing-side",
      "seed": 20260974,
      "parameters": {
        "mode": "hypotenuse",
        "legs": [
          8,
          15
        ],
        "hypotenuse": 17,
        "known": [
          8,
          15
        ]
      }
    },
    "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-pythagorean-missing-side-0003",
    "batch_id": "batch-20260912-geometry-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "3e068d606cd3480487e067b431f4ec3c0f6de588b33f441b2aa31844e56b75fe",
      "family_id": "qf-pythagorean-missing-side",
      "seed": 20260974,
      "semantic_template": "qf-pythagorean-missing-side/20260974"
    },
    "fields": {
      "title": "Missing Side by the Pythagorean Theorem",
      "stem": "A right triangle has leg lengths 8 and 15. Find the hypotenuse length c.",
      "answer": {
        "kind": "numeric",
        "value": 17,
        "explanation": "c=√(8²+15²)=17."
      },
      "skills": [
        "Pythagorean theorem",
        "square roots"
      ],
      "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": "在一個直角三角形中，兩股長分別為 8 與 15。求斜邊長 c。",
        "en": "A right triangle has leg lengths 8 and 15. Find the hypotenuse length c."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-pythagorean-missing-side, [hypotenuse, known, legs, mode]]",
      "after": "derived = [BASE-no-required-operation, no-invented-domain]",
      "relation": "implies",
      "rule_id": "R68_BANK_specific_keys_operations_and_numeric_guards",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按來源分bank：legacy raw SAFE/衍生BigInt無界，BASE Number.isInteger不偷加SAFE/百萬界。underscore operation、domain及寬/嚴keys各依本bank；原JSON完整保存。",
        "en": "Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。",
          "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [hypotenuse, 8, 15]",
      "after": "derived = [right triangle premise, unknown c>0, c^2=a^2+b^2]",
      "relation": "implies",
      "rule_id": "Pythagorean_GIVEN_right_triangle_TWO_legs_NOT_filled_hypotenuse",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原中英題給直角三角形與兩股a,b。只由兩個已知股長推c；參數內已填的hypotenuse不是計算oracle。定理用於已給的直角三角形，不在此倒用逆定理。",
        "en": "The ORIGINAL bilingual problem GIVES a right triangle and TWO legs.Derive c ONLY from these givens;the already-filled hypotenuse parameter is NOT an oracle.Apply Pythagoras under the GIVEN right-angle premise,not an unqualified converse."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。",
          "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "Pythagorean ORIGINAL given first leg squared := mul(8, 8)",
      "after": "Pythagorean ORIGINAL given first leg squared = 64",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。",
        "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Pythagorean ORIGINAL given first leg squared，不以小數近似替代。",
          "en": "Recompute Pythagorean ORIGINAL given first leg squared with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "8",
          "8"
        ],
        "output": "64",
        "label": "Pythagorean ORIGINAL given first leg squared"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "Pythagorean ORIGINAL given second leg squared := mul(15, 15)",
      "after": "Pythagorean ORIGINAL given second leg squared = 225",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。",
        "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Pythagorean ORIGINAL given second leg squared，不以小數近似替代。",
          "en": "Recompute Pythagorean ORIGINAL given second leg squared with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "15",
          "15"
        ],
        "output": "225",
        "label": "Pythagorean ORIGINAL given second leg squared"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "Pythagorean ORIGINAL sum of given leg squares := sum(64, 225)",
      "after": "Pythagorean ORIGINAL sum of given leg squares = 289",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。",
        "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Pythagorean ORIGINAL sum of given leg squares，不以小數近似替代。",
          "en": "Recompute Pythagorean ORIGINAL sum of given leg squares with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "64",
          "225"
        ],
        "output": "289",
        "label": "Pythagorean ORIGINAL sum of given leg squares"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "Pythagorean DERIVED positive root squared for reverse substitution := mul(17, 17)",
      "after": "Pythagorean DERIVED positive root squared for reverse substitution = 289",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。",
        "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Pythagorean DERIVED positive root squared for reverse substitution，不以小數近似替代。",
          "en": "Recompute Pythagorean DERIVED positive root squared for reverse substitution with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "17",
          "17"
        ],
        "output": "289",
        "label": "Pythagorean DERIVED positive root squared for reverse substitution"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "source roles = [hypotenuse, 289]",
      "after": "derived = [17, 289]",
      "relation": "implies",
      "rule_id": "Pythagorean_POSITIVE_length_selects_principal_exact_root",
      "conditions": [],
      "explanation": {
        "zh-Hant": "由未知邊平方=radicand，代回核value²相等；邊長必正故取正的主平方根，不取±兩支。本25題實際根皆精確整數，不用Math.sqrt近似或抄已填答案。",
        "en": "The unknown side has square radicand;substitute back to verify value² exactly.A POSITIVE length selects the positive principal root,not BOTH±branches.All25 ACTUAL roots are exact integers;do not use Math.sqrt approximations or copy filled answer metadata."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。",
          "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": 17
  },
  "conclusion": {
    "canonical_value": "17",
    "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": 63,
      "original_line_sha256": "45c307b7ad26ee87611519bfd50d92b5a68dc319a3319178a9cce974499493c1",
      "question_compact_sha256": "3e068d606cd3480487e067b431f4ec3c0f6de588b33f441b2aa31844e56b75fe",
      "english_row_compact_sha256": "b689fe6eadad773bcfc93ed5bdf4852442a1924920a571548d68f81e11a791bb",
      "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-euclid-pythagorean-theorem": {
        "sha256": "f91873f82805e9a6d9ee8358fa64afa78e7594fc6568999814e34c1205ad51c6",
        "english_sha256": "1ad53a259b7aa8574f8579d208fda5c28c60bbd7d60b814200022c5917b7a849",
        "original_path": "public/data/mko/pythagorean-theorem.json",
        "english_path": "public/data/i18n/editions/mko-euclid-pythagorean-theorem.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "345142be27643acca9d0fec2422ac7311b85bf142709391cd6b5b3a33c03cf8e",
    "original_candidate_sha256": "956798aa46064a6c83f8a05b32733f4b384f2f94f63a2ad455e4729d361a59a1",
    "original_candidate_line_sha256": "956798aa46064a6c83f8a05b32733f4b384f2f94f63a2ad455e4729d361a59a1"
  },
  "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-p69",
    "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": "e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed",
      "question_first_witness_sha256": "8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 7,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "5f048c2c6035ec9d51aec80bc2806478466276ea496664b78fc355e633a2993e",
      "arithmetic_steps": 4
    },
    "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."
  }
}