{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260920-rational-valid-representation-0007",
  "pilot_number": "R0068-34832",
  "number": 34832,
  "family_id": "qf-rational-valid-representation",
  "title": {
    "zh-Hant": "第 34832 題：qf-rational-valid-representation",
    "en": "Question 34832: Valid Rational Representation"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260920-rational-valid-representation-0007",
    "batch_id": "batch-20260920-rational-number-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-rational-number"
    ],
    "title_zh": "qf-rational-valid-representation",
    "stem_zh": "p=-6、q=7 都明示為整數。p/q 是否是有效有理數表示？",
    "answer": {
      "kind": "choice",
      "value": "是",
      "choices": [
        "是",
        "否"
      ],
      "explanation_zh": "q=7≠0，因此 -6/7 是有效表示。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 2,
      "skills": [
        "有理數表示",
        "非零分母"
      ]
    },
    "variant": {
      "family_id": "qf-rational-valid-representation",
      "seed": 20260927,
      "parameters": {
        "p": -6,
        "q": 7,
        "semantic_template": "qf-rational-valid-representation/{\"p\":-6,\"q\":7}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-20",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260920-rational-valid-representation-0007",
    "batch_id": "batch-20260920-rational-number-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "884f8a81b4cd826ec86458c8466ef64485fb03daea8754e1dd7b1bf80393cffc",
      "family_id": "qf-rational-valid-representation",
      "seed": 20260927,
      "semantic_template": "qf-rational-valid-representation/{\"p\":-6,\"q\":7}"
    },
    "fields": {
      "title": "Valid Rational Representation",
      "stem": "Both p=-6 and q=7 are explicitly integers. Is p/q a valid rational-number representation?",
      "answer": {
        "kind": "choice",
        "value": "Yes",
        "choices": [
          "Yes",
          "No"
        ],
        "explanation": "q=7≠0, so -6/7 is a valid representation."
      },
      "skills": [
        "rational representation",
        "nonzero denominator"
      ],
      "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": "p=-6、q=7 都明示為整數。p/q 是否是有效有理數表示？",
        "en": "Both p=-6 and q=7 are explicitly integers. Is p/q a valid rational-number representation?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-rational-valid-representation, [p, q]]",
      "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 = [-6, 7]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Rational_RAW_integer_pair_NONzero_DEN_before_any_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "p/q是有理數表示需p,q為整數且q非0。q=0合法回答No，連p=0也不能作0/0；此branch不嘗試除法，不假造數值。",
        "en": "A rational representation needs INTEGER p,q and q≠0.Zero denominator is a LEGAL No,including0/0.This branch does NOT divide or fabricate a numeric value."
      },
      "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": "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-20260920-rational-number-foundations",
      "batch_path": "public/data/questions/batches/batch-20260920-rational-number-foundations/questions.jsonl",
      "batch_sha256": "f8a35e94c5da1d738c06e068b6df3b749c9d386dbe61bd660711a5a939e50c05",
      "original_line": 7,
      "original_line_sha256": "0625c0633fcf21089192ed2a467b70beb44d2c037b9d02ea06e488944ba2503a",
      "question_compact_sha256": "884f8a81b4cd826ec86458c8466ef64485fb03daea8754e1dd7b1bf80393cffc",
      "english_row_compact_sha256": "accc52174cf953d626acf935b978cad1eb6456445ce9e31e3c9e74dedcc33890",
      "english_manifest_path": "public/data/i18n/editions/batch-20260920-rational-number-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260920-rational-number-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-rational-number": {
        "sha256": "f1b52aad1867316fd94d6e07d6e94237a202d6769454898a0831d8d1bb89f23f",
        "english_sha256": "7f9330a95c6c6cb3df1c1696d1ffa62bb4442ff453291c4176febb6d0d71ff5a",
        "original_path": "public/data/mko/rational-number.json",
        "english_path": "public/data/i18n/editions/mko-rational-number.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "345142be27643acca9d0fec2422ac7311b85bf142709391cd6b5b3a33c03cf8e",
    "original_candidate_sha256": "43b484f51c79fb48e947d59736e68a7e1163e6b2bbd415725de7e1585009bfca",
    "original_candidate_line_sha256": "43b484f51c79fb48e947d59736e68a7e1163e6b2bbd415725de7e1585009bfca"
  },
  "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": 2,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050",
      "arithmetic_steps": 0
    },
    "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."
  }
}