{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260930-r01-fraction-representation-validity-0017",
  "pilot_number": "R0063-32192",
  "number": 32192,
  "family_id": "qf-fraction-representation-validity",
  "title": {
    "zh-Hant": "第 32192 題：合法分數表示",
    "en": "Question 32192: Validity of a Fraction Representation"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260930-r01-fraction-representation-validity-0017",
    "batch_id": "batch-20260930-r01-fraction-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-fraction"
    ],
    "title_zh": "合法分數表示",
    "stem_zh": "對整數分子 p=4、分母 q=3，p/q 是合法的有理數表示嗎？回答是或否。",
    "answer": {
      "kind": "short_text",
      "value": "是",
      "explanation_zh": "分母條件為 q≠0；此處 q=3，因此答案為是。零分子不會取消分母條件。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 2,
      "skills": [
        "非零分母",
        "整數表示"
      ]
    },
    "variant": {
      "family_id": "qf-fraction-representation-validity",
      "seed": 202609301017,
      "parameters": {
        "operation": "representation_validity",
        "p": 4,
        "q": 3,
        "semantic_template": "qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":4,\"q\":3}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "json_schema",
        "producer_local_answer_invariants",
        "explanation_witness_accuracy"
      ],
      "warning_zh": "本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "Codex GPT-6 question producer",
      "generated_at": "2026-09-30",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260930-r01-fraction-representation-validity-0017",
    "batch_id": "batch-20260930-r01-fraction-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "288c203fa3446b5fab5ab9ab48beaad78d75e77ef862feae12d3f37ae4d1cb2b",
      "family_id": "qf-fraction-representation-validity",
      "seed": 202609301017,
      "semantic_template": "qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":4,\"q\":3}"
    },
    "fields": {
      "title": "Validity of a Fraction Representation",
      "stem": "For integer numerator p=4 and denominator q=3, is p/q a valid rational-number representation? Answer Yes or No.",
      "answer": {
        "kind": "short_text",
        "value": "Yes",
        "explanation": "q=3≠0, so 4/3 is a valid rational-number representation."
      },
      "skills": [
        "nonzero denominator",
        "integer representation"
      ],
      "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": "對整數分子 p=4、分母 q=3，p/q 是合法的有理數表示嗎？回答是或否。",
        "en": "For integer numerator p=4 and denominator q=3, is p/q a valid rational-number representation? Answer Yes or No."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-fraction-representation-validity, representation_validity, no-required-domain, []]",
      "after": "derived = [[nonzero_denominator_YesNo_STRING]]",
      "relation": "implies",
      "rule_id": "R63_SOURCE_bank_keys_operation_domain_output_roles_metadata_not_oracle",
      "conditions": [],
      "explanation": {
        "zh-Hant": "BASE來源沒有本輪legacy的通用operation/domain/額外欄位禁令；保metadata而不當答案。PULSE與legacy則核來源精確欄位、operation及domain。不要把tuple、/1或輸入界強套全部題族。",
        "en": "BASE sources do not acquire a generic legacy operation/domain or unknown-metadata ban.Retain metadata WITHOUT using it as an answer oracle.PULSE/legacy enforce their exact source keys,operation/domain.Do not impose universal tuples,/1 or input bounds."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "依原始輸入、型別、論域及明示前提反向代回核對；不是由結論唯一還原前提。來源綁定候選、獨立審查、形式證明與發布各自分開。",
          "en": "Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [4, 3, []]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Fraction_ALL_RAW_SAFE_integer_components_even_zero_den_validity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先驗全部raw分量的SAFE整數型別，包含q0／0/0資格題的分子。資格題可合法No；其他實際運算才要求所有用到的den非0。",
        "en": "Validate EVERY raw SAFE integer component,including the numerator at q0/0/0 eligibility.A validity task may legally return No;actual arithmetic requires ALL used denominators nonzero."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "依原始輸入、型別、論域及明示前提反向代回核對；不是由結論唯一還原前提。來源綁定候選、獨立審查、形式證明與發布各自分開。",
          "en": "Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate."
        }
      },
      "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-20260930-r01-fraction-foundations",
      "batch_path": "public/data/questions/batches/batch-20260930-r01-fraction-foundations/questions.jsonl",
      "batch_sha256": "e2b3f6511abc80a4dc23251454dabd91dee78b87fd84f708bbdd52180842f09f",
      "original_line": 17,
      "original_line_sha256": "e6bc981a7d4430d7c6ec0673e6156621cdd423e2302ecfa0ee90004ea12e9f76",
      "question_compact_sha256": "288c203fa3446b5fab5ab9ab48beaad78d75e77ef862feae12d3f37ae4d1cb2b",
      "english_row_compact_sha256": "40a04d3e4e8b5de520cbdbca446053c3e2f2bba3041ba2b198830c50e39bda1c",
      "english_manifest_path": "public/data/i18n/editions/batch-20260930-r01-fraction-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260930-r01-fraction-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-fraction": {
        "sha256": "aa89902ad405685be331872579647cec33e7ab6792273fe60ad8fefe6129f919",
        "english_sha256": "ea8b15d28832a77ca243cb2c04a33ac67244aca632c895666d9a33fa9b4982d4",
        "original_path": "public/data/mko/fraction.json",
        "english_path": "public/data/i18n/editions/mko-fraction.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "f3271d6047df957dbf3d61120bd3dd374784c828b17849887e14caf59d93f745",
    "original_candidate_sha256": "194382f6599362d8b6dd067a304789c930a4f4680c43fab452478fa8514c08ec",
    "original_candidate_line_sha256": "194382f6599362d8b6dd067a304789c930a4f4680c43fab452478fa8514c08ec"
  },
  "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-20261026-011-p64",
    "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": "acf03b776f4855e3869810bcbecf1116e3a2b11dfb1e2a5dfbcf8135ad24a7d0",
      "question_first_witness_sha256": "eadbbac3220988b52754f32450fb536d627217306d1ce28a49134f56c21bfa88"
    },
    "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."
  }
}