{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0001","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":1,\"b_scale\":2,\"ratio\":[1,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1/7, 7/6, 7/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(1, 2, 1/7, 7/6, 7/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171001,"parameters":{"a_scale":1,"b_scale":2,"ratio":[1,7],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[1,1],b_scale:[2,1],ratio:[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0002","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":2,\"b_scale\":3,\"ratio\":[2,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 1/4, 8/3, 4, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(2, 3, 1/4, 8/3, 4, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171002,"parameters":{"a_scale":2,"b_scale":3,"ratio":[2,8],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[2,1],b_scale:[3,1],ratio:[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0003","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":3,\"b_scale\":4,\"ratio\":[3,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 1/3, 9/2, 6, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(3, 4, 1/3, 9/2, 6, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171003,"parameters":{"a_scale":3,"b_scale":4,"ratio":[3,9],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[3,1],b_scale:[4,1],ratio:[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0004","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":4,\"b_scale\":5,\"ratio\":[4,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 2/5, 20/3, 25/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(4, 5, 2/5, 20/3, 25/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171004,"parameters":{"a_scale":4,"b_scale":5,"ratio":[4,10],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[4,1],b_scale:[5,1],ratio:[2,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0005","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":5,\"b_scale\":6,\"ratio\":[5,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 6, 5/11, 55/6, 11, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(5, 6, 5/11, 55/6, 11, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171005,"parameters":{"a_scale":5,"b_scale":6,"ratio":[5,11],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[5,1],b_scale:[6,1],ratio:[5,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0006","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":6,\"b_scale\":7,\"ratio\":[1,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 7, 1/7, 7, 49/6, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(6, 7, 1/7, 7, 49/6, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171006,"parameters":{"a_scale":6,"b_scale":7,"ratio":[1,7],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[6,1],b_scale:[7,1],ratio:[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0007","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":7,\"b_scale\":8,\"ratio\":[2,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 8, 1/4, 28/3, 32/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(7, 8, 1/4, 28/3, 32/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171007,"parameters":{"a_scale":7,"b_scale":8,"ratio":[2,8],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[7,1],b_scale:[8,1],ratio:[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0008","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":8,\"b_scale\":9,\"ratio\":[3,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 9, 1/3, 12, 27/2, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(8, 9, 1/3, 12, 27/2, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171008,"parameters":{"a_scale":8,"b_scale":9,"ratio":[3,9],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[8,1],b_scale:[9,1],ratio:[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0009","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":9,\"b_scale\":10,\"ratio\":[4,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 10, 2/5, 15, 50/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(9, 10, 2/5, 15, 50/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171009,"parameters":{"a_scale":9,"b_scale":10,"ratio":[4,10],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[9,1],b_scale:[10,1],ratio:[2,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0010","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":10,\"b_scale\":11,\"ratio\":[5,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 11, 5/11, 55/3, 121/6, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(10, 11, 5/11, 55/3, 121/6, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171010,"parameters":{"a_scale":10,"b_scale":11,"ratio":[5,11],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[10,1],b_scale:[11,1],ratio:[5,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0011","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":11,\"b_scale\":12,\"ratio\":[1,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 12, 1/7, 77/6, 14, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(11, 12, 1/7, 77/6, 14, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171011,"parameters":{"a_scale":11,"b_scale":12,"ratio":[1,7],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[11,1],b_scale:[12,1],ratio:[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0012","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":12,\"b_scale\":13,\"ratio\":[2,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 13, 1/4, 16, 52/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(12, 13, 1/4, 16, 52/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171012,"parameters":{"a_scale":12,"b_scale":13,"ratio":[2,8],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[12,1],b_scale:[13,1],ratio:[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0013","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":13,\"b_scale\":14,\"ratio\":[3,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 14, 1/3, 39/2, 21, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(13, 14, 1/3, 39/2, 21, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171013,"parameters":{"a_scale":13,"b_scale":14,"ratio":[3,9],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[13,1],b_scale:[14,1],ratio:[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0014","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":14,\"b_scale\":15,\"ratio\":[4,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 15, 2/5, 70/3, 25, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(14, 15, 2/5, 70/3, 25, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171014,"parameters":{"a_scale":14,"b_scale":15,"ratio":[4,10],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[14,1],b_scale:[15,1],ratio:[2,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0015","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":15,\"b_scale\":16,\"ratio\":[5,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 16, 5/11, 55/2, 88/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(15, 16, 5/11, 55/2, 88/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171015,"parameters":{"a_scale":15,"b_scale":16,"ratio":[5,11],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[15,1],b_scale:[16,1],ratio:[5,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0016","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":16,\"b_scale\":17,\"ratio\":[1,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 17, 1/7, 56/3, 119/6, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(16, 17, 1/7, 56/3, 119/6, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171016,"parameters":{"a_scale":16,"b_scale":17,"ratio":[1,7],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[16,1],b_scale:[17,1],ratio:[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0017","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":17,\"b_scale\":18,\"ratio\":[2,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 18, 1/4, 68/3, 24, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(17, 18, 1/4, 68/3, 24, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171017,"parameters":{"a_scale":17,"b_scale":18,"ratio":[2,8],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[17,1],b_scale:[18,1],ratio:[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0018","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":18,\"b_scale\":19,\"ratio\":[3,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 19, 1/3, 27, 57/2, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(18, 19, 1/3, 27, 57/2, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171018,"parameters":{"a_scale":18,"b_scale":19,"ratio":[3,9],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[18,1],b_scale:[19,1],ratio:[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0019","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":19,\"b_scale\":20,\"ratio\":[4,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 20, 2/5, 95/3, 100/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(19, 20, 2/5, 95/3, 100/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171019,"parameters":{"a_scale":19,"b_scale":20,"ratio":[4,10],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[19,1],b_scale:[20,1],ratio:[2,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0020","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":20,\"b_scale\":21,\"ratio\":[5,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 21, 5/11, 110/3, 77/2, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(20, 21, 5/11, 110/3, 77/2, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171020,"parameters":{"a_scale":20,"b_scale":21,"ratio":[5,11],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[20,1],b_scale:[21,1],ratio:[5,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0021","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":21,\"b_scale\":22,\"ratio\":[1,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 22, 1/7, 49/2, 77/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(21, 22, 1/7, 49/2, 77/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171021,"parameters":{"a_scale":21,"b_scale":22,"ratio":[1,7],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[21,1],b_scale:[22,1],ratio:[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0022","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":22,\"b_scale\":23,\"ratio\":[2,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 23, 1/4, 88/3, 92/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(22, 23, 1/4, 88/3, 92/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171022,"parameters":{"a_scale":22,"b_scale":23,"ratio":[2,8],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[22,1],b_scale:[23,1],ratio:[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0023","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":23,\"b_scale\":24,\"ratio\":[3,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 24, 1/3, 69/2, 36, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(23, 24, 1/3, 69/2, 36, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171023,"parameters":{"a_scale":23,"b_scale":24,"ratio":[3,9],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[23,1],b_scale:[24,1],ratio:[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0024","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":24,\"b_scale\":25,\"ratio\":[4,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 25, 2/5, 40, 125/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(24, 25, 2/5, 40, 125/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171024,"parameters":{"a_scale":24,"b_scale":25,"ratio":[4,10],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[24,1],b_scale:[25,1],ratio:[2,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0025","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-upper-geometric；資料={\"a_scale\":25,\"b_scale\":26,\"ratio\":[5,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 26, 5/11, 275/6, 143/3, 是, upper_comparison_proves_convergence)","explanation_zh":"Wave6第十一層核對=(25, 26, 5/11, 275/6, 143/3, 是, upper_comparison_proves_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-upper-geometric","seed":202611171025,"parameters":{"a_scale":25,"b_scale":26,"ratio":[5,11],"domain":"Exact_nonnegative_series_comparison","operation":"series-upper-geometric","semantic_template":"series-upper-geometric|{a_scale:[25,1],b_scale:[26,1],ratio:[5,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0026","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":2,\"b_scale\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(2, 1, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171026,"parameters":{"a_scale":2,"b_scale":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[2,1],b_scale:[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0027","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":4,\"b_scale\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 2, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(4, 2, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171027,"parameters":{"a_scale":4,"b_scale":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[4,1],b_scale:[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0028","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":6,\"b_scale\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 3, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(6, 3, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171028,"parameters":{"a_scale":6,"b_scale":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[6,1],b_scale:[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0029","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":8,\"b_scale\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 4, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(8, 4, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171029,"parameters":{"a_scale":8,"b_scale":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[8,1],b_scale:[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0030","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":10,\"b_scale\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 5, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(10, 5, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171030,"parameters":{"a_scale":10,"b_scale":5,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[10,1],b_scale:[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0031","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":12,\"b_scale\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 6, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(12, 6, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171031,"parameters":{"a_scale":12,"b_scale":6,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[12,1],b_scale:[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0032","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":14,\"b_scale\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 7, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(14, 7, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171032,"parameters":{"a_scale":14,"b_scale":7,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[14,1],b_scale:[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0033","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":16,\"b_scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 8, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(16, 8, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171033,"parameters":{"a_scale":16,"b_scale":8,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[16,1],b_scale:[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0034","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":18,\"b_scale\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 9, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(18, 9, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171034,"parameters":{"a_scale":18,"b_scale":9,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[18,1],b_scale:[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0035","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":20,\"b_scale\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 10, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(20, 10, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171035,"parameters":{"a_scale":20,"b_scale":10,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[20,1],b_scale:[10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0036","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":22,\"b_scale\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 11, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(22, 11, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171036,"parameters":{"a_scale":22,"b_scale":11,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[22,1],b_scale:[11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0037","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":24,\"b_scale\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 12, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(24, 12, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171037,"parameters":{"a_scale":24,"b_scale":12,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[24,1],b_scale:[12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0038","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":26,\"b_scale\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(26, 13, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(26, 13, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171038,"parameters":{"a_scale":26,"b_scale":13,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[26,1],b_scale:[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0039","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":28,\"b_scale\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(28, 14, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(28, 14, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171039,"parameters":{"a_scale":28,"b_scale":14,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[28,1],b_scale:[14,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0040","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":30,\"b_scale\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(30, 15, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(30, 15, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171040,"parameters":{"a_scale":30,"b_scale":15,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[30,1],b_scale:[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0041","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":32,\"b_scale\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(32, 16, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(32, 16, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171041,"parameters":{"a_scale":32,"b_scale":16,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[32,1],b_scale:[16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0042","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":34,\"b_scale\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(34, 17, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(34, 17, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171042,"parameters":{"a_scale":34,"b_scale":17,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[34,1],b_scale:[17,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0043","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":36,\"b_scale\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(36, 18, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(36, 18, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171043,"parameters":{"a_scale":36,"b_scale":18,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[36,1],b_scale:[18,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0044","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":38,\"b_scale\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(38, 19, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(38, 19, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171044,"parameters":{"a_scale":38,"b_scale":19,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[38,1],b_scale:[19,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0045","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":40,\"b_scale\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(40, 20, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(40, 20, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171045,"parameters":{"a_scale":40,"b_scale":20,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[40,1],b_scale:[20,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0046","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":42,\"b_scale\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(42, 21, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(42, 21, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171046,"parameters":{"a_scale":42,"b_scale":21,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[42,1],b_scale:[21,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0047","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":44,\"b_scale\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(44, 22, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(44, 22, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171047,"parameters":{"a_scale":44,"b_scale":22,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[44,1],b_scale:[22,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0048","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":46,\"b_scale\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(46, 23, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(46, 23, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171048,"parameters":{"a_scale":46,"b_scale":23,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[46,1],b_scale:[23,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0049","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":48,\"b_scale\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(48, 24, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(48, 24, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171049,"parameters":{"a_scale":48,"b_scale":24,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[48,1],b_scale:[24,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0050","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-lower-divergence；資料={\"a_scale\":50,\"b_scale\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(50, 25, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)","explanation_zh":"Wave6第十一層核對=(50, 25, a_n>=b_n>0_for_all_n, partial_sum_b=N*b_unbounded, 是, lower_comparison_proves_divergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-lower-divergence","seed":202611171050,"parameters":{"a_scale":50,"b_scale":25,"domain":"Exact_nonnegative_series_comparison","operation":"series-lower-divergence","semantic_template":"series-lower-divergence|{a_scale:[50,1],b_scale:[25,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0051","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[],\"prefix_b\":[],\"a_scale\":1,\"b_scale\":2,\"ratio\":[1,8],\"cutoff\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 0, 8/7, 16/7, 8/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(0, 0, 0, 8/7, 16/7, 8/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171051,"parameters":{"prefix_a":[],"prefix_b":[],"a_scale":1,"b_scale":2,"ratio":[1,8],"cutoff":0,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[1,1],b_scale:[2,1],cutoff:0,prefix_a:[],prefix_b:[],ratio:[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0052","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[2],\"prefix_b\":[1],\"a_scale\":2,\"b_scale\":3,\"ratio\":[2,9],\"cutoff\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1, 18/7, 27/7, 32/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(1, 2, 1, 18/7, 27/7, 32/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171052,"parameters":{"prefix_a":[2],"prefix_b":[1],"a_scale":2,"b_scale":3,"ratio":[2,9],"cutoff":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[2,1],b_scale:[3,1],cutoff:1,prefix_a:[[2,1]],prefix_b:[[1,1]],ratio:[2,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0053","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[3,4],\"prefix_b\":[1,2],\"a_scale\":3,\"b_scale\":4,\"ratio\":[3,10],\"cutoff\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 7, 3, 30/7, 40/7, 79/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(2, 7, 3, 30/7, 40/7, 79/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171053,"parameters":{"prefix_a":[3,4],"prefix_b":[1,2],"a_scale":3,"b_scale":4,"ratio":[3,10],"cutoff":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[3,1],b_scale:[4,1],cutoff:2,prefix_a:[[3,1],[4,1]],prefix_b:[[1,1],[2,1]],ratio:[3,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0054","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[4,5,6],\"prefix_b\":[1,2,3],\"a_scale\":4,\"b_scale\":5,\"ratio\":[4,11],\"cutoff\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 15, 6, 44/7, 55/7, 149/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(3, 15, 6, 44/7, 55/7, 149/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171054,"parameters":{"prefix_a":[4,5,6],"prefix_b":[1,2,3],"a_scale":4,"b_scale":5,"ratio":[4,11],"cutoff":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[4,1],b_scale:[5,1],cutoff:3,prefix_a:[[4,1],[5,1],[6,1]],prefix_b:[[1,1],[2,1],[3,1]],ratio:[4,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0055","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[5,6,7,8],\"prefix_b\":[1,2,3,4],\"a_scale\":5,\"b_scale\":6,\"ratio\":[5,12],\"cutoff\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 26, 10, 60/7, 72/7, 242/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(4, 26, 10, 60/7, 72/7, 242/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171055,"parameters":{"prefix_a":[5,6,7,8],"prefix_b":[1,2,3,4],"a_scale":5,"b_scale":6,"ratio":[5,12],"cutoff":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[5,1],b_scale:[6,1],cutoff:4,prefix_a:[[5,1],[6,1],[7,1],[8,1]],prefix_b:[[1,1],[2,1],[3,1],[4,1]],ratio:[5,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0056","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[],\"prefix_b\":[],\"a_scale\":6,\"b_scale\":7,\"ratio\":[1,8],\"cutoff\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 0, 48/7, 8, 48/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(0, 0, 0, 48/7, 8, 48/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171056,"parameters":{"prefix_a":[],"prefix_b":[],"a_scale":6,"b_scale":7,"ratio":[1,8],"cutoff":0,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[6,1],b_scale:[7,1],cutoff:0,prefix_a:[],prefix_b:[],ratio:[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0057","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[7],\"prefix_b\":[1],\"a_scale\":7,\"b_scale\":8,\"ratio\":[2,9],\"cutoff\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 7, 1, 9, 72/7, 16, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(1, 7, 1, 9, 72/7, 16, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171057,"parameters":{"prefix_a":[7],"prefix_b":[1],"a_scale":7,"b_scale":8,"ratio":[2,9],"cutoff":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[7,1],b_scale:[8,1],cutoff:1,prefix_a:[[7,1]],prefix_b:[[1,1]],ratio:[2,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0058","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[8,9],\"prefix_b\":[1,2],\"a_scale\":8,\"b_scale\":9,\"ratio\":[3,10],\"cutoff\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 17, 3, 80/7, 90/7, 199/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(2, 17, 3, 80/7, 90/7, 199/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171058,"parameters":{"prefix_a":[8,9],"prefix_b":[1,2],"a_scale":8,"b_scale":9,"ratio":[3,10],"cutoff":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[8,1],b_scale:[9,1],cutoff:2,prefix_a:[[8,1],[9,1]],prefix_b:[[1,1],[2,1]],ratio:[3,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0059","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[9,10,11],\"prefix_b\":[1,2,3],\"a_scale\":9,\"b_scale\":10,\"ratio\":[4,11],\"cutoff\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 30, 6, 99/7, 110/7, 309/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(3, 30, 6, 99/7, 110/7, 309/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171059,"parameters":{"prefix_a":[9,10,11],"prefix_b":[1,2,3],"a_scale":9,"b_scale":10,"ratio":[4,11],"cutoff":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[9,1],b_scale:[10,1],cutoff:3,prefix_a:[[9,1],[10,1],[11,1]],prefix_b:[[1,1],[2,1],[3,1]],ratio:[4,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0060","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[10,11,12,13],\"prefix_b\":[1,2,3,4],\"a_scale\":10,\"b_scale\":11,\"ratio\":[5,12],\"cutoff\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 46, 10, 120/7, 132/7, 442/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(4, 46, 10, 120/7, 132/7, 442/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171060,"parameters":{"prefix_a":[10,11,12,13],"prefix_b":[1,2,3,4],"a_scale":10,"b_scale":11,"ratio":[5,12],"cutoff":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[10,1],b_scale:[11,1],cutoff:4,prefix_a:[[10,1],[11,1],[12,1],[13,1]],prefix_b:[[1,1],[2,1],[3,1],[4,1]],ratio:[5,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0061","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[],\"prefix_b\":[],\"a_scale\":11,\"b_scale\":12,\"ratio\":[1,8],\"cutoff\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 0, 88/7, 96/7, 88/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(0, 0, 0, 88/7, 96/7, 88/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171061,"parameters":{"prefix_a":[],"prefix_b":[],"a_scale":11,"b_scale":12,"ratio":[1,8],"cutoff":0,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[11,1],b_scale:[12,1],cutoff:0,prefix_a:[],prefix_b:[],ratio:[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0062","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[12],\"prefix_b\":[1],\"a_scale\":12,\"b_scale\":13,\"ratio\":[2,9],\"cutoff\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 12, 1, 108/7, 117/7, 192/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(1, 12, 1, 108/7, 117/7, 192/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171062,"parameters":{"prefix_a":[12],"prefix_b":[1],"a_scale":12,"b_scale":13,"ratio":[2,9],"cutoff":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[12,1],b_scale:[13,1],cutoff:1,prefix_a:[[12,1]],prefix_b:[[1,1]],ratio:[2,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0063","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[13,14],\"prefix_b\":[1,2],\"a_scale\":13,\"b_scale\":14,\"ratio\":[3,10],\"cutoff\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 27, 3, 130/7, 20, 319/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(2, 27, 3, 130/7, 20, 319/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171063,"parameters":{"prefix_a":[13,14],"prefix_b":[1,2],"a_scale":13,"b_scale":14,"ratio":[3,10],"cutoff":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[13,1],b_scale:[14,1],cutoff:2,prefix_a:[[13,1],[14,1]],prefix_b:[[1,1],[2,1]],ratio:[3,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0064","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[14,15,16],\"prefix_b\":[1,2,3],\"a_scale\":14,\"b_scale\":15,\"ratio\":[4,11],\"cutoff\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 45, 6, 22, 165/7, 67, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(3, 45, 6, 22, 165/7, 67, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171064,"parameters":{"prefix_a":[14,15,16],"prefix_b":[1,2,3],"a_scale":14,"b_scale":15,"ratio":[4,11],"cutoff":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[14,1],b_scale:[15,1],cutoff:3,prefix_a:[[14,1],[15,1],[16,1]],prefix_b:[[1,1],[2,1],[3,1]],ratio:[4,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0065","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[15,16,17,18],\"prefix_b\":[1,2,3,4],\"a_scale\":15,\"b_scale\":16,\"ratio\":[5,12],\"cutoff\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 66, 10, 180/7, 192/7, 642/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(4, 66, 10, 180/7, 192/7, 642/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171065,"parameters":{"prefix_a":[15,16,17,18],"prefix_b":[1,2,3,4],"a_scale":15,"b_scale":16,"ratio":[5,12],"cutoff":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[15,1],b_scale:[16,1],cutoff:4,prefix_a:[[15,1],[16,1],[17,1],[18,1]],prefix_b:[[1,1],[2,1],[3,1],[4,1]],ratio:[5,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0066","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[],\"prefix_b\":[],\"a_scale\":16,\"b_scale\":17,\"ratio\":[1,8],\"cutoff\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 0, 128/7, 136/7, 128/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(0, 0, 0, 128/7, 136/7, 128/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171066,"parameters":{"prefix_a":[],"prefix_b":[],"a_scale":16,"b_scale":17,"ratio":[1,8],"cutoff":0,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[16,1],b_scale:[17,1],cutoff:0,prefix_a:[],prefix_b:[],ratio:[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0067","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[17],\"prefix_b\":[1],\"a_scale\":17,\"b_scale\":18,\"ratio\":[2,9],\"cutoff\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 17, 1, 153/7, 162/7, 272/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(1, 17, 1, 153/7, 162/7, 272/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171067,"parameters":{"prefix_a":[17],"prefix_b":[1],"a_scale":17,"b_scale":18,"ratio":[2,9],"cutoff":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[17,1],b_scale:[18,1],cutoff:1,prefix_a:[[17,1]],prefix_b:[[1,1]],ratio:[2,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0068","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[18,19],\"prefix_b\":[1,2],\"a_scale\":18,\"b_scale\":19,\"ratio\":[3,10],\"cutoff\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 37, 3, 180/7, 190/7, 439/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(2, 37, 3, 180/7, 190/7, 439/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171068,"parameters":{"prefix_a":[18,19],"prefix_b":[1,2],"a_scale":18,"b_scale":19,"ratio":[3,10],"cutoff":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[18,1],b_scale:[19,1],cutoff:2,prefix_a:[[18,1],[19,1]],prefix_b:[[1,1],[2,1]],ratio:[3,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0069","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[19,20,21],\"prefix_b\":[1,2,3],\"a_scale\":19,\"b_scale\":20,\"ratio\":[4,11],\"cutoff\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 60, 6, 209/7, 220/7, 629/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(3, 60, 6, 209/7, 220/7, 629/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171069,"parameters":{"prefix_a":[19,20,21],"prefix_b":[1,2,3],"a_scale":19,"b_scale":20,"ratio":[4,11],"cutoff":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[19,1],b_scale:[20,1],cutoff:3,prefix_a:[[19,1],[20,1],[21,1]],prefix_b:[[1,1],[2,1],[3,1]],ratio:[4,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0070","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[20,21,22,23],\"prefix_b\":[1,2,3,4],\"a_scale\":20,\"b_scale\":21,\"ratio\":[5,12],\"cutoff\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 86, 10, 240/7, 36, 842/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(4, 86, 10, 240/7, 36, 842/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171070,"parameters":{"prefix_a":[20,21,22,23],"prefix_b":[1,2,3,4],"a_scale":20,"b_scale":21,"ratio":[5,12],"cutoff":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[20,1],b_scale:[21,1],cutoff:4,prefix_a:[[20,1],[21,1],[22,1],[23,1]],prefix_b:[[1,1],[2,1],[3,1],[4,1]],ratio:[5,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0071","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[],\"prefix_b\":[],\"a_scale\":21,\"b_scale\":22,\"ratio\":[1,8],\"cutoff\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 0, 24, 176/7, 24, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(0, 0, 0, 24, 176/7, 24, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171071,"parameters":{"prefix_a":[],"prefix_b":[],"a_scale":21,"b_scale":22,"ratio":[1,8],"cutoff":0,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[21,1],b_scale:[22,1],cutoff:0,prefix_a:[],prefix_b:[],ratio:[1,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0072","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[22],\"prefix_b\":[1],\"a_scale\":22,\"b_scale\":23,\"ratio\":[2,9],\"cutoff\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 22, 1, 198/7, 207/7, 352/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(1, 22, 1, 198/7, 207/7, 352/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171072,"parameters":{"prefix_a":[22],"prefix_b":[1],"a_scale":22,"b_scale":23,"ratio":[2,9],"cutoff":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[22,1],b_scale:[23,1],cutoff:1,prefix_a:[[22,1]],prefix_b:[[1,1]],ratio:[2,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0073","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[23,24],\"prefix_b\":[1,2],\"a_scale\":23,\"b_scale\":24,\"ratio\":[3,10],\"cutoff\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 47, 3, 230/7, 240/7, 559/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(2, 47, 3, 230/7, 240/7, 559/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171073,"parameters":{"prefix_a":[23,24],"prefix_b":[1,2],"a_scale":23,"b_scale":24,"ratio":[3,10],"cutoff":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[23,1],b_scale:[24,1],cutoff:2,prefix_a:[[23,1],[24,1]],prefix_b:[[1,1],[2,1]],ratio:[3,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0074","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[24,25,26],\"prefix_b\":[1,2,3],\"a_scale\":24,\"b_scale\":25,\"ratio\":[4,11],\"cutoff\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 75, 6, 264/7, 275/7, 789/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(3, 75, 6, 264/7, 275/7, 789/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171074,"parameters":{"prefix_a":[24,25,26],"prefix_b":[1,2,3],"a_scale":24,"b_scale":25,"ratio":[4,11],"cutoff":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[24,1],b_scale:[25,1],cutoff:3,prefix_a:[[24,1],[25,1],[26,1]],prefix_b:[[1,1],[2,1],[3,1]],ratio:[4,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0075","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-eventual-tail；資料={\"prefix_a\":[25,26,27,28],\"prefix_b\":[1,2,3,4],\"a_scale\":25,\"b_scale\":26,\"ratio\":[5,12],\"cutoff\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 106, 10, 300/7, 312/7, 1042/7, 是, finite_prefix_does_not_change_tail_convergence)","explanation_zh":"Wave6第十一層核對=(4, 106, 10, 300/7, 312/7, 1042/7, 是, finite_prefix_does_not_change_tail_convergence)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-eventual-tail","seed":202611171075,"parameters":{"prefix_a":[25,26,27,28],"prefix_b":[1,2,3,4],"a_scale":25,"b_scale":26,"ratio":[5,12],"cutoff":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-eventual-tail","semantic_template":"series-eventual-tail|{a_scale:[25,1],b_scale:[26,1],cutoff:4,prefix_a:[[25,1],[26,1],[27,1],[28,1]],prefix_b:[[1,1],[2,1],[3,1],[4,1]],ratio:[5,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0076","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 1, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 1, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171076,"parameters":{"mode":"finite_sample","scale":1,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0077","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"divergent_upper\",\"scale\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(divergent_upper, a_n=2/n^2, b_n=2/n, a_n<=b_n, b_diverges_but_a_converges, 否)","explanation_zh":"Wave6第十一層核對=(divergent_upper, a_n=2/n^2, b_n=2/n, a_n<=b_n, b_diverges_but_a_converges, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171077,"parameters":{"mode":"divergent_upper","scale":2,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"divergent_upper\",scale:[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0078","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"signed_terms\",\"scale\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_terms, a_n=(-1)^n*3/n, nonnegative_hypothesis_fails, 否)","explanation_zh":"Wave6第十一層核對=(signed_terms, a_n=(-1)^n*3/n, nonnegative_hypothesis_fails, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171078,"parameters":{"mode":"signed_terms","scale":3,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"signed_terms\",scale:[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0079","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(unknown_reference, 4, comparison_holds_reference_status_not_proved, 否)","explanation_zh":"Wave6第十一層核對=(unknown_reference, 4, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171079,"parameters":{"mode":"unknown_reference","scale":4,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"unknown_reference\",scale:[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0080","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 5, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 5, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171080,"parameters":{"mode":"finite_sample","scale":5,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0081","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"divergent_upper\",\"scale\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(divergent_upper, a_n=6/n^2, b_n=6/n, a_n<=b_n, b_diverges_but_a_converges, 否)","explanation_zh":"Wave6第十一層核對=(divergent_upper, a_n=6/n^2, b_n=6/n, a_n<=b_n, b_diverges_but_a_converges, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171081,"parameters":{"mode":"divergent_upper","scale":6,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"divergent_upper\",scale:[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0082","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"signed_terms\",\"scale\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_terms, a_n=(-1)^n*7/n, nonnegative_hypothesis_fails, 否)","explanation_zh":"Wave6第十一層核對=(signed_terms, a_n=(-1)^n*7/n, nonnegative_hypothesis_fails, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171082,"parameters":{"mode":"signed_terms","scale":7,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"signed_terms\",scale:[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0083","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(unknown_reference, 8, comparison_holds_reference_status_not_proved, 否)","explanation_zh":"Wave6第十一層核對=(unknown_reference, 8, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171083,"parameters":{"mode":"unknown_reference","scale":8,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"unknown_reference\",scale:[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0084","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 9, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 9, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171084,"parameters":{"mode":"finite_sample","scale":9,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0085","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"divergent_upper\",\"scale\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(divergent_upper, a_n=10/n^2, b_n=10/n, a_n<=b_n, b_diverges_but_a_converges, 否)","explanation_zh":"Wave6第十一層核對=(divergent_upper, a_n=10/n^2, b_n=10/n, a_n<=b_n, b_diverges_but_a_converges, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171085,"parameters":{"mode":"divergent_upper","scale":10,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"divergent_upper\",scale:[10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0086","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"signed_terms\",\"scale\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_terms, a_n=(-1)^n*11/n, nonnegative_hypothesis_fails, 否)","explanation_zh":"Wave6第十一層核對=(signed_terms, a_n=(-1)^n*11/n, nonnegative_hypothesis_fails, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171086,"parameters":{"mode":"signed_terms","scale":11,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"signed_terms\",scale:[11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0087","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(unknown_reference, 12, comparison_holds_reference_status_not_proved, 否)","explanation_zh":"Wave6第十一層核對=(unknown_reference, 12, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171087,"parameters":{"mode":"unknown_reference","scale":12,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"unknown_reference\",scale:[12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0088","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 13, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 13, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171088,"parameters":{"mode":"finite_sample","scale":13,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0089","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"divergent_upper\",\"scale\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(divergent_upper, a_n=14/n^2, b_n=14/n, a_n<=b_n, b_diverges_but_a_converges, 否)","explanation_zh":"Wave6第十一層核對=(divergent_upper, a_n=14/n^2, b_n=14/n, a_n<=b_n, b_diverges_but_a_converges, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171089,"parameters":{"mode":"divergent_upper","scale":14,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"divergent_upper\",scale:[14,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0090","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"signed_terms\",\"scale\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_terms, a_n=(-1)^n*15/n, nonnegative_hypothesis_fails, 否)","explanation_zh":"Wave6第十一層核對=(signed_terms, a_n=(-1)^n*15/n, nonnegative_hypothesis_fails, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171090,"parameters":{"mode":"signed_terms","scale":15,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"signed_terms\",scale:[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0091","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(unknown_reference, 16, comparison_holds_reference_status_not_proved, 否)","explanation_zh":"Wave6第十一層核對=(unknown_reference, 16, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171091,"parameters":{"mode":"unknown_reference","scale":16,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"unknown_reference\",scale:[16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0092","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 17, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 17, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171092,"parameters":{"mode":"finite_sample","scale":17,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[17,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0093","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"divergent_upper\",\"scale\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(divergent_upper, a_n=18/n^2, b_n=18/n, a_n<=b_n, b_diverges_but_a_converges, 否)","explanation_zh":"Wave6第十一層核對=(divergent_upper, a_n=18/n^2, b_n=18/n, a_n<=b_n, b_diverges_but_a_converges, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171093,"parameters":{"mode":"divergent_upper","scale":18,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"divergent_upper\",scale:[18,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0094","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"signed_terms\",\"scale\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_terms, a_n=(-1)^n*19/n, nonnegative_hypothesis_fails, 否)","explanation_zh":"Wave6第十一層核對=(signed_terms, a_n=(-1)^n*19/n, nonnegative_hypothesis_fails, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171094,"parameters":{"mode":"signed_terms","scale":19,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"signed_terms\",scale:[19,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0095","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(unknown_reference, 20, comparison_holds_reference_status_not_proved, 否)","explanation_zh":"Wave6第十一層核對=(unknown_reference, 20, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171095,"parameters":{"mode":"unknown_reference","scale":20,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"unknown_reference\",scale:[20,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0096","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 21, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 21, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171096,"parameters":{"mode":"finite_sample","scale":21,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[21,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0097","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"divergent_upper\",\"scale\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(divergent_upper, a_n=22/n^2, b_n=22/n, a_n<=b_n, b_diverges_but_a_converges, 否)","explanation_zh":"Wave6第十一層核對=(divergent_upper, a_n=22/n^2, b_n=22/n, a_n<=b_n, b_diverges_but_a_converges, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171097,"parameters":{"mode":"divergent_upper","scale":22,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"divergent_upper\",scale:[22,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0098","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"signed_terms\",\"scale\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(signed_terms, a_n=(-1)^n*23/n, nonnegative_hypothesis_fails, 否)","explanation_zh":"Wave6第十一層核對=(signed_terms, a_n=(-1)^n*23/n, nonnegative_hypothesis_fails, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171098,"parameters":{"mode":"signed_terms","scale":23,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"signed_terms\",scale:[23,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0099","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(unknown_reference, 24, comparison_holds_reference_status_not_proved, 否)","explanation_zh":"Wave6第十一層核對=(unknown_reference, 24, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171099,"parameters":{"mode":"unknown_reference","scale":24,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"unknown_reference\",scale:[24,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261117-r01-series-comparison-test-0100","batch_id":"batch-20261015-advance-20261117-r01-series-comparison-test-foundations","language":"zh-Hant","source_mko_ids":["mko-series-comparison-test"],"title_zh":"級數比較判別法","stem_zh":"非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"finite_sample\",\"scale\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(finite_sample, 25, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)","explanation_zh":"Wave6第十一層核對=(finite_sample, 25, first_N_terms_compare_next_term_fails, 否, finite_samples_do_not_establish_eventual_forall)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["級數比較判別法"]},"variant":{"family_id":"qf-mod48-series-comparison-boundary","seed":202611171100,"parameters":{"mode":"finite_sample","scale":25,"domain":"Exact_nonnegative_series_comparison","operation":"series-comparison-boundary","semantic_template":"series-comparison-boundary|{mode:\"finite_sample\",scale:[25,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}