{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260930-r05-sequence-prefix-0003",
  "pilot_number": "R0069-35128",
  "number": 35128,
  "family_id": "qf-sequence-prefix",
  "title": {
    "zh-Hant": "第 35128 題：明示數列的有限前綴",
    "en": "Question 35128: Finite Prefix of an Explicit Sequence"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260930-r05-sequence-prefix-0003",
    "batch_id": "batch-20260930-r05-sequence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sequence"
    ],
    "title_zh": "明示數列的有限前綴",
    "stem_zh": "實數數列索引從 0，明示 a_n=(-10)+(-1)n，n∈N。列出長度 L=3 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。",
    "answer": {
      "kind": "short_text",
      "value": "[-10, -11, -12]",
      "explanation_zh": "依索引次序從 0 取恰好 3 項，得到 [-10, -11, -12]；這是明示公式的前綴，不是猜測規律。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 3,
      "skills": [
        "前綴長度",
        "索引次序"
      ]
    },
    "variant": {
      "family_id": "qf-sequence-prefix",
      "seed": 202609305203,
      "parameters": {
        "operation": "prefix",
        "u": -10,
        "d": -1,
        "L": 3,
        "semantic_template": "qf-sequence-prefix/{\"L\":3,\"d\":-1,\"operation\":\"prefix\",\"u\":-10}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "json_schema",
        "producer_local_answer_invariants",
        "explanation_witness_accuracy"
      ],
      "warning_zh": "本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "Codex GPT-6 question producer",
      "generated_at": "2026-09-30",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260930-r05-sequence-prefix-0003",
    "batch_id": "batch-20260930-r05-sequence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "4e1deade510125275626b2aa0223a6060295f8597fc9b7c51cc6e17748348c94",
      "family_id": "qf-sequence-prefix",
      "seed": 202609305203,
      "semantic_template": "qf-sequence-prefix/{\"L\":3,\"d\":-1,\"operation\":\"prefix\",\"u\":-10}"
    },
    "fields": {
      "title": "Finite Prefix of an Explicit Sequence",
      "stem": "The real sequence is indexed from 0 with a_n=(-10)+(-1)n. List the prefix [a_0,…,a_(L-1)] of length L=3; use [] when L=0.",
      "answer": {
        "kind": "short_text",
        "value": "[-10, -11, -12]",
        "explanation": "Take exactly 3 term(s) in index order beginning at 0. The explicit-formula prefix is [-10, -11, -12], not a guessed continuation rule."
      },
      "skills": [
        "prefix length",
        "index order"
      ],
      "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": "實數數列索引從 0，明示 a_n=(-10)+(-1)n，n∈N。列出長度 L=3 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。",
        "en": "The real sequence is indexed from 0 with a_n=(-10)+(-1)n. List the prefix [a_0,…,a_(L-1)] of length L=3; use [] when L=0."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-sequence-prefix, [L, d, operation, u]]",
      "after": "derived = [prefix, no-invented-domain]",
      "relation": "implies",
      "rule_id": "R69_SOURCE_specific_keys_operation_domain_AND_binary_contract",
      "conditions": [],
      "explanation": {
        "zh-Hant": "各bank的keys/operation/domain獨立：LDL/PULSE/function legacy為表內underscore，TREE是完整tree_*與明定domain，BASE signed較寬不偷加op/domain。所有算術保持binary primitive契約。",
        "en": "Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [-10, -1, 3, prefix]",
      "after": "derived = [a_0=u, a_n=u+n*d, zero based]",
      "relation": "implies",
      "rule_id": "Sequence_ALL_RAW_initial_step_and_count_EVEN_empty_prefix",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先驗全部raw u/d/count，即使prefix L=0也不跳過unused資料型別。此題已給公式/遞推與0-based起點，不從有限prefix猜一般規律。",
        "en": "Type ALL RAW u/d/count fields EVEN for prefix L=0.Indices start at0 and the formula/recurrence is GIVEN;do not infer a general rule from finite samples."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "Sequence prefix ORIGINAL index times step j=0 := mul(0, -1)",
      "after": "Sequence prefix ORIGINAL index times step j=0 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Sequence prefix ORIGINAL index times step j=0，不以小數近似替代。",
          "en": "Recompute Sequence prefix ORIGINAL index times step j=0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "0",
          "-1"
        ],
        "output": "0",
        "label": "Sequence prefix ORIGINAL index times step j=0"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "Sequence prefix ORIGINAL complete term j=0 := sum(-10, 0)",
      "after": "Sequence prefix ORIGINAL complete term j=0 = -10",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Sequence prefix ORIGINAL complete term j=0，不以小數近似替代。",
          "en": "Recompute Sequence prefix ORIGINAL complete term j=0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-10",
          "0"
        ],
        "output": "-10",
        "label": "Sequence prefix ORIGINAL complete term j=0"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "Sequence prefix ORIGINAL index times step j=1 := mul(1, -1)",
      "after": "Sequence prefix ORIGINAL index times step j=1 = -1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Sequence prefix ORIGINAL index times step j=1，不以小數近似替代。",
          "en": "Recompute Sequence prefix ORIGINAL index times step j=1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "-1"
        ],
        "output": "-1",
        "label": "Sequence prefix ORIGINAL index times step j=1"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "Sequence prefix ORIGINAL complete term j=1 := sum(-10, -1)",
      "after": "Sequence prefix ORIGINAL complete term j=1 = -11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Sequence prefix ORIGINAL complete term j=1，不以小數近似替代。",
          "en": "Recompute Sequence prefix ORIGINAL complete term j=1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-10",
          "-1"
        ],
        "output": "-11",
        "label": "Sequence prefix ORIGINAL complete term j=1"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "Sequence prefix ORIGINAL index times step j=2 := mul(2, -1)",
      "after": "Sequence prefix ORIGINAL index times step j=2 = -2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Sequence prefix ORIGINAL index times step j=2，不以小數近似替代。",
          "en": "Recompute Sequence prefix ORIGINAL index times step j=2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "-1"
        ],
        "output": "-2",
        "label": "Sequence prefix ORIGINAL index times step j=2"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "Sequence prefix ORIGINAL complete term j=2 := sum(-10, -2)",
      "after": "Sequence prefix ORIGINAL complete term j=2 = -12",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Sequence prefix ORIGINAL complete term j=2，不以小數近似替代。",
          "en": "Recompute Sequence prefix ORIGINAL complete term j=2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-10",
          "-2"
        ],
        "output": "-12",
        "label": "Sequence prefix ORIGINAL complete term j=2"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "source roles = [-10, -1, 3]",
      "after": "derived = [[-10, -11, -12], [-10, -11, -12]]",
      "relation": "implies",
      "rule_id": "Sequence_PREFIX_EXACT_length_L_indices0_to_Lminus1",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依索引順序取恰L項a0到a_(L−1)，不是取到aL；L=0顯示[]。原給定formula決定這些項，不宣稱prefix本身唯一決定未知規則。",
        "en": "Take EXACTLY L terms in index order from a0 through a_(L−1),NOT through aL.L=0 displays[].The GIVEN formula determines these terms;the prefix alone need not determine an unknown rule."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": "[-10, -11, -12]"
  },
  "conclusion": {
    "canonical_value": "[-10, -11, -12]",
    "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-20260930-r05-sequence-foundations",
      "batch_path": "public/data/questions/batches/batch-20260930-r05-sequence-foundations/questions.jsonl",
      "batch_sha256": "1fd40c248ceb344294f2436eadb0b3e48b2fe83a789029afd665bdc0de2c2b5f",
      "original_line": 53,
      "original_line_sha256": "fa4cf73bb21bdedd42b2f8fd8615d848ef3d9822a63e70484459d9da2604bf46",
      "question_compact_sha256": "4e1deade510125275626b2aa0223a6060295f8597fc9b7c51cc6e17748348c94",
      "english_row_compact_sha256": "9085a7f16725a232d6181c8d0d8920e5c17bfc7a389c2c8dba693ac964596e4a",
      "english_manifest_path": "public/data/i18n/editions/batch-20260930-r05-sequence-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260930-r05-sequence-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-sequence": {
        "sha256": "61e652778c86fb6151fba32a0e61c914e4f99a1c496dd1c3d933c1f9297782f7",
        "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": "63155b87d4994521b4a60f8f179750f57cbbd094e66cc42652608d1bbab47a9f",
    "original_candidate_sha256": "dd0b7abe5f10d54189590157fc69cf66500833a24b4ab833cb117dd15f94602a",
    "original_candidate_line_sha256": "dd0b7abe5f10d54189590157fc69cf66500833a24b4ab833cb117dd15f94602a",
    "mko_binding_revision": {
      "id": "edition-symbol-bindings-20261101",
      "path": "content/edition-symbol-bindings-20261101/revision.json",
      "sha256": "e9b4c69f2c4732074c37abb624c8ab8a70afc3645c12bf9df2268ef650ad7b6c",
      "previous_english_sha256": {
        "mko-sequence": "73ebcb30e2878e2fcb357eb7ed8f9eb08672f5b078965a636df48b982cf49fa3"
      }
    }
  },
  "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-p70",
    "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": "ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b",
      "question_first_witness_sha256": "11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 9,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "a96fd252dcd1a25e264cb837370cd8dd4936affb394f190304bde3d1b12f60ab",
      "arithmetic_steps": 6
    },
    "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."
  }
}