{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260930-r05-sequence-finite-index-validity-0009",
  "pilot_number": "R0069-35109",
  "number": 35109,
  "family_id": "qf-sequence-finite-index-validity",
  "title": {
    "zh-Hant": "第 35109 題：有限数列的索引邊界",
    "en": "Question 35109: Index Boundary of a Finite Sequence"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260930-r05-sequence-finite-index-validity-0009",
    "batch_id": "batch-20260930-r05-sequence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sequence"
    ],
    "title_zh": "有限数列的索引邊界",
    "stem_zh": "有限實數數列長度 L=2，索引從 0，可用索引須滿足 0≤n<L。n=1 是可用索引嗎？",
    "answer": {
      "kind": "short_text",
      "value": "是",
      "explanation_zh": "待判定索引與長度為 1, 2；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 3,
      "skills": [
        "零起始索引",
        "有限長度"
      ]
    },
    "variant": {
      "family_id": "qf-sequence-finite-index-validity",
      "seed": 202609305309,
      "parameters": {
        "operation": "finite_index",
        "L": 2,
        "n": 1,
        "semantic_template": "qf-sequence-finite-index-validity/{\"L\":2,\"n\":1,\"operation\":\"finite_index\"}"
      }
    },
    "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-finite-index-validity-0009",
    "batch_id": "batch-20260930-r05-sequence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "f78f297a27b912877c3f92ab981ba7c4adb088c9b15d0eb74454ee9a828f51ae",
      "family_id": "qf-sequence-finite-index-validity",
      "seed": 202609305309,
      "semantic_template": "qf-sequence-finite-index-validity/{\"L\":2,\"n\":1,\"operation\":\"finite_index\"}"
    },
    "fields": {
      "title": "Index Boundary of a Finite Sequence",
      "stem": "A finite real sequence has length L=2 and zero-based valid indices satisfying 0≤n<L. Is n=1 a valid index?",
      "answer": {
        "kind": "short_text",
        "value": "Yes",
        "explanation": "Check 0≤1<2; the answer is Yes. A sequence of length 0 has no valid indices."
      },
      "skills": [
        "zero-based indexing",
        "finite length"
      ],
      "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": "有限實數數列長度 L=2，索引從 0，可用索引須滿足 0≤n<L。n=1 是可用索引嗎？",
        "en": "A finite real sequence has length L=2 and zero-based valid indices satisfying 0≤n<L. Is n=1 a valid index?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-sequence-finite-index-validity, [L, n, operation]]",
      "after": "derived = [finite_index, 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, 1]",
      "after": "derived = [是, 是, 是]",
      "relation": "implies",
      "rule_id": "Sequence_FINITE_ZERO_based_index_BOTH_bounds_outside_is_No",
      "conditions": [],
      "explanation": {
        "zh-Hant": "長度L的合法索引恰0..L−1；n負或n≥L合法回答No，不把無效candidate誤當整題不合格。L=0無合法索引，L不是最後一個索引。",
        "en": "For length L,the valid indices are EXACTLY0..L−1.A negative n or n≥L is a LEGAL No,not a rejected candidate question.Length0 has no indices;L is not the last index."
      },
      "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": "是"
  },
  "conclusion": {
    "canonical_value": "是",
    "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": 84,
      "original_line_sha256": "a5086fdff1a38f7bef945edf9f96a3a4a32d16b64a011eb9ef9f29e566aaef1c",
      "question_compact_sha256": "f78f297a27b912877c3f92ab981ba7c4adb088c9b15d0eb74454ee9a828f51ae",
      "english_row_compact_sha256": "86220673f321a2e71cbced8e4f076f36bd66394eaf10dfabe72c2730153e4c72",
      "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": "8ce248e654901e83b374f7459cd7a731becc1ca695fe4a0c34bc683defb1b159",
    "original_candidate_line_sha256": "8ce248e654901e83b374f7459cd7a731becc1ca695fe4a0c34bc683defb1b159",
    "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": 2,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050",
      "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."
  }
}