{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0001","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[3,1],\"reference\":[1,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 2)","explanation_zh":"應用基礎核對=(3, 1, 2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203001,"parameters":{"approximation":[3,1],"reference":[1,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[3,1],\"reference\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0003","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[7,3],\"reference\":[3,3]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(7/3, 1, 4/3)","explanation_zh":"應用基礎核對=(7/3, 1, 4/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203003,"parameters":{"approximation":[7,3],"reference":[3,3],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[7,3],\"reference\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0004","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[9,4],\"reference\":[4,4]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 1, 5/4)","explanation_zh":"應用基礎核對=(9/4, 1, 5/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203004,"parameters":{"approximation":[9,4],"reference":[4,4],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[9,4],\"reference\":[4,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0005","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[11,5],\"reference\":[5,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(11/5, 5, 14/5)","explanation_zh":"應用基礎核對=(11/5, 5, 14/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203005,"parameters":{"approximation":[11,5],"reference":[5,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[11,5],\"reference\":[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0006","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[13,1],\"reference\":[6,2]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(13, 3, 10)","explanation_zh":"應用基礎核對=(13, 3, 10)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203006,"parameters":{"approximation":[13,1],"reference":[6,2],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[13,1],\"reference\":[6,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0007","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[15,2],\"reference\":[7,3]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(15/2, 7/3, 31/6)","explanation_zh":"應用基礎核對=(15/2, 7/3, 31/6)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203007,"parameters":{"approximation":[15,2],"reference":[7,3],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[15,2],\"reference\":[7,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0008","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[17,3],\"reference\":[8,4]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(17/3, 2, 11/3)","explanation_zh":"應用基礎核對=(17/3, 2, 11/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203008,"parameters":{"approximation":[17,3],"reference":[8,4],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[17,3],\"reference\":[8,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0009","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[19,4],\"reference\":[9,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(19/4, 9, 17/4)","explanation_zh":"應用基礎核對=(19/4, 9, 17/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203009,"parameters":{"approximation":[19,4],"reference":[9,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[19,4],\"reference\":[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0010","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[21,5],\"reference\":[1,2]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(21/5, 1/2, 37/10)","explanation_zh":"應用基礎核對=(21/5, 1/2, 37/10)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203010,"parameters":{"approximation":[21,5],"reference":[1,2],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[21,5],\"reference\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0011","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[23,1],\"reference\":[2,3]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(23, 2/3, 67/3)","explanation_zh":"應用基礎核對=(23, 2/3, 67/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203011,"parameters":{"approximation":[23,1],"reference":[2,3],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[23,1],\"reference\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0012","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[25,2],\"reference\":[3,4]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(25/2, 3/4, 47/4)","explanation_zh":"應用基礎核對=(25/2, 3/4, 47/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203012,"parameters":{"approximation":[25,2],"reference":[3,4],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[25,2],\"reference\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0013","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[27,3],\"reference\":[4,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(9, 4, 5)","explanation_zh":"應用基礎核對=(9, 4, 5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203013,"parameters":{"approximation":[27,3],"reference":[4,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[27,3],\"reference\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0014","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[29,4],\"reference\":[5,2]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(29/4, 5/2, 19/4)","explanation_zh":"應用基礎核對=(29/4, 5/2, 19/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203014,"parameters":{"approximation":[29,4],"reference":[5,2],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[29,4],\"reference\":[5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0015","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[31,5],\"reference\":[6,3]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(31/5, 2, 21/5)","explanation_zh":"應用基礎核對=(31/5, 2, 21/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203015,"parameters":{"approximation":[31,5],"reference":[6,3],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[31,5],\"reference\":[6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0016","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[33,1],\"reference\":[7,4]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(33, 7/4, 125/4)","explanation_zh":"應用基礎核對=(33, 7/4, 125/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203016,"parameters":{"approximation":[33,1],"reference":[7,4],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[33,1],\"reference\":[7,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0017","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[35,2],\"reference\":[8,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(35/2, 8, 19/2)","explanation_zh":"應用基礎核對=(35/2, 8, 19/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203017,"parameters":{"approximation":[35,2],"reference":[8,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[35,2],\"reference\":[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0018","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[37,3],\"reference\":[9,2]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(37/3, 9/2, 47/6)","explanation_zh":"應用基礎核對=(37/3, 9/2, 47/6)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203018,"parameters":{"approximation":[37,3],"reference":[9,2],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[37,3],\"reference\":[9,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0019","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[39,4],\"reference\":[1,3]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(39/4, 1/3, 113/12)","explanation_zh":"應用基礎核對=(39/4, 1/3, 113/12)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203019,"parameters":{"approximation":[39,4],"reference":[1,3],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[39,4],\"reference\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0020","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[41,5],\"reference\":[2,4]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(41/5, 1/2, 77/10)","explanation_zh":"應用基礎核對=(41/5, 1/2, 77/10)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203020,"parameters":{"approximation":[41,5],"reference":[2,4],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[41,5],\"reference\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0021","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[43,1],\"reference\":[3,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(43, 3, 40)","explanation_zh":"應用基礎核對=(43, 3, 40)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203021,"parameters":{"approximation":[43,1],"reference":[3,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[43,1],\"reference\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0022","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[45,2],\"reference\":[4,2]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(45/2, 2, 41/2)","explanation_zh":"應用基礎核對=(45/2, 2, 41/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203022,"parameters":{"approximation":[45,2],"reference":[4,2],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[45,2],\"reference\":[4,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0023","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[47,3],\"reference\":[5,3]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(47/3, 5/3, 14)","explanation_zh":"應用基礎核對=(47/3, 5/3, 14)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203023,"parameters":{"approximation":[47,3],"reference":[5,3],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[47,3],\"reference\":[5,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0024","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[49,4],\"reference\":[6,4]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(49/4, 3/2, 43/4)","explanation_zh":"應用基礎核對=(49/4, 3/2, 43/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203024,"parameters":{"approximation":[49,4],"reference":[6,4],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[49,4],\"reference\":[6,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0025","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-absolute-error；資料={\"approximation\":[51,5],\"reference\":[7,1]}。請依 [approximation,reference,absolute_error] 欄序回答。","answer":{"kind":"expression","value":"(51/5, 7, 16/5)","explanation_zh":"應用基礎核對=(51/5, 7, 16/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-absolute-error","seed":202610203025,"parameters":{"approximation":[51,5],"reference":[7,1],"domain":"Exact_rational_error","operation":"error-absolute-error","semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[51,5],\"reference\":[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0026","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[3,1],\"reference\":[1,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 2, 2)","explanation_zh":"應用基礎核對=(3, 1, 2, 2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203026,"parameters":{"approximation":[3,1],"reference":[1,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[3,1],\"reference\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0027","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[5,2],\"reference\":[2,2]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(5/2, 1, 3/2, 3/2)","explanation_zh":"應用基礎核對=(5/2, 1, 3/2, 3/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203027,"parameters":{"approximation":[5,2],"reference":[2,2],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[5,2],\"reference\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0028","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[7,3],\"reference\":[3,3]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(7/3, 1, 4/3, 4/3)","explanation_zh":"應用基礎核對=(7/3, 1, 4/3, 4/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203028,"parameters":{"approximation":[7,3],"reference":[3,3],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[7,3],\"reference\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0029","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[9,4],\"reference\":[4,4]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 1, 5/4, 5/4)","explanation_zh":"應用基礎核對=(9/4, 1, 5/4, 5/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203029,"parameters":{"approximation":[9,4],"reference":[4,4],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[9,4],\"reference\":[4,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0030","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[11,5],\"reference\":[5,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(11/5, 5, 14/5, 14/25)","explanation_zh":"應用基礎核對=(11/5, 5, 14/5, 14/25)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203030,"parameters":{"approximation":[11,5],"reference":[5,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[11,5],\"reference\":[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0031","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[13,1],\"reference\":[6,2]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(13, 3, 10, 10/3)","explanation_zh":"應用基礎核對=(13, 3, 10, 10/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203031,"parameters":{"approximation":[13,1],"reference":[6,2],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[13,1],\"reference\":[6,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0032","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[15,2],\"reference\":[7,3]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(15/2, 7/3, 31/6, 31/14)","explanation_zh":"應用基礎核對=(15/2, 7/3, 31/6, 31/14)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203032,"parameters":{"approximation":[15,2],"reference":[7,3],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[15,2],\"reference\":[7,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0033","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[17,3],\"reference\":[8,4]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(17/3, 2, 11/3, 11/6)","explanation_zh":"應用基礎核對=(17/3, 2, 11/3, 11/6)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203033,"parameters":{"approximation":[17,3],"reference":[8,4],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[17,3],\"reference\":[8,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0034","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[19,4],\"reference\":[9,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(19/4, 9, 17/4, 17/36)","explanation_zh":"應用基礎核對=(19/4, 9, 17/4, 17/36)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203034,"parameters":{"approximation":[19,4],"reference":[9,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[19,4],\"reference\":[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0035","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[21,5],\"reference\":[1,2]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(21/5, 1/2, 37/10, 37/5)","explanation_zh":"應用基礎核對=(21/5, 1/2, 37/10, 37/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203035,"parameters":{"approximation":[21,5],"reference":[1,2],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[21,5],\"reference\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0036","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[23,1],\"reference\":[2,3]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(23, 2/3, 67/3, 67/2)","explanation_zh":"應用基礎核對=(23, 2/3, 67/3, 67/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203036,"parameters":{"approximation":[23,1],"reference":[2,3],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[23,1],\"reference\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0037","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[25,2],\"reference\":[3,4]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(25/2, 3/4, 47/4, 47/3)","explanation_zh":"應用基礎核對=(25/2, 3/4, 47/4, 47/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203037,"parameters":{"approximation":[25,2],"reference":[3,4],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[25,2],\"reference\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0038","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[27,3],\"reference\":[4,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(9, 4, 5, 5/4)","explanation_zh":"應用基礎核對=(9, 4, 5, 5/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203038,"parameters":{"approximation":[27,3],"reference":[4,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[27,3],\"reference\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0039","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[29,4],\"reference\":[5,2]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(29/4, 5/2, 19/4, 19/10)","explanation_zh":"應用基礎核對=(29/4, 5/2, 19/4, 19/10)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203039,"parameters":{"approximation":[29,4],"reference":[5,2],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[29,4],\"reference\":[5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0040","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[31,5],\"reference\":[6,3]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(31/5, 2, 21/5, 21/10)","explanation_zh":"應用基礎核對=(31/5, 2, 21/5, 21/10)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203040,"parameters":{"approximation":[31,5],"reference":[6,3],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[31,5],\"reference\":[6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0041","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[33,1],\"reference\":[7,4]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(33, 7/4, 125/4, 125/7)","explanation_zh":"應用基礎核對=(33, 7/4, 125/4, 125/7)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203041,"parameters":{"approximation":[33,1],"reference":[7,4],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[33,1],\"reference\":[7,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0042","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[35,2],\"reference\":[8,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(35/2, 8, 19/2, 19/16)","explanation_zh":"應用基礎核對=(35/2, 8, 19/2, 19/16)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203042,"parameters":{"approximation":[35,2],"reference":[8,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[35,2],\"reference\":[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0043","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[37,3],\"reference\":[9,2]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(37/3, 9/2, 47/6, 47/27)","explanation_zh":"應用基礎核對=(37/3, 9/2, 47/6, 47/27)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203043,"parameters":{"approximation":[37,3],"reference":[9,2],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[37,3],\"reference\":[9,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0044","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[39,4],\"reference\":[1,3]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(39/4, 1/3, 113/12, 113/4)","explanation_zh":"應用基礎核對=(39/4, 1/3, 113/12, 113/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203044,"parameters":{"approximation":[39,4],"reference":[1,3],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[39,4],\"reference\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0045","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[41,5],\"reference\":[2,4]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(41/5, 1/2, 77/10, 77/5)","explanation_zh":"應用基礎核對=(41/5, 1/2, 77/10, 77/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203045,"parameters":{"approximation":[41,5],"reference":[2,4],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[41,5],\"reference\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0046","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[43,1],\"reference\":[3,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(43, 3, 40, 40/3)","explanation_zh":"應用基礎核對=(43, 3, 40, 40/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203046,"parameters":{"approximation":[43,1],"reference":[3,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[43,1],\"reference\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0047","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[45,2],\"reference\":[4,2]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(45/2, 2, 41/2, 41/4)","explanation_zh":"應用基礎核對=(45/2, 2, 41/2, 41/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203047,"parameters":{"approximation":[45,2],"reference":[4,2],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[45,2],\"reference\":[4,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0048","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[47,3],\"reference\":[5,3]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(47/3, 5/3, 14, 42/5)","explanation_zh":"應用基礎核對=(47/3, 5/3, 14, 42/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203048,"parameters":{"approximation":[47,3],"reference":[5,3],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[47,3],\"reference\":[5,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0049","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[49,4],\"reference\":[6,4]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(49/4, 3/2, 43/4, 43/6)","explanation_zh":"應用基礎核對=(49/4, 3/2, 43/4, 43/6)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203049,"parameters":{"approximation":[49,4],"reference":[6,4],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[49,4],\"reference\":[6,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0050","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-relative-error；資料={\"approximation\":[51,5],\"reference\":[7,1]}。請依 [approximation,reference,absolute_error,relative_error] 欄序回答。","answer":{"kind":"expression","value":"(51/5, 7, 16/5, 16/35)","explanation_zh":"應用基礎核對=(51/5, 7, 16/5, 16/35)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-relative-error","seed":202610203050,"parameters":{"approximation":[51,5],"reference":[7,1],"domain":"Exact_rational_error","operation":"error-relative-error","semantic_template":"qf-app20-error-relative-error/{\"approximation\":[51,5],\"reference\":[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0051","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[3,1],\"reference\":[1,1],\"tolerance\":[1,2]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 2, 1/2, 否)","explanation_zh":"應用基礎核對=(3, 1, 2, 1/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203051,"parameters":{"approximation":[3,1],"reference":[1,1],"tolerance":[1,2],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[3,1],\"reference\":[1,1],\"tolerance\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0052","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[5,2],\"reference\":[2,2],\"tolerance\":[2,3]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(5/2, 1, 3/2, 2/3, 否)","explanation_zh":"應用基礎核對=(5/2, 1, 3/2, 2/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203052,"parameters":{"approximation":[5,2],"reference":[2,2],"tolerance":[2,3],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[5,2],\"reference\":[2,2],\"tolerance\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0053","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[7,3],\"reference\":[3,3],\"tolerance\":[3,4]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(7/3, 1, 4/3, 3/4, 否)","explanation_zh":"應用基礎核對=(7/3, 1, 4/3, 3/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203053,"parameters":{"approximation":[7,3],"reference":[3,3],"tolerance":[3,4],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[7,3],\"reference\":[3,3],\"tolerance\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0054","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[9,4],\"reference\":[4,4],\"tolerance\":[4,5]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(9/4, 1, 5/4, 4/5, 否)","explanation_zh":"應用基礎核對=(9/4, 1, 5/4, 4/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203054,"parameters":{"approximation":[9,4],"reference":[4,4],"tolerance":[4,5],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[9,4],\"reference\":[4,4],\"tolerance\":[4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0055","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[11,5],\"reference\":[5,1],\"tolerance\":[5,6]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(11/5, 5, 14/5, 5/6, 否)","explanation_zh":"應用基礎核對=(11/5, 5, 14/5, 5/6, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203055,"parameters":{"approximation":[11,5],"reference":[5,1],"tolerance":[5,6],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[11,5],\"reference\":[5,1],\"tolerance\":[5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0056","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[13,1],\"reference\":[6,2],\"tolerance\":[6,7]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(13, 3, 10, 6/7, 否)","explanation_zh":"應用基礎核對=(13, 3, 10, 6/7, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203056,"parameters":{"approximation":[13,1],"reference":[6,2],"tolerance":[6,7],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[13,1],\"reference\":[6,2],\"tolerance\":[6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0057","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[15,2],\"reference\":[7,3],\"tolerance\":[1,8]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(15/2, 7/3, 31/6, 1/8, 否)","explanation_zh":"應用基礎核對=(15/2, 7/3, 31/6, 1/8, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203057,"parameters":{"approximation":[15,2],"reference":[7,3],"tolerance":[1,8],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[15,2],\"reference\":[7,3],\"tolerance\":[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0058","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[17,3],\"reference\":[8,4],\"tolerance\":[2,2]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(17/3, 2, 11/3, 1, 否)","explanation_zh":"應用基礎核對=(17/3, 2, 11/3, 1, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203058,"parameters":{"approximation":[17,3],"reference":[8,4],"tolerance":[2,2],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[17,3],\"reference\":[8,4],\"tolerance\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0059","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[19,4],\"reference\":[9,1],\"tolerance\":[3,3]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(19/4, 9, 17/4, 1, 否)","explanation_zh":"應用基礎核對=(19/4, 9, 17/4, 1, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203059,"parameters":{"approximation":[19,4],"reference":[9,1],"tolerance":[3,3],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[19,4],\"reference\":[9,1],\"tolerance\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0060","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[21,5],\"reference\":[1,2],\"tolerance\":[4,4]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(21/5, 1/2, 37/10, 1, 否)","explanation_zh":"應用基礎核對=(21/5, 1/2, 37/10, 1, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203060,"parameters":{"approximation":[21,5],"reference":[1,2],"tolerance":[4,4],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[21,5],\"reference\":[1,2],\"tolerance\":[4,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0061","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[23,1],\"reference\":[2,3],\"tolerance\":[5,5]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(23, 2/3, 67/3, 1, 否)","explanation_zh":"應用基礎核對=(23, 2/3, 67/3, 1, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203061,"parameters":{"approximation":[23,1],"reference":[2,3],"tolerance":[5,5],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[23,1],\"reference\":[2,3],\"tolerance\":[5,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0062","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[25,2],\"reference\":[3,4],\"tolerance\":[6,6]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(25/2, 3/4, 47/4, 1, 否)","explanation_zh":"應用基礎核對=(25/2, 3/4, 47/4, 1, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203062,"parameters":{"approximation":[25,2],"reference":[3,4],"tolerance":[6,6],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[25,2],\"reference\":[3,4],\"tolerance\":[6,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0063","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[27,3],\"reference\":[4,1],\"tolerance\":[1,7]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(9, 4, 5, 1/7, 否)","explanation_zh":"應用基礎核對=(9, 4, 5, 1/7, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203063,"parameters":{"approximation":[27,3],"reference":[4,1],"tolerance":[1,7],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[27,3],\"reference\":[4,1],\"tolerance\":[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0064","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[29,4],\"reference\":[5,2],\"tolerance\":[2,8]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(29/4, 5/2, 19/4, 1/4, 否)","explanation_zh":"應用基礎核對=(29/4, 5/2, 19/4, 1/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203064,"parameters":{"approximation":[29,4],"reference":[5,2],"tolerance":[2,8],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[29,4],\"reference\":[5,2],\"tolerance\":[2,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0065","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[31,5],\"reference\":[6,3],\"tolerance\":[3,2]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(31/5, 2, 21/5, 3/2, 否)","explanation_zh":"應用基礎核對=(31/5, 2, 21/5, 3/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203065,"parameters":{"approximation":[31,5],"reference":[6,3],"tolerance":[3,2],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[31,5],\"reference\":[6,3],\"tolerance\":[3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0066","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[33,1],\"reference\":[7,4],\"tolerance\":[4,3]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(33, 7/4, 125/4, 4/3, 否)","explanation_zh":"應用基礎核對=(33, 7/4, 125/4, 4/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203066,"parameters":{"approximation":[33,1],"reference":[7,4],"tolerance":[4,3],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[33,1],\"reference\":[7,4],\"tolerance\":[4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0067","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[35,2],\"reference\":[8,1],\"tolerance\":[5,4]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(35/2, 8, 19/2, 5/4, 否)","explanation_zh":"應用基礎核對=(35/2, 8, 19/2, 5/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203067,"parameters":{"approximation":[35,2],"reference":[8,1],"tolerance":[5,4],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[35,2],\"reference\":[8,1],\"tolerance\":[5,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0068","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[37,3],\"reference\":[9,2],\"tolerance\":[6,5]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(37/3, 9/2, 47/6, 6/5, 否)","explanation_zh":"應用基礎核對=(37/3, 9/2, 47/6, 6/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203068,"parameters":{"approximation":[37,3],"reference":[9,2],"tolerance":[6,5],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[37,3],\"reference\":[9,2],\"tolerance\":[6,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0069","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[39,4],\"reference\":[1,3],\"tolerance\":[1,6]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(39/4, 1/3, 113/12, 1/6, 否)","explanation_zh":"應用基礎核對=(39/4, 1/3, 113/12, 1/6, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203069,"parameters":{"approximation":[39,4],"reference":[1,3],"tolerance":[1,6],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[39,4],\"reference\":[1,3],\"tolerance\":[1,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0070","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[41,5],\"reference\":[2,4],\"tolerance\":[2,7]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(41/5, 1/2, 77/10, 2/7, 否)","explanation_zh":"應用基礎核對=(41/5, 1/2, 77/10, 2/7, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203070,"parameters":{"approximation":[41,5],"reference":[2,4],"tolerance":[2,7],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[41,5],\"reference\":[2,4],\"tolerance\":[2,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0071","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[43,1],\"reference\":[3,1],\"tolerance\":[3,8]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(43, 3, 40, 3/8, 否)","explanation_zh":"應用基礎核對=(43, 3, 40, 3/8, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203071,"parameters":{"approximation":[43,1],"reference":[3,1],"tolerance":[3,8],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[43,1],\"reference\":[3,1],\"tolerance\":[3,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0072","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[45,2],\"reference\":[4,2],\"tolerance\":[4,2]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(45/2, 2, 41/2, 2, 否)","explanation_zh":"應用基礎核對=(45/2, 2, 41/2, 2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203072,"parameters":{"approximation":[45,2],"reference":[4,2],"tolerance":[4,2],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[45,2],\"reference\":[4,2],\"tolerance\":[4,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0073","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[47,3],\"reference\":[5,3],\"tolerance\":[5,3]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(47/3, 5/3, 14, 5/3, 否)","explanation_zh":"應用基礎核對=(47/3, 5/3, 14, 5/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203073,"parameters":{"approximation":[47,3],"reference":[5,3],"tolerance":[5,3],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[47,3],\"reference\":[5,3],\"tolerance\":[5,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0074","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[49,4],\"reference\":[6,4],\"tolerance\":[6,4]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(49/4, 3/2, 43/4, 3/2, 否)","explanation_zh":"應用基礎核對=(49/4, 3/2, 43/4, 3/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203074,"parameters":{"approximation":[49,4],"reference":[6,4],"tolerance":[6,4],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[49,4],\"reference\":[6,4],\"tolerance\":[6,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0075","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-tolerance-audit；資料={\"approximation\":[51,5],\"reference\":[7,1],\"tolerance\":[1,5]}。請依 [approximation,reference,absolute_error,tolerance,within_tolerance] 欄序回答。","answer":{"kind":"expression","value":"(51/5, 7, 16/5, 1/5, 否)","explanation_zh":"應用基礎核對=(51/5, 7, 16/5, 1/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-tolerance-audit","seed":202610203075,"parameters":{"approximation":[51,5],"reference":[7,1],"tolerance":[1,5],"domain":"Exact_rational_error","operation":"error-tolerance-audit","semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[51,5],\"reference\":[7,1],\"tolerance\":[1,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0076","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[1,1],\"tolerance\":[1,2],\"candidate\":[1,1]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1, 1/2, 1/2, 3/2, 1, 是)","explanation_zh":"應用基礎核對=(1, 1/2, 1/2, 3/2, 1, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203076,"parameters":{"reference":[1,1],"tolerance":[1,2],"candidate":[1,1],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[1,1],\"reference\":[1,1],\"tolerance\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0077","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[2,2],\"tolerance\":[2,3],\"candidate\":[3,2]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1, 2/3, 1/3, 5/3, 3/2, 是)","explanation_zh":"應用基礎核對=(1, 2/3, 1/3, 5/3, 3/2, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203077,"parameters":{"reference":[2,2],"tolerance":[2,3],"candidate":[3,2],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[3,2],\"reference\":[2,2],\"tolerance\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0078","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[3,3],\"tolerance\":[3,4],\"candidate\":[5,3]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1, 3/4, 1/4, 7/4, 5/3, 是)","explanation_zh":"應用基礎核對=(1, 3/4, 1/4, 7/4, 5/3, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203078,"parameters":{"reference":[3,3],"tolerance":[3,4],"candidate":[5,3],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[5,3],\"reference\":[3,3],\"tolerance\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0079","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[4,4],\"tolerance\":[4,5],\"candidate\":[7,4]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1, 4/5, 1/5, 9/5, 7/4, 是)","explanation_zh":"應用基礎核對=(1, 4/5, 1/5, 9/5, 7/4, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203079,"parameters":{"reference":[4,4],"tolerance":[4,5],"candidate":[7,4],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[7,4],\"reference\":[4,4],\"tolerance\":[4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0080","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[5,1],\"tolerance\":[5,6],\"candidate\":[9,5]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(5, 5/6, 25/6, 35/6, 9/5, 否)","explanation_zh":"應用基礎核對=(5, 5/6, 25/6, 35/6, 9/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203080,"parameters":{"reference":[5,1],"tolerance":[5,6],"candidate":[9,5],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[9,5],\"reference\":[5,1],\"tolerance\":[5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0081","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[6,2],\"tolerance\":[6,7],\"candidate\":[11,1]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(3, 6/7, 15/7, 27/7, 11, 否)","explanation_zh":"應用基礎核對=(3, 6/7, 15/7, 27/7, 11, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203081,"parameters":{"reference":[6,2],"tolerance":[6,7],"candidate":[11,1],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[11,1],\"reference\":[6,2],\"tolerance\":[6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0082","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[7,3],\"tolerance\":[1,8],\"candidate\":[13,2]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(7/3, 1/8, 53/24, 59/24, 13/2, 否)","explanation_zh":"應用基礎核對=(7/3, 1/8, 53/24, 59/24, 13/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203082,"parameters":{"reference":[7,3],"tolerance":[1,8],"candidate":[13,2],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[13,2],\"reference\":[7,3],\"tolerance\":[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0083","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[8,4],\"tolerance\":[2,2],\"candidate\":[15,3]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(2, 1, 1, 3, 5, 否)","explanation_zh":"應用基礎核對=(2, 1, 1, 3, 5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203083,"parameters":{"reference":[8,4],"tolerance":[2,2],"candidate":[15,3],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[15,3],\"reference\":[8,4],\"tolerance\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0084","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[9,1],\"tolerance\":[3,3],\"candidate\":[17,4]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(9, 1, 8, 10, 17/4, 否)","explanation_zh":"應用基礎核對=(9, 1, 8, 10, 17/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203084,"parameters":{"reference":[9,1],"tolerance":[3,3],"candidate":[17,4],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[17,4],\"reference\":[9,1],\"tolerance\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0085","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[1,2],\"tolerance\":[4,4],\"candidate\":[19,5]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1, -1/2, 3/2, 19/5, 否)","explanation_zh":"應用基礎核對=(1/2, 1, -1/2, 3/2, 19/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203085,"parameters":{"reference":[1,2],"tolerance":[4,4],"candidate":[19,5],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[19,5],\"reference\":[1,2],\"tolerance\":[4,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0086","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[2,3],\"tolerance\":[5,5],\"candidate\":[21,1]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(2/3, 1, -1/3, 5/3, 21, 否)","explanation_zh":"應用基礎核對=(2/3, 1, -1/3, 5/3, 21, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203086,"parameters":{"reference":[2,3],"tolerance":[5,5],"candidate":[21,1],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[21,1],\"reference\":[2,3],\"tolerance\":[5,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0087","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[3,4],\"tolerance\":[6,6],\"candidate\":[23,2]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(3/4, 1, -1/4, 7/4, 23/2, 否)","explanation_zh":"應用基礎核對=(3/4, 1, -1/4, 7/4, 23/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203087,"parameters":{"reference":[3,4],"tolerance":[6,6],"candidate":[23,2],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[23,2],\"reference\":[3,4],\"tolerance\":[6,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0088","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[4,1],\"tolerance\":[1,7],\"candidate\":[25,3]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(4, 1/7, 27/7, 29/7, 25/3, 否)","explanation_zh":"應用基礎核對=(4, 1/7, 27/7, 29/7, 25/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203088,"parameters":{"reference":[4,1],"tolerance":[1,7],"candidate":[25,3],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[25,3],\"reference\":[4,1],\"tolerance\":[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0089","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[5,2],\"tolerance\":[2,8],\"candidate\":[27,4]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(5/2, 1/4, 9/4, 11/4, 27/4, 否)","explanation_zh":"應用基礎核對=(5/2, 1/4, 9/4, 11/4, 27/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203089,"parameters":{"reference":[5,2],"tolerance":[2,8],"candidate":[27,4],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[27,4],\"reference\":[5,2],\"tolerance\":[2,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0090","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[6,3],\"tolerance\":[3,2],\"candidate\":[29,5]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(2, 3/2, 1/2, 7/2, 29/5, 否)","explanation_zh":"應用基礎核對=(2, 3/2, 1/2, 7/2, 29/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203090,"parameters":{"reference":[6,3],"tolerance":[3,2],"candidate":[29,5],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[29,5],\"reference\":[6,3],\"tolerance\":[3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0091","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[7,4],\"tolerance\":[4,3],\"candidate\":[31,1]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(7/4, 4/3, 5/12, 37/12, 31, 否)","explanation_zh":"應用基礎核對=(7/4, 4/3, 5/12, 37/12, 31, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203091,"parameters":{"reference":[7,4],"tolerance":[4,3],"candidate":[31,1],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[31,1],\"reference\":[7,4],\"tolerance\":[4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0092","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[8,1],\"tolerance\":[5,4],\"candidate\":[33,2]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(8, 5/4, 27/4, 37/4, 33/2, 否)","explanation_zh":"應用基礎核對=(8, 5/4, 27/4, 37/4, 33/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203092,"parameters":{"reference":[8,1],"tolerance":[5,4],"candidate":[33,2],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[33,2],\"reference\":[8,1],\"tolerance\":[5,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0093","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[9,2],\"tolerance\":[6,5],\"candidate\":[35,3]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(9/2, 6/5, 33/10, 57/10, 35/3, 否)","explanation_zh":"應用基礎核對=(9/2, 6/5, 33/10, 57/10, 35/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203093,"parameters":{"reference":[9,2],"tolerance":[6,5],"candidate":[35,3],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[35,3],\"reference\":[9,2],\"tolerance\":[6,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0094","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[1,3],\"tolerance\":[1,6],\"candidate\":[37,4]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1/3, 1/6, 1/6, 1/2, 37/4, 否)","explanation_zh":"應用基礎核對=(1/3, 1/6, 1/6, 1/2, 37/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203094,"parameters":{"reference":[1,3],"tolerance":[1,6],"candidate":[37,4],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[37,4],\"reference\":[1,3],\"tolerance\":[1,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0095","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[2,4],\"tolerance\":[2,7],\"candidate\":[39,5]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 2/7, 3/14, 11/14, 39/5, 否)","explanation_zh":"應用基礎核對=(1/2, 2/7, 3/14, 11/14, 39/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203095,"parameters":{"reference":[2,4],"tolerance":[2,7],"candidate":[39,5],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[39,5],\"reference\":[2,4],\"tolerance\":[2,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0096","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[3,1],\"tolerance\":[3,8],\"candidate\":[41,1]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(3, 3/8, 21/8, 27/8, 41, 否)","explanation_zh":"應用基礎核對=(3, 3/8, 21/8, 27/8, 41, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203096,"parameters":{"reference":[3,1],"tolerance":[3,8],"candidate":[41,1],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[41,1],\"reference\":[3,1],\"tolerance\":[3,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0097","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[4,2],\"tolerance\":[4,2],\"candidate\":[43,2]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 0, 4, 43/2, 否)","explanation_zh":"應用基礎核對=(2, 2, 0, 4, 43/2, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203097,"parameters":{"reference":[4,2],"tolerance":[4,2],"candidate":[43,2],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[43,2],\"reference\":[4,2],\"tolerance\":[4,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0098","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[5,3],\"tolerance\":[5,3],\"candidate\":[45,3]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(5/3, 5/3, 0, 10/3, 15, 否)","explanation_zh":"應用基礎核對=(5/3, 5/3, 0, 10/3, 15, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203098,"parameters":{"reference":[5,3],"tolerance":[5,3],"candidate":[45,3],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[45,3],\"reference\":[5,3],\"tolerance\":[5,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0099","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[6,4],\"tolerance\":[6,4],\"candidate\":[47,4]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(3/2, 3/2, 0, 3, 47/4, 否)","explanation_zh":"應用基礎核對=(3/2, 3/2, 0, 3, 47/4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203099,"parameters":{"reference":[6,4],"tolerance":[6,4],"candidate":[47,4],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[47,4],\"reference\":[6,4],\"tolerance\":[6,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0100","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","language":"zh-Hant","source_mko_ids":["mko-numerical-approximation-error"],"title_zh":"精確有理誤差","stem_zh":"精確有理數。操作=error-error-interval；資料={\"reference\":[7,1],\"tolerance\":[1,5],\"candidate\":[49,5]}。請依 [reference,tolerance,lower,upper,candidate,in_interval] 欄序回答。","answer":{"kind":"expression","value":"(7, 1/5, 34/5, 36/5, 49/5, 否)","explanation_zh":"應用基礎核對=(7, 1/5, 34/5, 36/5, 49/5, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；relative error要求reference非零；不混淆截斷誤差與捨入誤差。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理誤差"]},"variant":{"family_id":"qf-app20-error-error-interval","seed":202610203100,"parameters":{"reference":[7,1],"tolerance":[1,5],"candidate":[49,5],"domain":"Exact_rational_error","operation":"error-error-interval","semantic_template":"qf-app20-error-error-interval/{\"candidate\":[49,5],\"reference\":[7,1],\"tolerance\":[1,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}