{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r02-supremum-and-infimum-0001","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[1,2],[-2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/2, -2/3, 3/4], 3/4, -2/3, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([1/2, -2/3, 3/4], 3/4, -2/3, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072001,"parameters":{"values":[[1,2],[-2,3],[3,4]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[1,2],[-2,3],[3,4]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0002","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[2,3],[-3,4],[5,5]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2/3, -3/4, 1], 1, -3/4, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([2/3, -3/4, 1], 1, -3/4, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072002,"parameters":{"values":[[2,3],[-3,4],[5,5]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[2,3],[-3,4],[5,5]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0003","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[3,4],[-4,5],[7,6]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3/4, -4/5, 7/6], 7/6, -4/5, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([3/4, -4/5, 7/6], 7/6, -4/5, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072003,"parameters":{"values":[[3,4],[-4,5],[7,6]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[3,4],[-4,5],[7,6]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0004","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[4,5],[-5,6],[9,7]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4/5, -5/6, 9/7], 9/7, -5/6, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([4/5, -5/6, 9/7], 9/7, -5/6, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072004,"parameters":{"values":[[4,5],[-5,6],[9,7]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[4,5],[-5,6],[9,7]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0005","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[5,6],[-6,7],[11,8]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([5/6, -6/7, 11/8], 11/8, -6/7, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([5/6, -6/7, 11/8], 11/8, -6/7, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072005,"parameters":{"values":[[5,6],[-6,7],[11,8]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[5,6],[-6,7],[11,8]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0006","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[6,7],[-7,8],[13,9]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([6/7, -7/8, 13/9], 13/9, -7/8, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([6/7, -7/8, 13/9], 13/9, -7/8, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072006,"parameters":{"values":[[6,7],[-7,8],[13,9]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[6,7],[-7,8],[13,9]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0007","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[7,8],[-8,9],[15,10]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([7/8, -8/9, 3/2], 3/2, -8/9, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([7/8, -8/9, 3/2], 3/2, -8/9, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072007,"parameters":{"values":[[7,8],[-8,9],[15,10]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[7,8],[-8,9],[15,10]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0008","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[8,9],[-9,10],[17,11]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([8/9, -9/10, 17/11], 17/11, -9/10, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([8/9, -9/10, 17/11], 17/11, -9/10, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072008,"parameters":{"values":[[8,9],[-9,10],[17,11]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[8,9],[-9,10],[17,11]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0009","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[9,10],[-10,11],[19,12]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([9/10, -10/11, 19/12], 19/12, -10/11, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([9/10, -10/11, 19/12], 19/12, -10/11, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072009,"parameters":{"values":[[9,10],[-10,11],[19,12]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[9,10],[-10,11],[19,12]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0010","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[10,11],[-11,12],[21,13]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([10/11, -11/12, 21/13], 21/13, -11/12, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([10/11, -11/12, 21/13], 21/13, -11/12, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072010,"parameters":{"values":[[10,11],[-11,12],[21,13]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[10,11],[-11,12],[21,13]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0011","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[11,12],[-12,13],[23,14]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([11/12, -12/13, 23/14], 23/14, -12/13, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([11/12, -12/13, 23/14], 23/14, -12/13, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072011,"parameters":{"values":[[11,12],[-12,13],[23,14]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[11,12],[-12,13],[23,14]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0012","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[12,13],[-13,14],[25,15]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([12/13, -13/14, 5/3], 5/3, -13/14, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([12/13, -13/14, 5/3], 5/3, -13/14, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072012,"parameters":{"values":[[12,13],[-13,14],[25,15]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[12,13],[-13,14],[25,15]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0013","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[13,14],[-14,15],[27,16]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([13/14, -14/15, 27/16], 27/16, -14/15, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([13/14, -14/15, 27/16], 27/16, -14/15, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072013,"parameters":{"values":[[13,14],[-14,15],[27,16]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[13,14],[-14,15],[27,16]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0014","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[14,15],[-15,16],[29,17]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([14/15, -15/16, 29/17], 29/17, -15/16, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([14/15, -15/16, 29/17], 29/17, -15/16, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072014,"parameters":{"values":[[14,15],[-15,16],[29,17]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[14,15],[-15,16],[29,17]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0015","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[15,16],[-16,17],[31,18]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([15/16, -16/17, 31/18], 31/18, -16/17, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([15/16, -16/17, 31/18], 31/18, -16/17, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072015,"parameters":{"values":[[15,16],[-16,17],[31,18]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[15,16],[-16,17],[31,18]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0016","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[16,17],[-17,18],[33,19]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([16/17, -17/18, 33/19], 33/19, -17/18, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([16/17, -17/18, 33/19], 33/19, -17/18, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072016,"parameters":{"values":[[16,17],[-17,18],[33,19]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[16,17],[-17,18],[33,19]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0017","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[17,18],[-18,19],[35,20]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([17/18, -18/19, 7/4], 7/4, -18/19, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([17/18, -18/19, 7/4], 7/4, -18/19, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072017,"parameters":{"values":[[17,18],[-18,19],[35,20]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[17,18],[-18,19],[35,20]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0018","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[18,19],[-19,20],[37,21]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([18/19, -19/20, 37/21], 37/21, -19/20, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([18/19, -19/20, 37/21], 37/21, -19/20, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072018,"parameters":{"values":[[18,19],[-19,20],[37,21]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[18,19],[-19,20],[37,21]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0019","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[19,20],[-20,21],[39,22]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([19/20, -20/21, 39/22], 39/22, -20/21, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([19/20, -20/21, 39/22], 39/22, -20/21, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072019,"parameters":{"values":[[19,20],[-20,21],[39,22]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[19,20],[-20,21],[39,22]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0020","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[20,21],[-21,22],[41,23]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([20/21, -21/22, 41/23], 41/23, -21/22, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([20/21, -21/22, 41/23], 41/23, -21/22, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072020,"parameters":{"values":[[20,21],[-21,22],[41,23]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[20,21],[-21,22],[41,23]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0021","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[21,22],[-22,23],[43,24]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([21/22, -22/23, 43/24], 43/24, -22/23, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([21/22, -22/23, 43/24], 43/24, -22/23, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072021,"parameters":{"values":[[21,22],[-22,23],[43,24]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[21,22],[-22,23],[43,24]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0022","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[22,23],[-23,24],[45,25]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([22/23, -23/24, 9/5], 9/5, -23/24, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([22/23, -23/24, 9/5], 9/5, -23/24, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072022,"parameters":{"values":[[22,23],[-23,24],[45,25]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[22,23],[-23,24],[45,25]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0023","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[23,24],[-24,25],[47,26]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([23/24, -24/25, 47/26], 47/26, -24/25, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([23/24, -24/25, 47/26], 47/26, -24/25, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072023,"parameters":{"values":[[23,24],[-24,25],[47,26]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[23,24],[-24,25],[47,26]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0024","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[24,25],[-25,26],[49,27]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([24/25, -25/26, 49/27], 49/27, -25/26, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([24/25, -25/26, 49/27], 49/27, -25/26, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072024,"parameters":{"values":[[24,25],[-25,26],[49,27]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[24,25],[-25,26],[49,27]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0025","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-finite-extrema；資料={\"values\":[[25,26],[-26,27],[51,28]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([25/26, -26/27, 51/28], 51/28, -26/27, 是, 是, finite_nonempty_set_extrema)","explanation_zh":"Wave6根層核對=([25/26, -26/27, 51/28], 51/28, -26/27, 是, 是, finite_nonempty_set_extrema)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-finite-extrema","seed":202611072025,"parameters":{"values":[[25,26],[-26,27],[51,28]],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-finite-extrema","semantic_template":"qf-mod38-supinf-finite-extrema/{\"values\":[[25,26],[-26,27],[51,28]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0026","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[1,2],[-2,3],[3,4]],\"candidate\":[3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, 是, 3/4, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(3/4, 是, 3/4, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072026,"parameters":{"values":[[1,2],[-2,3],[3,4]],"candidate":[3,4],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[3,4],\"values\":[[1,2],[-2,3],[3,4]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0027","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[2,3],[-3,4],[5,5]],\"candidate\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 是, 1, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(1, 是, 1, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072027,"parameters":{"values":[[2,3],[-3,4],[5,5]],"candidate":[1,1],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[1,1],\"values\":[[2,3],[-3,4],[5,5]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0028","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[3,4],[-4,5],[7,6]],\"candidate\":[7,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/6, 是, 7/6, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(7/6, 是, 7/6, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072028,"parameters":{"values":[[3,4],[-4,5],[7,6]],"candidate":[7,6],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[7,6],\"values\":[[3,4],[-4,5],[7,6]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0029","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[4,5],[-5,6],[9,7]],\"candidate\":[9,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/7, 是, 9/7, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(9/7, 是, 9/7, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072029,"parameters":{"values":[[4,5],[-5,6],[9,7]],"candidate":[9,7],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[9,7],\"values\":[[4,5],[-5,6],[9,7]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0030","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[5,6],[-6,7],[11,8]],\"candidate\":[11,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/8, 是, 11/8, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(11/8, 是, 11/8, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072030,"parameters":{"values":[[5,6],[-6,7],[11,8]],"candidate":[11,8],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[11,8],\"values\":[[5,6],[-6,7],[11,8]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0031","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[6,7],[-7,8],[13,9]],\"candidate\":[13,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/9, 是, 13/9, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(13/9, 是, 13/9, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072031,"parameters":{"values":[[6,7],[-7,8],[13,9]],"candidate":[13,9],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[13,9],\"values\":[[6,7],[-7,8],[13,9]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0032","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[7,8],[-8,9],[15,10]],\"candidate\":[3,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/2, 是, 3/2, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(3/2, 是, 3/2, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072032,"parameters":{"values":[[7,8],[-8,9],[15,10]],"candidate":[3,2],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[3,2],\"values\":[[7,8],[-8,9],[15,10]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0033","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[8,9],[-9,10],[17,11]],\"candidate\":[17,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/11, 是, 17/11, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(17/11, 是, 17/11, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072033,"parameters":{"values":[[8,9],[-9,10],[17,11]],"candidate":[17,11],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[17,11],\"values\":[[8,9],[-9,10],[17,11]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0034","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[9,10],[-10,11],[19,12]],\"candidate\":[19,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/12, 是, 19/12, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(19/12, 是, 19/12, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072034,"parameters":{"values":[[9,10],[-10,11],[19,12]],"candidate":[19,12],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[19,12],\"values\":[[9,10],[-10,11],[19,12]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0035","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[10,11],[-11,12],[21,13]],\"candidate\":[21,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21/13, 是, 21/13, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(21/13, 是, 21/13, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072035,"parameters":{"values":[[10,11],[-11,12],[21,13]],"candidate":[21,13],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[21,13],\"values\":[[10,11],[-11,12],[21,13]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0036","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[11,12],[-12,13],[23,14]],\"candidate\":[23,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/14, 是, 23/14, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(23/14, 是, 23/14, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072036,"parameters":{"values":[[11,12],[-12,13],[23,14]],"candidate":[23,14],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[23,14],\"values\":[[11,12],[-12,13],[23,14]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0037","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[12,13],[-13,14],[25,15]],\"candidate\":[5,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/3, 是, 5/3, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(5/3, 是, 5/3, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072037,"parameters":{"values":[[12,13],[-13,14],[25,15]],"candidate":[5,3],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[5,3],\"values\":[[12,13],[-13,14],[25,15]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0038","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[13,14],[-14,15],[27,16]],\"candidate\":[27,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(27/16, 是, 27/16, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(27/16, 是, 27/16, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072038,"parameters":{"values":[[13,14],[-14,15],[27,16]],"candidate":[27,16],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[27,16],\"values\":[[13,14],[-14,15],[27,16]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0039","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[14,15],[-15,16],[29,17]],\"candidate\":[29,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(29/17, 是, 29/17, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(29/17, 是, 29/17, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072039,"parameters":{"values":[[14,15],[-15,16],[29,17]],"candidate":[29,17],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[29,17],\"values\":[[14,15],[-15,16],[29,17]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0040","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[15,16],[-16,17],[31,18]],\"candidate\":[31,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(31/18, 是, 31/18, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(31/18, 是, 31/18, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072040,"parameters":{"values":[[15,16],[-16,17],[31,18]],"candidate":[31,18],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[31,18],\"values\":[[15,16],[-16,17],[31,18]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0041","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[16,17],[-17,18],[33,19]],\"candidate\":[33,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(33/19, 是, 33/19, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(33/19, 是, 33/19, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072041,"parameters":{"values":[[16,17],[-17,18],[33,19]],"candidate":[33,19],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[33,19],\"values\":[[16,17],[-17,18],[33,19]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0042","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[17,18],[-18,19],[35,20]],\"candidate\":[7,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/4, 是, 7/4, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(7/4, 是, 7/4, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072042,"parameters":{"values":[[17,18],[-18,19],[35,20]],"candidate":[7,4],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[7,4],\"values\":[[17,18],[-18,19],[35,20]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0043","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[18,19],[-19,20],[37,21]],\"candidate\":[37,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(37/21, 是, 37/21, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(37/21, 是, 37/21, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072043,"parameters":{"values":[[18,19],[-19,20],[37,21]],"candidate":[37,21],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[37,21],\"values\":[[18,19],[-19,20],[37,21]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0044","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[19,20],[-20,21],[39,22]],\"candidate\":[39,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(39/22, 是, 39/22, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(39/22, 是, 39/22, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072044,"parameters":{"values":[[19,20],[-20,21],[39,22]],"candidate":[39,22],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[39,22],\"values\":[[19,20],[-20,21],[39,22]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0045","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[20,21],[-21,22],[41,23]],\"candidate\":[41,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(41/23, 是, 41/23, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(41/23, 是, 41/23, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072045,"parameters":{"values":[[20,21],[-21,22],[41,23]],"candidate":[41,23],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[41,23],\"values\":[[20,21],[-21,22],[41,23]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0046","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[21,22],[-22,23],[43,24]],\"candidate\":[43,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(43/24, 是, 43/24, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(43/24, 是, 43/24, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072046,"parameters":{"values":[[21,22],[-22,23],[43,24]],"candidate":[43,24],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[43,24],\"values\":[[21,22],[-22,23],[43,24]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0047","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[22,23],[-23,24],[45,25]],\"candidate\":[9,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/5, 是, 9/5, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(9/5, 是, 9/5, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072047,"parameters":{"values":[[22,23],[-23,24],[45,25]],"candidate":[9,5],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[9,5],\"values\":[[22,23],[-23,24],[45,25]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0048","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[23,24],[-24,25],[47,26]],\"candidate\":[47,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(47/26, 是, 47/26, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(47/26, 是, 47/26, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072048,"parameters":{"values":[[23,24],[-24,25],[47,26]],"candidate":[47,26],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[47,26],\"values\":[[23,24],[-24,25],[47,26]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0049","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[24,25],[-25,26],[49,27]],\"candidate\":[49,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(49/27, 是, 49/27, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(49/27, 是, 49/27, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072049,"parameters":{"values":[[24,25],[-25,26],[49,27]],"candidate":[49,27],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[49,27],\"values\":[[24,25],[-25,26],[49,27]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0050","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-upper-bound-leastness；資料={\"values\":[[25,26],[-26,27],[51,28]],\"candidate\":[51,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(51/28, 是, 51/28, 是, upper_bound_and_leastness_are_separate)","explanation_zh":"Wave6根層核對=(51/28, 是, 51/28, 是, upper_bound_and_leastness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-upper-bound-leastness","seed":202611072050,"parameters":{"values":[[25,26],[-26,27],[51,28]],"candidate":[51,28],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-upper-bound-leastness","semantic_template":"qf-mod38-supinf-upper-bound-leastness/{\"candidate\":[51,28],\"values\":[[25,26],[-26,27],[51,28]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0051","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[1,2],[-2,3],[3,4]],\"candidate\":[-2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-2/3, 是, -2/3, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-2/3, 是, -2/3, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072051,"parameters":{"values":[[1,2],[-2,3],[3,4]],"candidate":[-2,3],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-2,3],\"values\":[[1,2],[-2,3],[3,4]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0052","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[2,3],[-3,4],[5,5]],\"candidate\":[-3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-3/4, 是, -3/4, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-3/4, 是, -3/4, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072052,"parameters":{"values":[[2,3],[-3,4],[5,5]],"candidate":[-3,4],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-3,4],\"values\":[[2,3],[-3,4],[5,5]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0053","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[3,4],[-4,5],[7,6]],\"candidate\":[-4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-4/5, 是, -4/5, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-4/5, 是, -4/5, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072053,"parameters":{"values":[[3,4],[-4,5],[7,6]],"candidate":[-4,5],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-4,5],\"values\":[[3,4],[-4,5],[7,6]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0054","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[4,5],[-5,6],[9,7]],\"candidate\":[-5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-5/6, 是, -5/6, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-5/6, 是, -5/6, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072054,"parameters":{"values":[[4,5],[-5,6],[9,7]],"candidate":[-5,6],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-5,6],\"values\":[[4,5],[-5,6],[9,7]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0055","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[5,6],[-6,7],[11,8]],\"candidate\":[-6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-6/7, 是, -6/7, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-6/7, 是, -6/7, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072055,"parameters":{"values":[[5,6],[-6,7],[11,8]],"candidate":[-6,7],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-6,7],\"values\":[[5,6],[-6,7],[11,8]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0056","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[6,7],[-7,8],[13,9]],\"candidate\":[-7,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-7/8, 是, -7/8, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-7/8, 是, -7/8, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072056,"parameters":{"values":[[6,7],[-7,8],[13,9]],"candidate":[-7,8],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-7,8],\"values\":[[6,7],[-7,8],[13,9]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0057","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[7,8],[-8,9],[15,10]],\"candidate\":[-8,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-8/9, 是, -8/9, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-8/9, 是, -8/9, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072057,"parameters":{"values":[[7,8],[-8,9],[15,10]],"candidate":[-8,9],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-8,9],\"values\":[[7,8],[-8,9],[15,10]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0058","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[8,9],[-9,10],[17,11]],\"candidate\":[-9,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-9/10, 是, -9/10, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-9/10, 是, -9/10, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072058,"parameters":{"values":[[8,9],[-9,10],[17,11]],"candidate":[-9,10],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-9,10],\"values\":[[8,9],[-9,10],[17,11]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0059","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[9,10],[-10,11],[19,12]],\"candidate\":[-10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-10/11, 是, -10/11, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-10/11, 是, -10/11, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072059,"parameters":{"values":[[9,10],[-10,11],[19,12]],"candidate":[-10,11],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-10,11],\"values\":[[9,10],[-10,11],[19,12]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0060","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[10,11],[-11,12],[21,13]],\"candidate\":[-11,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-11/12, 是, -11/12, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-11/12, 是, -11/12, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072060,"parameters":{"values":[[10,11],[-11,12],[21,13]],"candidate":[-11,12],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-11,12],\"values\":[[10,11],[-11,12],[21,13]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0061","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[11,12],[-12,13],[23,14]],\"candidate\":[-12,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-12/13, 是, -12/13, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-12/13, 是, -12/13, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072061,"parameters":{"values":[[11,12],[-12,13],[23,14]],"candidate":[-12,13],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-12,13],\"values\":[[11,12],[-12,13],[23,14]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0062","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[12,13],[-13,14],[25,15]],\"candidate\":[-13,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-13/14, 是, -13/14, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-13/14, 是, -13/14, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072062,"parameters":{"values":[[12,13],[-13,14],[25,15]],"candidate":[-13,14],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-13,14],\"values\":[[12,13],[-13,14],[25,15]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0063","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[13,14],[-14,15],[27,16]],\"candidate\":[-14,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-14/15, 是, -14/15, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-14/15, 是, -14/15, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072063,"parameters":{"values":[[13,14],[-14,15],[27,16]],"candidate":[-14,15],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-14,15],\"values\":[[13,14],[-14,15],[27,16]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0064","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[14,15],[-15,16],[29,17]],\"candidate\":[-15,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-15/16, 是, -15/16, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-15/16, 是, -15/16, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072064,"parameters":{"values":[[14,15],[-15,16],[29,17]],"candidate":[-15,16],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-15,16],\"values\":[[14,15],[-15,16],[29,17]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0065","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[15,16],[-16,17],[31,18]],\"candidate\":[-16,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-16/17, 是, -16/17, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-16/17, 是, -16/17, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072065,"parameters":{"values":[[15,16],[-16,17],[31,18]],"candidate":[-16,17],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-16,17],\"values\":[[15,16],[-16,17],[31,18]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0066","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[16,17],[-17,18],[33,19]],\"candidate\":[-17,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-17/18, 是, -17/18, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-17/18, 是, -17/18, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072066,"parameters":{"values":[[16,17],[-17,18],[33,19]],"candidate":[-17,18],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-17,18],\"values\":[[16,17],[-17,18],[33,19]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0067","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[17,18],[-18,19],[35,20]],\"candidate\":[-18,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-18/19, 是, -18/19, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-18/19, 是, -18/19, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072067,"parameters":{"values":[[17,18],[-18,19],[35,20]],"candidate":[-18,19],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-18,19],\"values\":[[17,18],[-18,19],[35,20]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0068","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[18,19],[-19,20],[37,21]],\"candidate\":[-19,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-19/20, 是, -19/20, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-19/20, 是, -19/20, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072068,"parameters":{"values":[[18,19],[-19,20],[37,21]],"candidate":[-19,20],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-19,20],\"values\":[[18,19],[-19,20],[37,21]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0069","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[19,20],[-20,21],[39,22]],\"candidate\":[-20,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-20/21, 是, -20/21, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-20/21, 是, -20/21, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072069,"parameters":{"values":[[19,20],[-20,21],[39,22]],"candidate":[-20,21],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-20,21],\"values\":[[19,20],[-20,21],[39,22]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0070","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[20,21],[-21,22],[41,23]],\"candidate\":[-21,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-21/22, 是, -21/22, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-21/22, 是, -21/22, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072070,"parameters":{"values":[[20,21],[-21,22],[41,23]],"candidate":[-21,22],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-21,22],\"values\":[[20,21],[-21,22],[41,23]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0071","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[21,22],[-22,23],[43,24]],\"candidate\":[-22,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-22/23, 是, -22/23, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-22/23, 是, -22/23, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072071,"parameters":{"values":[[21,22],[-22,23],[43,24]],"candidate":[-22,23],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-22,23],\"values\":[[21,22],[-22,23],[43,24]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0072","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[22,23],[-23,24],[45,25]],\"candidate\":[-23,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-23/24, 是, -23/24, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-23/24, 是, -23/24, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072072,"parameters":{"values":[[22,23],[-23,24],[45,25]],"candidate":[-23,24],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-23,24],\"values\":[[22,23],[-23,24],[45,25]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0073","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[23,24],[-24,25],[47,26]],\"candidate\":[-24,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-24/25, 是, -24/25, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-24/25, 是, -24/25, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072073,"parameters":{"values":[[23,24],[-24,25],[47,26]],"candidate":[-24,25],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-24,25],\"values\":[[23,24],[-24,25],[47,26]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0074","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[24,25],[-25,26],[49,27]],\"candidate\":[-25,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-25/26, 是, -25/26, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-25/26, 是, -25/26, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072074,"parameters":{"values":[[24,25],[-25,26],[49,27]],"candidate":[-25,26],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-25,26],\"values\":[[24,25],[-25,26],[49,27]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0075","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-lower-bound-greatestness；資料={\"values\":[[25,26],[-26,27],[51,28]],\"candidate\":[-26,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-26/27, 是, -26/27, 是, lower_bound_and_greatestness_are_separate)","explanation_zh":"Wave6根層核對=(-26/27, 是, -26/27, 是, lower_bound_and_greatestness_are_separate)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-lower-bound-greatestness","seed":202611072075,"parameters":{"values":[[25,26],[-26,27],[51,28]],"candidate":[-26,27],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-lower-bound-greatestness","semantic_template":"qf-mod38-supinf-lower-bound-greatestness/{\"candidate\":[-26,27],\"values\":[[25,26],[-26,27],[51,28]]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0076","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[0,1],\"right\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 2, 2, 0, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(0, 2, 2, 0, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072076,"parameters":{"left":[0,1],"right":[2,1],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[0,1],\"right\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0077","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[1,2],\"right\":[3,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, 3/2, 3/2, 1/2, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(1/2, 3/2, 3/2, 1/2, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072077,"parameters":{"left":[1,2],"right":[3,2],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[1,2],\"right\":[3,2]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0078","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[2,3],\"right\":[4,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2/3, 4/3, 4/3, 2/3, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(2/3, 4/3, 4/3, 2/3, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072078,"parameters":{"left":[2,3],"right":[4,3],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[2,3],\"right\":[4,3]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0079","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[3,4],\"right\":[5,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, 5/4, 5/4, 3/4, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(3/4, 5/4, 5/4, 3/4, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072079,"parameters":{"left":[3,4],"right":[5,4],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[3,4],\"right\":[5,4]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0080","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[4,5],\"right\":[6,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/5, 6/5, 6/5, 4/5, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(4/5, 6/5, 6/5, 4/5, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072080,"parameters":{"left":[4,5],"right":[6,5],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[4,5],\"right\":[6,5]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0081","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[5,6],\"right\":[7,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/6, 7/6, 7/6, 5/6, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(5/6, 7/6, 7/6, 5/6, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072081,"parameters":{"left":[5,6],"right":[7,6],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[5,6],\"right\":[7,6]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0082","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[6,7],\"right\":[8,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6/7, 8/7, 8/7, 6/7, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(6/7, 8/7, 8/7, 6/7, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072082,"parameters":{"left":[6,7],"right":[8,7],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[6,7],\"right\":[8,7]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0083","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[7,8],\"right\":[9,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/8, 9/8, 9/8, 7/8, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(7/8, 9/8, 9/8, 7/8, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072083,"parameters":{"left":[7,8],"right":[9,8],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[7,8],\"right\":[9,8]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0084","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[8,9],\"right\":[10,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/9, 10/9, 10/9, 8/9, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(8/9, 10/9, 10/9, 8/9, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072084,"parameters":{"left":[8,9],"right":[10,9],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[8,9],\"right\":[10,9]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0085","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[9,10],\"right\":[11,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/10, 11/10, 11/10, 9/10, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(9/10, 11/10, 11/10, 9/10, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072085,"parameters":{"left":[9,10],"right":[11,10],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[9,10],\"right\":[11,10]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0086","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[10,11],\"right\":[12,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10/11, 12/11, 12/11, 10/11, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(10/11, 12/11, 12/11, 10/11, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072086,"parameters":{"left":[10,11],"right":[12,11],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[10,11],\"right\":[12,11]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0087","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[11,12],\"right\":[13,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/12, 13/12, 13/12, 11/12, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(11/12, 13/12, 13/12, 11/12, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072087,"parameters":{"left":[11,12],"right":[13,12],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[11,12],\"right\":[13,12]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0088","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[12,13],\"right\":[14,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12/13, 14/13, 14/13, 12/13, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(12/13, 14/13, 14/13, 12/13, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072088,"parameters":{"left":[12,13],"right":[14,13],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[12,13],\"right\":[14,13]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0089","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[13,14],\"right\":[15,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/14, 15/14, 15/14, 13/14, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(13/14, 15/14, 15/14, 13/14, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072089,"parameters":{"left":[13,14],"right":[15,14],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[13,14],\"right\":[15,14]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0090","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[14,15],\"right\":[16,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14/15, 16/15, 16/15, 14/15, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(14/15, 16/15, 16/15, 14/15, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072090,"parameters":{"left":[14,15],"right":[16,15],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[14,15],\"right\":[16,15]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0091","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[15,16],\"right\":[17,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15/16, 17/16, 17/16, 15/16, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(15/16, 17/16, 17/16, 15/16, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072091,"parameters":{"left":[15,16],"right":[17,16],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[15,16],\"right\":[17,16]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0092","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[16,17],\"right\":[18,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16/17, 18/17, 18/17, 16/17, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(16/17, 18/17, 18/17, 16/17, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072092,"parameters":{"left":[16,17],"right":[18,17],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[16,17],\"right\":[18,17]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0093","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[17,18],\"right\":[19,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/18, 19/18, 19/18, 17/18, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(17/18, 19/18, 19/18, 17/18, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072093,"parameters":{"left":[17,18],"right":[19,18],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[17,18],\"right\":[19,18]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0094","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[18,19],\"right\":[20,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18/19, 20/19, 20/19, 18/19, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(18/19, 20/19, 20/19, 18/19, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072094,"parameters":{"left":[18,19],"right":[20,19],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[18,19],\"right\":[20,19]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0095","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[19,20],\"right\":[21,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/20, 21/20, 21/20, 19/20, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(19/20, 21/20, 21/20, 19/20, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072095,"parameters":{"left":[19,20],"right":[21,20],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[19,20],\"right\":[21,20]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0096","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[20,21],\"right\":[22,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20/21, 22/21, 22/21, 20/21, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(20/21, 22/21, 22/21, 20/21, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072096,"parameters":{"left":[20,21],"right":[22,21],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[20,21],\"right\":[22,21]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0097","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[21,22],\"right\":[23,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21/22, 23/22, 23/22, 21/22, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(21/22, 23/22, 23/22, 21/22, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072097,"parameters":{"left":[21,22],"right":[23,22],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[21,22],\"right\":[23,22]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0098","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[22,23],\"right\":[24,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22/23, 24/23, 24/23, 22/23, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(22/23, 24/23, 24/23, 22/23, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072098,"parameters":{"left":[22,23],"right":[24,23],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[22,23],\"right\":[24,23]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0099","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[23,24],\"right\":[25,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/24, 25/24, 25/24, 23/24, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(23/24, 25/24, 25/24, 23/24, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072099,"parameters":{"left":[23,24],"right":[25,24],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[23,24],\"right\":[25,24]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r02-supremum-and-infimum-0100","batch_id":"batch-20261014-advance-20261107-r02-supremum-and-infimum-foundations","language":"zh-Hant","source_mko_ids":["mko-supremum-and-infimum"],"title_zh":"上確界與下確界","stem_zh":"非空且相應有界的實值集合或明示有界開區間。操作=supinf-open-interval-nonattainment；資料={\"left\":[24,25],\"right\":[26,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24/25, 26/25, 26/25, 24/25, 否, 否, supremum_and_infimum_not_attained)","explanation_zh":"Wave6根層核對=(24/25, 26/25, 26/25, 24/25, 否, 否, supremum_and_infimum_not_attained)；依完整明示資料獨立重算；sup同時是上界與最小上界，inf對偶；兩項責任不可省略；sup與inf不必屬於集合，只有取到時才是maximum或minimum；空集與無界集另處理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上確界與下確界"]},"variant":{"family_id":"qf-mod38-supinf-open-interval-nonattainment","seed":202611072100,"parameters":{"left":[24,25],"right":[26,25],"domain":"Exact_bounded_real_set_extrema","operation":"supinf-open-interval-nonattainment","semantic_template":"qf-mod38-supinf-open-interval-nonattainment/{\"left\":[24,25],\"right\":[26,25]}"}},"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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}