{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261012-r04-set-membership-0003",
  "pilot_number": "R0010-05628",
  "number": 5628,
  "family_id": "qf-density12-membership-indexed-predicate-values",
  "title": {
    "zh-Hant": "第 5628 題：有限型別查詢的資格與隸屬真假",
    "en": "Question 5628: Typed Membership Queries and Truth Values"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261012-r04-set-membership-0003",
    "batch_id": "batch-20261008-advance-20261012-r04-set-membership-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-set-membership"
    ],
    "title_zh": "有限型別查詢的資格與隸屬真假",
    "stem_zh": "明示有限型別Fin(6)；完整特徵表bits=[0, 0, 0, 1, 1, 1]按索引從0給A的0／1隸屬，queries=[0, 1, 102]。依序列 (各查詢是否合型別, 合型別者的隸屬真假或不合型別)。",
    "answer": {
      "kind": "expression",
      "value": "([是, 是, 否], [假, 假, 不合型別])",
      "explanation_zh": "型別資格與隸屬真假=([是, 是, 否], [假, 假, 不合型別])。先核查型別再讀完整特徵表，型別外不等於隸屬為假；有限隸屬非全部集合論。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 1,
      "skills": [
        "有限型別查詢的資格與隸屬真假"
      ]
    },
    "variant": {
      "family_id": "qf-density12-membership-indexed-predicate-values",
      "seed": 202610124003,
      "parameters": {
        "n": 6,
        "bits": [
          0,
          0,
          0,
          1,
          1,
          1
        ],
        "queries": [
          0,
          1,
          102
        ],
        "operation": "density12_membership_indexed_predicate_values",
        "domain": "finite_typed_membership",
        "semantic_template": "qf-density12-membership-indexed-predicate-values/[\"nonmember\",\"nonmember\",\"untyped\"]"
      }
    },
    "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-r04-set-membership-0003",
    "batch_id": "batch-20261008-advance-20261012-r04-set-membership-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "0f27e0c0c6b42d3381f4ccc6db008e531c1568152cf76c4193775dabc9924d57",
      "family_id": "qf-density12-membership-indexed-predicate-values",
      "seed": 202610124003,
      "semantic_template": "qf-density12-membership-indexed-predicate-values/[\"nonmember\",\"nonmember\",\"untyped\"]"
    },
    "fields": {
      "title": "Typed Membership Queries and Truth Values",
      "stem": "The finite type is Fin(6)={0,…,5}. Complete characteristic table bits=[0, 0, 0, 1, 1, 1] uses 0/1 membership from index 0; ordered queries=[0, 1, 102]. Give (type-eligibility mask, membership truth values or ill-typed).",
      "answer": {
        "kind": "expression",
        "value": "([Yes, Yes, No], [False, False, ill-typed])",
        "explanation": "Check typing before reading the complete characteristic table; an outside-type query is not a False membership value. Finite membership does not constitute all of set theory. The exact result, retaining the requested order, is ([Yes, Yes, No], [False, False, ill-typed])."
      },
      "skills": [
        "Typed Membership Queries and Truth Values"
      ],
      "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": "明示有限型別Fin(6)；完整特徵表bits=[0, 0, 0, 1, 1, 1]按索引從0給A的0／1隸屬，queries=[0, 1, 102]。依序列 (各查詢是否合型別, 合型別者的隸屬真假或不合型別)。",
        "en": "The finite type is Fin(6)={0,…,5}. Complete characteristic table bits=[0, 0, 0, 1, 1, 1] uses 0/1 membership from index 0; ordered queries=[0, 1, 102]. Give (type-eligibility mask, membership truth values or ill-typed)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "declared finite type or bounded integer universe",
      "after": "membership truth is distinct from eligibility to ask the question",
      "relation": "implies",
      "rule_id": "finite_membership_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "型別外不等於隸屬為假；只在明示有限型別或整數集合中核對，並不宣稱全部集合論或無限制概括。",
        "en": "Being outside the type is not the same as false membership.Check only the declared finite type or integer set,not all set theory or unrestricted comprehension."
      },
      "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": "legal index=0∈Fin(6);bit=0",
      "after": "membership=假",
      "relation": "implies",
      "rule_id": "complete_characteristic_bit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整特徵表中1表示隸屬真、0表示假；兩者都仍是合法型別內的判定。",
        "en": "In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments."
      },
      "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": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "legal index=1∈Fin(6);bit=0",
      "after": "membership=假",
      "relation": "implies",
      "rule_id": "complete_characteristic_bit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整特徵表中1表示隸屬真、0表示假；兩者都仍是合法型別內的判定。",
        "en": "In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments."
      },
      "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": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "legal index=2∈Fin(6);bit=0",
      "after": "membership=假",
      "relation": "implies",
      "rule_id": "complete_characteristic_bit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整特徵表中1表示隸屬真、0表示假；兩者都仍是合法型別內的判定。",
        "en": "In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments."
      },
      "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": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "legal index=3∈Fin(6);bit=1",
      "after": "membership=真",
      "relation": "implies",
      "rule_id": "complete_characteristic_bit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整特徵表中1表示隸屬真、0表示假；兩者都仍是合法型別內的判定。",
        "en": "In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments."
      },
      "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": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "legal index=4∈Fin(6);bit=1",
      "after": "membership=真",
      "relation": "implies",
      "rule_id": "complete_characteristic_bit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整特徵表中1表示隸屬真、0表示假；兩者都仍是合法型別內的判定。",
        "en": "In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments."
      },
      "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": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "legal index=5∈Fin(6);bit=1",
      "after": "membership=真",
      "relation": "implies",
      "rule_id": "complete_characteristic_bit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整特徵表中1表示隸屬真、0表示假；兩者都仍是合法型別內的判定。",
        "en": "In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments."
      },
      "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": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "query=0;legal in Fin(6)=是",
      "after": "假",
      "relation": "implies",
      "rule_id": "typed_membership_query_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先檢型別再讀位元；不合型別不填成假，Fin(0)時所有整數查詢都在型別外。",
        "en": "Check typing before reading a bit;do not replace ill-typed with False.For Fin(0),every integer query is outside the type."
      },
      "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": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "query=1;legal in Fin(6)=是",
      "after": "假",
      "relation": "implies",
      "rule_id": "typed_membership_query_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先檢型別再讀位元；不合型別不填成假，Fin(0)時所有整數查詢都在型別外。",
        "en": "Check typing before reading a bit;do not replace ill-typed with False.For Fin(0),every integer query is outside the type."
      },
      "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": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "query=102;legal in Fin(6)=否",
      "after": "不合型別",
      "relation": "implies",
      "rule_id": "typed_membership_query_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先檢型別再讀位元；不合型別不填成假，Fin(0)時所有整數查詢都在型別外。",
        "en": "Check typing before reading a bit;do not replace ill-typed with False.For Fin(0),every integer query is outside the type."
      },
      "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": [
      [
        true,
        true,
        false
      ],
      [
        false,
        false,
        "不合型別"
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([是, 是, 否], [假, 假, 不合型別])",
    "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-r04-set-membership-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261012-r04-set-membership-foundations/questions.jsonl",
      "batch_sha256": "f10a826885fa19e57016c6a08b8d9a1fe86d7d44f9376d12639a973f92aeb8e2",
      "original_line": 3,
      "original_line_sha256": "603fe9f88b7425af2c756f7ff48925b0a96d865ae769b0a81662b7325c6c5105",
      "question_compact_sha256": "0f27e0c0c6b42d3381f4ccc6db008e531c1568152cf76c4193775dabc9924d57",
      "english_row_compact_sha256": "8358145fab9b81f0189a95a72cd0137fb56147c61f8ecc26d89ae11ac37ad6fc",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261012-r04-set-membership-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261012-r04-set-membership-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-set-membership": {
        "sha256": "2a438aa79c23e6d37869e1e63eb48420bcf2f114f44b58fe5bea386076b4f0db",
        "english_sha256": "3c93982fdf37b764e4dcea079fba39532642656286a8cfbae67470b6274a4e38",
        "original_path": "public/data/mko/set-membership.json",
        "english_path": "public/data/i18n/editions/mko-set-membership.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "aeab777a3897ae2c01315b86b5e9b9a43ffb59b075efae44fd95d447123d32f1",
    "original_candidate_sha256": "55ac00af78b89ef707936b2f89dd640cdb9d60af538e7976d1e363f55901ac48",
    "original_candidate_line_sha256": "55ac00af78b89ef707936b2f89dd640cdb9d60af538e7976d1e363f55901ac48"
  },
  "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": {
      "semantic_review_sha256": "0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06f",
      "question_first_witness_sha256": "0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fc"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 10,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "f9ca0888dd82acb1641d5b298fad2db84248dcafc3d5aed055461da1b368e691",
      "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."
  }
}