{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0001","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[1,2],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, -1/2, 1, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(1/2, -1/2, 1, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043001,"parameters":{"a":[1,2],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[1,2],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0002","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[2,3],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2/3, -1/2, 4/3, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(2/3, -1/2, 4/3, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043002,"parameters":{"a":[2,3],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[2,3],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0003","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[3,4],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, -1/2, 3/2, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(3/4, -1/2, 3/2, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043003,"parameters":{"a":[3,4],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[3,4],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0004","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[4,5],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/5, -1/2, 8/5, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(4/5, -1/2, 8/5, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043004,"parameters":{"a":[4,5],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[4,5],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0005","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[5,6],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/6, -1/2, 5/3, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(5/6, -1/2, 5/3, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043005,"parameters":{"a":[5,6],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[5,6],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0006","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[6,7],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6/7, -1/2, 12/7, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(6/7, -1/2, 12/7, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043006,"parameters":{"a":[6,7],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[6,7],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0007","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[7,8],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/8, -1/2, 7/4, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(7/8, -1/2, 7/4, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043007,"parameters":{"a":[7,8],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[7,8],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0008","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[8,9],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/9, -1/2, 16/9, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(8/9, -1/2, 16/9, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043008,"parameters":{"a":[8,9],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[8,9],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0009","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[9,10],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/10, -1/2, 9/5, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(9/10, -1/2, 9/5, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043009,"parameters":{"a":[9,10],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[9,10],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0010","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[10,11],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10/11, -1/2, 20/11, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(10/11, -1/2, 20/11, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043010,"parameters":{"a":[10,11],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[10,11],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0011","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[11,12],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/12, -1/2, 11/6, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(11/12, -1/2, 11/6, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043011,"parameters":{"a":[11,12],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[11,12],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0012","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[12,13],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12/13, -1/2, 24/13, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(12/13, -1/2, 24/13, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043012,"parameters":{"a":[12,13],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[12,13],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0013","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[13,14],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/14, -1/2, 13/7, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(13/14, -1/2, 13/7, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043013,"parameters":{"a":[13,14],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[13,14],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0014","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[14,15],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14/15, -1/2, 28/15, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(14/15, -1/2, 28/15, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043014,"parameters":{"a":[14,15],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[14,15],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0015","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[15,16],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15/16, -1/2, 15/8, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(15/16, -1/2, 15/8, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043015,"parameters":{"a":[15,16],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[15,16],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0016","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[16,17],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16/17, -1/2, 32/17, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(16/17, -1/2, 32/17, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043016,"parameters":{"a":[16,17],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[16,17],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0017","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[17,18],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/18, -1/2, 17/9, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(17/18, -1/2, 17/9, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043017,"parameters":{"a":[17,18],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[17,18],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0018","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[18,19],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18/19, -1/2, 36/19, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(18/19, -1/2, 36/19, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043018,"parameters":{"a":[18,19],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[18,19],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0019","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[19,20],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/20, -1/2, 19/10, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(19/20, -1/2, 19/10, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043019,"parameters":{"a":[19,20],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[19,20],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0020","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[20,21],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20/21, -1/2, 40/21, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(20/21, -1/2, 40/21, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043020,"parameters":{"a":[20,21],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[20,21],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0021","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[21,22],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21/22, -1/2, 21/11, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(21/22, -1/2, 21/11, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043021,"parameters":{"a":[21,22],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[21,22],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0022","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[22,23],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22/23, -1/2, 44/23, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(22/23, -1/2, 44/23, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043022,"parameters":{"a":[22,23],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[22,23],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0023","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[23,24],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/24, -1/2, 23/12, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(23/24, -1/2, 23/12, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043023,"parameters":{"a":[23,24],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[23,24],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0024","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[24,25],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24/25, -1/2, 48/25, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(24/25, -1/2, 48/25, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043024,"parameters":{"a":[24,25],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[24,25],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0025","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-geometric；資料={\"a\":[25,26],\"r\":[-1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25/26, -1/2, 25/13, 是, absolute_geometric_certificate)","explanation_zh":"Wave5第四層核對=(25/26, -1/2, 25/13, 是, absolute_geometric_certificate)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-geometric","seed":202611043025,"parameters":{"a":[25,26],"r":[-1,2],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-geometric","semantic_template":"qf-mod35-absseries-geometric/{\"a\":[25,26],\"r\":[-1,2]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0026","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":1,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 5, [1, -1/2, 1/3, -1/4, 1/5], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(1, 5, [1, -1/2, 1/3, -1/4, 1/5], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043026,"parameters":{"shift":1,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0027","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":2,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 5, [1/2, -1/3, 1/4, -1/5, 1/6], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(2, 5, [1/2, -1/3, 1/4, -1/5, 1/6], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043027,"parameters":{"shift":2,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":2}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0028","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":3,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 5, [1/3, -1/4, 1/5, -1/6, 1/7], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(3, 5, [1/3, -1/4, 1/5, -1/6, 1/7], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043028,"parameters":{"shift":3,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0029","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":4,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5, [1/4, -1/5, 1/6, -1/7, 1/8], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(4, 5, [1/4, -1/5, 1/6, -1/7, 1/8], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043029,"parameters":{"shift":4,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0030","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":5,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043030,"parameters":{"shift":5,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0031","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":6,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 5, [1/6, -1/7, 1/8, -1/9, 1/10], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(6, 5, [1/6, -1/7, 1/8, -1/9, 1/10], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043031,"parameters":{"shift":6,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":6}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0032","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":7,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 5, [1/7, -1/8, 1/9, -1/10, 1/11], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(7, 5, [1/7, -1/8, 1/9, -1/10, 1/11], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043032,"parameters":{"shift":7,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0033","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":8,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 5, [1/8, -1/9, 1/10, -1/11, 1/12], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(8, 5, [1/8, -1/9, 1/10, -1/11, 1/12], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043033,"parameters":{"shift":8,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0034","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":9,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 5, [1/9, -1/10, 1/11, -1/12, 1/13], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(9, 5, [1/9, -1/10, 1/11, -1/12, 1/13], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043034,"parameters":{"shift":9,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0035","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":10,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 5, [1/10, -1/11, 1/12, -1/13, 1/14], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(10, 5, [1/10, -1/11, 1/12, -1/13, 1/14], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043035,"parameters":{"shift":10,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0036","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":11,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 5, [1/11, -1/12, 1/13, -1/14, 1/15], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(11, 5, [1/11, -1/12, 1/13, -1/14, 1/15], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043036,"parameters":{"shift":11,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0037","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":12,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 5, [1/12, -1/13, 1/14, -1/15, 1/16], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(12, 5, [1/12, -1/13, 1/14, -1/15, 1/16], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043037,"parameters":{"shift":12,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0038","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":13,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 5, [1/13, -1/14, 1/15, -1/16, 1/17], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(13, 5, [1/13, -1/14, 1/15, -1/16, 1/17], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043038,"parameters":{"shift":13,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":13}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0039","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":14,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 5, [1/14, -1/15, 1/16, -1/17, 1/18], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(14, 5, [1/14, -1/15, 1/16, -1/17, 1/18], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043039,"parameters":{"shift":14,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":14}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0040","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":15,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 5, [1/15, -1/16, 1/17, -1/18, 1/19], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(15, 5, [1/15, -1/16, 1/17, -1/18, 1/19], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043040,"parameters":{"shift":15,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":15}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0041","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":16,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 5, [1/16, -1/17, 1/18, -1/19, 1/20], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(16, 5, [1/16, -1/17, 1/18, -1/19, 1/20], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043041,"parameters":{"shift":16,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":16}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0042","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":17,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 5, [1/17, -1/18, 1/19, -1/20, 1/21], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(17, 5, [1/17, -1/18, 1/19, -1/20, 1/21], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043042,"parameters":{"shift":17,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":17}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0043","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":18,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 5, [1/18, -1/19, 1/20, -1/21, 1/22], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(18, 5, [1/18, -1/19, 1/20, -1/21, 1/22], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043043,"parameters":{"shift":18,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":18}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0044","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":19,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 5, [1/19, -1/20, 1/21, -1/22, 1/23], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(19, 5, [1/19, -1/20, 1/21, -1/22, 1/23], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043044,"parameters":{"shift":19,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":19}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0045","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":20,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 5, [1/20, -1/21, 1/22, -1/23, 1/24], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(20, 5, [1/20, -1/21, 1/22, -1/23, 1/24], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043045,"parameters":{"shift":20,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":20}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0046","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":21,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 5, [1/21, -1/22, 1/23, -1/24, 1/25], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(21, 5, [1/21, -1/22, 1/23, -1/24, 1/25], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043046,"parameters":{"shift":21,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":21}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0047","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":22,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 5, [1/22, -1/23, 1/24, -1/25, 1/26], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(22, 5, [1/22, -1/23, 1/24, -1/25, 1/26], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043047,"parameters":{"shift":22,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":22}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0048","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":23,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 5, [1/23, -1/24, 1/25, -1/26, 1/27], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(23, 5, [1/23, -1/24, 1/25, -1/26, 1/27], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043048,"parameters":{"shift":23,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":23}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0049","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":24,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 5, [1/24, -1/25, 1/26, -1/27, 1/28], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(24, 5, [1/24, -1/25, 1/26, -1/27, 1/28], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043049,"parameters":{"shift":24,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":24}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0050","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":25,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 5, [1/25, -1/26, 1/27, -1/28, 1/29], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)","explanation_zh":"Wave5第四層核對=(25, 5, [1/25, -1/26, 1/27, -1/28, 1/29], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-conditional-alternating","seed":202611043050,"parameters":{"shift":25,"n":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-conditional-alternating","semantic_template":"qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":25}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0051","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,2],[-1,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/2, -1/3], [1/2, 1/3], 5/6, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/2, -1/3], [1/2, 1/3], 5/6, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043051,"parameters":{"terms":[[1,2],[-1,3]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,2],[-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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0052","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,3],[-1,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/3, -1/4], [1/3, 1/4], 7/12, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/3, -1/4], [1/3, 1/4], 7/12, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043052,"parameters":{"terms":[[1,3],[-1,4]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,3],[-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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0053","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,4],[-1,5]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/4, -1/5], [1/4, 1/5], 9/20, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/4, -1/5], [1/4, 1/5], 9/20, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043053,"parameters":{"terms":[[1,4],[-1,5]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,4],[-1,5]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0054","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,5],[-1,6]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/5, -1/6], [1/5, 1/6], 11/30, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/5, -1/6], [1/5, 1/6], 11/30, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043054,"parameters":{"terms":[[1,5],[-1,6]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,5],[-1,6]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0055","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,6],[-1,7]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/6, -1/7], [1/6, 1/7], 13/42, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/6, -1/7], [1/6, 1/7], 13/42, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043055,"parameters":{"terms":[[1,6],[-1,7]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,6],[-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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0056","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,7],[-1,8]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/7, -1/8], [1/7, 1/8], 15/56, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/7, -1/8], [1/7, 1/8], 15/56, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043056,"parameters":{"terms":[[1,7],[-1,8]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,7],[-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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0057","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,8],[-1,9]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/8, -1/9], [1/8, 1/9], 17/72, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/8, -1/9], [1/8, 1/9], 17/72, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043057,"parameters":{"terms":[[1,8],[-1,9]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,8],[-1,9]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0058","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,9],[-1,10]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/9, -1/10], [1/9, 1/10], 19/90, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/9, -1/10], [1/9, 1/10], 19/90, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043058,"parameters":{"terms":[[1,9],[-1,10]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,9],[-1,10]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0059","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,10],[-1,11]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/10, -1/11], [1/10, 1/11], 21/110, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/10, -1/11], [1/10, 1/11], 21/110, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043059,"parameters":{"terms":[[1,10],[-1,11]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,10],[-1,11]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0060","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,11],[-1,12]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/11, -1/12], [1/11, 1/12], 23/132, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/11, -1/12], [1/11, 1/12], 23/132, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043060,"parameters":{"terms":[[1,11],[-1,12]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,11],[-1,12]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0061","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,12],[-1,13]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/12, -1/13], [1/12, 1/13], 25/156, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/12, -1/13], [1/12, 1/13], 25/156, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043061,"parameters":{"terms":[[1,12],[-1,13]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,12],[-1,13]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0062","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,13],[-1,14]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/13, -1/14], [1/13, 1/14], 27/182, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/13, -1/14], [1/13, 1/14], 27/182, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043062,"parameters":{"terms":[[1,13],[-1,14]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,13],[-1,14]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0063","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,14],[-1,15]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/14, -1/15], [1/14, 1/15], 29/210, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/14, -1/15], [1/14, 1/15], 29/210, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043063,"parameters":{"terms":[[1,14],[-1,15]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,14],[-1,15]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0064","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,15],[-1,16]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/15, -1/16], [1/15, 1/16], 31/240, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/15, -1/16], [1/15, 1/16], 31/240, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043064,"parameters":{"terms":[[1,15],[-1,16]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,15],[-1,16]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0065","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,16],[-1,17]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/16, -1/17], [1/16, 1/17], 33/272, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/16, -1/17], [1/16, 1/17], 33/272, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043065,"parameters":{"terms":[[1,16],[-1,17]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,16],[-1,17]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0066","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,17],[-1,18]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/17, -1/18], [1/17, 1/18], 35/306, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/17, -1/18], [1/17, 1/18], 35/306, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043066,"parameters":{"terms":[[1,17],[-1,18]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,17],[-1,18]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0067","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,18],[-1,19]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/18, -1/19], [1/18, 1/19], 37/342, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/18, -1/19], [1/18, 1/19], 37/342, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043067,"parameters":{"terms":[[1,18],[-1,19]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,18],[-1,19]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0068","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,19],[-1,20]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/19, -1/20], [1/19, 1/20], 39/380, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/19, -1/20], [1/19, 1/20], 39/380, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043068,"parameters":{"terms":[[1,19],[-1,20]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,19],[-1,20]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0069","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,20],[-1,21]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/20, -1/21], [1/20, 1/21], 41/420, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/20, -1/21], [1/20, 1/21], 41/420, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043069,"parameters":{"terms":[[1,20],[-1,21]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,20],[-1,21]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0070","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,21],[-1,22]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/21, -1/22], [1/21, 1/22], 43/462, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/21, -1/22], [1/21, 1/22], 43/462, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043070,"parameters":{"terms":[[1,21],[-1,22]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,21],[-1,22]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0071","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,22],[-1,23]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/22, -1/23], [1/22, 1/23], 45/506, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/22, -1/23], [1/22, 1/23], 45/506, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043071,"parameters":{"terms":[[1,22],[-1,23]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,22],[-1,23]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0072","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,23],[-1,24]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/23, -1/24], [1/23, 1/24], 47/552, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/23, -1/24], [1/23, 1/24], 47/552, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043072,"parameters":{"terms":[[1,23],[-1,24]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,23],[-1,24]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0073","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,24],[-1,25]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/24, -1/25], [1/24, 1/25], 49/600, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/24, -1/25], [1/24, 1/25], 49/600, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043073,"parameters":{"terms":[[1,24],[-1,25]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,24],[-1,25]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0074","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,25],[-1,26]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/25, -1/26], [1/25, 1/26], 51/650, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/25, -1/26], [1/25, 1/26], 51/650, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043074,"parameters":{"terms":[[1,25],[-1,26]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,25],[-1,26]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0075","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-absolute-partial；資料={\"terms\":[[1,26],[-1,27]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/26, -1/27], [1/26, 1/27], 53/702, finite_absolute_partial_sum_only)","explanation_zh":"Wave5第四層核對=([1/26, -1/27], [1/26, 1/27], 53/702, finite_absolute_partial_sum_only)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-absolute-partial","seed":202611043075,"parameters":{"terms":[[1,26],[-1,27]],"domain":"Exact_absolute_or_conditional_series","operation":"absseries-absolute-partial","semantic_template":"qf-mod35-absseries-absolute-partial/{\"terms\":[[1,26],[-1,27]]}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0076","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":1,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(1, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043076,"parameters":{"shift":1,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0077","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":2,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(2, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043077,"parameters":{"shift":2,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":2}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0078","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":3,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(3, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043078,"parameters":{"shift":3,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0079","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":4,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(4, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043079,"parameters":{"shift":4,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0080","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":5,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(5, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043080,"parameters":{"shift":5,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0081","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":6,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(6, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043081,"parameters":{"shift":6,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":6}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0082","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":7,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(7, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043082,"parameters":{"shift":7,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0083","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":8,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(8, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043083,"parameters":{"shift":8,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0084","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":9,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(9, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043084,"parameters":{"shift":9,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0085","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":10,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(10, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043085,"parameters":{"shift":10,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0086","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":11,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(11, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043086,"parameters":{"shift":11,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0087","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":12,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(12, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043087,"parameters":{"shift":12,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0088","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":13,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(13, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043088,"parameters":{"shift":13,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":13}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0089","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":14,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(14, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043089,"parameters":{"shift":14,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":14}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0090","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":15,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(15, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043090,"parameters":{"shift":15,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":15}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0091","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":16,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(16, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043091,"parameters":{"shift":16,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":16}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0092","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":17,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(17, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043092,"parameters":{"shift":17,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":17}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0093","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":18,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(18, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043093,"parameters":{"shift":18,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":18}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0094","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":19,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(19, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043094,"parameters":{"shift":19,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":19}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0095","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":20,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(20, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043095,"parameters":{"shift":20,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":20}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0096","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":21,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(21, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043096,"parameters":{"shift":21,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":21}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0097","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":22,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(22, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043097,"parameters":{"shift":22,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":22}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0098","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":23,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(23, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043098,"parameters":{"shift":23,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":23}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0099","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":24,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(24, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043099,"parameters":{"shift":24,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":24}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r03-absolute-convergence-of-series-0100","batch_id":"batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-convergence-of-series"],"title_zh":"絕對收斂","stem_zh":"partial sums與absolute-series exact convergence certificate。操作=absseries-term-zero-boundary；資料={\"shift\":25,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 5, 是, 否, term_zero_not_absolute_convergence)","explanation_zh":"Wave5第四層核對=(25, 5, 是, 否, term_zero_not_absolute_convergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["絕對收斂"]},"variant":{"family_id":"qf-mod35-absseries-term-zero-boundary","seed":202611043100,"parameters":{"shift":25,"prefix_length":5,"domain":"Exact_absolute_or_conditional_series","operation":"absseries-term-zero-boundary","semantic_template":"qf-mod35-absseries-term-zero-boundary/{\"prefix_length\":5,\"shift\":25}"}},"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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}