{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r06-asymptotic-resource-bound-0001","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":1,\"p\":0,\"b\":1,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, 1, 0, 是, 是, 是, [1, 1], [1/1, 1])","explanation_zh":"第二批擴展核對=(1, 0, 1, 0, 是, 是, 是, [1, 1], [1/1, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196001,"parameters":{"a":1,"p":0,"b":1,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":1,\"b\":1,\"p\":0,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0002","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":2,\"p\":1,\"b\":2,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(2, 1, 2, 3, 是, 否, 否, [2, 1], 不存在)","explanation_zh":"第二批擴展核對=(2, 1, 2, 3, 是, 否, 否, [2, 1], 不存在)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196002,"parameters":{"a":2,"p":1,"b":2,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":2,\"b\":2,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0003","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":3,\"p\":2,\"b\":3,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 3, 0, 否, 是, 否, 不存在, [1/3, 1])","explanation_zh":"第二批擴展核對=(3, 2, 3, 0, 否, 是, 否, 不存在, [1/3, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196003,"parameters":{"a":3,"p":2,"b":3,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":3,\"b\":3,\"p\":2,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0004","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":4,\"p\":3,\"b\":4,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 4, 3, 是, 是, 是, [4, 1], [1/4, 1])","explanation_zh":"第二批擴展核對=(4, 3, 4, 3, 是, 是, 是, [4, 1], [1/4, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196004,"parameters":{"a":4,"p":3,"b":4,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":4,\"b\":4,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0005","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":5,\"p\":4,\"b\":5,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 5, 0, 否, 是, 否, 不存在, [1/5, 1])","explanation_zh":"第二批擴展核對=(5, 4, 5, 0, 否, 是, 否, 不存在, [1/5, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196005,"parameters":{"a":5,"p":4,"b":5,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":5,\"b\":5,\"p\":4,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0006","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":6,\"p\":5,\"b\":6,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(6, 5, 6, 3, 否, 是, 否, 不存在, [1/6, 1])","explanation_zh":"第二批擴展核對=(6, 5, 6, 3, 否, 是, 否, 不存在, [1/6, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196006,"parameters":{"a":6,"p":5,"b":6,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":6,\"b\":6,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0007","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":7,\"p\":0,\"b\":7,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(7, 0, 7, 0, 是, 是, 是, [7, 1], [1/7, 1])","explanation_zh":"第二批擴展核對=(7, 0, 7, 0, 是, 是, 是, [7, 1], [1/7, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196007,"parameters":{"a":7,"p":0,"b":7,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":7,\"b\":7,\"p\":0,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0008","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":8,\"p\":1,\"b\":1,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(8, 1, 1, 3, 是, 否, 否, [8, 1], 不存在)","explanation_zh":"第二批擴展核對=(8, 1, 1, 3, 是, 否, 否, [8, 1], 不存在)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196008,"parameters":{"a":8,"p":1,"b":1,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":8,\"b\":1,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0009","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":9,\"p\":2,\"b\":2,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(9, 2, 2, 0, 否, 是, 否, 不存在, [1/2, 1])","explanation_zh":"第二批擴展核對=(9, 2, 2, 0, 否, 是, 否, 不存在, [1/2, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196009,"parameters":{"a":9,"p":2,"b":2,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":9,\"b\":2,\"p\":2,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0010","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":10,\"p\":3,\"b\":3,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(10, 3, 3, 3, 是, 是, 是, [10, 1], [1/3, 1])","explanation_zh":"第二批擴展核對=(10, 3, 3, 3, 是, 是, 是, [10, 1], [1/3, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196010,"parameters":{"a":10,"p":3,"b":3,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":10,\"b\":3,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0011","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":11,\"p\":4,\"b\":4,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(11, 4, 4, 0, 否, 是, 否, 不存在, [1/4, 1])","explanation_zh":"第二批擴展核對=(11, 4, 4, 0, 否, 是, 否, 不存在, [1/4, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196011,"parameters":{"a":11,"p":4,"b":4,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":11,\"b\":4,\"p\":4,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0012","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":12,\"p\":5,\"b\":5,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(12, 5, 5, 3, 否, 是, 否, 不存在, [1/5, 1])","explanation_zh":"第二批擴展核對=(12, 5, 5, 3, 否, 是, 否, 不存在, [1/5, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196012,"parameters":{"a":12,"p":5,"b":5,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":12,\"b\":5,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0013","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":13,\"p\":0,\"b\":6,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(13, 0, 6, 0, 是, 是, 是, [13, 1], [1/6, 1])","explanation_zh":"第二批擴展核對=(13, 0, 6, 0, 是, 是, 是, [13, 1], [1/6, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196013,"parameters":{"a":13,"p":0,"b":6,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":13,\"b\":6,\"p\":0,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0014","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":14,\"p\":1,\"b\":7,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(14, 1, 7, 3, 是, 否, 否, [14, 1], 不存在)","explanation_zh":"第二批擴展核對=(14, 1, 7, 3, 是, 否, 否, [14, 1], 不存在)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196014,"parameters":{"a":14,"p":1,"b":7,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":14,\"b\":7,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0015","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":15,\"p\":2,\"b\":1,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(15, 2, 1, 0, 否, 是, 否, 不存在, [1/1, 1])","explanation_zh":"第二批擴展核對=(15, 2, 1, 0, 否, 是, 否, 不存在, [1/1, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196015,"parameters":{"a":15,"p":2,"b":1,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":15,\"b\":1,\"p\":2,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0016","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":16,\"p\":3,\"b\":2,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(16, 3, 2, 3, 是, 是, 是, [16, 1], [1/2, 1])","explanation_zh":"第二批擴展核對=(16, 3, 2, 3, 是, 是, 是, [16, 1], [1/2, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196016,"parameters":{"a":16,"p":3,"b":2,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":16,\"b\":2,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0017","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":17,\"p\":4,\"b\":3,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(17, 4, 3, 0, 否, 是, 否, 不存在, [1/3, 1])","explanation_zh":"第二批擴展核對=(17, 4, 3, 0, 否, 是, 否, 不存在, [1/3, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196017,"parameters":{"a":17,"p":4,"b":3,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":17,\"b\":3,\"p\":4,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0018","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":18,\"p\":5,\"b\":4,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(18, 5, 4, 3, 否, 是, 否, 不存在, [1/4, 1])","explanation_zh":"第二批擴展核對=(18, 5, 4, 3, 否, 是, 否, 不存在, [1/4, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196018,"parameters":{"a":18,"p":5,"b":4,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":18,\"b\":4,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0019","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":19,\"p\":0,\"b\":5,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(19, 0, 5, 0, 是, 是, 是, [19, 1], [1/5, 1])","explanation_zh":"第二批擴展核對=(19, 0, 5, 0, 是, 是, 是, [19, 1], [1/5, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196019,"parameters":{"a":19,"p":0,"b":5,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":19,\"b\":5,\"p\":0,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0020","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":20,\"p\":1,\"b\":6,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(20, 1, 6, 3, 是, 否, 否, [20, 1], 不存在)","explanation_zh":"第二批擴展核對=(20, 1, 6, 3, 是, 否, 否, [20, 1], 不存在)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196020,"parameters":{"a":20,"p":1,"b":6,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":20,\"b\":6,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0021","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":21,\"p\":2,\"b\":7,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(21, 2, 7, 0, 否, 是, 否, 不存在, [1/7, 1])","explanation_zh":"第二批擴展核對=(21, 2, 7, 0, 否, 是, 否, 不存在, [1/7, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196021,"parameters":{"a":21,"p":2,"b":7,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":21,\"b\":7,\"p\":2,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0022","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":22,\"p\":3,\"b\":1,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(22, 3, 1, 3, 是, 是, 是, [22, 1], [1/1, 1])","explanation_zh":"第二批擴展核對=(22, 3, 1, 3, 是, 是, 是, [22, 1], [1/1, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196022,"parameters":{"a":22,"p":3,"b":1,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":22,\"b\":1,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0023","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":23,\"p\":4,\"b\":2,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(23, 4, 2, 0, 否, 是, 否, 不存在, [1/2, 1])","explanation_zh":"第二批擴展核對=(23, 4, 2, 0, 否, 是, 否, 不存在, [1/2, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196023,"parameters":{"a":23,"p":4,"b":2,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":23,\"b\":2,\"p\":4,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0024","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":24,\"p\":5,\"b\":3,\"q\":3}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(24, 5, 3, 3, 否, 是, 否, 不存在, [1/3, 1])","explanation_zh":"第二批擴展核對=(24, 5, 3, 3, 否, 是, 否, 不存在, [1/3, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196024,"parameters":{"a":24,"p":5,"b":3,"q":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":24,\"b\":3,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0025","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-monomial-class；資料={\"a\":25,\"p\":0,\"b\":4,\"q\":0}。請依 [a,p,b,q,bigO,bigOmega,theta,O_witness,Omega_witness] 欄序回答。","answer":{"kind":"expression","value":"(25, 0, 4, 0, 是, 是, 是, [25, 1], [1/4, 1])","explanation_zh":"第二批擴展核對=(25, 0, 4, 0, 是, 是, 是, [25, 1], [1/4, 1])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-monomial-class","seed":202610196025,"parameters":{"a":25,"p":0,"b":4,"q":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-monomial-class","semantic_template":"qf-ext19-asymptotic-monomial-class/{\"a\":25,\"b\":4,\"p\":0,\"q\":0}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0026","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[0,1,0],\"coeffs_g\":[1,1,2,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0], [1, 1, 2, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 0], [1, 1, 2, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196026,"parameters":{"coeffs_f":[0,1,0],"coeffs_g":[1,1,2,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[0,1,0],\"coeffs_g\":[1,1,2,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0027","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[1,2,1],\"coeffs_g\":[1,2,0,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 1], [1, 2, 0, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([1, 2, 1], [1, 2, 0, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196027,"parameters":{"coeffs_f":[1,2,1],"coeffs_g":[1,2,0,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[1,2,1],\"coeffs_g\":[1,2,0,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0028","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[2,3,0],\"coeffs_g\":[1,3,1,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 0], [1, 3, 1, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([2, 3, 0], [1, 3, 1, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196028,"parameters":{"coeffs_f":[2,3,0],"coeffs_g":[1,3,1,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[2,3,0],\"coeffs_g\":[1,3,1,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0029","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[3,1,1],\"coeffs_g\":[1,4,2,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 1], [1, 4, 2, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([3, 1, 1], [1, 4, 2, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196029,"parameters":{"coeffs_f":[3,1,1],"coeffs_g":[1,4,2,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[3,1,1],\"coeffs_g\":[1,4,2,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0030","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[4,2,0],\"coeffs_g\":[1,5,0,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([4, 2, 0], [1, 5, 0, 0], 1, 1, 是, 是, 是)","explanation_zh":"第二批擴展核對=([4, 2, 0], [1, 5, 0, 0], 1, 1, 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196030,"parameters":{"coeffs_f":[4,2,0],"coeffs_g":[1,5,0,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[4,2,0],\"coeffs_g\":[1,5,0,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0031","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[5,3,1],\"coeffs_g\":[1,6,1,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([5, 3, 1], [1, 6, 1, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([5, 3, 1], [1, 6, 1, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196031,"parameters":{"coeffs_f":[5,3,1],"coeffs_g":[1,6,1,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[5,3,1],\"coeffs_g\":[1,6,1,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0032","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[6,1,0],\"coeffs_g\":[1,7,2,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([6, 1, 0], [1, 7, 2, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([6, 1, 0], [1, 7, 2, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196032,"parameters":{"coeffs_f":[6,1,0],"coeffs_g":[1,7,2,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[6,1,0],\"coeffs_g\":[1,7,2,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0033","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[7,2,1],\"coeffs_g\":[1,8,0,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([7, 2, 1], [1, 8, 0, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([7, 2, 1], [1, 8, 0, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196033,"parameters":{"coeffs_f":[7,2,1],"coeffs_g":[1,8,0,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[7,2,1],\"coeffs_g\":[1,8,0,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0034","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[8,3,0],\"coeffs_g\":[1,9,1,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([8, 3, 0], [1, 9, 1, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([8, 3, 0], [1, 9, 1, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196034,"parameters":{"coeffs_f":[8,3,0],"coeffs_g":[1,9,1,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[8,3,0],\"coeffs_g\":[1,9,1,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0035","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[9,1,1],\"coeffs_g\":[1,10,2,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([9, 1, 1], [1, 10, 2, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([9, 1, 1], [1, 10, 2, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196035,"parameters":{"coeffs_f":[9,1,1],"coeffs_g":[1,10,2,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[9,1,1],\"coeffs_g\":[1,10,2,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0036","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[10,2,0],\"coeffs_g\":[1,11,0,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([10, 2, 0], [1, 11, 0, 0], 1, 1, 是, 是, 是)","explanation_zh":"第二批擴展核對=([10, 2, 0], [1, 11, 0, 0], 1, 1, 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196036,"parameters":{"coeffs_f":[10,2,0],"coeffs_g":[1,11,0,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[10,2,0],\"coeffs_g\":[1,11,0,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0037","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[11,3,1],\"coeffs_g\":[1,12,1,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([11, 3, 1], [1, 12, 1, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([11, 3, 1], [1, 12, 1, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196037,"parameters":{"coeffs_f":[11,3,1],"coeffs_g":[1,12,1,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[11,3,1],\"coeffs_g\":[1,12,1,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0038","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[12,1,0],\"coeffs_g\":[1,13,2,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([12, 1, 0], [1, 13, 2, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([12, 1, 0], [1, 13, 2, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196038,"parameters":{"coeffs_f":[12,1,0],"coeffs_g":[1,13,2,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[12,1,0],\"coeffs_g\":[1,13,2,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0039","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[13,2,1],\"coeffs_g\":[1,14,0,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([13, 2, 1], [1, 14, 0, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([13, 2, 1], [1, 14, 0, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196039,"parameters":{"coeffs_f":[13,2,1],"coeffs_g":[1,14,0,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[13,2,1],\"coeffs_g\":[1,14,0,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0040","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[14,3,0],\"coeffs_g\":[1,15,1,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([14, 3, 0], [1, 15, 1, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([14, 3, 0], [1, 15, 1, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196040,"parameters":{"coeffs_f":[14,3,0],"coeffs_g":[1,15,1,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[14,3,0],\"coeffs_g\":[1,15,1,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0041","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[15,1,1],\"coeffs_g\":[1,16,2,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([15, 1, 1], [1, 16, 2, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([15, 1, 1], [1, 16, 2, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196041,"parameters":{"coeffs_f":[15,1,1],"coeffs_g":[1,16,2,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[15,1,1],\"coeffs_g\":[1,16,2,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0042","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[16,2,0],\"coeffs_g\":[1,17,0,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([16, 2, 0], [1, 17, 0, 0], 1, 1, 是, 是, 是)","explanation_zh":"第二批擴展核對=([16, 2, 0], [1, 17, 0, 0], 1, 1, 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196042,"parameters":{"coeffs_f":[16,2,0],"coeffs_g":[1,17,0,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[16,2,0],\"coeffs_g\":[1,17,0,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0043","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[17,3,1],\"coeffs_g\":[1,18,1,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([17, 3, 1], [1, 18, 1, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([17, 3, 1], [1, 18, 1, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196043,"parameters":{"coeffs_f":[17,3,1],"coeffs_g":[1,18,1,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[17,3,1],\"coeffs_g\":[1,18,1,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0044","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[18,1,0],\"coeffs_g\":[1,19,2,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([18, 1, 0], [1, 19, 2, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([18, 1, 0], [1, 19, 2, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196044,"parameters":{"coeffs_f":[18,1,0],"coeffs_g":[1,19,2,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[18,1,0],\"coeffs_g\":[1,19,2,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0045","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[19,2,1],\"coeffs_g\":[1,20,0,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([19, 2, 1], [1, 20, 0, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([19, 2, 1], [1, 20, 0, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196045,"parameters":{"coeffs_f":[19,2,1],"coeffs_g":[1,20,0,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[19,2,1],\"coeffs_g\":[1,20,0,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0046","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[20,3,0],\"coeffs_g\":[1,21,1,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([20, 3, 0], [1, 21, 1, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([20, 3, 0], [1, 21, 1, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196046,"parameters":{"coeffs_f":[20,3,0],"coeffs_g":[1,21,1,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[20,3,0],\"coeffs_g\":[1,21,1,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0047","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[21,1,1],\"coeffs_g\":[1,22,2,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([21, 1, 1], [1, 22, 2, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([21, 1, 1], [1, 22, 2, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196047,"parameters":{"coeffs_f":[21,1,1],"coeffs_g":[1,22,2,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[21,1,1],\"coeffs_g\":[1,22,2,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0048","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[22,2,0],\"coeffs_g\":[1,23,0,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([22, 2, 0], [1, 23, 0, 0], 1, 1, 是, 是, 是)","explanation_zh":"第二批擴展核對=([22, 2, 0], [1, 23, 0, 0], 1, 1, 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196048,"parameters":{"coeffs_f":[22,2,0],"coeffs_g":[1,23,0,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[22,2,0],\"coeffs_g\":[1,23,0,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0049","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[23,3,1],\"coeffs_g\":[1,24,1,1]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([23, 3, 1], [1, 24, 1, 1], 2, 3, 是, 否, 否)","explanation_zh":"第二批擴展核對=([23, 3, 1], [1, 24, 1, 1], 2, 3, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196049,"parameters":{"coeffs_f":[23,3,1],"coeffs_g":[1,24,1,1],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[23,3,1],\"coeffs_g\":[1,24,1,1]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0050","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-polynomial-degree；資料={\"coeffs_f\":[24,1,0],\"coeffs_g\":[1,25,2,0]}。請依 [coeffs_f,coeffs_g,degree_f,degree_g,bigO,bigOmega,theta] 欄序回答。","answer":{"kind":"expression","value":"([24, 1, 0], [1, 25, 2, 0], 1, 2, 是, 否, 否)","explanation_zh":"第二批擴展核對=([24, 1, 0], [1, 25, 2, 0], 1, 2, 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-polynomial-degree","seed":202610196050,"parameters":{"coeffs_f":[24,1,0],"coeffs_g":[1,25,2,0],"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-polynomial-degree","semantic_template":"qf-ext19-asymptotic-polynomial-degree/{\"coeffs_f\":[24,1,0],\"coeffs_g\":[1,25,2,0]}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0051","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":0,\"b\":1}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 1, 0, 是, 0n+1≤1(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(0, 1, 1, 0, 是, 0n+1≤1(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196051,"parameters":{"a":0,"b":1,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":0,\"b\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0052","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":1,\"b\":3}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 4, 0, 是, 1n+3≤4(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(1, 3, 4, 0, 是, 1n+3≤4(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196052,"parameters":{"a":1,"b":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":1,\"b\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0053","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":2,\"b\":5}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 7, 0, 是, 2n+5≤7(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(2, 5, 7, 0, 是, 2n+5≤7(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196053,"parameters":{"a":2,"b":5,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":2,\"b\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0054","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":3,\"b\":7}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, 10, 0, 是, 3n+7≤10(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(3, 7, 10, 0, 是, 3n+7≤10(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196054,"parameters":{"a":3,"b":7,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":3,\"b\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0055","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":4,\"b\":9}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(4, 9, 13, 0, 是, 4n+9≤13(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(4, 9, 13, 0, 是, 4n+9≤13(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196055,"parameters":{"a":4,"b":9,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":4,\"b\":9}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0056","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":5,\"b\":11}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(5, 11, 16, 0, 是, 5n+11≤16(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(5, 11, 16, 0, 是, 5n+11≤16(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196056,"parameters":{"a":5,"b":11,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":5,\"b\":11}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0057","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":6,\"b\":13}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(6, 13, 19, 0, 是, 6n+13≤19(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(6, 13, 19, 0, 是, 6n+13≤19(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196057,"parameters":{"a":6,"b":13,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":6,\"b\":13}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0058","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":7,\"b\":15}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(7, 15, 22, 0, 是, 7n+15≤22(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(7, 15, 22, 0, 是, 7n+15≤22(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196058,"parameters":{"a":7,"b":15,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":7,\"b\":15}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0059","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":8,\"b\":17}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(8, 17, 25, 0, 是, 8n+17≤25(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(8, 17, 25, 0, 是, 8n+17≤25(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196059,"parameters":{"a":8,"b":17,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":8,\"b\":17}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0060","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":9,\"b\":19}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(9, 19, 28, 0, 是, 9n+19≤28(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(9, 19, 28, 0, 是, 9n+19≤28(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196060,"parameters":{"a":9,"b":19,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":9,\"b\":19}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0061","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":10,\"b\":21}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(10, 21, 31, 0, 是, 10n+21≤31(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(10, 21, 31, 0, 是, 10n+21≤31(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196061,"parameters":{"a":10,"b":21,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":10,\"b\":21}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0062","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":11,\"b\":23}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(11, 23, 34, 0, 是, 11n+23≤34(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(11, 23, 34, 0, 是, 11n+23≤34(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196062,"parameters":{"a":11,"b":23,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":11,\"b\":23}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0063","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":12,\"b\":25}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(12, 25, 37, 0, 是, 12n+25≤37(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(12, 25, 37, 0, 是, 12n+25≤37(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196063,"parameters":{"a":12,"b":25,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":12,\"b\":25}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0064","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":13,\"b\":27}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(13, 27, 40, 0, 是, 13n+27≤40(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(13, 27, 40, 0, 是, 13n+27≤40(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196064,"parameters":{"a":13,"b":27,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":13,\"b\":27}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0065","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":14,\"b\":29}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(14, 29, 43, 0, 是, 14n+29≤43(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(14, 29, 43, 0, 是, 14n+29≤43(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196065,"parameters":{"a":14,"b":29,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":14,\"b\":29}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0066","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":15,\"b\":31}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(15, 31, 46, 0, 是, 15n+31≤46(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(15, 31, 46, 0, 是, 15n+31≤46(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196066,"parameters":{"a":15,"b":31,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":15,\"b\":31}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0067","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":16,\"b\":33}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(16, 33, 49, 0, 是, 16n+33≤49(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(16, 33, 49, 0, 是, 16n+33≤49(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196067,"parameters":{"a":16,"b":33,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":16,\"b\":33}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0068","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":17,\"b\":35}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(17, 35, 52, 0, 是, 17n+35≤52(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(17, 35, 52, 0, 是, 17n+35≤52(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196068,"parameters":{"a":17,"b":35,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":17,\"b\":35}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0069","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":18,\"b\":37}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(18, 37, 55, 0, 是, 18n+37≤55(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(18, 37, 55, 0, 是, 18n+37≤55(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196069,"parameters":{"a":18,"b":37,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":18,\"b\":37}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0070","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":19,\"b\":39}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(19, 39, 58, 0, 是, 19n+39≤58(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(19, 39, 58, 0, 是, 19n+39≤58(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196070,"parameters":{"a":19,"b":39,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":19,\"b\":39}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0071","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":20,\"b\":41}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(20, 41, 61, 0, 是, 20n+41≤61(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(20, 41, 61, 0, 是, 20n+41≤61(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196071,"parameters":{"a":20,"b":41,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":20,\"b\":41}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0072","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":21,\"b\":43}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(21, 43, 64, 0, 是, 21n+43≤64(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(21, 43, 64, 0, 是, 21n+43≤64(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196072,"parameters":{"a":21,"b":43,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":21,\"b\":43}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0073","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":22,\"b\":45}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(22, 45, 67, 0, 是, 22n+45≤67(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(22, 45, 67, 0, 是, 22n+45≤67(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196073,"parameters":{"a":22,"b":45,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":22,\"b\":45}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0074","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":23,\"b\":47}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(23, 47, 70, 0, 是, 23n+47≤70(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(23, 47, 70, 0, 是, 23n+47≤70(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196074,"parameters":{"a":23,"b":47,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":23,\"b\":47}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0075","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-linear-witness；資料={\"a\":24,\"b\":49}。請依 [a,b,C,N,valid,witness_inequality] 欄序回答。","answer":{"kind":"expression","value":"(24, 49, 73, 0, 是, 24n+49≤73(n+1) 對所有 n≥0)","explanation_zh":"第二批擴展核對=(24, 49, 73, 0, 是, 24n+49≤73(n+1) 對所有 n≥0)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-linear-witness","seed":202610196075,"parameters":{"a":24,"b":49,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-linear-witness","semantic_template":"qf-ext19-asymptotic-linear-witness/{\"a\":24,\"b\":49}"}},"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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0076","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":0,\"q\":1,\"bound\":0}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 0, [[0, 1, 0]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(0, 1, 0, [[0, 1, 0]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196076,"parameters":{"p":0,"q":1,"bound":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":0,\"p\":0,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0077","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":1,\"q\":3,\"bound\":1}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 1, [[0, 0, 0], [1, 1, 1]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(1, 3, 1, [[0, 0, 0], [1, 1, 1]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196077,"parameters":{"p":1,"q":3,"bound":1,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":1,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0078","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":2,\"q\":5,\"bound\":2}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 2, [[0, 0, 0], [1, 1, 1], [2, 4, 32]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(2, 5, 2, [[0, 0, 0], [1, 1, 1], [2, 4, 32]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196078,"parameters":{"p":2,"q":5,"bound":2,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":2,\"p\":2,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0079","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":3,\"q\":1,\"bound\":3}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 3, [[0, 0, 0], [1, 1, 1], [2, 8, 2], [3, 27, 3]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(3, 1, 3, [[0, 0, 0], [1, 1, 1], [2, 8, 2], [3, 27, 3]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196079,"parameters":{"p":3,"q":1,"bound":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":3,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0080","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":4,\"q\":3,\"bound\":4}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 4, [[0, 0, 0], [1, 1, 1], [2, 16, 8], [3, 81, 27], [4, 256, 64]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(4, 3, 4, [[0, 0, 0], [1, 1, 1], [2, 16, 8], [3, 81, 27], [4, 256, 64]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196080,"parameters":{"p":4,"q":3,"bound":4,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":4,\"p\":4,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0081","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":5,\"q\":5,\"bound\":5}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 5, [[0, 0, 0], [1, 1, 1], [2, 32, 32], [3, 243, 243], [4, 1024, 1024], [5, 3125, 3125]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(5, 5, 5, [[0, 0, 0], [1, 1, 1], [2, 32, 32], [3, 243, 243], [4, 1024, 1024], [5, 3125, 3125]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196081,"parameters":{"p":5,"q":5,"bound":5,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":5,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0082","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":0,\"q\":1,\"bound\":6}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 6, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3], [4, 1, 4], [5, 1, 5], [6, 1, 6]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(0, 1, 6, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3], [4, 1, 4], [5, 1, 5], [6, 1, 6]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196082,"parameters":{"p":0,"q":1,"bound":6,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":6,\"p\":0,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0083","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":1,\"q\":3,\"bound\":0}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 0, [[0, 0, 0]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(1, 3, 0, [[0, 0, 0]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196083,"parameters":{"p":1,"q":3,"bound":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":0,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0084","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":2,\"q\":5,\"bound\":1}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 1, [[0, 0, 0], [1, 1, 1]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(2, 5, 1, [[0, 0, 0], [1, 1, 1]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196084,"parameters":{"p":2,"q":5,"bound":1,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":1,\"p\":2,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0085","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":3,\"q\":1,\"bound\":2}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 2, [[0, 0, 0], [1, 1, 1], [2, 8, 2]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(3, 1, 2, [[0, 0, 0], [1, 1, 1], [2, 8, 2]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196085,"parameters":{"p":3,"q":1,"bound":2,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":2,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0086","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":4,\"q\":3,\"bound\":3}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 3, [[0, 0, 0], [1, 1, 1], [2, 16, 8], [3, 81, 27]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(4, 3, 3, [[0, 0, 0], [1, 1, 1], [2, 16, 8], [3, 81, 27]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196086,"parameters":{"p":4,"q":3,"bound":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":3,\"p\":4,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0087","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":5,\"q\":5,\"bound\":4}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 4, [[0, 0, 0], [1, 1, 1], [2, 32, 32], [3, 243, 243], [4, 1024, 1024]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(5, 5, 4, [[0, 0, 0], [1, 1, 1], [2, 32, 32], [3, 243, 243], [4, 1024, 1024]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196087,"parameters":{"p":5,"q":5,"bound":4,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":4,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0088","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":0,\"q\":1,\"bound\":5}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 5, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3], [4, 1, 4], [5, 1, 5]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(0, 1, 5, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3], [4, 1, 4], [5, 1, 5]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196088,"parameters":{"p":0,"q":1,"bound":5,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":5,\"p\":0,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0089","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":1,\"q\":3,\"bound\":6}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 6, [[0, 0, 0], [1, 1, 1], [2, 2, 8], [3, 3, 27], [4, 4, 64], [5, 5, 125], [6, 6, 216]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(1, 3, 6, [[0, 0, 0], [1, 1, 1], [2, 2, 8], [3, 3, 27], [4, 4, 64], [5, 5, 125], [6, 6, 216]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196089,"parameters":{"p":1,"q":3,"bound":6,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":6,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0090","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":2,\"q\":5,\"bound\":0}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 0, [[0, 0, 0]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(2, 5, 0, [[0, 0, 0]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196090,"parameters":{"p":2,"q":5,"bound":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":0,\"p\":2,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0091","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":3,\"q\":1,\"bound\":1}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 1, [[0, 0, 0], [1, 1, 1]], 是, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(3, 1, 1, [[0, 0, 0], [1, 1, 1]], 是, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196091,"parameters":{"p":3,"q":1,"bound":1,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":1,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0092","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":4,\"q\":3,\"bound\":2}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 2, [[0, 0, 0], [1, 1, 1], [2, 16, 8]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(4, 3, 2, [[0, 0, 0], [1, 1, 1], [2, 16, 8]], 否, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196092,"parameters":{"p":4,"q":3,"bound":2,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":2,\"p\":4,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0093","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":5,\"q\":5,\"bound\":3}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 3, [[0, 0, 0], [1, 1, 1], [2, 32, 32], [3, 243, 243]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(5, 5, 3, [[0, 0, 0], [1, 1, 1], [2, 32, 32], [3, 243, 243]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196093,"parameters":{"p":5,"q":5,"bound":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":3,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0094","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":0,\"q\":1,\"bound\":4}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 4, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3], [4, 1, 4]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(0, 1, 4, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3], [4, 1, 4]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196094,"parameters":{"p":0,"q":1,"bound":4,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":4,\"p\":0,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0095","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":1,\"q\":3,\"bound\":5}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 5, [[0, 0, 0], [1, 1, 1], [2, 2, 8], [3, 3, 27], [4, 4, 64], [5, 5, 125]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(1, 3, 5, [[0, 0, 0], [1, 1, 1], [2, 2, 8], [3, 3, 27], [4, 4, 64], [5, 5, 125]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196095,"parameters":{"p":1,"q":3,"bound":5,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":5,\"p\":1,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0096","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":2,\"q\":5,\"bound\":6}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 6, [[0, 0, 0], [1, 1, 1], [2, 4, 32], [3, 9, 243], [4, 16, 1024], [5, 25, 3125], [6, 36, 7776]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(2, 5, 6, [[0, 0, 0], [1, 1, 1], [2, 4, 32], [3, 9, 243], [4, 16, 1024], [5, 25, 3125], [6, 36, 7776]], 是, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196096,"parameters":{"p":2,"q":5,"bound":6,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":6,\"p\":2,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0097","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":3,\"q\":1,\"bound\":0}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 0, [[0, 0, 0]], 是, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(3, 1, 0, [[0, 0, 0]], 是, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196097,"parameters":{"p":3,"q":1,"bound":0,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":0,\"p\":3,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0098","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":4,\"q\":3,\"bound\":1}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 1, [[0, 0, 0], [1, 1, 1]], 是, [否, 是, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(4, 3, 1, [[0, 0, 0], [1, 1, 1]], 是, [否, 是, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196098,"parameters":{"p":4,"q":3,"bound":1,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":1,\"p\":4,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0099","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":5,\"q\":5,\"bound\":2}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 2, [[0, 0, 0], [1, 1, 1], [2, 32, 32]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(5, 5, 2, [[0, 0, 0], [1, 1, 1], [2, 32, 32]], 是, [是, 是, 是], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196099,"parameters":{"p":5,"q":5,"bound":2,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":2,\"p\":5,\"q\":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、一般程式證明、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-20261019-r06-asymptotic-resource-bound-0100","batch_id":"batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations","language":"zh-Hant","source_mko_ids":["mko-asymptotic-resource-bound"],"title_zh":"漸近資源界","stem_zh":"明示非負函數族。操作=asymptotic-benchmark-insufficiency；資料={\"p\":0,\"q\":1,\"bound\":3}。請依 [p,q,bound,samples,sample_le,asymptotic_class,samples_sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 3, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)","explanation_zh":"第二批擴展核對=(0, 1, 3, [[0, 1, 0], [1, 1, 1], [2, 1, 2], [3, 1, 3]], 否, [是, 否, 否], 否, 有限benchmark不足以證全尾段)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；全尾段量化；有限benchmark不證Big-O或Theta；成本模型必須固定。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["漸近資源界"]},"variant":{"family_id":"qf-ext19-asymptotic-benchmark-insufficiency","seed":202610196100,"parameters":{"p":0,"q":1,"bound":3,"domain":"Nat_nonnegative_asymptotics","operation":"asymptotic-benchmark-insufficiency","semantic_template":"qf-ext19-asymptotic-benchmark-insufficiency/{\"bound\":3,\"p\":0,\"q\":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、一般程式證明、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"}}