{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0001","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=0x^0，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1]","explanation_zh":"零常數原函數係數=[0/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086001,"parameters":{"c":0,"n":0,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"zero_primitive\"],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0002","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-2x^1，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, -1/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, -1/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086002,"parameters":{"c":-2,"n":1,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-2\",1],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0003","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=3x^2，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 1/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 1/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086003,"parameters":{"c":3,"n":2,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"3\",2],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0004","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-4x^3，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, -1/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, -1/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086004,"parameters":{"c":-4,"n":3,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-4\",3],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0005","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=5x^4，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 1/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 1/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086005,"parameters":{"c":5,"n":4,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"5\",4],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0006","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-6x^5，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -1/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -1/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086006,"parameters":{"c":-6,"n":5,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-6\",5],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0007","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=7x^0，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 7/1]","explanation_zh":"零常數原函數係數=[0/1, 7/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086007,"parameters":{"c":7,"n":0,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"7\",0],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0008","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-8x^1，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, -4/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, -4/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086008,"parameters":{"c":-8,"n":1,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-8\",1],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0009","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=9x^2，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 3/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 3/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086009,"parameters":{"c":9,"n":2,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"9\",2],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0010","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-10x^3，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, -5/2]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, -5/2]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086010,"parameters":{"c":-10,"n":3,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-10\",3],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0011","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=11x^4，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 11/5]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 11/5]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086011,"parameters":{"c":11,"n":4,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"11\",4],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0012","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-12x^5，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -2/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -2/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086012,"parameters":{"c":-12,"n":5,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-12\",5],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0013","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=13x^0，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 13/1]","explanation_zh":"零常數原函數係數=[0/1, 13/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086013,"parameters":{"c":13,"n":0,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"13\",0],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0014","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-14x^1，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, -7/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, -7/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086014,"parameters":{"c":-14,"n":1,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-14\",1],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0015","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=15x^2，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 5/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 5/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086015,"parameters":{"c":15,"n":2,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"15\",2],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0016","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-16x^3，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, -4/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, -4/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086016,"parameters":{"c":-16,"n":3,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-16\",3],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0017","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=17x^4，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 17/5]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 17/5]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086017,"parameters":{"c":17,"n":4,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"17\",4],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0018","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-18x^5，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -3/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -3/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086018,"parameters":{"c":-18,"n":5,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-18\",5],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0019","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=19x^0，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 19/1]","explanation_zh":"零常數原函數係數=[0/1, 19/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086019,"parameters":{"c":19,"n":0,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"19\",0],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0020","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-20x^1，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, -10/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, -10/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086020,"parameters":{"c":-20,"n":1,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-20\",1],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0021","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=21x^2，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 7/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 7/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086021,"parameters":{"c":21,"n":2,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"21\",2],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0022","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-22x^3，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, -11/2]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, -11/2]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086022,"parameters":{"c":-22,"n":3,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-22\",3],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0023","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=23x^4，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 23/5]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 23/5]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086023,"parameters":{"c":23,"n":4,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"23\",4],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0024","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-24x^5，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -4/1]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 0/1, 0/1, 0/1, 0/1, -4/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086024,"parameters":{"c":-24,"n":5,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"-24\",5],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0025","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"單項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=25x^0，n為0至5。求常數項固定零的原函數升冪有理係數，整數也保留 /1。","answer":{"kind":"expression","value":"[0/1, 25/1]","explanation_zh":"零常數原函數係數=[0/1, 25/1]。係數除以次方加一；n=5 時可有七個係數，零多項式規約為 [0/1]。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["單項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-monomial","seed":202610086025,"parameters":{"c":25,"n":0,"operation":"monomial_primitive","domain":"reals","semantic_template":"qf-antiderivative-monomial/{\"inputs\":[\"25\",0],\"operation\":\"monomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0026","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[0]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1]","explanation_zh":"零常數原函數係數=[0/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086026,"parameters":{"f":[0],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"0\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0027","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 3/1]","explanation_zh":"零常數原函數係數=[0/1, 3/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086027,"parameters":{"f":[3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0028","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-10, 3, 1, 3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -10/1, 3/2, 1/3, 3/4]","explanation_zh":"零常數原函數係數=[0/1, -10/1, 3/2, 1/3, 3/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086028,"parameters":{"f":[-10,3,1,3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-10\",\"3\",\"1\",\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0029","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-9, 4, -1, 4]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -9/1, 2/1, -1/3, 1/1]","explanation_zh":"零常數原函數係數=[0/1, -9/1, 2/1, -1/3, 1/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086029,"parameters":{"f":[-9,4,-1,4],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-9\",\"4\",\"-1\",\"4\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0030","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-8, 5, 0, 1]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -8/1, 5/2, 0/1, 1/4]","explanation_zh":"零常數原函數係數=[0/1, -8/1, 5/2, 0/1, 1/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086030,"parameters":{"f":[-8,5,0,1],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-8\",\"5\",\"0\",\"1\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0031","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-7, 6, 1, 2]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -7/1, 3/1, 1/3, 1/2]","explanation_zh":"零常數原函數係數=[0/1, -7/1, 3/1, 1/3, 1/2]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086031,"parameters":{"f":[-7,6,1,2],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-7\",\"6\",\"1\",\"2\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0032","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-6, 7, -1, 3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -6/1, 7/2, -1/3, 3/4]","explanation_zh":"零常數原函數係數=[0/1, -6/1, 7/2, -1/3, 3/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086032,"parameters":{"f":[-6,7,-1,3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-6\",\"7\",\"-1\",\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0033","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-5, 8, 0, 4]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -5/1, 4/1, 0/1, 1/1]","explanation_zh":"零常數原函數係數=[0/1, -5/1, 4/1, 0/1, 1/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086033,"parameters":{"f":[-5,8,0,4],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-5\",\"8\",\"0\",\"4\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0034","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-4, 9, 1, 1]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -4/1, 9/2, 1/3, 1/4]","explanation_zh":"零常數原函數係數=[0/1, -4/1, 9/2, 1/3, 1/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086034,"parameters":{"f":[-4,9,1,1],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-4\",\"9\",\"1\",\"1\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0035","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-3, 10, -1, 2]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -3/1, 5/1, -1/3, 1/2]","explanation_zh":"零常數原函數係數=[0/1, -3/1, 5/1, -1/3, 1/2]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086035,"parameters":{"f":[-3,10,-1,2],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-3\",\"10\",\"-1\",\"2\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0036","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-2, 11, 0, 3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -2/1, 11/2, 0/1, 3/4]","explanation_zh":"零常數原函數係數=[0/1, -2/1, 11/2, 0/1, 3/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086036,"parameters":{"f":[-2,11,0,3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-2\",\"11\",\"0\",\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0037","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-1, 12, 1, 4]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, -1/1, 6/1, 1/3, 1/1]","explanation_zh":"零常數原函數係數=[0/1, -1/1, 6/1, 1/3, 1/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086037,"parameters":{"f":[-1,12,1,4],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"-1\",\"12\",\"1\",\"4\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0038","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[0, 13, -1, 1]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 0/1, 13/2, -1/3, 1/4]","explanation_zh":"零常數原函數係數=[0/1, 0/1, 13/2, -1/3, 1/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086038,"parameters":{"f":[0,13,-1,1],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"0\",\"13\",\"-1\",\"1\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0039","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[1, 14, 0, 2]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 1/1, 7/1, 0/1, 1/2]","explanation_zh":"零常數原函數係數=[0/1, 1/1, 7/1, 0/1, 1/2]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086039,"parameters":{"f":[1,14,0,2],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"1\",\"14\",\"0\",\"2\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0040","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[2, 15, 1, 3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 2/1, 15/2, 1/3, 3/4]","explanation_zh":"零常數原函數係數=[0/1, 2/1, 15/2, 1/3, 3/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086040,"parameters":{"f":[2,15,1,3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"2\",\"15\",\"1\",\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0041","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[3, 16, -1, 4]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 3/1, 8/1, -1/3, 1/1]","explanation_zh":"零常數原函數係數=[0/1, 3/1, 8/1, -1/3, 1/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086041,"parameters":{"f":[3,16,-1,4],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"3\",\"16\",\"-1\",\"4\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0042","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[4, 17, 0, 1]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 4/1, 17/2, 0/1, 1/4]","explanation_zh":"零常數原函數係數=[0/1, 4/1, 17/2, 0/1, 1/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086042,"parameters":{"f":[4,17,0,1],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"4\",\"17\",\"0\",\"1\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0043","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[5, 18, 1, 2]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 5/1, 9/1, 1/3, 1/2]","explanation_zh":"零常數原函數係數=[0/1, 5/1, 9/1, 1/3, 1/2]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086043,"parameters":{"f":[5,18,1,2],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"5\",\"18\",\"1\",\"2\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0044","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[6, 19, -1, 3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 6/1, 19/2, -1/3, 3/4]","explanation_zh":"零常數原函數係數=[0/1, 6/1, 19/2, -1/3, 3/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086044,"parameters":{"f":[6,19,-1,3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"6\",\"19\",\"-1\",\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0045","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[7, 20, 0, 4]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 7/1, 10/1, 0/1, 1/1]","explanation_zh":"零常數原函數係數=[0/1, 7/1, 10/1, 0/1, 1/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086045,"parameters":{"f":[7,20,0,4],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"7\",\"20\",\"0\",\"4\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0046","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[8, 21, 1, 1]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 8/1, 21/2, 1/3, 1/4]","explanation_zh":"零常數原函數係數=[0/1, 8/1, 21/2, 1/3, 1/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086046,"parameters":{"f":[8,21,1,1],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"8\",\"21\",\"1\",\"1\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0047","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[9, 22, -1, 2]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 9/1, 11/1, -1/3, 1/2]","explanation_zh":"零常數原函數係數=[0/1, 9/1, 11/1, -1/3, 1/2]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086047,"parameters":{"f":[9,22,-1,2],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"9\",\"22\",\"-1\",\"2\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0048","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[10, 23, 0, 3]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 10/1, 23/2, 0/1, 3/4]","explanation_zh":"零常數原函數係數=[0/1, 10/1, 23/2, 0/1, 3/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086048,"parameters":{"f":[10,23,0,3],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"10\",\"23\",\"0\",\"3\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0049","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[11, 24, 1, 4]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 11/1, 12/1, 1/3, 1/1]","explanation_zh":"零常數原函數係數=[0/1, 11/1, 12/1, 1/3, 1/1]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086049,"parameters":{"f":[11,24,1,4],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"11\",\"24\",\"1\",\"4\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0050","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"多項式的零常數原函數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[12, 25, -1, 1]。求常數項固定零的原函數升冪有理係數，採最簡正分母。","answer":{"kind":"expression","value":"[0/1, 12/1, 25/2, -1/3, 1/4]","explanation_zh":"零常數原函數係數=[0/1, 12/1, 25/2, -1/3, 1/4]。逐係數積成指定的 canonical polynomial primitive，不聲稱一般反導函數唯一性已被有限資料證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多項式的零常數原函數"]},"variant":{"family_id":"qf-antiderivative-polynomial","seed":202610086050,"parameters":{"f":[12,25,-1,1],"operation":"polynomial_primitive","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-polynomial/{\"inputs\":[\"12\",\"25\",\"-1\",\"1\"],\"operation\":\"polynomial_primitive\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0051","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[0]；候選 F 的升冪有理係數為 [[7,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[0/1]；目標係數=[0/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086051,"parameters":{"f":[0],"F":[[7,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"0\"],[]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0052","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-11, 2, 0, 2]；候選 F 的升冪有理係數為 [[-12,1],[-11,1],[1,1],[0,1],[3,2]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[-11/1, 2/1, 0/1, 6/1]；目標係數=[-11/1, 2/1, 0/1, 2/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086052,"parameters":{"f":[-11,2,0,2],"F":[[-12,1],[-11,1],[1,1],[0,1],[3,2]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-11\",\"2\",\"0\",\"2\"],[\"-11/1\",\"1/1\",\"0/1\",\"3/2\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0053","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-10, 3, 1, 3]；候選 F 的升冪有理係數為 [[-11,1],[-10,1],[3,2],[1,3],[3,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[-10/1, 3/1, 1/1, 3/1]；目標係數=[-10/1, 3/1, 1/1, 3/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086053,"parameters":{"f":[-10,3,1,3],"F":[[-11,1],[-10,1],[3,2],[1,3],[3,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-10\",\"3\",\"1\",\"3\"],[\"-10/1\",\"3/2\",\"1/3\",\"3/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0054","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-9, 4, -1, 4]；候選 F 的升冪有理係數為 [[-10,1],[-9,1],[2,1],[-1,3],[2,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[-9/1, 4/1, -1/1, 8/1]；目標係數=[-9/1, 4/1, -1/1, 4/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086054,"parameters":{"f":[-9,4,-1,4],"F":[[-10,1],[-9,1],[2,1],[-1,3],[2,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-9\",\"4\",\"-1\",\"4\"],[\"-9/1\",\"2/1\",\"-1/3\",\"2/1\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0055","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-8, 5, 0, 1]；候選 F 的升冪有理係數為 [[-9,1],[-8,1],[5,2],[0,1],[1,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[-8/1, 5/1, 0/1, 1/1]；目標係數=[-8/1, 5/1, 0/1, 1/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086055,"parameters":{"f":[-8,5,0,1],"F":[[-9,1],[-8,1],[5,2],[0,1],[1,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-8\",\"5\",\"0\",\"1\"],[\"-8/1\",\"5/2\",\"0/1\",\"1/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0056","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-7, 6, 1, 2]；候選 F 的升冪有理係數為 [[-8,1],[-7,1],[3,1],[1,3],[3,2]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[-7/1, 6/1, 1/1, 6/1]；目標係數=[-7/1, 6/1, 1/1, 2/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086056,"parameters":{"f":[-7,6,1,2],"F":[[-8,1],[-7,1],[3,1],[1,3],[3,2]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-7\",\"6\",\"1\",\"2\"],[\"-7/1\",\"3/1\",\"1/3\",\"3/2\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0057","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-6, 7, -1, 3]；候選 F 的升冪有理係數為 [[-7,1],[-6,1],[7,2],[-1,3],[3,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[-6/1, 7/1, -1/1, 3/1]；目標係數=[-6/1, 7/1, -1/1, 3/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086057,"parameters":{"f":[-6,7,-1,3],"F":[[-7,1],[-6,1],[7,2],[-1,3],[3,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-6\",\"7\",\"-1\",\"3\"],[\"-6/1\",\"7/2\",\"-1/3\",\"3/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0058","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-5, 8, 0, 4]；候選 F 的升冪有理係數為 [[-6,1],[-5,1],[4,1],[0,1],[2,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[-5/1, 8/1, 0/1, 8/1]；目標係數=[-5/1, 8/1, 0/1, 4/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086058,"parameters":{"f":[-5,8,0,4],"F":[[-6,1],[-5,1],[4,1],[0,1],[2,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-5\",\"8\",\"0\",\"4\"],[\"-5/1\",\"4/1\",\"0/1\",\"2/1\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0059","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-4, 9, 1, 1]；候選 F 的升冪有理係數為 [[-5,1],[-4,1],[9,2],[1,3],[1,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[-4/1, 9/1, 1/1, 1/1]；目標係數=[-4/1, 9/1, 1/1, 1/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086059,"parameters":{"f":[-4,9,1,1],"F":[[-5,1],[-4,1],[9,2],[1,3],[1,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-4\",\"9\",\"1\",\"1\"],[\"-4/1\",\"9/2\",\"1/3\",\"1/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0060","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-3, 10, -1, 2]；候選 F 的升冪有理係數為 [[-4,1],[-3,1],[5,1],[-1,3],[3,2]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[-3/1, 10/1, -1/1, 6/1]；目標係數=[-3/1, 10/1, -1/1, 2/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086060,"parameters":{"f":[-3,10,-1,2],"F":[[-4,1],[-3,1],[5,1],[-1,3],[3,2]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-3\",\"10\",\"-1\",\"2\"],[\"-3/1\",\"5/1\",\"-1/3\",\"3/2\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0061","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-2, 11, 0, 3]；候選 F 的升冪有理係數為 [[-3,1],[-2,1],[11,2],[0,1],[3,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[-2/1, 11/1, 0/1, 3/1]；目標係數=[-2/1, 11/1, 0/1, 3/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086061,"parameters":{"f":[-2,11,0,3],"F":[[-3,1],[-2,1],[11,2],[0,1],[3,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-2\",\"11\",\"0\",\"3\"],[\"-2/1\",\"11/2\",\"0/1\",\"3/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0062","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-1, 12, 1, 4]；候選 F 的升冪有理係數為 [[-2,1],[-1,1],[6,1],[1,3],[2,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[-1/1, 12/1, 1/1, 8/1]；目標係數=[-1/1, 12/1, 1/1, 4/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086062,"parameters":{"f":[-1,12,1,4],"F":[[-2,1],[-1,1],[6,1],[1,3],[2,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"-1\",\"12\",\"1\",\"4\"],[\"-1/1\",\"6/1\",\"1/3\",\"2/1\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0063","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[0, 13, -1, 1]；候選 F 的升冪有理係數為 [[-1,1],[0,1],[13,2],[-1,3],[1,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[0/1, 13/1, -1/1, 1/1]；目標係數=[0/1, 13/1, -1/1, 1/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086063,"parameters":{"f":[0,13,-1,1],"F":[[-1,1],[0,1],[13,2],[-1,3],[1,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"0\",\"13\",\"-1\",\"1\"],[\"0/1\",\"13/2\",\"-1/3\",\"1/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0064","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[1, 14, 0, 2]；候選 F 的升冪有理係數為 [[0,1],[1,1],[7,1],[0,1],[3,2]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[1/1, 14/1, 0/1, 6/1]；目標係數=[1/1, 14/1, 0/1, 2/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086064,"parameters":{"f":[1,14,0,2],"F":[[0,1],[1,1],[7,1],[0,1],[3,2]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"1\",\"14\",\"0\",\"2\"],[\"1/1\",\"7/1\",\"0/1\",\"3/2\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0065","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[2, 15, 1, 3]；候選 F 的升冪有理係數為 [[1,1],[2,1],[15,2],[1,3],[3,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[2/1, 15/1, 1/1, 3/1]；目標係數=[2/1, 15/1, 1/1, 3/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086065,"parameters":{"f":[2,15,1,3],"F":[[1,1],[2,1],[15,2],[1,3],[3,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"2\",\"15\",\"1\",\"3\"],[\"2/1\",\"15/2\",\"1/3\",\"3/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0066","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[3, 16, -1, 4]；候選 F 的升冪有理係數為 [[2,1],[3,1],[8,1],[-1,3],[2,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[3/1, 16/1, -1/1, 8/1]；目標係數=[3/1, 16/1, -1/1, 4/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086066,"parameters":{"f":[3,16,-1,4],"F":[[2,1],[3,1],[8,1],[-1,3],[2,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"3\",\"16\",\"-1\",\"4\"],[\"3/1\",\"8/1\",\"-1/3\",\"2/1\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0067","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[4, 17, 0, 1]；候選 F 的升冪有理係數為 [[3,1],[4,1],[17,2],[0,1],[1,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[4/1, 17/1, 0/1, 1/1]；目標係數=[4/1, 17/1, 0/1, 1/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086067,"parameters":{"f":[4,17,0,1],"F":[[3,1],[4,1],[17,2],[0,1],[1,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"4\",\"17\",\"0\",\"1\"],[\"4/1\",\"17/2\",\"0/1\",\"1/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0068","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[5, 18, 1, 2]；候選 F 的升冪有理係數為 [[4,1],[5,1],[9,1],[1,3],[3,2]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[5/1, 18/1, 1/1, 6/1]；目標係數=[5/1, 18/1, 1/1, 2/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086068,"parameters":{"f":[5,18,1,2],"F":[[4,1],[5,1],[9,1],[1,3],[3,2]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"5\",\"18\",\"1\",\"2\"],[\"5/1\",\"9/1\",\"1/3\",\"3/2\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0069","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[6, 19, -1, 3]；候選 F 的升冪有理係數為 [[5,1],[6,1],[19,2],[-1,3],[3,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[6/1, 19/1, -1/1, 3/1]；目標係數=[6/1, 19/1, -1/1, 3/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086069,"parameters":{"f":[6,19,-1,3],"F":[[5,1],[6,1],[19,2],[-1,3],[3,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"6\",\"19\",\"-1\",\"3\"],[\"6/1\",\"19/2\",\"-1/3\",\"3/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0070","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[7, 20, 0, 4]；候選 F 的升冪有理係數為 [[6,1],[7,1],[10,1],[0,1],[2,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[7/1, 20/1, 0/1, 8/1]；目標係數=[7/1, 20/1, 0/1, 4/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086070,"parameters":{"f":[7,20,0,4],"F":[[6,1],[7,1],[10,1],[0,1],[2,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"7\",\"20\",\"0\",\"4\"],[\"7/1\",\"10/1\",\"0/1\",\"2/1\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0071","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[8, 21, 1, 1]；候選 F 的升冪有理係數為 [[7,1],[8,1],[21,2],[1,3],[1,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[8/1, 21/1, 1/1, 1/1]；目標係數=[8/1, 21/1, 1/1, 1/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086071,"parameters":{"f":[8,21,1,1],"F":[[7,1],[8,1],[21,2],[1,3],[1,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"8\",\"21\",\"1\",\"1\"],[\"8/1\",\"21/2\",\"1/3\",\"1/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0072","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[9, 22, -1, 2]；候選 F 的升冪有理係數為 [[8,1],[9,1],[11,1],[-1,3],[3,2]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[9/1, 22/1, -1/1, 6/1]；目標係數=[9/1, 22/1, -1/1, 2/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086072,"parameters":{"f":[9,22,-1,2],"F":[[8,1],[9,1],[11,1],[-1,3],[3,2]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"9\",\"22\",\"-1\",\"2\"],[\"9/1\",\"11/1\",\"-1/3\",\"3/2\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0073","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[10, 23, 0, 3]；候選 F 的升冪有理係數為 [[9,1],[10,1],[23,2],[0,1],[3,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[10/1, 23/1, 0/1, 3/1]；目標係數=[10/1, 23/1, 0/1, 3/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086073,"parameters":{"f":[10,23,0,3],"F":[[9,1],[10,1],[23,2],[0,1],[3,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"10\",\"23\",\"0\",\"3\"],[\"10/1\",\"23/2\",\"0/1\",\"3/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0074","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[11, 24, 1, 4]；候選 F 的升冪有理係數為 [[10,1],[11,1],[12,1],[1,3],[2,1]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"否","explanation_zh":"候選導數係數=[11/1, 24/1, 1/1, 8/1]；目標係數=[11/1, 24/1, 1/1, 4/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086074,"parameters":{"f":[11,24,1,4],"F":[[10,1],[11,1],[12,1],[1,3],[2,1]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"11\",\"24\",\"1\",\"4\"],[\"11/1\",\"12/1\",\"1/3\",\"2/1\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0075","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"候選原函數的係數資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[12, 25, -1, 1]；候選 F 的升冪有理係數為 [[11,1],[12,1],[25,2],[-1,3],[1,4]]，每對是 [分子,正分母]。是否有 F′=f 的多項式恆等？","answer":{"kind":"short_text","value":"是","explanation_zh":"候選導數係數=[12/1, 25/1, -1/1, 1/1]；目標係數=[12/1, 25/1, -1/1, 1/1]。按係數恆等逐項核對，不在單點或有限點試值；F 的常數項不影響資格。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["候選原函數的係數資格"]},"variant":{"family_id":"qf-antiderivative-candidate","seed":202610086075,"parameters":{"f":[12,25,-1,1],"F":[[11,1],[12,1],[25,2],[-1,3],[1,4]],"operation":"primitive_candidate","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-candidate/{\"inputs\":[[\"12\",\"25\",\"-1\",\"1\"],[\"12/1\",\"25/2\",\"-1/3\",\"1/4\"]],\"operation\":\"primitive_candidate\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0076","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[1, 2]，F0 為零常數 canonical primitive。令 F=F0+(0)，求 F(0)，採最簡正分母分數。","answer":{"kind":"expression","value":"0/1","explanation_zh":"含常數原函數值=0/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086076,"parameters":{"f":[1,2],"C":0,"x":0,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[\"constant_value\",\"0\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0077","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[0]，F0 為零常數 canonical primitive。令 F=F0+(1)，求 F(3)，採最簡正分母分數。","answer":{"kind":"expression","value":"1/1","explanation_zh":"含常數原函數值=1/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086077,"parameters":{"f":[0],"C":1,"x":3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[\"constant_value\",\"1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0078","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-10, 3, 1, 3]，F0 為零常數 canonical primitive。令 F=F0+(-10)，求 F(3)，採最簡正分母分數。","answer":{"kind":"expression","value":"173/4","explanation_zh":"含常數原函數值=173/4。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086078,"parameters":{"f":[-10,3,1,3],"C":-10,"x":3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-10\",\"3\",\"1\",\"3\"],\"-10\",\"3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0079","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-9, 4, -1, 4]，F0 為零常數 canonical primitive。令 F=F0+(-9)，求 F(-1)，採最簡正分母分數。","answer":{"kind":"expression","value":"10/3","explanation_zh":"含常數原函數值=10/3。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086079,"parameters":{"f":[-9,4,-1,4],"C":-9,"x":-1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-9\",\"4\",\"-1\",\"4\"],\"-9\",\"-1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0080","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-8, 5, 0, 1]，F0 為零常數 canonical primitive。令 F=F0+(-8)，求 F(2)，採最簡正分母分數。","answer":{"kind":"expression","value":"-10/1","explanation_zh":"含常數原函數值=-10/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086080,"parameters":{"f":[-8,5,0,1],"C":-8,"x":2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-8\",\"5\",\"0\",\"1\"],\"-8\",\"2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0081","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-7, 6, 1, 2]，F0 為零常數 canonical primitive。令 F=F0+(-7)，求 F(-3)，採最簡正分母分數。","answer":{"kind":"expression","value":"145/2","explanation_zh":"含常數原函數值=145/2。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086081,"parameters":{"f":[-7,6,1,2],"C":-7,"x":-3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-7\",\"6\",\"1\",\"2\"],\"-7\",\"-3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0082","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-6, 7, -1, 3]，F0 為零常數 canonical primitive。令 F=F0+(-6)，求 F(1)，採最簡正分母分數。","answer":{"kind":"expression","value":"-97/12","explanation_zh":"含常數原函數值=-97/12。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086082,"parameters":{"f":[-6,7,-1,3],"C":-6,"x":1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-6\",\"7\",\"-1\",\"3\"],\"-6\",\"1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0083","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-5, 8, 0, 4]，F0 為零常數 canonical primitive。令 F=F0+(-5)，求 F(-2)，採最簡正分母分數。","answer":{"kind":"expression","value":"37/1","explanation_zh":"含常數原函數值=37/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086083,"parameters":{"f":[-5,8,0,4],"C":-5,"x":-2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-5\",\"8\",\"0\",\"4\"],\"-5\",\"-2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0084","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-4, 9, 1, 1]，F0 為零常數 canonical primitive。令 F=F0+(-4)，求 F(3)，採最簡正分母分數。","answer":{"kind":"expression","value":"215/4","explanation_zh":"含常數原函數值=215/4。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086084,"parameters":{"f":[-4,9,1,1],"C":-4,"x":3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-4\",\"9\",\"1\",\"1\"],\"-4\",\"3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0085","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-3, 10, -1, 2]，F0 為零常數 canonical primitive。令 F=F0+(-3)，求 F(-1)，採最簡正分母分數。","answer":{"kind":"expression","value":"35/6","explanation_zh":"含常數原函數值=35/6。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086085,"parameters":{"f":[-3,10,-1,2],"C":-3,"x":-1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-3\",\"10\",\"-1\",\"2\"],\"-3\",\"-1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0086","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-2, 11, 0, 3]，F0 為零常數 canonical primitive。令 F=F0+(-2)，求 F(2)，採最簡正分母分數。","answer":{"kind":"expression","value":"28/1","explanation_zh":"含常數原函數值=28/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086086,"parameters":{"f":[-2,11,0,3],"C":-2,"x":2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-2\",\"11\",\"0\",\"3\"],\"-2\",\"2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0087","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[-1, 12, 1, 4]，F0 為零常數 canonical primitive。令 F=F0+(-1)，求 F(-3)，採最簡正分母分數。","answer":{"kind":"expression","value":"128/1","explanation_zh":"含常數原函數值=128/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086087,"parameters":{"f":[-1,12,1,4],"C":-1,"x":-3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"-1\",\"12\",\"1\",\"4\"],\"-1\",\"-3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0088","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[0, 13, -1, 1]，F0 為零常數 canonical primitive。令 F=F0+(0)，求 F(1)，採最簡正分母分數。","answer":{"kind":"expression","value":"77/12","explanation_zh":"含常數原函數值=77/12。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086088,"parameters":{"f":[0,13,-1,1],"C":0,"x":1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"0\",\"13\",\"-1\",\"1\"],\"0\",\"1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0089","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[1, 14, 0, 2]，F0 為零常數 canonical primitive。令 F=F0+(1)，求 F(-2)，採最簡正分母分數。","answer":{"kind":"expression","value":"35/1","explanation_zh":"含常數原函數值=35/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086089,"parameters":{"f":[1,14,0,2],"C":1,"x":-2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"1\",\"14\",\"0\",\"2\"],\"1\",\"-2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0090","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[2, 15, 1, 3]，F0 為零常數 canonical primitive。令 F=F0+(2)，求 F(3)，採最簡正分母分數。","answer":{"kind":"expression","value":"581/4","explanation_zh":"含常數原函數值=581/4。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086090,"parameters":{"f":[2,15,1,3],"C":2,"x":3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"2\",\"15\",\"1\",\"3\"],\"2\",\"3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0091","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[3, 16, -1, 4]，F0 為零常數 canonical primitive。令 F=F0+(3)，求 F(-1)，採最簡正分母分數。","answer":{"kind":"expression","value":"28/3","explanation_zh":"含常數原函數值=28/3。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086091,"parameters":{"f":[3,16,-1,4],"C":3,"x":-1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"3\",\"16\",\"-1\",\"4\"],\"3\",\"-1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0092","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[4, 17, 0, 1]，F0 為零常數 canonical primitive。令 F=F0+(4)，求 F(2)，採最簡正分母分數。","answer":{"kind":"expression","value":"50/1","explanation_zh":"含常數原函數值=50/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086092,"parameters":{"f":[4,17,0,1],"C":4,"x":2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"4\",\"17\",\"0\",\"1\"],\"4\",\"2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0093","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[5, 18, 1, 2]，F0 為零常數 canonical primitive。令 F=F0+(5)，求 F(-3)，採最簡正分母分數。","answer":{"kind":"expression","value":"205/2","explanation_zh":"含常數原函數值=205/2。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086093,"parameters":{"f":[5,18,1,2],"C":5,"x":-3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"5\",\"18\",\"1\",\"2\"],\"5\",\"-3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0094","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[6, 19, -1, 3]，F0 為零常數 canonical primitive。令 F=F0+(6)，求 F(1)，採最簡正分母分數。","answer":{"kind":"expression","value":"263/12","explanation_zh":"含常數原函數值=263/12。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086094,"parameters":{"f":[6,19,-1,3],"C":6,"x":1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"6\",\"19\",\"-1\",\"3\"],\"6\",\"1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0095","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[7, 20, 0, 4]，F0 為零常數 canonical primitive。令 F=F0+(7)，求 F(-2)，採最簡正分母分數。","answer":{"kind":"expression","value":"49/1","explanation_zh":"含常數原函數值=49/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086095,"parameters":{"f":[7,20,0,4],"C":7,"x":-2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"7\",\"20\",\"0\",\"4\"],\"7\",\"-2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0096","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[8, 21, 1, 1]，F0 為零常數 canonical primitive。令 F=F0+(8)，求 F(3)，採最簡正分母分數。","answer":{"kind":"expression","value":"623/4","explanation_zh":"含常數原函數值=623/4。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086096,"parameters":{"f":[8,21,1,1],"C":8,"x":3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"8\",\"21\",\"1\",\"1\"],\"8\",\"3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0097","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[9, 22, -1, 2]，F0 為零常數 canonical primitive。令 F=F0+(9)，求 F(-1)，採最簡正分母分數。","answer":{"kind":"expression","value":"71/6","explanation_zh":"含常數原函數值=71/6。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086097,"parameters":{"f":[9,22,-1,2],"C":9,"x":-1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"9\",\"22\",\"-1\",\"2\"],\"9\",\"-1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0098","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[10, 23, 0, 3]，F0 為零常數 canonical primitive。令 F=F0+(10)，求 F(2)，採最簡正分母分數。","answer":{"kind":"expression","value":"88/1","explanation_zh":"含常數原函數值=88/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086098,"parameters":{"f":[10,23,0,3],"C":10,"x":2,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"10\",\"23\",\"0\",\"3\"],\"10\",\"2\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0099","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[11, 24, 1, 4]，F0 為零常數 canonical primitive。令 F=F0+(11)，求 F(-3)，採最簡正分母分數。","answer":{"kind":"expression","value":"158/1","explanation_zh":"含常數原函數值=158/1。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086099,"parameters":{"f":[11,24,1,4],"C":11,"x":-3,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"11\",\"24\",\"1\",\"4\"],\"11\",\"-3\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r06-antiderivative-0100","batch_id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","language":"zh-Hant","source_mko_ids":["mko-antiderivative"],"title_zh":"含實際常數的原函數值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。升冪係數 f=[12, 25, -1, 1]，F0 為零常數 canonical primitive。令 F=F0+(12)，求 F(1)，採最簡正分母分數。","answer":{"kind":"expression","value":"437/12","explanation_zh":"含常數原函數值=437/12。此題保留實際 C 與求值點，不混同忽略 C 的原函數資格檢查。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["含實際常數的原函數值"]},"variant":{"family_id":"qf-antiderivative-shifted-value","seed":202610086100,"parameters":{"f":[12,25,-1,1],"C":12,"x":1,"operation":"shifted_primitive_value","domain":"reals","representation":"ascending_powers","semantic_template":"qf-antiderivative-shifted-value/{\"inputs\":[[\"12\",\"25\",\"-1\",\"1\"],\"12\",\"1\"],\"operation\":\"shifted_primitive_value\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}