{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r03-continuity-0001","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=0x+(0)，求 f(0)。","answer":{"kind":"short_text","value":"0","explanation_zh":"點值=0。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083001,"parameters":{"m":0,"b":0,"a":0,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"value_b\",\"0\"],\"operation\":\"continuous_affine_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-r03-continuity-0002","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-2x+(-11)，求 f(0)。","answer":{"kind":"short_text","value":"-11","explanation_zh":"點值=-11。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083002,"parameters":{"m":-2,"b":-11,"a":0,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"value_b\",\"-11\"],\"operation\":\"continuous_affine_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-r03-continuity-0003","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=3x+(-10)，求 f(3)。","answer":{"kind":"short_text","value":"-1","explanation_zh":"點值=-1。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083003,"parameters":{"m":3,"b":-10,"a":3,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"3\",\"-10\",\"3\"],\"operation\":\"continuous_affine_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-r03-continuity-0004","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-4x+(-9)，求 f(4)。","answer":{"kind":"short_text","value":"-25","explanation_zh":"點值=-25。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083004,"parameters":{"m":-4,"b":-9,"a":4,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-4\",\"-9\",\"4\"],\"operation\":\"continuous_affine_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-r03-continuity-0005","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=5x+(-8)，求 f(1)。","answer":{"kind":"short_text","value":"-3","explanation_zh":"點值=-3。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083005,"parameters":{"m":5,"b":-8,"a":1,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"5\",\"-8\",\"1\"],\"operation\":\"continuous_affine_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-r03-continuity-0006","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-6x+(-7)，求 f(2)。","answer":{"kind":"short_text","value":"-19","explanation_zh":"點值=-19。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083006,"parameters":{"m":-6,"b":-7,"a":2,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-6\",\"-7\",\"2\"],\"operation\":\"continuous_affine_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-r03-continuity-0007","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=7x+(-6)，求 f(3)。","answer":{"kind":"short_text","value":"15","explanation_zh":"點值=15。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083007,"parameters":{"m":7,"b":-6,"a":3,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"7\",\"-6\",\"3\"],\"operation\":\"continuous_affine_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-r03-continuity-0008","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-8x+(-5)，求 f(4)。","answer":{"kind":"short_text","value":"-37","explanation_zh":"點值=-37。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083008,"parameters":{"m":-8,"b":-5,"a":4,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-8\",\"-5\",\"4\"],\"operation\":\"continuous_affine_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-r03-continuity-0009","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=9x+(-4)，求 f(1)。","answer":{"kind":"short_text","value":"5","explanation_zh":"點值=5。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083009,"parameters":{"m":9,"b":-4,"a":1,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"9\",\"-4\",\"1\"],\"operation\":\"continuous_affine_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-r03-continuity-0010","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-10x+(-3)，求 f(2)。","answer":{"kind":"short_text","value":"-23","explanation_zh":"點值=-23。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083010,"parameters":{"m":-10,"b":-3,"a":2,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-10\",\"-3\",\"2\"],\"operation\":\"continuous_affine_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-r03-continuity-0011","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=11x+(-2)，求 f(3)。","answer":{"kind":"short_text","value":"31","explanation_zh":"點值=31。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083011,"parameters":{"m":11,"b":-2,"a":3,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"11\",\"-2\",\"3\"],\"operation\":\"continuous_affine_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-r03-continuity-0012","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-12x+(-1)，求 f(4)。","answer":{"kind":"short_text","value":"-49","explanation_zh":"點值=-49。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083012,"parameters":{"m":-12,"b":-1,"a":4,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-12\",\"-1\",\"4\"],\"operation\":\"continuous_affine_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-r03-continuity-0013","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=13x+(0)，求 f(1)。","answer":{"kind":"short_text","value":"13","explanation_zh":"點值=13。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083013,"parameters":{"m":13,"b":0,"a":1,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"13\",\"0\",\"1\"],\"operation\":\"continuous_affine_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-r03-continuity-0014","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-14x+(1)，求 f(2)。","answer":{"kind":"short_text","value":"-27","explanation_zh":"點值=-27。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083014,"parameters":{"m":-14,"b":1,"a":2,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-14\",\"1\",\"2\"],\"operation\":\"continuous_affine_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-r03-continuity-0015","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=15x+(2)，求 f(3)。","answer":{"kind":"short_text","value":"47","explanation_zh":"點值=47。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083015,"parameters":{"m":15,"b":2,"a":3,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"15\",\"2\",\"3\"],\"operation\":\"continuous_affine_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-r03-continuity-0016","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-16x+(3)，求 f(4)。","answer":{"kind":"short_text","value":"-61","explanation_zh":"點值=-61。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083016,"parameters":{"m":-16,"b":3,"a":4,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-16\",\"3\",\"4\"],\"operation\":\"continuous_affine_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-r03-continuity-0017","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=17x+(4)，求 f(1)。","answer":{"kind":"short_text","value":"21","explanation_zh":"點值=21。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083017,"parameters":{"m":17,"b":4,"a":1,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"17\",\"4\",\"1\"],\"operation\":\"continuous_affine_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-r03-continuity-0018","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-18x+(5)，求 f(2)。","answer":{"kind":"short_text","value":"-31","explanation_zh":"點值=-31。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083018,"parameters":{"m":-18,"b":5,"a":2,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-18\",\"5\",\"2\"],\"operation\":\"continuous_affine_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-r03-continuity-0019","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=19x+(6)，求 f(3)。","answer":{"kind":"short_text","value":"63","explanation_zh":"點值=63。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083019,"parameters":{"m":19,"b":6,"a":3,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"19\",\"6\",\"3\"],\"operation\":\"continuous_affine_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-r03-continuity-0020","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-20x+(7)，求 f(4)。","answer":{"kind":"short_text","value":"-73","explanation_zh":"點值=-73。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083020,"parameters":{"m":-20,"b":7,"a":4,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-20\",\"7\",\"4\"],\"operation\":\"continuous_affine_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-r03-continuity-0021","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=21x+(8)，求 f(1)。","answer":{"kind":"short_text","value":"29","explanation_zh":"點值=29。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083021,"parameters":{"m":21,"b":8,"a":1,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"21\",\"8\",\"1\"],\"operation\":\"continuous_affine_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-r03-continuity-0022","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-22x+(9)，求 f(2)。","answer":{"kind":"short_text","value":"-35","explanation_zh":"點值=-35。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083022,"parameters":{"m":-22,"b":9,"a":2,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-22\",\"9\",\"2\"],\"operation\":\"continuous_affine_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-r03-continuity-0023","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=23x+(10)，求 f(3)。","answer":{"kind":"short_text","value":"79","explanation_zh":"點值=79。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083023,"parameters":{"m":23,"b":10,"a":3,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"23\",\"10\",\"3\"],\"operation\":\"continuous_affine_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-r03-continuity-0024","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=-24x+(11)，求 f(4)。","answer":{"kind":"short_text","value":"-85","explanation_zh":"點值=-85。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083024,"parameters":{"m":-24,"b":11,"a":4,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"-24\",\"11\",\"4\"],\"operation\":\"continuous_affine_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-r03-continuity-0025","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"連續仿射模型的點值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。連續仿射函數 f(x)=25x+(12)，求 f(1)。","answer":{"kind":"short_text","value":"37","explanation_zh":"點值=37。只求這個明示仿射模型的點值，不以一個讀值證明任意函數連續。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續仿射模型的點值"]},"variant":{"family_id":"qf-continuity-affine-value","seed":202610083025,"parameters":{"m":25,"b":12,"a":1,"operation":"continuous_affine_value","domain":"reals","semantic_template":"qf-continuity-affine-value/{\"inputs\":[\"25\",\"12\",\"1\"],\"operation\":\"continuous_affine_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-r03-continuity-0026","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-12 時 f(x)=1x+(-1)，x>-12 時 f(x)=-1x+(-25)，另明示點值 f(-12)=-13。函數在 a=-12 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=-13；右極限=-13；點值=-13。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083026,"parameters":{"a":-12,"left_m":1,"left_b":-1,"right_m":-1,"right_b":-25,"value":-13,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-13\",\"-13\",\"-13\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0027","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-11 時 f(x)=2x+(24)，x>-11 時 f(x)=-2x+(-20)，另明示點值 f(-11)=3。函數在 a=-11 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=2；右極限=2；點值=3。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083027,"parameters":{"a":-11,"left_m":2,"left_b":24,"right_m":-2,"right_b":-20,"value":3,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"2\",\"2\",\"3\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0028","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-10 時 f(x)=3x+(29)，x>-10 時 f(x)=-3x+(-29)，另明示點值 f(-10)=0。函數在 a=-10 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-1；右極限=1；點值=0。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083028,"parameters":{"a":-10,"left_m":3,"left_b":29,"right_m":-3,"right_b":-29,"value":0,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-1\",\"1\",\"0\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0029","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-9 時 f(x)=4x+(26)，x>-9 時 f(x)=-1x+(-19)，另明示點值 f(-9)=-10。函數在 a=-9 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=-10；右極限=-10；點值=-10。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083029,"parameters":{"a":-9,"left_m":4,"left_b":26,"right_m":-1,"right_b":-19,"value":-10,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-10\",\"-10\",\"-10\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0030","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-8 時 f(x)=1x+(0)，x>-8 時 f(x)=-2x+(-24)，另明示點值 f(-8)=-9。函數在 a=-8 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-8；右極限=-8；點值=-9。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083030,"parameters":{"a":-8,"left_m":1,"left_b":0,"right_m":-2,"right_b":-24,"value":-9,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-8\",\"-8\",\"-9\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0031","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-7 時 f(x)=2x+(6)，x>-7 時 f(x)=-3x+(-27)，另明示點值 f(-7)=-8。函數在 a=-7 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-8；右極限=-6；點值=-8。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083031,"parameters":{"a":-7,"left_m":2,"left_b":6,"right_m":-3,"right_b":-27,"value":-8,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-8\",\"-6\",\"-8\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0032","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-6 時 f(x)=3x+(11)，x>-6 時 f(x)=-1x+(-13)，另明示點值 f(-6)=-7。函數在 a=-6 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=-7；右極限=-7；點值=-7。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083032,"parameters":{"a":-6,"left_m":3,"left_b":11,"right_m":-1,"right_b":-13,"value":-7,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-7\",\"-7\",\"-7\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0033","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-5 時 f(x)=4x+(15)，x>-5 時 f(x)=-2x+(-15)，另明示點值 f(-5)=-6。函數在 a=-5 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-5；右極限=-5；點值=-6。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083033,"parameters":{"a":-5,"left_m":4,"left_b":15,"right_m":-2,"right_b":-15,"value":-6,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-5\",\"-5\",\"-6\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0034","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-4 時 f(x)=1x+(-1)，x>-4 時 f(x)=-3x+(-15)，另明示點值 f(-4)=-5。函數在 a=-4 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-5；右極限=-3；點值=-5。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083034,"parameters":{"a":-4,"left_m":1,"left_b":-1,"right_m":-3,"right_b":-15,"value":-5,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-5\",\"-3\",\"-5\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0035","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-3 時 f(x)=2x+(2)，x>-3 時 f(x)=-1x+(-7)，另明示點值 f(-3)=-4。函數在 a=-3 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=-4；右極限=-4；點值=-4。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083035,"parameters":{"a":-3,"left_m":2,"left_b":2,"right_m":-1,"right_b":-7,"value":-4,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-4\",\"-4\",\"-4\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0036","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-2 時 f(x)=3x+(4)，x>-2 時 f(x)=-2x+(-6)，另明示點值 f(-2)=-3。函數在 a=-2 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-2；右極限=-2；點值=-3。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083036,"parameters":{"a":-2,"left_m":3,"left_b":4,"right_m":-2,"right_b":-6,"value":-3,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-2\",\"-2\",\"-3\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0037","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-1 時 f(x)=4x+(2)，x>-1 時 f(x)=-3x+(-3)，另明示點值 f(-1)=-2。函數在 a=-1 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=-2；右極限=0；點值=-2。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083037,"parameters":{"a":-1,"left_m":4,"left_b":2,"right_m":-3,"right_b":-3,"value":-2,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-2\",\"0\",\"-2\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0038","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<0 時 f(x)=1x+(-1)，x>0 時 f(x)=-1x+(-1)，另明示點值 f(0)=-1。函數在 a=0 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=-1；右極限=-1；點值=-1。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083038,"parameters":{"a":0,"left_m":1,"left_b":-1,"right_m":-1,"right_b":-1,"value":-1,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"-1\",\"-1\",\"-1\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0039","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<1 時 f(x)=2x+(-1)，x>1 時 f(x)=-2x+(3)，另明示點值 f(1)=0。函數在 a=1 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=1；右極限=1；點值=0。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083039,"parameters":{"a":1,"left_m":2,"left_b":-1,"right_m":-2,"right_b":3,"value":0,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"1\",\"1\",\"0\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0040","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<2 時 f(x)=3x+(-5)，x>2 時 f(x)=-3x+(9)，另明示點值 f(2)=1。函數在 a=2 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=1；右極限=3；點值=1。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083040,"parameters":{"a":2,"left_m":3,"left_b":-5,"right_m":-3,"right_b":9,"value":1,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"1\",\"3\",\"1\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0041","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<3 時 f(x)=4x+(-10)，x>3 時 f(x)=-1x+(5)，另明示點值 f(3)=2。函數在 a=3 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=2；右極限=2；點值=2。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083041,"parameters":{"a":3,"left_m":4,"left_b":-10,"right_m":-1,"right_b":5,"value":2,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"2\",\"2\",\"2\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0042","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<4 時 f(x)=1x+(0)，x>4 時 f(x)=-2x+(12)，另明示點值 f(4)=3。函數在 a=4 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=4；右極限=4；點值=3。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083042,"parameters":{"a":4,"left_m":1,"left_b":0,"right_m":-2,"right_b":12,"value":3,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"4\",\"4\",\"3\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0043","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<5 時 f(x)=2x+(-6)，x>5 時 f(x)=-3x+(21)，另明示點值 f(5)=4。函數在 a=5 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=4；右極限=6；點值=4。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083043,"parameters":{"a":5,"left_m":2,"left_b":-6,"right_m":-3,"right_b":21,"value":4,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"4\",\"6\",\"4\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0044","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<6 時 f(x)=3x+(-13)，x>6 時 f(x)=-1x+(11)，另明示點值 f(6)=5。函數在 a=6 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=5；右極限=5；點值=5。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083044,"parameters":{"a":6,"left_m":3,"left_b":-13,"right_m":-1,"right_b":11,"value":5,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"5\",\"5\",\"5\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0045","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<7 時 f(x)=4x+(-21)，x>7 時 f(x)=-2x+(21)，另明示點值 f(7)=6。函數在 a=7 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=7；右極限=7；點值=6。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083045,"parameters":{"a":7,"left_m":4,"left_b":-21,"right_m":-2,"right_b":21,"value":6,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"7\",\"7\",\"6\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0046","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<8 時 f(x)=1x+(-1)，x>8 時 f(x)=-3x+(33)，另明示點值 f(8)=7。函數在 a=8 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=7；右極限=9；點值=7。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083046,"parameters":{"a":8,"left_m":1,"left_b":-1,"right_m":-3,"right_b":33,"value":7,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"7\",\"9\",\"7\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0047","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<9 時 f(x)=2x+(-10)，x>9 時 f(x)=-1x+(17)，另明示點值 f(9)=8。函數在 a=9 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=8；右極限=8；點值=8。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083047,"parameters":{"a":9,"left_m":2,"left_b":-10,"right_m":-1,"right_b":17,"value":8,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"8\",\"8\",\"8\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0048","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<10 時 f(x)=3x+(-20)，x>10 時 f(x)=-2x+(30)，另明示點值 f(10)=9。函數在 a=10 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=10；右極限=10；點值=9。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083048,"parameters":{"a":10,"left_m":3,"left_b":-20,"right_m":-2,"right_b":30,"value":9,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"10\",\"10\",\"9\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0049","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<11 時 f(x)=4x+(-34)，x>11 時 f(x)=-3x+(45)，另明示點值 f(11)=10。函數在 a=11 是否連續？","answer":{"kind":"short_text","value":"否","explanation_zh":"左極限=10；右極限=12；點值=10。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083049,"parameters":{"a":11,"left_m":4,"left_b":-34,"right_m":-3,"right_b":45,"value":10,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"10\",\"12\",\"10\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0050","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"兩側與明示點值的連續資格","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<12 時 f(x)=1x+(-1)，x>12 時 f(x)=-1x+(23)，另明示點值 f(12)=11。函數在 a=12 是否連續？","answer":{"kind":"short_text","value":"是","explanation_zh":"左極限=11；右極限=11；點值=11。兩側極限與實際點值三者都相等才符合；有去心極限不保證補定點值正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩側與明示點值的連續資格"]},"variant":{"family_id":"qf-continuity-piecewise-point","seed":202610083050,"parameters":{"a":12,"left_m":1,"left_b":-1,"right_m":-1,"right_b":23,"value":11,"operation":"piecewise_continuity","domain":"reals","semantic_template":"qf-continuity-piecewise-point/{\"inputs\":[\"11\",\"11\",\"11\"],\"operation\":\"piecewise_continuity\"}"}},"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-r03-continuity-0051","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-12)²)/(x−(-12)) 在 x≠-12 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-24","explanation_zh":"補定點值=-24。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083051,"parameters":{"a":-12,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-12\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0052","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-11)²)/(x−(-11)) 在 x≠-11 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-22","explanation_zh":"補定點值=-22。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083052,"parameters":{"a":-11,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-11\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0053","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-10)²)/(x−(-10)) 在 x≠-10 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-20","explanation_zh":"補定點值=-20。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083053,"parameters":{"a":-10,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-10\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0054","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-9)²)/(x−(-9)) 在 x≠-9 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-18","explanation_zh":"補定點值=-18。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083054,"parameters":{"a":-9,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-9\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0055","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-8)²)/(x−(-8)) 在 x≠-8 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-16","explanation_zh":"補定點值=-16。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083055,"parameters":{"a":-8,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-8\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0056","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-7)²)/(x−(-7)) 在 x≠-7 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-14","explanation_zh":"補定點值=-14。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083056,"parameters":{"a":-7,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-7\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0057","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-6)²)/(x−(-6)) 在 x≠-6 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-12","explanation_zh":"補定點值=-12。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083057,"parameters":{"a":-6,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-6\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0058","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-5)²)/(x−(-5)) 在 x≠-5 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-10","explanation_zh":"補定點值=-10。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083058,"parameters":{"a":-5,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-5\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0059","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-4)²)/(x−(-4)) 在 x≠-4 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-8","explanation_zh":"補定點值=-8。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083059,"parameters":{"a":-4,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-4\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0060","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-3)²)/(x−(-3)) 在 x≠-3 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-6","explanation_zh":"補定點值=-6。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083060,"parameters":{"a":-3,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-3\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0061","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-2)²)/(x−(-2)) 在 x≠-2 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-4","explanation_zh":"補定點值=-4。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083061,"parameters":{"a":-2,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-2\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0062","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(-1)²)/(x−(-1)) 在 x≠-1 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"-2","explanation_zh":"補定點值=-2。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083062,"parameters":{"a":-1,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"-1\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0063","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(0)²)/(x−(0)) 在 x≠0 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"0","explanation_zh":"補定點值=0。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083063,"parameters":{"a":0,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"0\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0064","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(1)²)/(x−(1)) 在 x≠1 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"2","explanation_zh":"補定點值=2。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083064,"parameters":{"a":1,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"1\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0065","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(2)²)/(x−(2)) 在 x≠2 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"4","explanation_zh":"補定點值=4。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083065,"parameters":{"a":2,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"2\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0066","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(3)²)/(x−(3)) 在 x≠3 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"6","explanation_zh":"補定點值=6。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083066,"parameters":{"a":3,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"3\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0067","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(4)²)/(x−(4)) 在 x≠4 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"8","explanation_zh":"補定點值=8。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083067,"parameters":{"a":4,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"4\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0068","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(5)²)/(x−(5)) 在 x≠5 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"10","explanation_zh":"補定點值=10。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083068,"parameters":{"a":5,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"5\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0069","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(6)²)/(x−(6)) 在 x≠6 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"12","explanation_zh":"補定點值=12。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083069,"parameters":{"a":6,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"6\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0070","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(7)²)/(x−(7)) 在 x≠7 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"14","explanation_zh":"補定點值=14。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083070,"parameters":{"a":7,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"7\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0071","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(8)²)/(x−(8)) 在 x≠8 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"16","explanation_zh":"補定點值=16。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083071,"parameters":{"a":8,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"8\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0072","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(9)²)/(x−(9)) 在 x≠9 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"18","explanation_zh":"補定點值=18。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083072,"parameters":{"a":9,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"9\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0073","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(10)²)/(x−(10)) 在 x≠10 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"20","explanation_zh":"補定點值=20。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083073,"parameters":{"a":10,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"10\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0074","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(11)²)/(x−(11)) 在 x≠11 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"22","explanation_zh":"補定點值=22。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083074,"parameters":{"a":11,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"11\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0075","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"原商式的連續補定值","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。原商 (x²−(12)²)/(x−(12)) 在 x≠12 定義。另建 g(a)=V 的全域延拓，哪個 V 使 g 在 a 連續？","answer":{"kind":"short_text","value":"24","explanation_zh":"補定點值=24。原商未在 a 定義；答案指定的是新延拓 g 的補定值，不追改原商或把未定義值設零。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["原商式的連續補定值"]},"variant":{"family_id":"qf-continuity-removable-extension","seed":202610083075,"parameters":{"a":12,"operation":"removable_continuous_extension","domain":"reals","semantic_template":"qf-continuity-removable-extension/{\"inputs\":[\"12\"],\"operation\":\"removable_continuous_extension\"}"}},"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-r03-continuity-0076","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-12 時 f(x)=1x+(0)，x>-12 時 f(x)=-1x+(-24)，點值 f(-12)=-12。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(0, 0)","explanation_zh":"點缺陷=(0, 0)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083076,"parameters":{"a":-12,"left_m":1,"left_b":0,"right_m":-1,"right_b":-24,"value":-12,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"0\",\"0\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0077","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-11 時 f(x)=2x+(12)，x>-11 時 f(x)=-2x+(-34)，點值 f(-11)=-11。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(1, -1)","explanation_zh":"點缺陷=(1, -1)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083077,"parameters":{"a":-11,"left_m":2,"left_b":12,"right_m":-2,"right_b":-34,"value":-11,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"1\",\"-1\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0078","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-10 時 f(x)=3x+(22)，x>-10 時 f(x)=-3x+(-37)，點值 f(-10)=-10。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(2, 3)","explanation_zh":"點缺陷=(2, 3)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083078,"parameters":{"a":-10,"left_m":3,"left_b":22,"right_m":-3,"right_b":-37,"value":-10,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"2\",\"3\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0079","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-9 時 f(x)=4x+(30)，x>-9 時 f(x)=-1x+(-21)，點值 f(-9)=-9。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(3, -3)","explanation_zh":"點缺陷=(3, -3)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083079,"parameters":{"a":-9,"left_m":4,"left_b":30,"right_m":-1,"right_b":-21,"value":-9,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"3\",\"-3\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0080","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-8 時 f(x)=1x+(4)，x>-8 時 f(x)=-2x+(-19)，點值 f(-8)=-8。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(4, 5)","explanation_zh":"點缺陷=(4, 5)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083080,"parameters":{"a":-8,"left_m":1,"left_b":4,"right_m":-2,"right_b":-19,"value":-8,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"4\",\"5\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0081","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-7 時 f(x)=2x+(12)，x>-7 時 f(x)=-3x+(-33)，點值 f(-7)=-7。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(5, -5)","explanation_zh":"點缺陷=(5, -5)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083081,"parameters":{"a":-7,"left_m":2,"left_b":12,"right_m":-3,"right_b":-33,"value":-7,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"5\",\"-5\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0082","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-6 時 f(x)=3x+(18)，x>-6 時 f(x)=-1x+(-5)，點值 f(-6)=-6。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(6, 7)","explanation_zh":"點缺陷=(6, 7)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083082,"parameters":{"a":-6,"left_m":3,"left_b":18,"right_m":-1,"right_b":-5,"value":-6,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"6\",\"7\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0083","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-5 時 f(x)=4x+(22)，x>-5 時 f(x)=-2x+(-22)，點值 f(-5)=-5。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(7, -7)","explanation_zh":"點缺陷=(7, -7)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083083,"parameters":{"a":-5,"left_m":4,"left_b":22,"right_m":-2,"right_b":-22,"value":-5,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"7\",\"-7\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0084","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-4 時 f(x)=1x+(8)，x>-4 時 f(x)=-3x+(-7)，點值 f(-4)=-4。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(8, 9)","explanation_zh":"點缺陷=(8, 9)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083084,"parameters":{"a":-4,"left_m":1,"left_b":8,"right_m":-3,"right_b":-7,"value":-4,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"8\",\"9\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0085","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-3 時 f(x)=2x+(12)，x>-3 時 f(x)=-1x+(-15)，點值 f(-3)=-3。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(9, -9)","explanation_zh":"點缺陷=(9, -9)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083085,"parameters":{"a":-3,"left_m":2,"left_b":12,"right_m":-1,"right_b":-15,"value":-3,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"9\",\"-9\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0086","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-2 時 f(x)=3x+(14)，x>-2 時 f(x)=-2x+(5)，點值 f(-2)=-2。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(10, 11)","explanation_zh":"點缺陷=(10, 11)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083086,"parameters":{"a":-2,"left_m":3,"left_b":14,"right_m":-2,"right_b":5,"value":-2,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"10\",\"11\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0087","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<-1 時 f(x)=4x+(14)，x>-1 時 f(x)=-3x+(-15)，點值 f(-1)=-1。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(11, -11)","explanation_zh":"點缺陷=(11, -11)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083087,"parameters":{"a":-1,"left_m":4,"left_b":14,"right_m":-3,"right_b":-15,"value":-1,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"11\",\"-11\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0088","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<0 時 f(x)=1x+(12)，x>0 時 f(x)=-1x+(13)，點值 f(0)=0。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(12, 13)","explanation_zh":"點缺陷=(12, 13)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083088,"parameters":{"a":0,"left_m":1,"left_b":12,"right_m":-1,"right_b":13,"value":0,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"12\",\"13\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0089","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<1 時 f(x)=2x+(12)，x>1 時 f(x)=-2x+(-10)，點值 f(1)=1。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(13, -13)","explanation_zh":"點缺陷=(13, -13)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083089,"parameters":{"a":1,"left_m":2,"left_b":12,"right_m":-2,"right_b":-10,"value":1,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"13\",\"-13\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0090","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<2 時 f(x)=3x+(10)，x>2 時 f(x)=-3x+(23)，點值 f(2)=2。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(14, 15)","explanation_zh":"點缺陷=(14, 15)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083090,"parameters":{"a":2,"left_m":3,"left_b":10,"right_m":-3,"right_b":23,"value":2,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"14\",\"15\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0091","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<3 時 f(x)=4x+(6)，x>3 時 f(x)=-1x+(-9)，點值 f(3)=3。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(15, -15)","explanation_zh":"點缺陷=(15, -15)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083091,"parameters":{"a":3,"left_m":4,"left_b":6,"right_m":-1,"right_b":-9,"value":3,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"15\",\"-15\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0092","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<4 時 f(x)=1x+(16)，x>4 時 f(x)=-2x+(29)，點值 f(4)=4。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(16, 17)","explanation_zh":"點缺陷=(16, 17)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083092,"parameters":{"a":4,"left_m":1,"left_b":16,"right_m":-2,"right_b":29,"value":4,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"16\",\"17\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0093","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<5 時 f(x)=2x+(12)，x>5 時 f(x)=-3x+(3)，點值 f(5)=5。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(17, -17)","explanation_zh":"點缺陷=(17, -17)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083093,"parameters":{"a":5,"left_m":2,"left_b":12,"right_m":-3,"right_b":3,"value":5,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"17\",\"-17\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0094","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<6 時 f(x)=3x+(6)，x>6 時 f(x)=-1x+(31)，點值 f(6)=6。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(18, 19)","explanation_zh":"點缺陷=(18, 19)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083094,"parameters":{"a":6,"left_m":3,"left_b":6,"right_m":-1,"right_b":31,"value":6,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"18\",\"19\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0095","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<7 時 f(x)=4x+(-2)，x>7 時 f(x)=-2x+(2)，點值 f(7)=7。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(19, -19)","explanation_zh":"點缺陷=(19, -19)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083095,"parameters":{"a":7,"left_m":4,"left_b":-2,"right_m":-2,"right_b":2,"value":7,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"19\",\"-19\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0096","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<8 時 f(x)=1x+(20)，x>8 時 f(x)=-3x+(53)，點值 f(8)=8。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(20, 21)","explanation_zh":"點缺陷=(20, 21)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083096,"parameters":{"a":8,"left_m":1,"left_b":20,"right_m":-3,"right_b":53,"value":8,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"20\",\"21\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0097","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<9 時 f(x)=2x+(12)，x>9 時 f(x)=-1x+(-3)，點值 f(9)=9。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(21, -21)","explanation_zh":"點缺陷=(21, -21)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083097,"parameters":{"a":9,"left_m":2,"left_b":12,"right_m":-1,"right_b":-3,"value":9,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"21\",\"-21\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0098","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<10 時 f(x)=3x+(2)，x>10 時 f(x)=-2x+(53)，點值 f(10)=10。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(22, 23)","explanation_zh":"點缺陷=(22, 23)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083098,"parameters":{"a":10,"left_m":3,"left_b":2,"right_m":-2,"right_b":53,"value":10,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"22\",\"23\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0099","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<11 時 f(x)=4x+(-10)，x>11 時 f(x)=-3x+(21)，點值 f(11)=11。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(23, -23)","explanation_zh":"點缺陷=(23, -23)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083099,"parameters":{"a":11,"left_m":4,"left_b":-10,"right_m":-3,"right_b":21,"value":11,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"23\",\"-23\"],\"operation\":\"point_defects\"}"}},"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-r03-continuity-0100","batch_id":"batch-20261007-advance-20261008-r03-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-continuity"],"title_zh":"左右極限相對點值的缺陷","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。當 x<12 時 f(x)=1x+(24)，x>12 時 f(x)=-1x+(49)，點值 f(12)=12。求 (左極限−點值, 右極限−點值)。","answer":{"kind":"expression","value":"(24, 25)","explanation_zh":"點缺陷=(24, 25)。在明示兩側仿射模型中求精確差，斜率與共同平移不另創造相同缺陷的變種。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["左右極限相對點值的缺陷"]},"variant":{"family_id":"qf-continuity-point-defects","seed":202610083100,"parameters":{"a":12,"left_m":1,"left_b":24,"right_m":-1,"right_b":49,"value":12,"operation":"point_defects","domain":"reals","semantic_template":"qf-continuity-point-defects/{\"inputs\":[\"24\",\"25\"],\"operation\":\"point_defects\"}"}},"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"}}