{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260920-rational-denominator-sign-normalization-0020",
  "pilot_number": "R0068-34770",
  "number": 34770,
  "family_id": "qf-rational-denominator-sign-normalization",
  "title": {
    "zh-Hant": "第 34770 題：qf-rational-denominator-sign-normalization",
    "en": "Question 34770: Denominator-Sign Normalization"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260920-rational-denominator-sign-normalization-0020",
    "batch_id": "batch-20260920-rational-number-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-rational-number"
    ],
    "title_zh": "qf-rational-denominator-sign-normalization",
    "stem_zh": "將 7/-2 正規化為分母為正的精確表示。",
    "answer": {
      "kind": "short_text",
      "value": "-7/2",
      "explanation_zh": "q=-2 為負，只將負號移到分子，得到 -7/2；比值未改變，未做 gcd 約分或最簡化。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 3,
      "skills": [
        "分母符號正規化"
      ]
    },
    "variant": {
      "family_id": "qf-rational-denominator-sign-normalization",
      "seed": 20261040,
      "parameters": {
        "p": 7,
        "q": -2,
        "semantic_template": "qf-rational-denominator-sign-normalization/{\"p\":7,\"q\":-2}"
      }
    },
    "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-denominator-sign-normalization-0020",
    "batch_id": "batch-20260920-rational-number-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "152424e361162ba618c7bb5d8d18e70a1025e20d08a27cd918c490c18dca92ae",
      "family_id": "qf-rational-denominator-sign-normalization",
      "seed": 20261040,
      "semantic_template": "qf-rational-denominator-sign-normalization/{\"p\":7,\"q\":-2}"
    },
    "fields": {
      "title": "Denominator-Sign Normalization",
      "stem": "Normalize 7/-2 to an exact representation with a positive denominator.",
      "answer": {
        "kind": "short_text",
        "value": "-7/2",
        "explanation": "Because q=-2 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."
      },
      "skills": [
        "denominator-sign normalization"
      ],
      "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": "將 7/-2 正規化為分母為正的精確表示。",
        "en": "Normalize 7/-2 to an exact representation with a positive denominator."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-rational-denominator-sign-normalization, [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 = [7, -2]",
      "after": "derived = [-7, 2, -7/2]",
      "relation": "implies",
      "rule_id": "Rational_SIGN_ONLY_simultaneous_sign_flip_NO_gcd_reduction",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只在分母負時同乘−1，使分母正；本題不約分！2/2、0/4、−2/6都可能是正確sign-only答案；正分母則原表示不變，不能偷換成最簡分數。",
        "en": "ONLY when the denominator is negative,multiply BOTH components by−1.This task DOES NOT REDUCE:2/2,0/4,−2/6 may be correct sign-only answers.A positive denominator leaves the original representation unchanged.Do not silently substitute lowest terms."
      },
      "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": "-7/2"
  },
  "conclusion": {
    "canonical_value": "-7/2",
    "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": 45,
      "original_line_sha256": "6501bba50a95865501402eebd1105bd35da17e092d0848f044b1b774b6f881af",
      "question_compact_sha256": "152424e361162ba618c7bb5d8d18e70a1025e20d08a27cd918c490c18dca92ae",
      "english_row_compact_sha256": "a091bb6ca166f284f8a69947f750e8b73fd0aafa74873aa77ff5cd90d2d9d8f3",
      "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": "ffbf2ebed6965ffa06ad6390a8db06af4321ad1faeae4a1ae359685b43eb4d6d",
    "original_candidate_line_sha256": "ffbf2ebed6965ffa06ad6390a8db06af4321ad1faeae4a1ae359685b43eb4d6d"
  },
  "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": "d80592ab5f324f1fd92f3acba50e95f004caa31efbac1e8384ec7ee306cc3724",
      "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."
  }
}