{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261014-advance-20261107-r07-subsequence-0090",
  "pilot_number": "R0039-20465",
  "number": 20465,
  "family_id": "qf-mod38-subseq-finite-prefix-boundary",
  "title": {
    "zh-Hant": "第 20465 題：子數列",
    "en": "Question 20465: A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261014-advance-20261107-r07-subsequence-0090",
    "batch_id": "batch-20261014-advance-20261107-r07-subsequence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-subsequence"
    ],
    "title_zh": "子數列",
    "stem_zh": "自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[14,19,24,29,34,39]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "([14, 19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)",
      "explanation_zh": "Wave6根層核對=([14, 19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "子數列"
      ]
    },
    "variant": {
      "family_id": "qf-mod38-subseq-finite-prefix-boundary",
      "seed": 202611077090,
      "parameters": {
        "indices": [
          14,
          19,
          24,
          29,
          34,
          39
        ],
        "domain": "Symbolic_affine_subsequence_index",
        "operation": "subseq-finite-prefix-boundary",
        "semantic_template": "qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[14,19,24,29,34,39]}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_or_symbolic_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-14",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261014-advance-20261107-r07-subsequence-0090",
    "batch_id": "batch-20261014-advance-20261107-r07-subsequence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "05a9035ef4926fb70a78bd0aa2ffbf95302f62aa133d6828af57028d93159c65",
      "family_id": "qf-mod38-subseq-finite-prefix-boundary",
      "seed": 202611077090,
      "semantic_template": "qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[14,19,24,29,34,39]}"
    },
    "fields": {
      "title": "A Finite Increasing List Is Not an Already-Supplied Infinite Certificate",
      "stem": "Supplied finite natural-index list=[14, 19, 24, 29, 34, 39]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).",
      "answer": {
        "kind": "expression",
        "value": "([14, 19, 24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)",
        "explanation": "Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([14, 19, 24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."
      },
      "skills": [
        "A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"
      ],
      "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": "自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[14,19,24,29,34,39]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Supplied finite natural-index list=[14, 19, 24, 29, 34, 39]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source operation=subseq-finite-prefix-boundary;original snapshot and mathematics retained",
      "after": "explicit ordered source output fields=[indices, finite_prefix_increasing, infinite_certificate_supplied, boundary]",
      "relation": "implies",
      "rule_id": "source_ordered_interface_explicit_without_javascript",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原題快照保留歷史介面標記；本頁直接列來源欄位順序，不需JavaScript或外部表。欄位標籤不是額外數學證據，No保持原題的聲稱範圍。",
        "en": "Retain the historical interface marker in the original snapshot while listing ordered source fields here,without JavaScript or external lookup.Field labels are not additional mathematical evidence,and No retains the source claim scope."
      },
      "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": "subsequence finite prefix adjacent index1 difference := sub(19, 14)",
      "after": "subsequence finite prefix adjacent index1 difference = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。",
        "en": "Substitute original roles and established intermediates exactly,retaining indices,signs,denominators and the proof's applicability conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 subsequence finite prefix adjacent index1 difference，不以小數近似替代。",
          "en": "Recompute subsequence finite prefix adjacent index1 difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "19",
          "14"
        ],
        "output": "5",
        "label": "subsequence finite prefix adjacent index1 difference"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "ORIGINAL finite adjacent positions=[0, 1];actual indices=[14, 19]",
      "after": "exact forward difference=5;strictly increasing here=是",
      "relation": "implies",
      "rule_id": "subseq_finite_order_each_actual_adjacent_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。",
        "en": "Check every adjacent pair in original order without sorting or deduplicating to repair the prefix.Positive differences at all finite adjacent positions certify this prefix's strict increase."
      },
      "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": "subsequence finite prefix adjacent index2 difference := sub(24, 19)",
      "after": "subsequence finite prefix adjacent index2 difference = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。",
        "en": "Substitute original roles and established intermediates exactly,retaining indices,signs,denominators and the proof's applicability conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 subsequence finite prefix adjacent index2 difference，不以小數近似替代。",
          "en": "Recompute subsequence finite prefix adjacent index2 difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "24",
          "19"
        ],
        "output": "5",
        "label": "subsequence finite prefix adjacent index2 difference"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "ORIGINAL finite adjacent positions=[1, 2];actual indices=[19, 24]",
      "after": "exact forward difference=5;strictly increasing here=是",
      "relation": "implies",
      "rule_id": "subseq_finite_order_each_actual_adjacent_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。",
        "en": "Check every adjacent pair in original order without sorting or deduplicating to repair the prefix.Positive differences at all finite adjacent positions certify this prefix's strict increase."
      },
      "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": "subsequence finite prefix adjacent index3 difference := sub(29, 24)",
      "after": "subsequence finite prefix adjacent index3 difference = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。",
        "en": "Substitute original roles and established intermediates exactly,retaining indices,signs,denominators and the proof's applicability conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 subsequence finite prefix adjacent index3 difference，不以小數近似替代。",
          "en": "Recompute subsequence finite prefix adjacent index3 difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "29",
          "24"
        ],
        "output": "5",
        "label": "subsequence finite prefix adjacent index3 difference"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "ORIGINAL finite adjacent positions=[2, 3];actual indices=[24, 29]",
      "after": "exact forward difference=5;strictly increasing here=是",
      "relation": "implies",
      "rule_id": "subseq_finite_order_each_actual_adjacent_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。",
        "en": "Check every adjacent pair in original order without sorting or deduplicating to repair the prefix.Positive differences at all finite adjacent positions certify this prefix's strict increase."
      },
      "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": "subsequence finite prefix adjacent index4 difference := sub(34, 29)",
      "after": "subsequence finite prefix adjacent index4 difference = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。",
        "en": "Substitute original roles and established intermediates exactly,retaining indices,signs,denominators and the proof's applicability conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 subsequence finite prefix adjacent index4 difference，不以小數近似替代。",
          "en": "Recompute subsequence finite prefix adjacent index4 difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "34",
          "29"
        ],
        "output": "5",
        "label": "subsequence finite prefix adjacent index4 difference"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "ORIGINAL finite adjacent positions=[3, 4];actual indices=[29, 34]",
      "after": "exact forward difference=5;strictly increasing here=是",
      "relation": "implies",
      "rule_id": "subseq_finite_order_each_actual_adjacent_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。",
        "en": "Check every adjacent pair in original order without sorting or deduplicating to repair the prefix.Positive differences at all finite adjacent positions certify this prefix's strict increase."
      },
      "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": "subsequence finite prefix adjacent index5 difference := sub(39, 34)",
      "after": "subsequence finite prefix adjacent index5 difference = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。",
        "en": "Substitute original roles and established intermediates exactly,retaining indices,signs,denominators and the proof's applicability conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 subsequence finite prefix adjacent index5 difference，不以小數近似替代。",
          "en": "Recompute subsequence finite prefix adjacent index5 difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "39",
          "34"
        ],
        "output": "5",
        "label": "subsequence finite prefix adjacent index5 difference"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "ORIGINAL finite adjacent positions=[4, 5];actual indices=[34, 39]",
      "after": "exact forward difference=5;strictly increasing here=是",
      "relation": "implies",
      "rule_id": "subseq_finite_order_each_actual_adjacent_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。",
        "en": "Check every adjacent pair in original order without sorting or deduplicating to repair the prefix.Positive differences at all finite adjacent positions certify this prefix's strict increase."
      },
      "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": "ORIGINAL finite index list=[14, 19, 24, 29, 34, 39];ALL adjacent strict flags=[是, 是, 是, 是, 是]",
      "after": "this finite prefix increasing=是;INFINITE certificate supplied by original data=否;finite_prefix_not_infinite_subsequence_certificate",
      "relation": "implies",
      "rule_id": "subseq_prefix_No_not_nonextendability_or_sorting",
      "conditions": [],
      "explanation": {
        "zh-Hant": "No指原資料沒指定所有後續索引的通用law。合格有限prefix可另構造延伸，例如最後值後逐次加1，但這不確定原未指定continuation；若prefix本身已不遞增，其實際相鄰違例才是阻礙。",
        "en": "The No says the original data do not specify a universal law for all later indices.A valid finite prefix can be separately extended,for example by adding1 after its last value,but that does not determine an unspecified original continuation.If the prefix already fails,its actual adjacent violation is the obstruction."
      },
      "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": [
      [
        14,
        19,
        24,
        29,
        34,
        39
      ],
      true,
      false,
      "finite_increasing_prefix_not_infinite_subsequence_certificate"
    ]
  },
  "conclusion": {
    "canonical_value": "([14, 19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)",
    "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-20261014-advance-20261107-r07-subsequence-foundations",
      "batch_path": "public/data/questions/batches/batch-20261014-advance-20261107-r07-subsequence-foundations/questions.jsonl",
      "batch_sha256": "9ba8fa0ce8414b0f93d4e18a0af4fe49e8c59529895aa0a7d8920db4ef56b98f",
      "original_line": 90,
      "original_line_sha256": "9c22e865e1b1e0b955579198c769a6c4171864fdb827f5cad959ac128ab6f412",
      "question_compact_sha256": "05a9035ef4926fb70a78bd0aa2ffbf95302f62aa133d6828af57028d93159c65",
      "english_row_compact_sha256": "70325603df607aac51913606d83f1306420e6372a17541f36528baeeb8ddf274",
      "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261107-r07-subsequence-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261107-r07-subsequence-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-subsequence": {
        "sha256": "f4791c70590c6e099961027b14a591894bd691565f6e1bc8cd191792d0e2a44f",
        "english_sha256": "e54379f1fd9f6ccb9ef4be2d69a165c97d4e793ec8b2ecf051c61d8e2163b155",
        "original_path": "public/data/mko/source13-20261018-subsequence.json",
        "english_path": "public/data/i18n/editions/mko-subsequence.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "521929dfe9b0919224c38312ad78e5fa56457fc886faaa12b137edd83962251e",
    "original_candidate_sha256": "3ca119a5aaa97dfec86af2abbf3e31001725dcd41dfbaa717672a26e1f4a9d71",
    "original_candidate_line_sha256": "3ca119a5aaa97dfec86af2abbf3e31001725dcd41dfbaa717672a26e1f4a9d71"
  },
  "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-20261026-008-p40",
    "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": "6e11e35fafe32f16900ce9b522d01acb7b2ee6b463ab179392076cfbe1af8034",
      "question_first_witness_sha256": "cc0fa361fc25151729e70264340d2eae94f179f6f2a2edfe80ba5704fbbd0682"
    },
    "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": "a3fb8cae34e3dc4d8170a8938bfd2223b8db5fb22e106b18c67499dafe59e80c",
      "arithmetic_steps": 5
    },
    "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."
  }
}