{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261012-r04-set-membership-0058",
  "pilot_number": "R0010-05608",
  "number": 5608,
  "family_id": "qf-density12-membership-deletion-residual",
  "title": {
    "zh-Hant": "第 5608 題：原隸屬資格與刪除後集合",
    "en": "Question 5608: Original Membership and Set Deletion"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261012-r04-set-membership-0058",
    "batch_id": "batch-20261008-advance-20261012-r04-set-membership-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-set-membership"
    ],
    "title_zh": "原隸屬資格與刪除後集合",
    "stem_zh": "有限整數集合A=[-7, 0, 7]，x=-7。依序答 (原本x∈A的真假, 遞增A\\{x})，保留空集。",
    "answer": {
      "kind": "expression",
      "value": "(真, [0, 7])",
      "explanation_zh": "隸屬資格與刪除結果=(真, [0, 7])。依原集合判隸屬，再排除等於x者；不屬A的候選不改集合，有限隸屬非全部集合論。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 1,
      "skills": [
        "原隸屬資格與刪除後集合"
      ]
    },
    "variant": {
      "family_id": "qf-density12-membership-deletion-residual",
      "seed": 202610124058,
      "parameters": {
        "A": [
          -7,
          0,
          7
        ],
        "x": -7,
        "operation": "density12_membership_deletion_residual",
        "domain": "finite_integer_membership",
        "semantic_template": "qf-density12-membership-deletion-residual/[true,[0,7]]"
      }
    },
    "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-0058",
    "batch_id": "batch-20261008-advance-20261012-r04-set-membership-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "0f5c0ecf56b2d99796493fd1d117fbf1d00fbf47e0661e26ec49d6dd5d46482c",
      "family_id": "qf-density12-membership-deletion-residual",
      "seed": 202610124058,
      "semantic_template": "qf-density12-membership-deletion-residual/[true,[0,7]]"
    },
    "fields": {
      "title": "Original Membership and Set Deletion",
      "stem": "Finite integer set A=[-7, 0, 7], x=-7. Give (original truth of x∈A, increasing A\\{x}), retaining [].",
      "answer": {
        "kind": "expression",
        "value": "(True, [0, 7])",
        "explanation": "Judge membership in the original set, then remove elements equal to x; a candidate outside A leaves the set unchanged. The exact result, retaining the requested order, is (True, [0, 7])."
      },
      "skills": [
        "Original Membership and Set Deletion"
      ],
      "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": "有限整數集合A=[-7, 0, 7]，x=-7。依序答 (原本x∈A的真假, 遞增A\\{x})，保留空集。",
        "en": "Finite integer set A=[-7, 0, 7], x=-7. Give (original truth of x∈A, increasing A\\{x}), retaining []."
      }
    }
  ],
  "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": "original A=[-7, 0, 7];x=-7",
      "after": "original membership=真",
      "relation": "implies",
      "rule_id": "original_set_membership_before_change",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先讀原集合隸屬，不以插入或刪除後的集合回填原判定。",
        "en": "Read original membership before changing the set;do not use the resulting set to overwrite the original judgment."
      },
      "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": "operation=delete x=-7;original A=[-7, 0, 7]",
      "after": "[0, 7]",
      "relation": "implies",
      "rule_id": "finite_set_membership_update",
      "conditions": [],
      "explanation": {
        "zh-Hant": "插入已在者不重列，刪除不在者不改集合；輸出按數值去重排序，原始來源仍保留。",
        "en": "Inserting an existing element adds no duplicate,and deleting an absent element leaves the set unchanged.Sort the result numerically while retaining the original source."
      },
      "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,
      [
        0,
        7
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "(真, [0, 7])",
    "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": 58,
      "original_line_sha256": "d8c691629ea195507d85ef8634e76c0f31e59b8a5129122ab4cb5c445a088bf3",
      "question_compact_sha256": "0f5c0ecf56b2d99796493fd1d117fbf1d00fbf47e0661e26ec49d6dd5d46482c",
      "english_row_compact_sha256": "f6488652b61641e8bfce415d9c9314bfd22d9e416d7ca3f84a2f4448537ed1c0",
      "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": "31f24ebd1fd7585f76521958e8b03d66204c08052f439fff467eab272803f42c",
    "original_candidate_line_sha256": "31f24ebd1fd7585f76521958e8b03d66204c08052f439fff467eab272803f42c"
  },
  "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": 3,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "3022b2c237534a39360d271a1c7ff2422347a188e9f4a1811b278cc7e7804b0d",
      "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."
  }
}