{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261005-advance-20261006-r01-order-relation-0037",
  "pilot_number": "R0067-34087",
  "number": 34087,
  "family_id": "qf-order-finite-extrema",
  "title": {
    "zh-Hant": "第 34087 題：有限實數集合的最小與最大值",
    "en": "Question 34087: Minimum and Maximum of a Finite Real Set"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261005-advance-20261006-r01-order-relation-0037",
    "batch_id": "batch-20261005-advance-20261006-r01-order-relation-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-order-relation"
    ],
    "title_zh": "有限實數集合的最小與最大值",
    "stem_zh": "依實數順序，明示非空有限整數集合 {-11, 0, 13}，求 (最小值, 最大值)。",
    "answer": {
      "kind": "expression",
      "value": "(-11, 13)",
      "explanation_zh": "極值=(-11, 13)。集合非空才能取兩個極值；逐值比較不假設資料原本已排序，單元素時兩者相同。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 2,
      "skills": [
        "有限實數集合的最小與最大值"
      ]
    },
    "variant": {
      "family_id": "qf-order-finite-extrema",
      "seed": 202610061037,
      "parameters": {
        "values": [
          -11,
          0,
          13
        ],
        "operation": "finite_extrema",
        "semantic_template": "qf-order-finite-extrema/{\"inputs\":[\"-11\",\"13\"],\"operation\":\"finite_extrema\"}"
      }
    },
    "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": "2026-10-05",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261005-advance-20261006-r01-order-relation-0037",
    "batch_id": "batch-20261005-advance-20261006-r01-order-relation-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "37001e74fd3b9fa3c4ba2a1c7fb06b8320530072dba40f3ffaa9dd17bebab496",
      "family_id": "qf-order-finite-extrema",
      "seed": 202610061037,
      "semantic_template": "qf-order-finite-extrema/{\"inputs\":[\"-11\",\"13\"],\"operation\":\"finite_extrema\"}"
    },
    "fields": {
      "title": "Minimum and Maximum of a Finite Real Set",
      "stem": "Under the usual real order, the explicit finite nonempty set has elements {-11, 0, 13}. Give (minimum, maximum).",
      "answer": {
        "kind": "expression",
        "value": "(-11, 13)",
        "explanation": "Order the given elements to obtain (-11, 13). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."
      },
      "skills": [
        "Minimum and Maximum of a Finite Real Set"
      ],
      "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": "依實數順序，明示非空有限整數集合 {-11, 0, 13}，求 (最小值, 最大值)。",
        "en": "Under the usual real order, the explicit finite nonempty set has elements {-11, 0, 13}. Give (minimum, maximum)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-order-finite-extrema, [operation, values]]",
      "after": "derived = [finite_extrema, no-invented-domain]",
      "relation": "implies",
      "rule_id": "R67_SOURCE_specific_keys_operation_domain_and_numeric_bank",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本bank核keys與operation/domain：legacy為各表underscore，MOD50用local hyphen；BASE參數較寬不加未知欄限制。Number.isInteger與SAFE兩種來源界分開，原JSON數字表示仍完整保存。",
        "en": "Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以本題原始角色、完整前提及欄序反查本步；區分單向推論與等價，並保留原題與英文、MKO、AST及審查狀態。不把有限核對冒充獨立審查或一般形式證明。",
          "en": "Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [[-11, 0, 13]]",
      "after": "derived = [[-11, 0, 13], [[-11, 是], [0, 是], [13, 是]], -11, 13]",
      "relation": "implies",
      "rule_id": "Order_FINITE_nonempty_DISTINCT_set_ALL_extrema_bounds",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這是非空、至多100個不同元素的有限set，非允重複的觀測列。逐元素核min≤x≤max且兩端確在set；singleton的min=max，空集不在此定義切片。",
        "en": "This is a NONEMPTY finite SET of at most100 DISTINCT elements,not an observation multiset.Audit min≤x≤max for EVERY element and attainment at both endpoints.A singleton has equal extrema;the empty set is outside THIS protocol."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以本題原始角色、完整前提及欄序反查本步；區分單向推論與等價，並保留原題與英文、MKO、AST及審查狀態。不把有限核對冒充獨立審查或一般形式證明。",
          "en": "Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      -11,
      13
    ]
  },
  "conclusion": {
    "canonical_value": "(-11, 13)",
    "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-20261005-advance-20261006-r01-order-relation-foundations",
      "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r01-order-relation-foundations/questions.jsonl",
      "batch_sha256": "7445d3cd6c8f4cc77448d51656238ce18229a8b5084f76112e419933e63d33a8",
      "original_line": 37,
      "original_line_sha256": "ccd24f591e54173f387185969538372ec92e984215da2ce67c84df69cc08c3af",
      "question_compact_sha256": "37001e74fd3b9fa3c4ba2a1c7fb06b8320530072dba40f3ffaa9dd17bebab496",
      "english_row_compact_sha256": "4ede708fa4b1116d6e6219a47aa240132ffc4707c5f77c283cc062bd9356864f",
      "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r01-order-relation-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r01-order-relation-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-order-relation": {
        "sha256": "95554189da3a451f8a69edd139e154fd9254524119837ea1643487a5646a2dc3",
        "english_sha256": "3bb53f0ce66755124a9e09f8d185cdebfbb4e6f8cc93a7733a5c08ceba6bdcd6",
        "original_path": "public/data/mko/order-relation.json",
        "english_path": "public/data/i18n/editions/mko-order-relation.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "6bb156cec7bdb6baf2497762702fc01f94fd1db55a5926bc575b12ff9237a4de",
    "original_candidate_sha256": "0432d639a76297ce577828c71d1a5f7adedd31c3b11709c70faed612c7fe6d1e",
    "original_candidate_line_sha256": "0432d639a76297ce577828c71d1a5f7adedd31c3b11709c70faed612c7fe6d1e"
  },
  "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-20261026-012-p68",
    "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": "c89efa383b67bb2cf25bcf16160b9f5f614bbe5e5e791f4d7f58234d17a3371c",
      "question_first_witness_sha256": "12766d451c5375842b4fc2843ae94807ec55f15763a916558026912a13873d57"
    },
    "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": "40b3b5ae17111c30e8f4c5d493ed369d805131b254cd2689732272647831a7f5",
      "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."
  }
}