{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260930-r05-sequence-explicit-term-0015",
  "pilot_number": "R0069-35090",
  "number": 35090,
  "family_id": "qf-sequence-explicit-term",
  "title": {
    "zh-Hant": "第 35090 題：零起始通項計算",
    "en": "Question 35090: Term of a Zero-Based Explicit Sequence"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260930-r05-sequence-explicit-term-0015",
    "batch_id": "batch-20260930-r05-sequence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sequence"
    ],
    "title_zh": "零起始通項計算",
    "stem_zh": "實數數列索引從 0，明示 a_n=(2)+(-3)n，n∈N={0,1,2,…}。求索引 n=4 的項。",
    "answer": {
      "kind": "short_text",
      "value": "-10",
      "explanation_zh": "把明示索引代入通項，a_4=2+(-3)×4=-10；不涉及數列極限。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 3,
      "skills": [
        "零起始索引",
        "明示通項"
      ]
    },
    "variant": {
      "family_id": "qf-sequence-explicit-term",
      "seed": 202609305015,
      "parameters": {
        "operation": "explicit_term",
        "u": 2,
        "d": -3,
        "n": 4,
        "semantic_template": "qf-sequence-explicit-term/{\"d\":-3,\"n\":4,\"operation\":\"explicit_term\",\"u\":2}"
      }
    },
    "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-explicit-term-0015",
    "batch_id": "batch-20260930-r05-sequence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "d1cb039a3b088c8e42a4fc612843f8abbf810cf9765a291ce5efc5420d847a94",
      "family_id": "qf-sequence-explicit-term",
      "seed": 202609305015,
      "semantic_template": "qf-sequence-explicit-term/{\"d\":-3,\"n\":4,\"operation\":\"explicit_term\",\"u\":2}"
    },
    "fields": {
      "title": "Term of a Zero-Based Explicit Sequence",
      "stem": "The real sequence is indexed from 0 and has the explicit rule a_n=(2)+(-3)n for n∈N={0,1,2,…}. Find the term at n=4.",
      "answer": {
        "kind": "short_text",
        "value": "-10",
        "explanation": "Substitute the explicit zero-based index: a_4=2+(-3)×4=-10. No limit claim is involved."
      },
      "skills": [
        "zero-based indexing",
        "explicit term formula"
      ],
      "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=(2)+(-3)n，n∈N={0,1,2,…}。求索引 n=4 的項。",
        "en": "The real sequence is indexed from 0 and has the explicit rule a_n=(2)+(-3)n for n∈N={0,1,2,…}. Find the term at n=4."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-sequence-explicit-term, [d, n, operation, u]]",
      "after": "derived = [explicit_term, 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 = [2, -3, 4, explicit_term]",
      "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 ORIGINAL zero-based n times common difference := mul(4, -3)",
      "after": "Sequence ORIGINAL zero-based n times common difference = -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 ORIGINAL zero-based n times common difference，不以小數近似替代。",
          "en": "Recompute Sequence ORIGINAL zero-based n times common difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "4",
          "-3"
        ],
        "output": "-12",
        "label": "Sequence ORIGINAL zero-based n times common difference"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "Sequence ORIGINAL initial plus n common differences := sum(2, -12)",
      "after": "Sequence ORIGINAL initial plus n common differences = -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 ORIGINAL initial plus n common differences，不以小數近似替代。",
          "en": "Recompute Sequence ORIGINAL initial plus n common differences with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "2",
          "-12"
        ],
        "output": "-10",
        "label": "Sequence ORIGINAL initial plus n common differences"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "source roles = [2, -3, 4]",
      "after": "derived = [-10]",
      "relation": "implies",
      "rule_id": "Sequence_EXPLICIT_complete_substitution_NO_limit_claim",
      "conditions": [],
      "explanation": {
        "zh-Hant": "把本n代入u+n*d，n=0回a0=u，d負亦合法。衍生BigInt不重套raw SAFE，不從一個term推出極限。",
        "en": "Substitute THIS n into u+n*d.At n=0 recover a0=u;negative d is allowed.Derived BigInts are not recapped at RAW SAFE;one term does not prove a limit."
      },
      "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"
  },
  "conclusion": {
    "canonical_value": "-10",
    "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": 15,
      "original_line_sha256": "321d21b4ae988246c7b3a307059891b0da892daf136c9bf87efaa4a2fba693b0",
      "question_compact_sha256": "d1cb039a3b088c8e42a4fc612843f8abbf810cf9765a291ce5efc5420d847a94",
      "english_row_compact_sha256": "1dab07e5538e5cc191f6d1e1dcf43ddbd9b0d0e13bf238552b92094559363f6e",
      "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": "394b08f0ed5bd555ee2dac96ad68f858163883656e39002b85139706e2e222b3",
    "original_candidate_line_sha256": "394b08f0ed5bd555ee2dac96ad68f858163883656e39002b85139706e2e222b3",
    "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": 5,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "6833945d2ccb3fba451309a3b259cd864cbd51dc3eff9242dc8c3036e0f56d85",
      "arithmetic_steps": 2
    },
    "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."
  }
}