{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260915-finite-set-intersection-0010",
  "pilot_number": "R0063-32035",
  "number": 32035,
  "family_id": "qf-finite-set-intersection",
  "title": {
    "zh-Hant": "第 32035 題：有限集合交集",
    "en": "Question 32035: Finite Set Intersection"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260915-finite-set-intersection-0010",
    "batch_id": "batch-20260915-finite-set-operations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-set-operations"
    ],
    "title_zh": "有限集合交集",
    "stem_zh": "令 A={391, 392, 394}，B={393, 395, 396}。求 A∩B（元素只列一次並依遞增排序）。",
    "answer": {
      "kind": "short_text",
      "value": "∅",
      "explanation_zh": "沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 1,
      "skills": [
        "集合交集",
        "外延相等"
      ]
    },
    "variant": {
      "family_id": "qf-finite-set-intersection",
      "seed": 20260949,
      "parameters": {
        "A": [
          391,
          392,
          394
        ],
        "B": [
          393,
          395,
          396
        ],
        "semantic_template": "qf-finite-set-intersection/{\"A\":[391,392,394],\"B\":[393,395,396]}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-15",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260915-finite-set-intersection-0010",
    "batch_id": "batch-20260915-finite-set-operations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "68557c927903b03a9488e23f3c15df0882548ebdca53a7605a153c97311a44b6",
      "family_id": "qf-finite-set-intersection",
      "seed": 20260949,
      "semantic_template": "qf-finite-set-intersection/{\"A\":[391,392,394],\"B\":[393,395,396]}"
    },
    "fields": {
      "title": "Finite Set Intersection",
      "stem": "Let A={391, 392, 394} and B={393, 395, 396}. Find A∩B, listing each element once in increasing order.",
      "answer": {
        "kind": "short_text",
        "value": "∅",
        "explanation": "The intersection retains exactly the elements common to A and B, giving ∅."
      },
      "skills": [
        "set intersection",
        "extensional equality"
      ],
      "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": "令 A={391, 392, 394}，B={393, 395, 396}。求 A∩B（元素只列一次並依遞增排序）。",
        "en": "Let A={391, 392, 394} and B={393, 395, 396}. Find A∩B, listing each element once in increasing order."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-finite-set-intersection, no-required-operation, no-required-domain, []]",
      "after": "derived = [[numeric_sorted_set_STRING_or_empty]]",
      "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 = [A ORIGINAL, [391, 392, 394]]",
      "after": "derived = [[391, 392, 394]]",
      "relation": "implies",
      "rule_id": "Sets_BASE_distinct_integer_lists_no_SAFE_or100cap_no_silent_repair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "此BASE集合題先驗distinct整數list，重複不得偷偷修成合法。只對衍生顯示排序，原資料不改；不搬用其他bank的SAFE或100元素界。",
        "en": "THIS BASE set bank requires distinct integer lists;do not silently repair duplicates.Sort ONLY derived display,retaining originals.Do not import another bank SAFE/100-element bound."
      },
      "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": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "source roles = [B ORIGINAL, [393, 395, 396]]",
      "after": "derived = [[393, 395, 396]]",
      "relation": "implies",
      "rule_id": "Sets_BASE_distinct_integer_lists_no_SAFE_or100cap_no_silent_repair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "此BASE集合題先驗distinct整數list，重複不得偷偷修成合法。只對衍生顯示排序，原資料不改；不搬用其他bank的SAFE或100元素界。",
        "en": "THIS BASE set bank requires distinct integer lists;do not silently repair duplicates.Sort ONLY derived display,retaining originals.Do not import another bank SAFE/100-element bound."
      },
      "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": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "source roles = [qf-finite-set-intersection, 391, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [是, 否, 否]",
      "relation": "implies",
      "rule_id": "Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐完整A∪B的label分開驗屬A／屬B，再用本題的或、且、A且非B判保留。A\\B不是B\\A，不依排列或圖形猜。",
        "en": "For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\\B is not B\\A;do not infer from order or pictures."
      },
      "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": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "source roles = [qf-finite-set-intersection, 392, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [是, 否, 否]",
      "relation": "implies",
      "rule_id": "Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐完整A∪B的label分開驗屬A／屬B，再用本題的或、且、A且非B判保留。A\\B不是B\\A，不依排列或圖形猜。",
        "en": "For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\\B is not B\\A;do not infer from order or pictures."
      },
      "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": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "source roles = [qf-finite-set-intersection, 393, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [否, 是, 否]",
      "relation": "implies",
      "rule_id": "Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐完整A∪B的label分開驗屬A／屬B，再用本題的或、且、A且非B判保留。A\\B不是B\\A，不依排列或圖形猜。",
        "en": "For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\\B is not B\\A;do not infer from order or pictures."
      },
      "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": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "source roles = [qf-finite-set-intersection, 394, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [是, 否, 否]",
      "relation": "implies",
      "rule_id": "Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐完整A∪B的label分開驗屬A／屬B，再用本題的或、且、A且非B判保留。A\\B不是B\\A，不依排列或圖形猜。",
        "en": "For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\\B is not B\\A;do not infer from order or pictures."
      },
      "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": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "source roles = [qf-finite-set-intersection, 395, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [否, 是, 否]",
      "relation": "implies",
      "rule_id": "Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐完整A∪B的label分開驗屬A／屬B，再用本題的或、且、A且非B判保留。A\\B不是B\\A，不依排列或圖形猜。",
        "en": "For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\\B is not B\\A;do not infer from order or pictures."
      },
      "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": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "source roles = [qf-finite-set-intersection, 396, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [否, 是, 否]",
      "relation": "implies",
      "rule_id": "Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐完整A∪B的label分開驗屬A／屬B，再用本題的或、且、A且非B判保留。A\\B不是B\\A，不依排列或圖形猜。",
        "en": "For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\\B is not B\\A;do not infer from order or pictures."
      },
      "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": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "source roles = [qf-finite-set-intersection, [391, 392, 394], [393, 395, 396]]",
      "after": "derived = [[], ∅, not-requested]",
      "relation": "implies",
      "rule_id": "Sets_COMPLETE_extensional_result_numeric_order_reverse_difference_separate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "列完所有label才輸出遞增且每元素一次的集合，空用∅。差集另算B\\A對照方向；原A/B及其來源雜湊保持不變。",
        "en": "AFTER every label,display the complete numeric increasing set once per element,or∅.For difference ALSO compute B\\A to distinguish direction.Keep original A/B and source hashes."
      },
      "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": "∅"
  },
  "conclusion": {
    "canonical_value": "∅",
    "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-20260915-finite-set-operations",
      "batch_path": "public/data/questions/batches/batch-20260915-finite-set-operations/questions.jsonl",
      "batch_sha256": "f64b473d5731f99d54cfcb62ad382b4c148843223705bb9fd97a25b0a0b97c7e",
      "original_line": 35,
      "original_line_sha256": "dec15b6d654ea7d6c9dd3585f1d8904b23f0d6006ac0cce86a9f8d736b1c953e",
      "question_compact_sha256": "68557c927903b03a9488e23f3c15df0882548ebdca53a7605a153c97311a44b6",
      "english_row_compact_sha256": "1edda5362ad76bce1f55426f9dd526f96c8bd9a5dc40364d65f759e6425cee03",
      "english_manifest_path": "public/data/i18n/editions/batch-20260915-finite-set-operations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260915-finite-set-operations.en.jsonl"
    },
    "mko_bindings": {
      "mko-set-operations": {
        "sha256": "e857b27da045df1a33d58d7cd56b319d6c8ec23162a8cfc3c15f7c70d30f317b",
        "english_sha256": "3cad86e57536464f92b934935e0803aa9aee386b3c235758ae9da575c56f3ac3",
        "original_path": "public/data/mko/set-operations.json",
        "english_path": "public/data/i18n/editions/mko-set-operations.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "f3271d6047df957dbf3d61120bd3dd374784c828b17849887e14caf59d93f745",
    "original_candidate_sha256": "9ede499a14ec10a31e73acbc9631c715e28d9e49b88063852ad996d74b71b83c",
    "original_candidate_line_sha256": "9ede499a14ec10a31e73acbc9631c715e28d9e49b88063852ad996d74b71b83c"
  },
  "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": 10,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "0ad2a3db21080309b4235f495a8d79d027914c1d6740ebcd86d256dba34fce0d",
      "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."
  }
}