{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261011-r06-sample-space-0055",
  "pilot_number": "R0008-04905",
  "number": 4905,
  "family_id": "qf-density11-sample-list-completeness-defects",
  "title": {
    "zh-Hant": "第 4905 題：基本結果清單的漏列與域外項",
    "en": "Question 4905: Missing and Outside Elementary Outcomes"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261011-r06-sample-space-0055",
    "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sample-space"
    ],
    "title_zh": "基本結果清單的漏列與域外項",
    "stem_zh": "基本可能結果S={0,…,4}；待核原列=[0, 1, 2, 3, -5]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。",
    "answer": {
      "kind": "expression",
      "value": "([4], [-5])",
      "explanation_zh": "清單漏列與域外項=([4], [-5])。分別比較S與清單的兩側差；重列不補足漏項，域外數字不是合法基本結果，不指定概率。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 1,
      "skills": [
        "基本結果清單的漏列與域外項"
      ]
    },
    "variant": {
      "family_id": "qf-density11-sample-list-completeness-defects",
      "seed": 202610116055,
      "parameters": {
        "n": 5,
        "candidates": [
          0,
          1,
          2,
          3,
          -5
        ],
        "operation": "density11_sample_list_completeness_defects",
        "domain": "finite_possible_outcome_protocol",
        "semantic_template": "qf-density11-sample-list-completeness-defects/[[4],[-5]]"
      }
    },
    "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-20261011-r06-sample-space-0055",
    "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "a0dbecbab7a63ccf9e8f698ab658cf08ac08f038b76908da6d788e9b9dfe5b27",
      "family_id": "qf-density11-sample-list-completeness-defects",
      "seed": 202610116055,
      "semantic_template": "qf-density11-sample-list-completeness-defects/[[4],[-5]]"
    },
    "fields": {
      "title": "Missing and Outside Elementary Outcomes",
      "stem": "Elementary outcomes are Fin(5)={0,…,4}. Candidate raw list=[0, 1, 2, 3, -5]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.",
      "answer": {
        "kind": "expression",
        "value": "([4], [-5])",
        "explanation": "Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([4], [-5])."
      },
      "skills": [
        "Missing and Outside Elementary Outcomes"
      ],
      "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": "基本可能結果S={0,…,4}；待核原列=[0, 1, 2, 3, -5]。依序列 (漏列的S元素, 列中S外元素)，去重後遞增。",
        "en": "Elementary outcomes are Fin(5)={0,…,4}. Candidate raw list=[0, 1, 2, 3, -5]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "explicit finite possible-outcome protocol",
      "after": "no probability law,equiprobability or independence inferred",
      "relation": "implies",
      "rule_id": "possible_outcomes_not_probabilities",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這裡列可能基本結果、記錄或事件資格，不指定概率；所有組合可發生不等於等可能或兩階段獨立。",
        "en": "These tasks list possible outcomes,recordings or event membership without assigning probabilities.All combinations being possible does not imply equiprobability or independence."
      },
      "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": "valid source outcome=0",
      "after": "listed=是",
      "relation": "implies",
      "rule_id": "source_outcome_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依完整S逐項找漏列，不以重列其他項補足。",
        "en": "Inspect every element of complete S for omissions;repeating another item cannot fill a gap."
      },
      "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": "valid source outcome=1",
      "after": "listed=是",
      "relation": "implies",
      "rule_id": "source_outcome_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依完整S逐項找漏列，不以重列其他項補足。",
        "en": "Inspect every element of complete S for omissions;repeating another item cannot fill a gap."
      },
      "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": "valid source outcome=2",
      "after": "listed=是",
      "relation": "implies",
      "rule_id": "source_outcome_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依完整S逐項找漏列，不以重列其他項補足。",
        "en": "Inspect every element of complete S for omissions;repeating another item cannot fill a gap."
      },
      "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": "valid source outcome=3",
      "after": "listed=是",
      "relation": "implies",
      "rule_id": "source_outcome_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依完整S逐項找漏列，不以重列其他項補足。",
        "en": "Inspect every element of complete S for omissions;repeating another item cannot fill a gap."
      },
      "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": "valid source outcome=4",
      "after": "listed=否",
      "relation": "implies",
      "rule_id": "source_outcome_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依完整S逐項找漏列，不以重列其他項補足。",
        "en": "Inspect every element of complete S for omissions;repeating another item cannot fill a gap."
      },
      "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": "candidate list element=-5",
      "after": "inside S=否",
      "relation": "implies",
      "rule_id": "candidate_space_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "候選列中的域外數字仍不具基本結果資格。",
        "en": "An outside-domain number in the candidate list is still not a possible outcome."
      },
      "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": "candidate list element=0",
      "after": "inside S=是",
      "relation": "implies",
      "rule_id": "candidate_space_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "候選列中的域外數字仍不具基本結果資格。",
        "en": "An outside-domain number in the candidate list is still not a possible outcome."
      },
      "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": "candidate list element=1",
      "after": "inside S=是",
      "relation": "implies",
      "rule_id": "candidate_space_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "候選列中的域外數字仍不具基本結果資格。",
        "en": "An outside-domain number in the candidate list is still not a possible outcome."
      },
      "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": "candidate list element=2",
      "after": "inside S=是",
      "relation": "implies",
      "rule_id": "candidate_space_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "候選列中的域外數字仍不具基本結果資格。",
        "en": "An outside-domain number in the candidate list is still not a possible outcome."
      },
      "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": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "candidate list element=3",
      "after": "inside S=是",
      "relation": "implies",
      "rule_id": "candidate_space_inventory_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "候選列中的域外數字仍不具基本結果資格。",
        "en": "An outside-domain number in the candidate list is still not a possible outcome."
      },
      "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": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "S=[0, 1, 2, 3, 4];normalized candidate list=[-5, 0, 1, 2, 3]",
      "after": "([4], [-5])",
      "relation": "implies",
      "rule_id": "sample_list_two_sided_defects",
      "conditions": [],
      "explanation": {
        "zh-Hant": "第一欄是S缺列，第二欄是列中S外項；兩側差不可交換。",
        "en": "The first field lists omitted S-elements and the second lists outside entries;do not swap the two differences."
      },
      "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": [
      [
        4
      ],
      [
        -5
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([4], [-5])",
    "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-20261011-r06-sample-space-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r06-sample-space-foundations/questions.jsonl",
      "batch_sha256": "a3c5671d763c26ec164aeff524d6308ad28eb3415359ccb057a20ba767acdcc9",
      "original_line": 55,
      "original_line_sha256": "a761086fd3ace021c6ddc9a41ddc001433257e6af42f14d7a801110f630c1bef",
      "question_compact_sha256": "a0dbecbab7a63ccf9e8f698ab658cf08ac08f038b76908da6d788e9b9dfe5b27",
      "english_row_compact_sha256": "c7a647e06a5bcb922e48b2b9def21c675ba92ce6d17f94a4fcf927c95798212b",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r06-sample-space-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r06-sample-space-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-sample-space": {
        "sha256": "c58b0d07252ece257a4143fd10f0f25b249023f4ed50bc6d393f4752a91267f7",
        "english_sha256": "ba452c266ef8c6ab4b549a3ccb6bc04a19fc7fafef1934d17f821c9ef4c04756",
        "original_path": "public/data/mko/sample-space.json",
        "english_path": "public/data/i18n/editions/mko-sample-space.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "6dc34e24b0f43c50e49365ca1a1153175f8661d5290c9236df5527bb047157eb",
    "original_candidate_sha256": "c9bf11e731ecc9eb1a9fd8d0e046d75544d77d38be41f6eca415f835809c1250",
    "original_candidate_line_sha256": "c9bf11e731ecc9eb1a9fd8d0e046d75544d77d38be41f6eca415f835809c1250"
  },
  "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-20261026-004-p9",
    "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": "b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289",
      "question_first_witness_sha256": "caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 12,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "60d48486e3336bd563af5ad878e7fd9f714c11147def6a9f95391c943193667e",
      "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."
  }
}