{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261011-advance-20261015-r05-sequence-0091",
  "pilot_number": "R0013-07141",
  "number": 7141,
  "family_id": "qf-density15-sequence-five-term-prefix-deltas",
  "title": {
    "zh-Hant": "第 7141 題：五項累加與有序差",
    "en": "Question 7141: Five Prefix Sums and Four Ordered Differences"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261011-advance-20261015-r05-sequence-0091",
    "batch_id": "batch-20261011-advance-20261015-r05-sequence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sequence"
    ],
    "title_zh": "五項累加與有序差",
    "stem_zh": "N從0起，明示有限索引。原序五項=[3, 0, 3, -1, 1]。求 (五個截至各位置的前綴和, 四個後項減前項, 五值皆相同資格)。",
    "answer": {
      "kind": "expression",
      "value": "([3, 3, 6, 5, 6], [-3, 3, -4, 2], 否)",
      "explanation_zh": "五項前綴和與有序差列=([3, 3, 6, 5, 6], [-3, 3, -4, 2], 否)。逐項累加及逐鄰相減，不去重、不排序。有限前綴和不是無窮級數或極限。數列次序與重複保留，有限前綴不推定唯一無限規則。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 2,
      "skills": [
        "五項累加與有序差"
      ]
    },
    "variant": {
      "family_id": "qf-density15-sequence-five-term-prefix-deltas",
      "seed": 202610155091,
      "parameters": {
        "values": [
          3,
          0,
          3,
          -1,
          1
        ],
        "domain": "finite_zero_based_sequence_protocol",
        "operation": "density15_sequence_five_term_prefix_deltas",
        "semantic_template": "qf-density15-sequence-five-term-prefix-deltas/[3,0,3,-1,1]"
      }
    },
    "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": "2026-10-11",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261011-advance-20261015-r05-sequence-0091",
    "batch_id": "batch-20261011-advance-20261015-r05-sequence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "e5316cc7d2f3da5f6d67e10147e0f7caef0a24ccad1a0b4e526f523f276feba0",
      "family_id": "qf-density15-sequence-five-term-prefix-deltas",
      "seed": 202610155091,
      "semantic_template": "qf-density15-sequence-five-term-prefix-deltas/[3,0,3,-1,1]"
    },
    "fields": {
      "title": "Five Prefix Sums and Four Ordered Differences",
      "stem": "N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[3, 0, 3, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).",
      "answer": {
        "kind": "expression",
        "value": "([3, 3, 6, 5, 6], [-3, 3, -4, 2], No)",
        "explanation": "Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([3, 3, 6, 5, 6], [-3, 3, -4, 2], No)."
      },
      "skills": [
        "Five Prefix Sums and Four Ordered Differences"
      ],
      "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": "N從0起，明示有限索引。原序五項=[3, 0, 3, -1, 1]。求 (五個截至各位置的前綴和, 四個後項減前項, 五值皆相同資格)。",
        "en": "N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[3, 0, 3, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "N starts at0;ordered finite indices and repeated values retained",
      "after": "given recurrences differ from guessing an infinite rule from observations",
      "relation": "implies",
      "rule_id": "finite_ordered_sequence_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "數列有序且可重複，有限前綴本身不能決定唯一無限規則；若題目另明示遞推，則只依該規則推導，不擅自補規則。",
        "en": "Sequences are ordered and may repeat.A finite observed prefix alone does not determine a unique infinite rule;when a recurrence is explicitly supplied,use that rule rather than inventing one."
      },
      "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": "finite prefix sum through0 := sum(0, 3)",
      "after": "finite prefix sum through0 = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原序把本項加到先前前綴和，重複項仍要加。",
        "en": "Add the current term to the preceding prefix sum in original order,including repeats."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite prefix sum through0，不以小數近似替代。",
          "en": "Recompute finite prefix sum through0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "3"
        ],
        "output": "3",
        "label": "finite prefix sum through0"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "finite prefix sum through1 := sum(3, 0)",
      "after": "finite prefix sum through1 = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原序把本項加到先前前綴和，重複項仍要加。",
        "en": "Add the current term to the preceding prefix sum in original order,including repeats."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite prefix sum through1，不以小數近似替代。",
          "en": "Recompute finite prefix sum through1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "3",
          "0"
        ],
        "output": "3",
        "label": "finite prefix sum through1"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "finite prefix sum through2 := sum(3, 3)",
      "after": "finite prefix sum through2 = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原序把本項加到先前前綴和，重複項仍要加。",
        "en": "Add the current term to the preceding prefix sum in original order,including repeats."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite prefix sum through2，不以小數近似替代。",
          "en": "Recompute finite prefix sum through2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "3",
          "3"
        ],
        "output": "6",
        "label": "finite prefix sum through2"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "finite prefix sum through3 := sum(6, -1)",
      "after": "finite prefix sum through3 = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原序把本項加到先前前綴和，重複項仍要加。",
        "en": "Add the current term to the preceding prefix sum in original order,including repeats."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite prefix sum through3，不以小數近似替代。",
          "en": "Recompute finite prefix sum through3 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "6",
          "-1"
        ],
        "output": "5",
        "label": "finite prefix sum through3"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "finite prefix sum through4 := sum(5, 1)",
      "after": "finite prefix sum through4 = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原序把本項加到先前前綴和，重複項仍要加。",
        "en": "Add the current term to the preceding prefix sum in original order,including repeats."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite prefix sum through4，不以小數近似替代。",
          "en": "Recompute finite prefix sum through4 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "5",
          "1"
        ],
        "output": "6",
        "label": "finite prefix sum through4"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "finite adjacent delta0 := sub(0, 3)",
      "after": "finite adjacent delta0 = -3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "有序差取後項減前項，不排序或去重。",
        "en": "Take each ordered next-minus-previous difference without sorting or deduplication."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite adjacent delta0，不以小數近似替代。",
          "en": "Recompute finite adjacent delta0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "0",
          "3"
        ],
        "output": "-3",
        "label": "finite adjacent delta0"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "finite adjacent delta1 := sub(3, 0)",
      "after": "finite adjacent delta1 = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "有序差取後項減前項，不排序或去重。",
        "en": "Take each ordered next-minus-previous difference without sorting or deduplication."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite adjacent delta1，不以小數近似替代。",
          "en": "Recompute finite adjacent delta1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "3",
          "0"
        ],
        "output": "3",
        "label": "finite adjacent delta1"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "finite adjacent delta2 := sub(-1, 3)",
      "after": "finite adjacent delta2 = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "有序差取後項減前項，不排序或去重。",
        "en": "Take each ordered next-minus-previous difference without sorting or deduplication."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite adjacent delta2，不以小數近似替代。",
          "en": "Recompute finite adjacent delta2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-1",
          "3"
        ],
        "output": "-4",
        "label": "finite adjacent delta2"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "finite adjacent delta3 := sub(1, -1)",
      "after": "finite adjacent delta3 = 2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "有序差取後項減前項，不排序或去重。",
        "en": "Take each ordered next-minus-previous difference without sorting or deduplication."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 finite adjacent delta3，不以小數近似替代。",
          "en": "Recompute finite adjacent delta3 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "1",
          "-1"
        ],
        "output": "2",
        "label": "finite adjacent delta3"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "[3, 0, 3, -1, 1]",
      "after": "all five values equal=否",
      "relation": "implies",
      "rule_id": "finite_prefix_not_infinite_sum",
      "conditions": [],
      "explanation": {
        "zh-Hant": "前綴和是有限五項的累加，不是無窮級數或極限；此處相同資格也只核對這五項。",
        "en": "These prefix sums are finite accumulations of five terms,not an infinite series or limit.The constant-value verdict concerns only these five terms."
      },
      "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": [
      [
        "3",
        "3",
        "6",
        "5",
        "6"
      ],
      [
        "-3",
        "3",
        "-4",
        "2"
      ],
      false
    ]
  },
  "conclusion": {
    "canonical_value": "([3, 3, 6, 5, 6], [-3, 3, -4, 2], 否)",
    "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-20261011-advance-20261015-r05-sequence-foundations",
      "batch_path": "public/data/questions/batches/batch-20261011-advance-20261015-r05-sequence-foundations/questions.jsonl",
      "batch_sha256": "e8a28d58ec052ac711318299c789c1b43033dbf1739c5b39fa88b9544e87f61b",
      "original_line": 91,
      "original_line_sha256": "1df5657f9ef53f3b05747b5ed0abb01e19306629035db016c0aedccc3873dbbd",
      "question_compact_sha256": "e5316cc7d2f3da5f6d67e10147e0f7caef0a24ccad1a0b4e526f523f276feba0",
      "english_row_compact_sha256": "7fcee22005f83e97bc2e63915a4cac889abde771f0cfe31d703c009f05cf0a95",
      "english_manifest_path": "public/data/i18n/editions/batch-20261011-advance-20261015-r05-sequence-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261011-advance-20261015-r05-sequence-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-sequence": {
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        "english_sha256": "24722e5fa3e44eb82dbc3fccbd220761d9b4aa84bdf79ad9d04bad0d83621dde",
        "original_path": "public/data/mko/sequence.json",
        "english_path": "public/data/i18n/editions/mko-sequence.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "944e5a6e7ddc77eb28f9280c1b90da6c7083069b4790cbeb7488d009328efce8",
    "original_candidate_sha256": "c37f30e0ee1d7475c9ed17a18c6fd1782b30e3b6335ab6bfee3f1a39c81d7b6b",
    "original_candidate_line_sha256": "c37f30e0ee1d7475c9ed17a18c6fd1782b30e3b6335ab6bfee3f1a39c81d7b6b",
    "mko_binding_revision": {
      "id": "edition-symbol-bindings-20261101",
      "path": "content/edition-symbol-bindings-20261101/revision.json",
      "sha256": "e9b4c69f2c4732074c37abb624c8ab8a70afc3645c12bf9df2268ef650ad7b6c",
      "previous_english_sha256": {
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    }
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      "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-p14",
    "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": {
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      "question_first_witness_sha256": "0e1039f4cf022bf35af4e5531651c9a2b7ca7a5fdacac34fb1e4bcd9a81f6299"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 11,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "6eb8765f0116912602b993b640e747fdf9cc93f8730300df73dfc523d0568874",
      "arithmetic_steps": 9
    },
    "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."
  }
}